Computational problem solving
in university physics education
Students’ beliefs, knowledge, and motivation
Madelen Bodin
Department of Physics
Umeå 2012
This work is protected by the Swedish Copyright Legislation (Act 1960:729)
ISBN: 978-91-7459-398-3
ISSN: 1652-5051
Cover: Madelen Bodin
Electronic version available at http://umu.diva-portal.org/
Printed by: Print & Media, Umeå University
Umeå, Sweden, 2012
To my family
Thanks
It has been an exciting journey during these years as a PhD student in
physics education research. I started this journey as a physicist and I am
grateful that I've had the privilege to gain insight into the fascination field of
how, why, and when people learn. There are many people that have been
involved during this journey and contributed with support, encouragements,
criticism, laughs, inspiration, and love.
First I would like to thank Mikael Winberg who encouraged me to apply as
a PhD student and who later became my supervisor. You have been
invaluable as a research partner and constantly given me constructive
comments on my work. Thanks also to Sune Pettersson and Sylvia Benkert
who introduced me to this field of research. Many thanks to Jonas Larsson,
Martin Servin, and Patrik Norqvist who let me borrow their students and
also have contributed with valuable ideas and comments. Special thanks to
the students who shared their learning experiences during my studies.
It has been a privilege to be a member of the National Graduate School in
Science and Technology Education (FontD). Thanks for providing courses
and possibilities to networking with research colleagues from all over the
world. Thanks also to all student colleagues in cohort 3 for all feedback and
fun. Special thanks to Lena Tibell for being a friend and a research partner.
Thanks also to Åke Ingerman for invaluable feedback on my 90 % seminar.
Many thanks to my friends and colleagues at the departments of Physics
and Science and mathematics education for providing support and feedback
on seminars and papers. Special thanks to Karin, Phimpoo, and Jenny for
being roommates, friends, and colleagues.
And to the most important persons in my life: Kenneth - without your love
and support I couldn't have done this; Tora, Stina, and Milla - thanks for just
being there.
Table of Contents
1!
Introduction
1.1!
1.2!
2!
1.3!
2.2.1!
2.2.2!
2.2.3!
2.2.4!
2.2.5!
2.2.6!
3.1!
3.3!
3.4!
3.5!
3.5.1!
3.5.2!
3.6!
3.6.1!
3.6.2!
5!
Overview of the thesis
Why learning physics?
Problem solving in physics
Observations
Physics principles
Mathematics
Modeling
Computational physics
Simulations
Conceptual framework
3.2!
4!
Context of the study
Learning and teaching physics
2.1!
2.2!
3!
Aim of the thesis
3.7!
Knowledge representation
Structures in knowledge
Concepts and meaning
Visual representations
Beliefs
Epistemological beliefs
Expectancy and value beliefs
Motivation
Autonomy
Indicators of motivation
Experts, novices, and computational physics
Research questions
Methods
5.1!
5.1.1!
5.1.2!
5.2!
5.2.1!
5.2.2!
5.2.3!
5.3!
5.3.1!
5.3.2!
5.3.3!
5.3.4!
5.4!
The context of the study
The sample
The task
Data collection methods
Questionnaires
Interviews
Students’ written reports and Matlab code
Analysis
Multivariate statistical analysis
Content analysis
Network analysis
SOLO analysis
Methodological issues
1!
1!
2!
5!
6!
6!
7!
8!
8!
9!
9!
10!
11!
14!
14!
15!
17!
18!
18!
18!
19!
19!
20!
21!
21!
23!
25!
25!
25!
26!
26!
26!
26!
27!
27!
27!
28!
31!
33!
33!
i
5.4.1!
6!
Validity
5.4.2!
Reliability
Results
6.1!
Paper I: Role of beliefs and emotions in numerical problem solving
in university physics education
6.2!
34!
36!
36!
Paper II: Mapping university students’ epistemic framing of computational
physics using network analysis
6.3!
34!
36!
Paper III: Mapping university physics teachers' and students'
conceptualization of simulation competence in physics education using network
analysis
6.4!
7!
and code development
Discussion of main findings
7.1!
7.2!
7.3!
8!
9!
ii
Paper IV: Students' progress in computational physics: mental models
7.4!
Critical aspects of computational physics
Teachers' and students epistemic framing
Positive and negative learning effects
Network analysis as a tool
Conclusions
Bibliography
38!
39!
41!
41!
42!
44!
45!
47!
49!
List of papers
The thesis is based on the following papers.
Paper I: Bodin, M., & Winberg, M. (2012). Role of beliefs and emotions in
numerical problem solving in university physics education. Phys. Rev. ST
Phys. Educ. Res., 8, 010108. DOI: 10.1103/PhysRevSTPER.8.010108
Paper II: Bodin, M. (in-press). Mapping students' epistemic framing of
computational physics using network analysis. Phys. Rev. ST Phys. Educ.
Res.
Paper III: Bodin, M. (2011). Mapping university teachers' and students'
conceptualization of simulation competence in physics education using
network analysis. Manuscript submitted for publication.
Paper IV: Bodin, M. (2011). Students’ progress during an assignment in
computational physics: mental models and code development. Manuscript
submitted for publication.
Paper I and Paper II are reproduced under the terms of the Creative
Commons Attribution 3.0 License. Further distribution of this work must
maintain attribution to the author(s) and the published article’s title,
journal citation, and DOI.
iii
iv
Introduction
1 Introduction
Physics education research is research about how we learn, teach,
understand, and use physics. The fundamental research questions are
intriguing as they address how human intelligence relates to the laws of
nature and how we explain the world around us. As an applied science,
physics education research has the prospect of improving teaching and
learning in terms of new tools and methods. Physics education research is an
interdisciplinary research area and combines two fields with different
research traditions. Education research is influenced by, e.g., social studies,
psychology, and neuroscience. Physics is a traditional academic subject but
is also integrated in a number of other fields such as chemistry, biology,
computer science, and even economy and sociology. Physics education
research can therefore be approached in many ways depending on the
particular questions asked and the context chosen for the research, as well as
find applications outside physics.
1.1
Aim of the thesis
The teaching and learning situation in focus in this thesis moves across the
fields of physics, mathematics, computer science, and the problem solving
associated with these fields. It is situated in a university context and the
assignment in focus is a physics problem in classical mechanics where
students use computational physics to develop a simulation.
This work strives at contributing to understanding of the cognitive and
affective learning experiences from a computational physics assignment
where competencies from several fields interact. The assignment is thus not
limited to finding a sole physics solution but includes numerics, computer
science, as well as visualization and interactivity. Will this complex situation
help or hinder the student from developing a coherent view of how physics is
used to model and understand the world? The overall research questions
treated in this thesis are:
!
What are the critical aspects of using computational problem solving in
physics education?
!
How do teachers and students frame a learning situation in
computational physics? Do teachers and students agree about learning
objectives, approaches, and difficulties?
1
Introduction
!
What are the consequences in terms of positive or negative learning
experiences when using computational problem solving in physics
education?
My aim with this thesis is to contribute to the metacognitive
understanding of how students learn computational physics and to provide
university teachers with knowledge about effects of using computational
thinking in university physics education.
1.2
Context of the study
The context for this thesis is physics education at university level. Studying
physics at university level can have several purposes. A physics student can
aim at becoming a scientist and therefore chooses a traditional physics
education. Another student may have a different career in mind and chooses
an engineering approach of physics studies. A third student is interested in
becoming a schoolteacher and chooses to study physics where the
pedagogical aspects in combination with physics play important roles. The
motivation to study physics may differ in these three exemplified cases but
the understanding of physics as a subject should not differ (Heuvelen, 1991).
The academic physics education is often concentrated on learning physics
concepts, solving physics problems, and using physics principles in order to
explain phenomena and predict physical processes (McDermott, 2001;
Redish, 1999). The engineering approach tends to focus more on methods
and tools for solving physics problems as emphasize may be directed
towards constructing technology and finding solutions to technological and
scientific issues (Redish, Saul, & Steinberg, 1998). The teacher student is, on
the other hand, besides learning the physics subject, interested in
metacognitive aspects such as, how physics is learned, what students have
difficulties with, and how the teacher's knowledge can be implemented in a
classroom situation (Arons, 1997). Studying these different approaches and
interests in learning and teaching physics all contribute to knowledge about
how students learn physics and how teaching can be improved.
The term computational scientific thinking has been used in a number of
contexts during the past years as a way to approach science that would not
be available otherwise (Landau, 2008). Ken Wilson proposed computation
to be the third leg of science, together with theory and experiment, due to
breakthroughs in science because of new computational models, findings
that actually awarded Wilson a Nobel prize in 1975 (Denning, 2009).
Approaching science with a computational mind would therefore be
expected to be present in tertiary physics education but this is generally not
the case, even though several initiatives have been taken in this direction
(Johnston, 2006; Landau, 2006).
2
Introduction
The following definition of computational physics was proposed by the
editor in chief of Computing in Science and Engineering, Norman Chonacky
in relation to a, in the U.S., nation-wide survey among teachers about how
computational approaches were used in undergraduate physics education:
"By computation in physics here we mean uses of computing
that are intimately connected with content and not its
presentation. There seems to be no concurrence on which
role(s) are appropriate for computing in physics, but there is a
distinction we can draw between computers used for
instructional methodologies and computers used for
computational physics. We’re interested in the latter where,
as in calculus, we use computation to derive solutions to
problems." (Fuller, 2006)
Using computation in physics education is not a new approach. Numerical
methods have for long been important resources in solving complex physics
problems. However, without resources such as computers and numerical
methods, calculating numerical solutions is a very time-consuming business.
In recent years the interest in the field of implementing computational
physics in conventional physics education has increased in the physics
education community and some of these reasons are:
!
The accessibility to computers in education has increased. Computers
are becoming a natural tool in education and most students already use
computers in their everyday life (Botet & Trizac, 2005).
!
Increasing computer capacity gives possibilities to graphical and
computational challenges. Computer processors are getting more and
more powerful and computations as well as rendering of graphics in real
time open up for technologies for visualization of physics (Johnston,
2006).
!
Problem solving and simulation environments open up possibilities to
work with realistic problems. Software together with increasing
computer capacity give even more possibilities to approach realistic
physics problems, problems that are not possible to solve without using
numerical methods and computers (Chabay & Sherwood, 2008).
!
Computation has in recent years been considered as important as theory
and experiments in science and would therefore be expected to be
represented on the same terms in education (Landau, 2006).
3
Introduction
!
Competence in computational physics gives access to new types of jobs
in emerging industries that often are considered attractive and
motivating to students, e.g. in movie visual effects, computer games
development, interaction technology, and computational design
(Denning, 2009).
Computers in physics education thus seem to offer extensive possibilities
to investigate physical phenomena as well as solving realistic problems.
However, what will the students actually learn? Is solving complex problems
with computational physics a way to gain knowledge in physics or is physics
learning hindered by learning other competencies such as programming and
numerical modeling of physics? Figure 1 illustrates how this increased
complexity adds another dimension to traditional problem solving skills in
physics, math, and modeling.
Analytical problem solving
Computational problem solving
Figure 1: Model of competences used for describing the main difference between analytical and
computational problem solving in physics. Computational problem solving adds one dimension,
programming skills, to the analytical model.
My purpose with this thesis is to investigate cognitive and affective
aspects related to students' and teachers' experience with computation and
simulation in physics education. There is a huge difference in student
activity between developing a simulation and using a simulation. I have
focused on the situation in which students with computational approaches
develop a visual interactive simulation as a solution to a physics problem.
4
Introduction
1.3
Overview of the thesis
This thesis comprises an introductory section and four papers.
Chapter 2 consists of a background to learning and teaching physics, This
deals with characteristics of physics as a subject and presents previous
research on teaching and learning physics. This gives an ontology, i.e., a
description of what is out there to know and how I decide what questions
that are of interest.
In the conceptual framework, chapter 3, the issues concerning my
epistemological views of teaching and learning physics are treated, i.e., what
can we know about this field and how can we know that. This part deals with
how knowledge can be represented, the influence of personal beliefs and
attitudes on learning, and what role motivation plays in learning.
The research questions investigated in the four papers in this thesis are
presented in chapter 4 and they are further covered in the four
accompanying research articles.
In the methodological framework in chapter 5 issues concerning methods
are described. Methodology deals with the precise procedures that can be
used to acquire the knowledge necessary to answer the research questions,
i.e., what data and how it should be collected and how the data should be
analyzed. In the methodological framework I describe and discuss the
methods for data collection and analysis and their relevance for answering
the research questions.
The results from the studies are presented as a summary of the four
papers in chapter 6.
In chapter 7 the main findings are summarized and discussed and chapter
8 concludes the thesis.
5
Learning and teaching physics
2 Learning and teaching physics
In this chapter and the following, chapter 3, I describe what my choice of
research questions is based upon. This thesis is not only about teaching and
learning physics but also about applying knowledge and skills from several
disciplines in order to solve and simulate a realistic physics problem using
computational methods. The questions in focus deal with what can be
learned from the students' experiences in terms of cognitive and affective
aspects.
2.1
Why learning physics?
Physics is a unique subject since it involves many levels of abstractions in
different forms of representations, e.g., conceptual (laws, principles),
mathematical formalism (equations), experimental (equipment, skills),
descriptive (text, tables, graphs) (Roth, 1995). Hence, what it actually means
to understand physics is a challenging question. Knowing a phenomenon's
causes, effects, and how to interact with it are some of the attributes related
to understanding (Greca & Moreira, 2000) which also fit the purposes of
learning physics.
Physics is formulated in order to try to explain the world we live in.
Therefore we have invented physics as a tool in order to gain knowledge
about our environment and ourselves. Brody (1993) refers to physics as an
epistemic cycle where physics is not a finished product but is instead the
process of creating that product, physics itself. This is expected to give
physics knowledge a particular epistemological touch (Roth &
Roychoudhury, 1994) where knowledge about physics can lead to knowledge
about how and why we learn. Humans are fit to handle the physical
conditions that the world provides, such as space, time, and mass. Our
bodies have generally no problem to act in this world, but when it comes to
formulating and communicating what we experience, our brains seem to be
less comfortable. Classical mechanics is what our bodies most easily can
experience and observe, and thus what is easiest to collect empirical data
about. Some of the most fundamental aspects of physics, such as energy and
momentum conservation and Newton's laws of motion, are based on
empiricism from classical mechanics, and therefore have a position as
fundamental for all physics. In physics education we generally start to learn
mechanics in order to practice how to model what we experience before we
move to more abstract phenomena, such as electricity, magnetism, and
quantum mechanics.
Physics education research has a long tradition and is mainly associated
with the traditional learning motifs, approaching physics concepts,
6
Learning and teaching physics
principles, and problem solving with the purpose of learning conceptual
physics and solving analytical problems. Much of the focus is also devoted to
finding answers to how novice students can develop the type of intuitive
knowledge that expertise in the field seems to possess (Chi, Feltovich, &
Glaser, 1981; Larkin, McDermott, Simon, & Simon, 1980). Results so far
show that in general there are no short cuts, but there do exist better or
worse ways of learning physics (Redish, 1999). An active engagement in
learning, rather than passive reception, has for long been promoted to
stimulate the cognitive development according to constructivist views on
learning as well as motivational aspects (Benware & Deci, 1984; Heuvelen,
1991; McDermott, 2001; Prince, 2004). To actively engage in the physics
studies, e.g., discuss problem solving strategies in groups, or to work with
interactive computer environments for investigating phenomena or solving
problems, usually promote a more coherent view of physics (Redish &
Steinberg, 1999) (Laws, 1997) (Evans & Gibbons, 2007) while passive
learning, e.g., listening to lectures and means-ends problem solving, tend to
leave the student with physics as consisting of isolated facts (Reif, 1995)
(Halloun & Hestenes, 1998).
2.2
Problem solving in physics
The main activity in practicing physics is to solve problems. I will here refer
to any question that regards physics to be seen as a physics problem, which
can be solved by using observations, mathematics, and modeling. If the
problem is simple, an observation can be enough to find an answer. If the
problem is complex, we might need numerical methods to simulate the
problem and provide visualizations we can interact with to find solutions
and answers.
Problem solving in physics education is a vast area of research and covers
many aspects of how students as well as teachers experience problem solving
in the learning and teaching process as shown, for example, in the review by
Hsu, Brewe, Foster, and Harper (2004). The meaning of a physics problem
is very broad and can be anything on the continuum from a closed problem,
with a unique mathematical solution, to an open problem, which has no
single answer and which can have several solutions. In physics education,
traditional textbooks usually offer physics problems that are reduced to an
idealized context and illustrate a single physics principle. The purpose is to
train students to be familiar with physics principles and the corresponding
mathematical formalism. These problems are typically quantitative, focusing
on finding appropriate formulas and manipulating the equations to solve for
a numerical value, i.e., encouraging a means-ends strategy. Previous studies
have shown that problems where means-ends strategies can be used, can
usually be solved without applying any conceptual understanding of physics
7
Learning and teaching physics
principles (Larkin et al., 1980; Sabella & Redish, 2007). Being able to
mathematically manipulate equations is indeed one aspect of being
proficient in physics problem solving. However, students also need to model
and solve open and more complex problems in order to develop expert-like
problem solving skills as well as to achieve a coherent knowledge in physics
(Hestenes, 1992; McDermott, 1991; Redish & Steinberg, 1999).
2.2.1
Observations
Before a problem can be solved there need to be some sort of data. We need
to know something about the context of the problem. This data can be
provided by observations, for example the type of information that is given
in a physics problem about velocity, mass, etc. Observational data can also
be obtained by conducting a systematic experiment. Data can also be
represented by known quantities, e.g., that the problem is set on earth,
which means that we know or can easily find the gravitational acceleration or
the distance to the center of earth.
2.2.2
Physics principles
When solving a physics problem there are a number of physics principles
that can be applied in order to model the problem or to check whether the
solution is reasonable or not. These physics principles are based on
empirical data, discussed, and developed within the physics community for
many years and considered to be general in the physical systems they
represent. Some principles are considered as scientific laws of nature, which
represent theories that describe nature. Some examples are Newton's laws of
motion and the conservation laws, e.g., energy, momentum, and electric
charge. A law within physics does not claim to hold the truth. It is simply the
best agreement that the model expressed by the law is a very good
description and has not yet been proven to not be valid. For example,
Newton laws of motion are regarded as excellent when explaining our
macroscopic world but they do not explain effects arising in the microscopic
world where quantum effects have to be considered. Research on student
epistemologies, however, show that novice students often comprehend
physics principles as the truth, believing that knowledge is something that is
possessed by authority (Hammer, 1994). Physics principles are necessary
tools for problem solving but it is also important to understand their origin
in order to know how to model physics.
8
Learning and teaching physics
2.2.3
Mathematics
Mathematics is the language we use to understand and communicate physics
as well as other sciences. Most physics students need some mathematics
experience prior to studying physics. However, mathematics in physics
seems to differ from mathematics in math courses (Bing & Redish, 2009;
Martínez-Torregrosa, López-Gay, & Gras-Martí, 2006; Redish, 2005).
Mathematics used in physics is applied, focusing on using mathematical
methods, e.g. differential equations and vector analysis, with physics
principles, in contrast to mathematics courses where abstractions and proofs
play larger roles. This causes trouble among students who are unable to
transfer their mathematical knowledge into the applied context that physics
comprises. This is reported in several studies among tertiary physics
students. Students have been found to have trouble, even after one semester
of calculus, expressing physics relationships algebraically (Clement,
Lochhead, & Monk, 1981) and to lack knowledge of concepts such as
"derivative" and "integration" (Breitenberger, 1992). Bing and Redish (2009)
studied different ways of how students frame the use of mathematics in
physics. They found that even though students had knowledge and skills of
how to apply certain mathematics in order to solve a problem, they often got
stuck in a frame that would not lead them right. If, for example, students
failed to solve a problem due to the wrong mathematical approach, they were
unable to map the physics to the appropriate math without assistance.
Knowing how to use mathematics in physics is therefore an important issue
in order to be proficient in physics problem solving.
2.2.4
Modeling
Modeling plays a central role in science. Modeling is about constructing
models that can describe and predict a phenomenon or a process. Solving a
physics problem includes knowledge about physics principles relevant for
the task and the mathematical formulations needed for the computations.
Depending on the complexity of the physics problem it is often necessary to
simplify the model in order to be able to calculate a solution. Typical
simplifications that are made are omission of air resistance when modeling
an object thrown through the air, or to consider the raindrop as spherical
when modeling the rainbow. This might cause discrepancies between the
student's personal experiences and what the model describes. To understand
what properties that can be neglected and when and what has to apply, such
as a certain physics principle, requires fundamental understanding of the
physics principles as well as how to apply the mathematical methods.
Hestenes (1987, 1992) suggests that physics should be taught with a
modeling approach in order to train students to use physics principles and
9
Learning and teaching physics
mathematical methods from the beginning. This would help student to learn
more efficiently and develop a more coherent view of physics. Other studies
support modeling as an epistemological framework for teaching, both using
the model to teach the content of physics and the modeling activity to teach
scientific knowledge and procedures (Etkina, Warren, & Gentile, 2006;
Greca & Moreira, 2002; Halloun, 1996).
2.2.5
Computational physics
With computational methods other dimensions of physics problem solving
can be reached and complex problems can be available for solving that
would not be possible to solve using only paper and pen. This typically
means realistic problems with many interacting objects. An example of a
physics problem that requires computational methods and is central in this
thesis is how to model an elastic macroscopic object sliding over a rough
surface; how can the friction coefficient be determined? This problem
requires a physical model for the object as well as the ground, numerical
methods that calculate all relevant force interactions using appropriate time
steps, and physics principles, such as energy and momentum conservation.
Skills in computational thinking means to be able to give structure to
calculations, i.e., to organize the mathematical operations that are needed to
solve a numerical problem. Computational methods are everyday tools for
physicists and engineers. Still many physics educators hesitate to use
computational approaches when teaching physics (Fuller, 2006). Numerics
are usually provided as numerics courses rather than integrated in physics
courses. Previous research has shown that students have problems
integrating mathematics into the physics context because students are not
able to transfer knowledge between the contexts of mathematics and physics
courses (Bing & Redish, 2009; Redish, 2005). The same effect could
therefore be expected when students are exposed to numerical methods in
physics courses. A computation approach to problem solving does not only
require knowledge about how to use a chosen numerical method together
with the physics but also how to tell the computer to do the calculations, i.e.,
to program the computer. This provides a complex situation for a physics
student, having to deal with many competencies, which might obstruct
elaboration of physics knowledge. However, with computational methods
complex and realistic physics problems can be exposed to students. A
computational physics problem, e.g., simulating force interactions between
many particles, is seldom possible to solve using only a means-ends strategy,
and is thus a type of problem that is suitable for a modeling approach in
teaching. However, the importance of designing activities is discussed in
several studies. Buffler, Pillay, Lubben, and Fearick (2008) suggested a
framework for designing computational problems for physics students based
10
Learning and teaching physics
on feedback on students mathematical models prior to programming in
order to facilitate for students to focus on the physics. Cabellero (2011)
designed and tested a computational assignment in classical mechanics and
identified some common students mistakes in three categories: initial
condition errors, force calculation errors, and errors with Newton's second
law. This leads to suggestions for adding additional material to the
assignment but also on focusing instructional effort on qualitative analysis of
solutions. There are few studies on students' cognitive or affective
experiences of solving physics problems with computational approaches.
Therefore the studies conveyed within this thesis and the corresponding
results fill a knowledge gap about these learning situations.
2.2.6
Simulations
Computational physics has the purpose of simulating the problem that is
investigated. Simulations are theoretical experiments and provide insight
into computational models of physics systems, which can be manipulated
and interacted with in order to explain their properties. A simulation is often
represented by a visualization of the computed data. Using computers and
simulations in physics education has been subject of several studies with
different approaches. Monaghan and Clement (1999) proposed that using
computer simulations can facilitate students' own mental simulation in
order to form a framework for visualization and problem solving. Another
approach was made by Vreman de Olde and de Jong (2004) in which
students were stimulated into a more active learning mode by letting them
create assignments for each other on electrical circuits in a computer
simulation environment.
When simulations are mentioned in the same sentence as physics
education it can mean different things. Environments for computational
physics and simulations may differ significantly with regard to the learning
conditions they provide, representing different levels of autonomy and
requiring more or less knowledge and skills in modeling, programming,
mathematics, or conceptual physics. Questions have been raised whether
simulation activities actually help students learn physics (Steinberg, 2000).
A simulation environment does not necessarily provide active engagement of
the learner. Many simulation environments that are supposed to engage
students and help them develop their schemata for physical problem solving,
are rather functioning as passive learning environments offering small
opportunities for students to actually participate in the simulation process. I
will here differ between three ways of working with simulations in physics
education: using pre-made simulations (or animations), using simulations as
tools, and building simulations.
11
Learning and teaching physics
!
Students can use simulations to illustrate a phenomenon. An animation
can also illustrate a phenomenon but where the animation rather is an
artistic illustration, the simulation is based on computation of the
equations of physics. An animation does not offer any possibilities to
interactivity. A simulation, however, illuminates certain aspects of the
physics involved in the phenomenon and offers interactivity, e.g., to
change parameters in order to investigate what happens under other
conditions. Simulation applets like PhET (Perkins et al., 2006) or many
of the applets that can be found on the internet may provide interactivity
in terms of possibilities to change parameters and investigate different
phenomena but do not require any computational skills.
!
Students can use simulations as tools to solve problems. In this case we
have a simulation environment that is used for declaring systems for
investigation and testing of models within the physics that is covered by
the simulation environment. This situation does not generally need
knowledge about the physical and numerical models. An example of a
simulation tool is Algodoo (Bodin, Bodin, Ernerfelt, & Persson, 2011),
which provides a graphical interface but uses advanced numerical
solvers for calculating physics interactions.
!
Students can build simulations using different problem solving
environments and tools. This can span from programming the physics
and math to visualize a phenomenon to using simulation environments
with built-in physics- and math-engines. Pure programming
environments, such as C++ and Java, are common among scientists and
provide a very open approach to numerical problem solving of physics.
Maple, Mathematica, Matlab, and Octave provide some support in terms
of functions and graphics but do require a computational thinking
approach (Chonacky & Winch, 2005). Easy Java Simulations (Christian
& Esquembre, 2007) and VPython (Chabay & Sherwood, 2008) are
environments which provide support in computation as well as
visualization through physics engines and visualization libraries.
To use simulations can provide visual representations of complex
phenomena and help students develop their conceptual understanding. To
build simulations is expected to require a more active participation from the
student giving possibilities to actually model and control physical systems.
These different types of simulation environments are therefore believed to
provide different learning outcomes. The point of interest in this work is to
study a situation where the student is given as much control over the
simulation as possible. In order to stimulate the acquisition of expert-like
12
Learning and teaching physics
cognitive structures for problem solving, this approach is expected to
provide positive learning outcomes.
The difference between a simulation and a visualization is not
straightforward in many cases. The result from a simulation is usually a
visualization but visualizations can also be provided as fictive animations.
Scientific visualization is a competence and research area in itself, both in
terms of developing visualizations and to interpret visual representations
(Hansen & Johnson, 2005). Many agree that visualizations should have a
central role in science education as well (Gilbert, 2005). Humans have an
excellent memory for visual information and tend to remember a particular
visualization’s meaning rather than the actual visualization (J. R. Anderson,
2004; Crilly, Blackwell, & Clarkson, 2006). Visual representations of data
are invaluable when it comes to, e.g., interpret the data generated from a
computational model (Naps et al., 2002). However, visualizations are
expected to provide, as for simulations, different learning outcomes
depending on how they are used in physics education. Tools for animation
and simulation together with the Internet have made visualizations of
physics phenomena accessible to every teacher and student, both in terms of
studying visualizations and creating visualizations. In this work I refer to
visualization as the visual feedback that is generated to the students as they
build their simulations.
13
Conceptual framework
3 Conceptual framework
In this chapter I present the underlying background that I have used in order
to investigate the research question. More details on the framework
concerning the specific studies are provided in Papers I - IV.
3.1
Knowledge representation
Knowledge itself exists in many forms in the research literature. Alexander et
al. (1991) provided a summary of up to thirty different types of knowledge
constructs that have previously been used in research and to this list several
more can be added. When knowledge is referred to in education it is often in
terms of using and creating knowledge and skills associated with a subject.
Common categorizations are conceptual, procedural, and metacognitive
knowledge (J. R. Anderson, 2004; de Jong & Ferguson-Hessler, 1996;
Jonassen, 2009). This is also how I will refer to knowledge.
There are many ways of describing an individual's complex thinking in
and about physics and learning physics in terms of cognition. The term
cognition refers to the mental processes associated with, e.g., remembering,
solving problems, and making decisions. The general consensus among
cognitive scientists, psychologists, and neuroscientists is that understanding
happens when knowledge components interact and form structures (J. R.
Anderson, 2004). These knowledge components can have different
properties (Merrill, 2000), levels (Grayson, Anderson, & Crossley, 2001),
distinctions in meaning (L. W. Anderson & Krathwohl, 2001), and how they
are used (Novak, 2010), but they are linked by the underlying idea of
knowledge as represented by knowledge components that are connected in
some pattern.
The common components in cognitive frameworks for learning and
memory form a knowledge base consisting of declarative and procedural
knowledge, i.e., concepts forming a vocabulary for the field in order to
communicate and procedures for applying the knowledge (J. R. Anderson,
2004). Also metacognitive components, such as beliefs, are considered to
play important roles (Flavell, 1979; Kuhn, 2000). One frequently used
framework for learning is Bloom's revised framework, which apply these
different types of knowledge, described below, to different cognitive
processes, from remembering facts to generating new knowledge (L. W.
Anderson & Krathwohl, 2001).
Concepts - conceptual knowledge. To possess conceptual knowledge
is to understand what the conceptual vocabulary means, i.e., to understand
the meaning of physics concepts and how they are connected to form physics
principles. Novice students often possess alternative conceptions, i.e., have
14
Conceptual framework
adapted ideas of how physics concepts are related that are not consistent
with the laws of physics, e.g., an object in motion requires a force acting on
the object, or that electric charges are consumed in an electric circuit
(Dykstra, Boyle, & Monarch, 1992 ; Slotta, Chi, & Joram, 1995).
Actions - procedural knowledge. Procedural knowledge in physics
means to know how to do in order to solve a physics problem. This includes
strategies, methods, and tools for modeling, problem solving, and
computations in order to solve a problem (Hestenes, 1987).
Beliefs - metacognitive knowledge. Metacognitive knowledge refers
to knowledge about the learning process, both in general terms and one's
own learning process (Veenman, Hout-Wolters, & Afflerbach, 2006). A
common construct that captures metacognitive aspects of learning is beliefs.
I here distinguish between two types of beliefs that I have found useful in
order to explain the background to my work; epistemological beliefs relating
to knowledge and learning (Hofer & Pintrich, 2002), and value beliefs, which
captures attitudes and reasons for engaging in activities (Eccles & Wigfield,
2002). Beliefs are further considered in section 3.5.
3.2
Structures in knowledge
The organization of knowledge is described in several ways in the literature
about physics education research. Schemas (Chi et al., 1981), scripts (Redish,
2004), mental models (Corpuz & Rebello, 2011; Greca & Moreira, 2000;
Larkin, 1983), and frames (Elby & Hammer, 2010; Hammer, Elby, Scherr, &
Redish, 2005) are some of the constructs that are used in order to describe
how physics knowledge is internally represented in the human mind. What
follows is a short description of the differences between these constructs and
how they have been used in previous research in order to investigate
memory, understanding, and learning.
Schemas are formed by chunks of knowledge organized in an associative
pattern that are activated by a stimuli (Chi et al., 1981; Derry, 1996; Redish,
2004). Schemata facilitate both encoding and retrieval of information and is
based on the assumption that what we remember is related to what we
already know (J. R. Anderson, 2004). Schemas correspond to an active
process depending on new experiences and learning. Schemas can also be
seen as run schedules (event schemas) that are activated by particular tasks
or situations and are sometimes referred to as scripts (Schank & Abelson,
1977).
Mental models. According to Johnson-Laird (Johnson-Laird, 1983),
mental models are personal constructions of situations in the real world that
we can use, test, and mentally manipulate to understand, explain, and
predict phenomena. Mental models can be seen as internalized, organized
knowledge structures, representing spatial, temporal, and causal
15
Conceptual framework
relationships of a concept, that are used to solve problems (Rapp, 2005).
Mental models are actually never complete, but constructed as
understanding of, e.g., a physics phenomenon, and correspond to abstract
representations of memory. Thus mental models can be seen as working
models for comprehension of different situations. Investigating mental
models in education research is expected to give information of the type of
memory that students build in different learning situations. This information
can be used to suggest circumstances in teaching and learning under which
accurate mental models can be constructed. However, mental models rely on
a person’s individual understanding and beliefs, and do therefore not always
correspond to a valid or reliable representation (Rapp, 2005).
Due to the abstract character of mental models and their ability to change
over time they are difficult to define. Carley and Palmquist (1992) addressed
a number of issues in order to develop methods for assessing mental models.
Mental models are internal representations held by the individual in contrast
to external representations such as concept models or mathematical models
(Greca & Moreira, 2002). An important issue concerns language as being
the key to mental models, i.e., mental models can be represented by words.
Mental models are also assumed to be represented as networks of concepts
and the meaning of a concept for an individual lies in its relations to other
concepts in the individual’s mental model.
Framing corresponds to an intuitive reaction when exposed to some kind
of activity and deals with the question ”What is going on here?” The
construct has previously been used in linguistics, cognitive psychology, and
anthropology. Tannen and Wallat (1993) defined framing in terms of
individual reasoning and summarized the concept of frame as the set of
expectations, based on previous experience, an individual has about a given
situation or, widely spoken, a community of practice. Minsky (1975) used
frame as describing the cognitive structure that a person recalls (memory)
when entering a new situation, e.g. a learning situation. When a person
enters the situation a frame that represents a previous situation is loaded. If
the frame doesn't fit, it is replaced or revised until it fits the situation. In an
educational setting, a student's framing used for interpreting a learning
situation can be expected to be based on cognitive and context-specific
experiences concerning, e.g., prior knowledge, skills, and beliefs, but also
social aspects, such as relations to other people, and on what resources that
are available for learning, such as literature and teachers. Due to the
particular context of a learning situation that is recalled in this thesis I have
chosen to call these building blocks involved in creating knowledge epistemic
elements and consequently epistemic framing is chosen to describe the
organization of these epistemic elements. Epistemic or epistemological
framing have previously been used in research when investigating students'
16
Conceptual framework
expectations (Bing & Redish, 2009; Elby & Hammer, 2010; Scherr &
Hammer, 2009; Shaffer, 2006).
Networks can be used to represent the relations between knowledge
components. The knowledge components are referred to as nodes and the
links between them as edges. A common representation is the semantic
network that encodes the structure of conceptual knowledge (Hartley &
Barnden, 1997).
Several studies have applied networks as representations of knowledge.
Shavelson (1972) employed a network approach to investigate the structure
of content of an exercise in relation to cognition after a teacher intervention
in the context of classical mechanics using the number of connections
between specific concepts as evidence of learning. In a study about digital
learning environments Shaffer et al. (2009) visualized epistemic frames
using an epistemic network analysis approach where the components
consisted of knowledge as well as beliefs, giving a time-resolved
development of students' epistemic framing. Jonassen and Henning (1996)
assumed that semantic adjacency between concepts in a text could be
approximated by geometric space and that cognitive structures could be
modeled through semantic networks based on geometric adjacency. Carley
(1997) proposed networks as representations of conceptual structures and
developed a toolkit for building and analyzing networks as representations of
mental models in different contexts (Carley & Palmquist, 1992). Koponen
and Pehkonen (2010) investigated structures of experts' and novices' physics
knowledge using concept networks comprising concepts, laws, and
principles as nodes, and procedures, such as modeling and experiments, as
edges, resulting in networks that can be used to interpret coherence in
physics knowledge. Also concept maps are forms of networks linking
knowledge components by their associative and causal meaning (Novak,
2010).
3.3
Concepts and meaning
Knowledge about a subject can be investigated by studying the language
associated with that subject (Alexander et al., 1991). Language is, in the
research done in these studies, assumed to be the key to students’ minds.
What they experience and learn is expressed in their own words. According
to Vygotski! and Kozulin (1986), language is assumed to mediate thought
and this assumption is used in order to represent students' mental models
and epistemic frames as networks, using the concepts they express and how
they interact. Noble (1963) suggested that the meaningfulness of a word was
proportional to the number of its associates. When students acquire
conceptual knowledge in physics, concepts would increase its associations
17
Conceptual framework
and thus increase their meaningfulness. The concepts students use and how
they use them in relation to other concepts can thus be a measure of their
conceptual knowledge (Brookes & Etkina, 2009; Koponen & Pehkonen,
2010; McBride, Zollman, & Rebello, 2010).
3.4
Visual representations
Previous research has shown that visualizations can help students build
mental models for comprehension but visualizations by themselves do not
necessarily lead to enhanced learning (Rapp, 2005). An interactive
visualization is expected to stimulate cognitive engagement and an
important feature would be to which degree a student can take control and
interact with the visualization to study characteristics of a problem solution.
In a study by Monaghan and Clement (2000) it was shown that students
who interacted with a visual simulation used mental imagery to solve the
problem while students who only were exposed to numeric interventions of
the same simulation used mechanical algorithms dominated by numeric
procession. The authors suggested that with a combination of numeric and
visual feedback, students would, in the ideal situation, integrate their
numeric and visual representation to provide a coherent model of the
problem.
3.5
3.5.1
Beliefs
Epistemological beliefs
Students' beliefs about learning have in previous research been shown to be
an important actor in the learning process of physics (Adams et al., 2006;
Buehl & Alexander, 2005; Hammer, 1994; Schommer, 1993). In the context
of introductory physics, Hammer (1994) used a framework consisting of
three dimensions; structure of physics, content of physics knowledge, and
learning physics when characterizing students' epistemological beliefs.
Student beliefs were found to influence students' work in the course and
were also consistent across physics content. Hammer found, for example,
that if students believed that physics knowledge consisted of facts rather that
general principles, it was reflected in how these students solved problems
and explained phenomena, relating to isolated facts rather than using
physics laws and principles. Students' choice of strategies in order to solve a
physics problem was also expected to be influenced by their beliefs about
problem solving. Students might have problems facing a more open-ended,
ill-structured task since the problem solving strategies generally taught in
physics problem solving represent means-ends strategies, i.e., searching for
equations that contains the same variables for the known and unknown
18
Conceptual framework
information in the task. Students need to believe that standardized equation
matching is not always sufficient for solving engineering and scientific
problems (Ogilvie, 2009).
3.5.2
Expectancy and value beliefs
Previous research on motivation in learning has also put emphasis on the
importance of student beliefs. The expectancy-value framework is an
important contribution to research on motivation in learning in order to
predict academic achievement and holds expectancy beliefs and value beliefs
as the two most important variables in achievement behavior (Eccles &
Wigfield, 2002). Expectancy beliefs in terms of self-perceptions of
competence have shown to be strong predictors of performance (Eccles &
Wigfield, 2002) as well as cognitive engagement and learning strategies
(Pintrich, Marx, & Boyle, 1993). Value beliefs refer to the reasons the student
may have for engaging in a task, such as interest, value, and do mainly affect
choice behavior and predict, for example, what courses the student will
enroll in. (Eccles & Wigfield, 2002)
Students may also have beliefs about how to explain their achievement
outcomes which has shown to be connected to beliefs about ability as well as
value. Weiner (1992) found that the most important attributions for how the
students performed in a task were ability, effort, task difficulty, and luck. For
example, attributing ability to an outcome has stronger influence on
expectancy of success, and thus actual performance, than attributing effort.
Negative perceptions about own capability to complete the task, i.e., selfefficacy (Bandura, 1993), are strongly related to expectancy beliefs about
failure (Eccles & Wigfield, 2002) and are expected be related to choices of
less optimal strategies for learning.
3.6
Motivation
Motivation is what keeps us going when doing an activity, for example
engaging in a learning activity. Motivation can vary in type as well as
intensity (Ryan & Deci, 2000). The type of motivation has to do with the
reasons for engaging in an activity, e.g., a student gets motivated to do an
assignment because he or she gets paid, or by realizing the value of
completing the assignment in terms of learning the skills needed for a
profession. In self-determination theory (Ryan & Deci, 2000) the type of
motivation is found on a intrinsic-extrinsic continuum where intrinsic
motivation is described as a will to engage in an activity because it gives
satisfaction, while extrinsic motivation is driven by a separable outcome.
Ryan and Deci proposed that extrinsic motivation could vary and also
consist of intrinsic aspects, depending on the degree of internalization and
19
Conceptual framework
integration of extrinsic goals.
Intrinsic motivation exists within an
individual and is, besides a self-determined behavior, manifested by positive
emotions of enjoyment and satisfaction. The intrinsic character of extrinsic
motivation is, due to internalization of goals, also experienced as selfdetermined behavior, leading to increased engagement and positive
emotions and thus difficult to distinguish from true intrinsic motivation.
3.6.1
Autonomy
There are many perspectives on the role and origin of autonomy, i.e., selfdetermination, which is considered as an important variable in motivational
frameworks (Ryan & Deci, 2000). Autonomy is a multidimensional
construct and can take different forms depending on, e.g., stage of learning
and context. It can be associated with the characteristics of a learning
situation, e.g., how a task is designed in terms of the number of possible
solution pathways and teacher support for autonomy, but also with
characteristics of the learner herself, personal autonomy. A general
description of personal autonomy is the learners' possibility to take charge or
control of their own learning (Benson, 2001). The level of responsibility for
learning a student is capable of handling is thus expected to be dependent on
the student's knowledge and skills but also on epistemological beliefs,
values, and goals associated with the task. Candy (1988) suggested that a
learner's autonomy in a given learning situation has two main dimensions:
situational autonomy and epistemological autonomy. While situational
autonomy is associated with independence from outside direction and the
degree to which skills and knowledge are suited for the situation,
epistemological autonomy is rather involved in the learner's ability to make
judgments about the content to be learned and about strategies of inquiry.
Littlewood (1996) argues for both ability and willingness as components for
autonomy, where willingness in turn involves motivation as well as
confidence (i.e., perceived ability) to work autonomously with a task.
Willingness and ability can be seen as interdependent since the more
knowledge and skills the student possesses, the more confident the student
feels about working independently. Autonomy can be considered as being an
important entity in the constructionist learning framework (Harel & Papert,
1991) where tasks are designed to motivate students to use their own
knowledge in order to build things and thus create new knowledge.
Autonomous behavior is encouraged by the guidance from teachers as well
as the feedback from the results of their exercises, e.g., a computer
simulation or a physical product, such as a building or a construction. Many
problem-solving and simulation environments provide scope for
autonomous behavior and are designed with a constructionist learning
20
Conceptual framework
approach in mind, e.g., Logo environment (Papert, 1993), Boxer (diSessa,
2000), SodaConstructor (Shaffer, 2006), and Algodoo, (Bodin et al., 2011).
3.6.2
Indicators of motivation
The emotions that students experience in relation to a learning situation are
often considered as good indicators of motivation in learning. (Pekrun,
1992). According to self-determination theory (Ryan & Deci, 2000), intrinsic
motivation generates positive emotions and indicate a will to engage in
activity. Positive emotions, such as enjoyment or excitement, are also
proposed to indicate a deeper cognitive engagement (Pekrun, Goetz, Titz, &
Perry, 2002). Emotions expressing pleasure, control, and concentration are
part of the flow framework (Csíkszentmihályi, 1990). Flow is described as an
intense feeling of active well-being and is experienced when perceived skills
and challenge of a task are above a threshold level and in balance. If flow is
within reach, emotions like control and enjoyment function as activators that
encourage the learner to increase their skills or the level of challenge to
achieve balance. If the discrepancy between skills and challenge is too large,
negative emotions like boredom, anxiety, uneasiness, or relaxation
interrupts behavior, which might cause the learner to turn to another
activity.
3.7
Experts, novices, and computational physics
University teachers in physics usually possess long-time experience within
their fields. Their knowledge is often considered as tacit (Polanyi, 1967), i.e.,
not easily verbalized, automated and adapted as an expert level of knowledge
(Dreyfus & Dreyfus, 1986). Tacit knowledge can also be related to the welldeveloped schema, or large chunks of interrelated physics principles and
concepts, an expert activates when approaching a physics problem solving
situation (Chi et al., 1981). A novice student can be considered to not yet
possess appropriate schemas for physics problems and therefore has to rely
on isolated facts and principles and a means-ends strategy for problem
solving rather than a knowledge development strategy (Larkin et al., 1980).
During a means-ends analysis of a problem there is a continuous evaluation
between the problem state and the goal state. The focus lies on the quantity
to be found and on trying to find expressions that connect that unknown
quantity with the variables given in the problem, i.e., a formula-centered
problem solving strategy (Larkin et al., 1980). In a knowledge development
strategy, as is used in an expert sense, known information, e.g., physics
principles, is used in order to develop new information, which leads towards
the solution. A problem that can be solved using a means-ends strategy does
not necessarily require any prior knowledge, just a set of actions, which in
21
Conceptual framework
the physics problem case means to search for equations that contains the
unknown, e.g., as in the end-of-the-chapter physics problems described
above. In order to avoid means-ends strategies for problem solving,
Hestenes (1987) suggests that problem solving should be taught with a
modeling approach, just as the expert approaches a problem by creating an
abstract model of the given information in the problem statement and then
develop the model in order to include also the unknown or searched
information.
A computational physics problem, e.g., simulating force interactions
between many particles, is seldom possible to solve using only a means-ends
strategy, and is thus a type of problem that is suitable for a modeling
approach in teaching. A numerical problem needs to be modeled, using not
only appropriate physics principles, but also appropriate mathematical
models as well as programming algorithms, and there is no unknown
quantity to search for. Numerical problem solving in physics is therefore
expected to force students to use an expert-like, knowledge development
strategy in order to solve the problem. Solving complex problems also
provides scope for autonomy and possibilities to be in control of the learning
process, i.e., aspects of a learning situation that is considered as central in
most motivational frameworks (Ryan & Deci, 2000).
Research shows that most students hold novice-like knowledge structures.
Teachers need to be aware of possible misconceptions that students hold as
well as their beliefs (Grayson, 2004). Many never develop expert-like physics
knowledge and keep stating physics problems based on surface features
instead of recognizing the physics principle that is applicable for the
problem. In order to develop expert-like problem solving skills as well as to
achieve a coherent physics knowledge students also need to solve open and
more complex problems (McDermott, 1991; Redish & Steinberg, 1999).
22
Research questions
4 Research questions
As discussed in the previous chapters there are many components that may
affect learning in physics and the desired transition from novice towards
expert. In this work I have the following research questions in focus:
!
What are the critical aspects of using computational problem solving in
physics education?
!
How do teachers and students frame a learning situation in
computational physics? Do teachers and students agree about learning
objectives, approaches, and difficulties?
!
What are the consequences in terms of positive or negative learning
experiences when using computational problem solving in physics
education?
In the papers these questions are developed and investigated as more
specific questions:
!
What are the relationships between students’ prior knowledge,
epistemological and value beliefs, and emotional experiences (control,
concentration, and pleasure) and how do they interact with the quality of
performance in a learning situation with many degrees of freedom?
(Paper I)
!
What are the students focusing on, in terms of knowledge and beliefs,
when describing a numerical problem-solving task, before and after
doing the task? (Paper II)
!
What role does physics knowledge take in describing a numerical
problem-solving situation? (Paper II)
!
When teachers say that something is important, how is this described in
an epistemic network? (Paper III)
!
How do students' epistemic networks change between before and after
the task? (Paper III)
!
How do students' and teachers' epistemic networks differ? Are students
and teachers focusing on the same critical aspects? (Paper III)
23
Research questions
!
How do students' mental models change during the assignment? (Paper
IV)
!
How do students programming code change during the assignment?
(Paper IV)
!
Are there any relations between progress in students' mental models, the
characteristics of the code, and the structure of the lab report? (Paper
IV)
In addition to these educational research question I have introduced a,
from an educational research perspective, novel method for extracting,
investigating, and visualizing mental models, namely network modeling.
24
Methods
5 Methods
The empirical data used in the studies presented in this thesis originates
from different data collection methods. Both fixed and flexible approaches
are used in a mixed-method research design in order to carry out the
investigations. Fixed research designs are typically well planned, e.g., an
experiment or a survey, and could generate quantitative as well as qualitative
data. A flexible design has room for development as the investigation
continues, e.g., observations or interviews, and could also generate
quantitative as well as qualitative data (Robson, 2002). Flexible designs are
sometimes accused of being less scientific than the fixed design. However,
scientific method, i.e., to consider systematics, objectivity, and ethics, must
be the backbone of all research. The results are extracted using adequate
methods of analysis, chosen due to their possibility of revealing patterns of
interest in the collected data that correspond to the posed research
questions.
5.1
The context of the study
The studies that form the basis for this thesis were carried out at the same
university in Sweden. The same assignment in computational physics was
used in all studies, except for the teacher interviews in Paper III. Three
different student groups, from three different years, and four university
teachers have contributed to the data.
5.1.1
The sample
The students participating in the studies were university students at their
second year of their engineering physics education. Three different student
groups, corresponding to a total of 87 students, from three consecutive
years, contributed to the data sets. Students mean age was 22 at the time of
the data collection. The students have contributed to the data set, either by
responses to questionnaires, written lab reports, or as interviewees. There
were only about 15% women and therefore no analysis concerning gender
issues has been performed. Prior to the assignment subject for investigation,
students had studied courses corresponding to mathematics 45 ECTS
(European Credit Transfer System, where 60 ECTS corresponds to one year
of full time studies), programming 7.5 ECTS, classical mechanics 9 ECTS,
and numerical methods 4.5 ECTS.
In one of the studies, presented in Paper III, four university teachers from
the departments of physics, math, and computer science contributed to the
collected data.
25
Methods
5.1.2
The task
The instruction to the assignment subject for investigation is found in the
Appendix. The assignment was part of a five-week course (7.5 ECTS) in
mathematical modeling of physics. Prior to this assignment the course
treated mathematical methods of physics in vector algebra. Students had
also worked with a simulation environment for investigating electromagnetic
phenomena.
Students were given about seven days of full time studies to complete the
task, of which five days were teacher assisted computer lab time. This time is
estimated due to the fact that the time for completing the assignment span
over Christmas break giving about two weeks for holidays, which students
could have used for self-studies. An intermediate deadline was set right
before Christmas break in order to let the students turn in a preliminary
report with a functioning simulation code to gain bonus marks for the
examination of the course.
5.2
Data collection methods
The data collection methods were chosen based on what information that I
wanted to retrieve in order to answer the research questions. I considered
both quantitative and qualitative data to be necessary sources of information
in order to cover the scope of the research questions.
5.2.1
Questionnaires
Questionnaires are commonly used for descriptive data about personal
characteristics and their interrelations. A research questionnaire requires an
extensive development design procedure based on the theoretical issues that
are subject for the data collection to make sure the survey is measuring data
that can be used to answer the research question (Robson, 2002).
Questionnaires were used in order to collect data that would provide
information about students’ knowledge, beliefs, attitudes, and perceived
emotions and mental effort in the learning situations forming the context of
this research. Questionnaires were the main data collecting method in Paper
I and used as complements in the other papers.
5.2.2
Interviews
Interviews were used to collect data in three of the articles. Interviews can be
performed in many structural ways, from letting the interviewees respond to
a questionnaire to letting them talk freely about anything. The interviews in
this study have been semi-structured, meaning that for a particular set of
26
Methods
interviewees the same questions concerning a specific topic were posed to
everyone and about the same time was allocated for every interview
(Gillham, 2005). I performed all the interviews myself following interview
guides that were prepared prior to the interview. All interviews were audio
recorded and transcribed verbatim by me. Interviews were used in Papers II,
III, and IV.
5.2.3
Students’ written reports and Matlab code
A third source of data used for investigation in this thesis was the students'
written reports from their assignment in computational physics. The reports
consisted of a text where the answers to a number of questions posed in the
lab instruction were supposed to be expressed in running text together with
graphs and plots from the simulation. The students were also instructed to
attach the Matlab code to their simulation. The purpose of using the lab
reports as data was to collect information of students' performance in the
assignment and use this as a measure of their cognitive position after the
assignment. Students' written reports were used as data sources in two of the
papers, Papers I and IV. In Paper IV the students' Matlab code was also
subject for analysis. Students were then asked to submit the Matlab code
they had produced during each day during the assignment resulting in about
five code samples from each student.
5.3
Analysis
Methods for analysis were chosen in order to extract the appropriate
information from the collected data.
5.3.1
Multivariate statistical analysis
Multivariate statistical analysis involves statistical analysis of several
variables collected at the same time in order to capture different aspects of a
particular situation. A multivariate analysis approach gives information
about how the variables are interacting in a specific situation and is also
helpful in order to reduce a large number of variables. Projection methods
are also adequate when there is noise in the data and when matrices have
more variables than observations, which is common in small-scale studies
like those presented in this thesis.
In this thesis questionnaire data has been subject for multivariate analysis
in order to investigate interrelations between questionnaire items and to
reduce the large number of variables that the questionnaires generated. The
statistical methods used are the projection methods of principal component
analysis (PCA) and it’s regression counterpart, partial least squares analysis
27
Methods
(PLS) (Joliffe, 1986). The statistical software used for these analyses was
Simca P12 (Umetrics, 2009). These methods are described more in detail in
Paper I.
5.3.2
Content analysis
Analyzing textual data for educational purposes is usually done by a
qualitative approach. I have used a mix of quantitative and qualitative
analysis in order to extract meaning from the interview transcripts and the
students' written reports. When I started to consider representing students’
and teachers’ knowledge and beliefs structures as visual networks I came
across computer assisted methods of text mining and found that they could
be useful in order to extract information from the interview transcripts.
Semantic networks for content analysis as well as for knowledge
representation have in previous research been proposed as useful tools
(Atteveldt, 2008; Carley & Palmquist, 1992; Hartley & Barnden, 1997;
Shavelson, 1972) and in order to prepare the data for a network analysis,
textual preprocessing in terms of content analysis had to be performed.
Content analysis is often referred to as the methods of systematically
studying the quantitative content of texts, e.g., frequency of certain concepts
or length of utterances in a conversation (Robson, 2002). I have used
content analysis in the wider meaning, including qualitative as well as
quantitative aspects which is in line with the definition of content analysis as
stated by Markoff, Shapiro, and Weitman (1975):
"Content Analysis [is] any methodological measurement
applied to text for social science purposes. [..] the term refers
to any systematic reduction of a flow of text, that is, recorded
language, to a standard set of statistically manipulable
symbols representing the presence, the intensity, or the
frequency of some characteristics relevant to social science."
(Markoff et al., 1975, p.5)
Also Krippendorff (2004) argues for content analysis as a tool for making
inferences about the message context rather than just measuring aspects of
the message content.
"Content analysis is a research technique for making
replicable and valid inferences from texts (or other
meaningful matter) to the contexts of their use."
(Krippendorff, 2004, p. 18)
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Methods
Two applications of semantic network analysis have been used for content
analysis in the studies presented in this thesis:
1.
Coding of the textual data into epistemic elements using a
qualitative analysis in order to meet the research questions
followed by network analysis as a tool for visualization and
further interpretation.
2. Computer-assisted text-mining of textual data into contextdependent concepts visualized as networks followed by a
qualitative analysis in order to meet the research questions.
Epistemic elements are here statements expressing beliefs, knowledge
or resources used in the learning situation. In the first method the interview
transcripts were manually coded using a mix of confirmatory and
exploratory approaches in order to find what epistemic elements that would
constitute the networks. The confirmatory aspects meant that in order to
categorize the meaning in the transcripts, statements expressing the
principle categories of beliefs elements, knowledge elements, and resource
elements, specific for the particular learning situation, were initially
searched for. Beliefs were defined as statements expressing any opinion,
goal, attitude, strategy, value, etc., that was associated with teaching and
learning. Within the knowledge category any expression stating knowledge
or skill about the sub-categories physics, math, programming, modeling, and
problem solving, were registered as a knowledge element. The next step
followed a more exploratory approach where elements within these principle
categories were added as they were found to show relevance in the data set.
These codes for epistemic elements were then replacing the actual
expressions in the interviews, reducing the transcript to text document
consisting only of codes for epistemic elements. These epistemic elements
were then subject for network analysis, presented in the next section. This
method of content analysis was used in the study presented in Paper II.
Context-dependent concepts are generalized words associated with
the particular context. In the second method the textual data was
preprocessed in order to reduce the text documents to consist of a limited
number of context-dependent concepts that were explicitly describing the
particular context of computational problem solving in physics education.
These context-dependent concepts and their semantic relations would later
constitute the networks. The text documents were initially run through a
text-mining tool, Automap (Diesner & Carley, 2004). Automap is part of a
toolkit for network analysis developed by Carley, Diesner, Reminga, and
Tsvetovat (2007) and has functions for preprocessing texts, such as concept
lists, delete lists, thesauri, as well as to generate networks. The textual data
29
Methods
were initially run through Automap in order to generate a union word list
that covered all words that occurred in the entire text documents subject for
analysis. The word list could be sorted alphabetically or according to
frequency or relative frequency of words. This list was then manually treated
in order to create a list of context-dependent concepts that could be used as a
thesaurus for replacement of words into context-dependent concepts. Only
words that had any meaning in the particular context were kept in the
thesaurus. In questionable cases, e.g., words with multiple meanings, I
consulted the original textual data in order to locate the words and
determine their relevance. In order to further reduce the number of words,
generalizations were made, e.g., words like simulations, simulate, and
simulating were coded as "simulation". This procedure was repeated in an
iterative process until the list of context-dependent elements were
considered to still cover the meaning in the textual data but represent a
manageable number of concepts. For every preprocessing action, i.e.,
replacing words with the context-dependent concepts, the transcripts were
read through in order to make sure that meanings in the texts were kept
intact. When all the replacements were done the text-documents were
prepare for the next step of analysis, network analysis that would visualize
the meaning in the textual data as networks of relations between contextdependent concepts.
This method was used in Paper III, where 26 concepts were considered to
carry the meaning in the interview transcripts corresponding to the textual
data, and Paper IV, where 101 concepts were used. Since the sets of concepts
use in each study were strongly context dependent, it was necessary to
generate a set of concepts for every situation depending on how fine-grained
or general the analysis was planned to be. The smaller number of contextdependent concepts, used in Paper III gave a more coarse-grained base for
further analysis, while more detailed information was kept in the study in
Paper IV.
Comparison between the two approaches. Content analysis by
coding the interview transcripts into epistemic elements corresponds to
traditional qualitative analysis of textual data. It is a very time-consuming
procedure but the information provided is rich and corresponds to elements
representing the researchers knowledge base in the specific context.
However, there is a limit to how much textual data that is possible to
manually code. A computer-assisted text-mining approach is a fast way of
determining the content of textual data and it is possible to analyze large
amounts of data. There is however always difficulties associated with
deciding which words that should constitute the set of concepts, especially
when words have multiple meanings. To ensure reliability in this coding
process it is desirable to return to the original textual data and double-check
questionable cases. This is particularly important if only a few or small
30
Methods
samples are used. If large amounts of textual data is analyzed a few
misinterpretations of concepts is expected to cause less noise.
By investigating occurrences of epistemic elements and contextdependent concepts in the reduced interview transcripts and lab reports
information was revealed about what focus students and teachers had. In
order to also investigate relations between these elements and concepts
networks were built using elements and concepts as nodes and their
semantic adjacency as links. This procedure is described in the next section.
5.3.3
Network analysis
Network modeling makes it possible to visualize and understand the
complexity of a system with many interacting components or agents.
Common applications of network modeling are, for example, social
interactions, biological systems, information systems, and semantic
patterns. Increasing computer capacity have made possible to investigate
networks with billions of interacting agents, for example as in biological and
computer networks. Studies of life systems and drug design are examples of
applications of biological network analysis (Junker & Schreiber, 2008).
Previous studies in network analysis are also associated with, e.g., social
interactions (Wasserman & Faust, 1994), or semantic networks (Steyvers,
2005). In social network analysis the focus is on investigating relations
between people in order to answer questions concerning economic, political,
or social importance, for example, about terrorist networks (Borgatti, Mehra,
Brass, & Labianca, 2009), or to understand the spreading of human diseases,
e.g., SARS and the swine flu (Pastor-Satorras & Vespignani, 2001). Semantic
networks represents the relation between concepts and can be used to
represent knowledge within a context (Carley, 1997; Hartley & Barnden,
1997) as I will discuss further on in this section.
If a system is small, with only a few nodes and links, it can generally be
visualized as is. Many systems, however, are very large and need to be
described in a simplified manner. Depending on what information we want
to draw from a network there are different methods of analysis. Investigating
the formation of a network might require other methods than investigating
the dynamics of a network. The formation of a network is often studied by a
modularity approach where modules are formed according to higher density
within the modules and a sparser structure between modules (Newman,
2006). For a system's behavior, e.g., how local interactions between few
nodes induce a flow through the whole system, it is interesting to understand
the network's dynamic structure and how the links regulate the flow. The
map equation (Rosvall, Axelsson, & Bergstrom, 2009) is an informationtheoretic algorithm which can optimize the path of a random walker in a
network and describe how information flows in the network. Groups of
31
Methods
nodes cluster into modules where information flows quickly. The links
between modules represent information paths, which connect the clusters
and reveal the whole networks dynamic structure. In previous research the
map equation has been used in networks to show the flow of information
within the scientific community by studying cross citations of scientific
journals (Rosvall & Bergstrom, 2008). The results revealed a bidirectional
structure between basic sciences and a directed flow from applied sciences
referring back to basic sciences giving information of how knowledge was
flowing among scientists within different subject fields.
The choice of using network analysis as a tool for investigating students'
and teachers' epistemic framings, conceptualizations, and mental models
was based upon previous research about representing knowledge and beliefs
as maps of concepts (Carley & Palmquist, 1992; Hartley & Barnden, 1997;
Novak, 2010; Shaffer et al., 2009; Shavelson, 1972). The content analysis
described in the previous section provided the epistemic elements and the
context-dependent concepts that would form the node sets used for building
the networks. In order to complete the networks the relation between the
concepts were needed. Two approaches were used also here: 1) determining
the relations between epistemic elements manually, as described in Paper II,
and 2) generating the networks automatically based on adjacency between
context-dependent concepts, an approach used in Paper III and IV.
Manual building of networks. In order to map students' epistemic
framing the relations between the epistemic elements, described in the
previous section about content analysis, were determined manually, a
procedure described in detail in Paper II. The decision of a relation between
two epistemic elements where mainly based on adjacency, i.e., elements that
were close were linked in most cases, but also other connections between
elements within a sentence or a paragraph could be considered as links. The
weight of each link was equal to one and all links were bidirectional, i.e., I
did not consider the direction of the link between two elements.
Automatic generating of networks. The second approach
corresponded an automatic generation of networks. The tool Automap
(Diesner & Carley, 2004), used for the text mining procedure used for coding
textual data into context-dependent concepts, was used also here in order to
generate semantic networks from the coded text documents. These networks
were based only on adjacency between concepts, using a window of two, i.e.,
only elements that were adjacent were links. The unit of analysis was chosen
to be a paragraph, i.e., only concepts within a paragraph could form a
relation.
Comparison between the two approaches. By automatic generation
of networks there is a risk that the network will not capture the intended
information. The choice of window size in this case is critical. With a too
large window, however, there is a risk that too many concepts will be linked,
32
Methods
giving a network with no distinguishable information. A too small window
leads to a risk that important links will be lost. A manual building of
networks is a very time-consuming process but is expected to capture all the
relevant information in the textual data and thus a suitable approach for case
studies. However, the more automatic procedure has in the studies of Paper
III and IV shown to reveal intelligible results also on small samples. The
automatic approach is fast and expected to be reliable enough to be used on
large amounts of textual data where students' mental representations of
knowledge and beliefs relatively easily can be determined. However, the
networks generated suing a more automated process were in these cases
further analyzed using a qualitative approach where the networks were used
as indicators of where interesting information could be found, taking the
analysis one step further. Some context-dependent concepts of particular
interest were chosen as prompts in order to locate what type of information
their interactions with other concepts carried. Using this approach resulted
in determining a number of key aspects associated with computational
physics, as described in Paper III.
This is an area that needs further research in order to determine how
content analysis and network analysis can be developed towards different
implementations in research as well as in educational development.
5.3.4
SOLO analysis
There are different ways of determining the quality of an assignment. The
SOLO (Structure of the Observed Learning Outcome) taxonomy (Biggs &
Collis, 1982), is a tool for determining quality of learning outcome in terms
of complexity based on how students use arguments when explaining and
performing a task. The SOLO taxonomy was used for analysis of students'
lab reports in order to determine their quality and get a measure of students'
performance and is described more in detail in Paper I.
5.4
Methodological issues
The purpose with research is to find explanations to phenomena and to find
new ways of investigating phenomena. A desire for generalization of results
is always present but sometimes it is necessary to investigate a smaller
sample or even a case in order to test ideas that could be taken to further
research. The studies presented in this thesis are based on small samples
and cases and different methods have been used for data collection as well as
analysis corresponding to a mixed-method design where both fixed and
flexible approaches have been taken (Robson, 2002).
33
Methods
5.4.1
Validity
Validity in research is whether the chosen methods, used for data collection
and analysis, are appropriate for measuring the constructs they are supposed
to measure. For quantitative data subject for statistical analysis, validation
can be done using statistical tools. This was the case in Paper I where the
questionnaire data was subject for multivariate analysis methods which
provided support for cross-validation and correlation patterns. There are
some threats to validity in flexible research designs that generate qualitative
data, which I have tried to overcome in this work. The interviews were all
audio recorded and transcribed by myself in order to document as much as
possible from the interview sessions. When coding the interview transcripts
into epistemic elements (Paper II) I mainly used the transcripts but I kept
returning to the recordings when I wanted to make sure that I've interpreted
students intentions and meanings correctly. I did this coding myself and
there is always a risk with using only one researcher. However, the choice for
content analysis were based on theoretical assumptions of what epistemic
elements that were intended to be captured and I chose to reanalyze the data
at several occasions with several months apart until the necessary features of
the interviews were covered by appropriate epistemic elements. The
categorization of words into context-dependent concepts as used in Paper III
and IV corresponded to a less sensitive analysis method but used a more
exploratory approach than the study in paper II. The categorization
procedure was repeated in an iterative process in order to capture all the
necessary information that was assumed to describe the particular situation.
Using triangulation is a way to increase validity in research. I have in these
studies used both quantitative and qualitative approaches, using different
methods for data collection as well as for analysis. In order to answer the
overall research questions, results from all studies are considered in order to
cover the different aspects these approaches have given.
5.4.2
Reliability
Reliability in research is extremely important. In order to be completely
reliable an investigation carried out by a research group should generate the
same results if repeated by another research group. For flexible research
designs this is very difficult to accomplish since the situation for the study
changes, especially in education research where unpredictable humans are
the subjects for investigations. Different students, different teachers,
different curriculums, different environments, even the time of the day or
whether it is summer or winter could affect data collection. When collecting
and analyzing qualitative data it is suggested to refer to consistency rather
than reliability (Lincoln & Guba, 1985). The investigations have been
34
Methods
performed on three consecutive groups of students and generated consistent
results where it has been possible. Student beliefs and attitudes, using the
same instrument, have been measured in all studies giving student profiles
that were consistent through the student groups. A rich description of the
studies that have been performed facilitate for reproduction of results and I
have tried to include as much information as possible that had to do with the
context, the data collection, and the analysis.
35
Results
6 Results
This chapter presents a summary of the papers and the results according to
the research questions that are associated with each paper. In the end of this
section the main findings are summarized in relation to the overall research
questions presented in chapter 3.
6.1
Paper I: Role of beliefs and emotions in numerical
problem solving in university physics education
This study aimed at investigating the correlations between personal
characteristics, such as prior knowledge and beliefs, and the emotions that
are involved in a high autonomy learning situation, and these variables’
effect on student performance. The research question is posed as:
!
What are the relationships between students’ prior knowledge,
epistemological and value beliefs, and emotional experiences (control,
concentration, and pleasure) and how do they interact with the quality of
performance in a learning situation with many degrees of freedom?
The results show that expert-like beliefs about physics and learning physics
together with prior knowledge were the most important predictors of the
quality of high performance on a task in computational physics offering
several degrees of freedom. Feelings corresponding to control and
concentration, i.e., emotions that are assumed to indicate a high level of
motivation were also important in predicting performance. Unexpectedly,
intrinsic motivation, as indicated by enjoyment and interest, together with
students’ personal interest and utility value beliefs did not predict
performance. This indicates that although a certain degree of enjoyment is
probably necessary, motivated behavior is rather regulated by integration
and identification of expert-like beliefs about learning. Motivated behavior is
thus more strongly associated with concentration and control during
learning. The results suggest that the development of students’
epistemological beliefs is important for students’ ability to learn from
realistic high-autonomy problem-solving situations in physics education.
6.2
Paper II: Mapping university students’ epistemic
framing of computational physics using network
analysis
The purpose of the second paper was twofold, having educational as well as
methodological issues in focus. The educational purpose was to investigate
36
Results
changes in students’ epistemic framing before and after doing an assignment
in numerical problem solving. Epistemic frames are here referred to as the
students’ knowledge and beliefs structures that are activated and revealed
when describing (before the task) and recalling (after the task) the
assignment in individual interviews. The epistemic networks are built upon
epistemic elements, representing different aspects of knowledge and beliefs,
as nodes that are connected with links in terms of the interaction between
these epistemic elements. The epistemic elements are defined using a
thematic coding approach of transcribed student interviews. The purpose
was to find, for the context, relevant statements that expressed physics,
math, programming, and modeling, but also metacognitive elements
expressing epistemology, value, and attributions. The methodological issues
also concerned using network analysis as a novel tool for extracting,
analyzing, and visualizing the students’ epistemic networks from the
transcribed interviews. The research questions of interest in this paper was:
!
What are the students focusing on, in terms of knowledge and beliefs,
when describing a numerical problem-solving task, before and after
doing the task?
!
What role does physics knowledge take in describing a numerical
problem-solving situation?
The results showed that students had different focus before and after the
task, revealed by how the epistemic elements were clustered in each case.
Before the task students used descriptive elements and expressed the task in
terms of values about learning, in particular Matlab, but also in terms of
interest and real world connection. In general they expressed confidence that
they would manage the task due to previous knowledge. However, they did
express concerns about difficulties with getting started with the assignment
but expected that with help from other students and reading the instruction
carefully they would indeed manage the task. After the assignment students'
attention turned towards actual experiences of the task where
troubleshooting and aspects relating to modeling and programming were in
focus.
Students' use of physics was shown in a 100 % increase in number of
unique physics elements in the interviews after the modeling activity. This
indicates that, even though no measures on physics knowledge were done in
this study, that students were more comfortable with expressing the task in
terms of physics concepts after the exercise suggesting an increased
understanding of how to use the concepts in this new context of
computational physics. This increase was not shown for any other category
of epistemic elements.
37
Results
6.3
Paper III: Mapping university physics teachers' and
students' conceptualization of simulation competence
in physics education using network analysis
In the third paper an approach to analyze and visualize epistemic networks
was used in order to investigate teachers' and students' conceptualization of
computational physics. The data was based on interviews with four
university teachers with experience from education in computational physics
and visualization and six students in computational physics with the purpose
of extracting beliefs structures concerning competencies involved in
computational physics, such as physics, math, programming, and modeling.
The interview transcripts were analyzed using computer-based content
analysis generating context-dependent concepts. Semantic networks based
on adjacency between concepts were created and visualized as epistemic
networks. The research questions were:
!
When teachers say that something is important, how is this described in
an epistemic network?
!
How do students' epistemic networks change between before and after
the task?
!
How do students' and teachers' epistemic networks differ? Are students
and teachers focusing on the same critical aspects?
These epistemic networks showed that there were similarities as well as
differences between how teachers and students framed this particular
learning context. The similarities were found in a basic structure where
context-dependent concepts describing physics, math, problem solving,
programming, and modeling formed a rather stable structure for both
teachers and students indicating that they agree about the main
characteristics of computational physics. The differences were in the
meaning of how these context-dependent concepts interacted and where the
focus was. Using the teachers’ networks six key aspects about using
computational approaches in physics education could be identified. Teachers
saw possibilities to solve deeper and more interesting problems, facilitation
of fundamental understanding, and possibilities to control and test the
solution but also saw risks that fundamental physics understanding could be
hampered if demands of programming and mathematical skills were too
large. Students agreed with most of these key aspects, especially after the
task. What students did emphasize more was the visual feedback from the
simulations and graphs that they used to test and control the simulation.
38
Results
Students were not all convinced that computational physics would help
develop fundamental understanding of physics and math.
A result from this study not reported in the submitted article but still an
interesting result, was that the epistemic networks did differ between
university teachers with different academic backgrounds. The epistemic
networks indicated that the main issue for a teacher with formal background
in physics was to use physics principles when investigating a simulation or a
solution while for a teacher with formal background in math the focus was
on the numerical algorithms. A consequence from this result could be that
teachers and teacher assistants with different educational background focus
on different aspects of an assignment in computational physics. For
example, it could be very difficult to debug and solve a computational
physics problem if physics principles such as conservation of energy and
momentum are not considered. In order to guide students to solve such a
problem the teacher needs to instruct students to also consider physics
principles, which might not be the case if the teacher lacks formal education
in physics. The other way around is of course also possible. Numerical
solutions are usually discrete, meaning that unexpected results due to
numerical errors might occur and in that case it is important to understand
that the a chosen numerical solution has limitations. From a methodological
point of view this result shows additional evidence of that epistemic network
analysis is a useful method in order to describe cognitive focus.
6.4
Paper IV: Students' progress in computational physics:
mental models and code development
The fourth paper focuses on the students' cognitive process during a oneweek computational physics assignment. Students' mental models were
monitored using interviews at several occasions during the assignment. As a
complement the code the students produce each day was collected in order
to get data on students achievements. The interview data was analyzed by
content analysis followed by semantic network analysis. The content analysis
reduced the transcripts to consist of 101 unique concepts that were content
bearing in this particular context. Semantic networks were then created from
the reduced transcripts using semantic adjacency as links between concepts.
These semantic networks were then assumed to represent students' mental
model at the time of the interview. The programming code was also
subjected to network analysis in order to find trends in how students built
the code for this particular simulation assignment. Students' lab reports
were subject for the same content and semantic network analysis in order to
see if they reflected students' mental models. The results were presented
partly as a compound view of students' shifts in their mental models but also
39
Results
as a case study, where two students with different beliefs profiles were more
carefully investigated.
!
How do students' mental models change during the assignment?
!
How do students programming code change during the assignment?
!
Are there any relations between progress in students' mental models, the
characteristics of the code, and the structure of the lab report?
The semantic networks revealed an interesting shift in the students'
mental models where the focus moved from being concerned about the
difficulties with writing the programming code towards using more and
more physics related concepts, especially energy conservation, and
expressing less concern about coding difficulties. This was an expected
pattern, as similar results were provided in Paper II, but it also means that
the method chosen to analyze and visualize mental models did give
intelligible results.
The case study showed that students with different beliefs profiles did not
use the same concepts when describing difficulties, strategies, and
expectations, i.e., they focused on different things. The student with expertlike beliefs focused on how to perform tests on the simulation and to check
its performance and had already a coherent view of the whole assignment.
The student with novice-like beliefs was focused on the first steps of the
assignment and had not yet started to look forward towards a general
application.
The student with expert-like beliefs also used a more general coding
approach, developing a code that would apply to all steps in the assignment.
The code thus was only slightly changed between the submissions and kept
its general structure all the way into the lab report. A student with novicelike beliefs started with an approach that would solve only the first step in
the assignment, coding a special case rather than a general case. As the
assignment turned more complex this student had to rewrite large parts of
the code in order to match the general case and solve all steps in the
assignment.
40
Discussion of main findings
7 Discussion of main findings
I here summarize and discuss the main findings as answers to the research
questions stated in chapter 4 given by the empirical data in relation to
previous research.
7.1
!
Critical aspects of computational physics
What are the critical aspects of computational problem solving in
physics education with respect to the relationship between student
characteristics, progress, and performance?
Students' beliefs about physics and learning physics have in these studies
shown to be important predictors of performance in computational physics.
The task described and investigated in this thesis corresponded to a learning
situation which provided many degrees of freedom and participants who
believed that invested effort and taking responsibility of one's own learning,
performed better in this task. The learning situation's characteristics were
also mirrored in the students' perceived control and concentration emotions,
which are important indicators of motivation, showing that this assignment
provided scope for self-determined behavior.
Even though previous research stresses the importance of including
students' motivation in successful learning (Eccles & Wigfield, 2002; Ryan &
Deci, 2000) it is mainly the cognitive aspect of motivation, represented by
the emotions concentration and control, that contribute to performance in
the particular context described in this thesis. Emotions expressing
enjoyment and value are often used as indicators of intrinsic motivation
(Pekrun, 1992; Turner, Meyer, & Schweinle, 2003), but in Paper I they
showed little correlation with performance in this particular context. Thus,
the results imply that it is not enough to just be interested and value the task
as useful in order to perform well, the task must also be optimized for
cognitive engagement in order to motivate students.
The assignment used in these studies represented a complex learning
situation where knowledge and skills from several domains were needed in
order to perform well. The learning situation also provided several degrees
of freedom where students could choose when, where, and how to solve the
problem, characteristics that are related to the level of autonomy of a task.
Previous research has, however, shown that not all students perform well in
a high autonomy learning situation. It is mainly those students who already
possess expert-like beliefs that are more likely to be favored by a learning
situation with many degrees of freedom (Redish et al., 1998; Windschitl &
Andre, 1998). Autonomy is one of the needs, i.e., reasons to engage in an
41
Discussion of main findings
activity, in self-determination theory, together with competence and
relatedness (Deci & Ryan, 1980), and is suggested to be indicated by
perceived emotions of control (Ryan & Deci, 2000). The results reported in
Paper I show that competence and control are indeed predictors of
performance and correlated with epistemological beliefs and prior
knowledge. This indicates that students who experienced self-determination
also reported expert-like epistemological beliefs and scored high on
performance, which supports previous research on these correlations.
Thus, epistemological beliefs and prior knowledge are not only reliable
predictors of performance but also important to consider when designing
learning to support self-determined behavior. Students with novice-like
beliefs tend to view knowledge as consisting of isolated facts and something
possessed and transferred by authority. They risk experiencing difficulties
with approaching an assignment that requires a coherent use of different
knowledge and skills and several alternatives to reach a solution. Students
need to feel competent but if their view of competence differs from what is
expected from the assignment I suggest they need triggers to motivate them
towards a self-determined behavior, such as positive and constructive
feedback on competence.
7.2
!
Teachers' and students epistemic framing
How do teachers and students frame a learning situation in
computational physics? Do teachers and students agree about learning
objectives, approaches, and difficulties?
Teacher’s beliefs have in previous research been suggested to have impact
on how teaching is performed and how teaching material is developed
(Henderson, Yerushalmi, Kuo, Heller, & Heller, 2007; Louca, Elby,
Hammer, & Kagey, 2004; Yerushalmi, Henderson, Heller, Heller, & Kuo,
2007). In Paper III, teachers' beliefs about computational physics were
investigated using a network analysis approach in order to map what
teachers believed was important aspects of computational physics. Since
there is an assumption that teachers' intentions correspond to students'
expectation a comparison between teachers' and students' epistemic
networks was included in the study.
One of the most important aspects is that teachers view computational
problem solving in physics as something that students can actively engage in
to a higher degree than analytical problems, which have limitations in what
type of questions and phenomena they can treat. Teachers claim that
possibilities to test, interact with, and control the solution open up for
increased understanding of physics, as well as math and the numerical
methods. This mirrors teachers’ epistemological beliefs, i.e., how they
42
Discussion of main findings
believe their students learn and how they want them to learn. The teachers
interviewed in Paper III all expressed beliefs about learning corresponding
to active engagement and making use of previous knowledge to develop new
knowledge. However, no observations of teaching have been made in these
studies and previous research has also shown that even though teachers
believe that students should be actively engaged in their own learning it is
not always reflected in how the teachers teach (Van Driel, Verloop, Inge Van
Werven, & Dekkers, 1997).
Teachers see the possibilities for students to investigate more realistic
physics problems with the use of numerical tools and expect that students
will develop a deeper understanding of physics as well as math and
numerical methods. Students do agree with these beliefs to some extent but
do not express development of fundamental understanding to the same
degree. If they do, it is related to the visual feedback. The feedback aspects of
the visualizations of the problems are present in all interview studies and
seem to encourage a motivated behavior where students stick to the task,
possibly indicating a deepened cognitive activity, which could eventually lead
to development of expert-like knowledge, and thus beliefs.
Teachers believe that the students would appreciate complex problems
because the teachers see both the possibilities of solving more interesting
problems but also to be able to look beyond the more surface-like and
idealized features that analytical problems are limited to offer and develop a
deeper understanding. However, the students are not expected to have the
problem solving experiences associated with numerical tools or subject
knowledge that experts have. They have not acquired that knowledge yet.
This might cause a gap between what teachers teach and what students learn
(McDermott, 1991). Students express that they probably won't acquire any
deeper understanding of physics because they are occupied with the
numerical implementation. Maybe they are not able to see the possibilities to
reach deepened physics understanding because they actually do need more
practice and more experience in order to construct the mental
representations that are useful as working models for developing conceptual
knowledge in physics. However, students are confronted with physics
principles as well as mathematical methods and programming issues during
the assignment, but the impact on how they conceptualize the learning
situation is dominated by an increased used of physics. This indicates
increased physics awareness.
In the present case of computational physics the teachers shared many of
the beliefs about the learning situation, as reported in Paper IV, but there are
differences that mainly have to do with the subject field the teacher
originally belongs to. A teacher with his/her roots in computer science may
not at first hand consider that a student’s problem with a solution could be
troubleshooted by applying fundamental physics laws. On the other hand a
43
Discussion of main findings
teacher schooled in physics or math may lack the insight in how data
structures and algorithms contribute in order to build effective computer
programs. This thesis does not investigate aspects of learning computer
science but previous research in this field stresses the importance of gaining
knowledge about, e.g., concurrency, data structures, and algorithms, in order
to become proficient programmers (Moström, 2011).
7.3
!
Positive and negative learning effects
What are the consequences in terms of positive or negative learning
experiences from using computational problem solving in physics
education?
The results from Papers I and IV show that students who already possess
expert-like beliefs seem more likely to be favored by a learning situation that
provides conditions for autonomous learning behavior. This is in line with
previous research (Redish et al., 1998; Windschitl & Andre, 1998).
The results from Papers II, III, and IV imply that the visualization aspects
of the particular assignment used in these studies are very important for the
students. They use the visual simulation and graphs to evaluate their
numerical solution and they also express the visual feedback as a resource
for better understanding. The results also show that students to a higher
degree use physics concepts after the task, which indicates that students feel
more confident with physics terms. Previous research has shown that
whether a problem used visual feedback or numerical feedback had influence
on how students solved problems (Monaghan & Clement, 2000). With a
numerical solution students were more likely to use algorithmic arguments
while a visualization made students use mental imagery to solve the
problem. Monaghan and Clement suggested that a combination of visual and
numerical representations could lead to better, more coherent
understanding of phenomena involved in a problem. The assignment used as
context in my studies did encourage both modalities and is thus expected to
lead to a more coherent understanding of the task than if only one of the
numeric or visual feedbacks were provided. The results from Papers II, III,
and IV did show an increased awareness in physics in terms of using more
concepts expressing physics. However, the cognitive depth in how these
concepts are used are not investigated in detail but I suggest that students'
learning experiences points towards an increased understanding of physics
in this particular context indicated by the increased interactivity between
physics concepts and other context-dependent concepts.
44
Discussion of main findings
7.4
!
Network analysis as a tool
What are the strengths and weaknesses of using network analysis as a
tool for analyzing and visualizing knowledge and beliefs structure?
Network analysis seems to be a useful tool for extracting different types of
representations from textual data, generated from interviews, lab reports, or
programming code. The idea of expressing cognitive structures as networks
is not new and there are several studies besides mine where networks are
used as representations of epistemic framing (Shaffer et al., 2009), mental
models (Carley & Palmquist, 1992; Jonassen & Henning, 1996; Shavelson,
1972), and knowledge structures (Koponen & Pehkonen, 2010). My
contribution to this field is to develop relatively simple content analysis
methods to generate semantic networks and visualize them using a map
generator optimized for dynamic clustering of nodes (Rosvall et al., 2009).
In the studies reported in this thesis network analysis has been used with
different approaches. In the study reported in Paper II, the content analysis,
based on manual coding of interview transcripts, was visualized as epistemic
networks describing students' epistemic framing of a computational physics
assignment. The epistemic networks revealed structures in students' framing
showing how students' focus changed between before and after the
assignment.
In Papers III and IV network analysis was used as computer-assisted
content analysis. The textual data was subjected to text-mining processes
where words were categorized according to their content-bearing
characteristics in the particular context. The textual data could then be
reduced to contain only a limited number of context-dependent concepts, 26
concepts in Paper III and 101 concepts in Paper IV, which were assumed to
still maintain the content and meaning of the texts. This content and
meaning were visualized by generating semantic networks from the reduced
texts, allowing concepts that were close and belonging to the same sentence
to be connected. The resulting epistemic networks could then be regarded as
representations of the conceptualization of the investigated texts. I further
assumed that these networks based on interviews could be interpreted as
mental models, revealing what was on an individuals mind at the time of the
interview.
Even though the applications of epistemic networks are somewhat
different between the studies in Papers II, III, and IV the method follows the
same basic procedure. Striking is that the semi-automated content analysis
approach used in Papers III and IV does give intelligible information from
the data that is very similar to the qualitative analysis performed in Paper II,
categorizing and connecting statements manually. Thus, an automated
45
Discussion of main findings
process seems useful in order to indicate patterns of content and meaning in
many contexts that can be represented textually.
One critical issue lies in how the concepts that would represent the
context are chosen. I have used two approaches: One that is similar to
traditional qualitative coding of textual data where epistemic elements
(statements) expressing knowledge and beliefs are identified as nodes in the
epistemic network, Paper II. The choice of epistemic elements was based
upon a confirmatory approach where certain types of knowledge, beliefs, and
resources (principle categories) were searched for but the actual epistemic
elements were defined using an exploratory approach. The other way of
choosing concepts among a complete word list followed an even more
exploratory approach. The only limitation was that they would represent a
meaning in the context. Using a smaller number of concepts generate a
coarse-grained network as investigated in Paper III, while more concepts, as
in Paper IV, would give a finer grained network with more information.
Another critical issue concerns how the linking is determined and how I
know that the resulting network represent the structure of meaning of the
original data. Since I have used very simple linking options, based almost
only on adjacency, there are limitations to what questions these networks
can give information about. In Paper II, the relations between the epistemic
elements were qualitatively treated, where links were defined considering
semantic adjacency. By using the original transcripts as references it was
possible to make sure that no important links were missing. However, the
linking was limited to only show that there was a relation, not what type of
relation. In order to add meaning to the networks the links could contain
more information, e.g., direction, strength, meaning (Carley & Palmquist,
1992), and that information could be provided in a visualization. I suggest
this as an area of research that needs to be developed further in order to
capture more fine-grained information and facilitate qualitative
interpretation of the networks.
46
Conclusions
8 Conclusions
The work I present in this thesis contributes to physics education research in
several aspects. Using interactive tools for modeling physics and technology,
building simulations, and interactive solutions is expected to grow in tertiary
physics education as well as in secondary and even primary education due to
increased use of interactive tools and environment in learning. Knowledge
about students' affective and cognitive reactions in these learning situations
is therefore important to consider. I have provided the following
contributions to this field of physics education research:
!
I have investigated a new and emerging area in tertiary physics
education, namely computational physics.
!
I have shown that students' epistemological beliefs are important
predictors for students' performance.
!
I have shown that is not enough to be interested and value the task as
useful in order to perform well, the task must also be optimized for
cognitive engagement in order to motivate students.
!
I have shown that students increase their physics awareness during an
assignment in computational physics.
!
I have introduced a novel method of modeling knowledge and beliefs
structures using network analysis in educational research.
This thesis highlights some of the critical aspects that are related to
teaching in computational physics. Introducing learning activities offering
possibilities for high autonomy and complexity but it is important to
consider how students' beliefs, epistemological as well as value, might
influence student behavior. Computational physics is not easy to students.
There are many aspects that students need to relate to and as a teacher it is
important to guide the student to a coherent view of the computational
problem without losing physics, mathematical, or programming aspects. To
keep focus on the importance of how physics principles are used in
troubleshooting problem solutions is one suggestion to help students to a
coherent view. I suggest that teachers emphasize the limitations and
possibilities that numerical methods may provide in solving physics
problems.
Improved understanding of how complex learning situations, such as in
computational physics, affect student with different profiles in cognitive as
47
Conclusions
well as in motivational aspects could provide a good platform for
development of assignments to support efficient learning. Further
development of methods for modeling of knowledge and beliefs structures is
therefore suggested as an emerging area of research.
48
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1. Margareta Enghag (2004): MINIPROJECTS AND CONTEXT RICH PROBLEMS –
Case studies with qualitative analysis of motivation, learner ownership and
competence in small group work in physics. (licentiate thesis) Linköping University
2. Carl-Johan Rundgren (2006): Meaning-Making in Molecular Life Science Education –
upper secondary school students’ interpretation of visualizations of proteins. (licentiate
thesis) Linköping University
3. Michal Drechsler (2005): Textbooks’, teachers’, and students´ understanding of
models used to explain acid-base reactions. ISSN: 1403-8099, ISBN: 91-85335-40-1.
(licentiate thesis) Karlstad University
4. Margareta Enghag (2007): Two dimensions of Student Ownership of Learning during
Small-Group Work with Miniprojects and context rich Problems in Physics. ISSN:
1651-4238, ISBN: 91-85485-31-4. (Doctoral Dissertation) Mälardalen University
5. Maria Åström (2007): Integrated and Subject-specific. An empirical exploration of
Science education in Swedish compulsory schools. (Licentiate thesis) Linköping
university
6. Ola Magntorn (2007): Reading Nature: developing ecological literacy through
teaching. (Doctoral Dissertation) Linköping University
7. Maria Andreé (2007): Den levda läroplanen. En studie av naturorienterande
undervisningspraktiker i grundskolan. ISSN: 1400-478X, HLS Förlag: ISBN 978-917656-632-9 (Doctoral Dissertation, LHS)
8. Mattias Lundin (2007): Students' participation in the realization of school science
activities.(Doctoral Dissertation) Linköping University
9. Michal Drechsler (2007): Models in chemistry education. A study of teaching and
learning acids and bases in Swedish upper secondary schools ISBN 978-91-7063-1122 (Doctoral Dissertation) Karlstad University
10. Proceedings from FontD Vadstena-meeting, April 2006.
11. Eva Blomdahl (2007): Teknik i skolan. En studie av teknikundervisning för yngre
skolbarn. ISSN: 1400-478X, HLS Förlag: ISBN 978-91-7656-635-0 (Doctoral
Dissertation, LHS)
12. Iann Lundegård (2007): På väg mot pluralism. Elever i situerade samtal kring hållbar
utveckling. ISSN:1400-478X, HLS Förlag: ISBN 978-91-7656-642-8 (Doctoral
Dissertation, LHS)
13. Lena Hansson (2007): ”Enligt fysiken eller enligt mig själv?” – Gymnasieelever,
fysiken och grundantaganden om världen. (Doctoral Dissertation) Linköping
University.
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14. Christel Persson (2008): Sfärernas symfoni i förändring? Lärande i miljö för hållbar
utveckling med naturvetenskaplig utgångspunkt. En longitudinell studie i
grundskolans tidigare årskurser. (Doctoral Dissertation) Linköping University
15. Eva Davidsson (2008): Different Images of Science – a study of how science is
constituted in exhibitions. ISBN: 978-91-977100-1-5 (Doctoral Dissertation) Malmö
University
16. Magnus Hultén (2008): Naturens kanon. Formering och förändring av innehållet i
folkskolans och grundskolans naturvetenskap 1842-2007. ISBN: 978-91-7155-612-7
(Doctoral Dissertation) Stockholm University
17. Lars-Erik Björklund (2008): Från Novis till Expert: Förtrogenhetskunskap i kognitiv
och didaktisk belysning. (Doctoral Dissertation) Linköping University.
18. Anders Jönsson (2008): Educative assessment for/of teacher competency. A study of
assessment and learning in the “Interactive examination” for student teachers. ISBN:
978-91-977100-3-9 (Doctoral Dissertation) Malmö University
19. Pernilla Nilsson (2008): Learning to teach and teaching to learn - primary science
student teachers' complex journey from learners to teachers. (Doctoral Dissertation)
Linköping University
20. Carl-Johan Rundgren (2008): VISUAL THINKING, VISUAL SPEECH - a Semiotic
Perspective on Meaning-Making in Molecular Life Science. (Doctoral Dissertation)
Linköping University
21. Per Sund (2008): Att urskilja selektiva traditioner i miljöundervisningens
socialisationsinnehåll – implikationer för undervisning för hållbar utveckling. ISBN:
978-91-85485-88-8 (Doctoral Dissertation) Mälardalen University
22. Susanne Engström (2008): Fysiken spelar roll! I undervisning om hållbara
energisystem - fokus på gymnasiekursen Fysik A. ISBN: 978-91-85485-96-3
(Licentiate thesis) Mälardalen University
23. Britt Jakobsson (2008): Learning science through aesthetic experience in elementary
school science. Aesthetic judgement, metaphor and art. ISBN: 978-91-7155-654-7.
(Doctoral Dissertation) Stockholm university
24. Gunilla Gunnarsson (2008): Den laborativa klassrumsverksamhetens interaktioner En studie om vilket meningsskapande år 7-elever kan erbjudas i möten med den
laborativa verksamhetens instruktioner, artefakter och språk inom elementär ellära,
samt om lärares didaktiska handlingsmönster i dessa möten. (Doctoral Dissertation)
Linköping University
25. Pernilla Granklint Enochson (2008): Elevernas föreställningar om kroppens organ och
kroppens hälsa utifrån ett skolsammanhang. (Licentiate thesis) Linköping University
26. Maria Åström (2008): Defining Integrated Science Education and putting it to test
(Doctoral Dissertation) Linköping University
27. Niklas Gericke (2009): Science versus School-science. Multiple models in genetics –
The depiction of gene function in upper secondary textbooks and its influence on
students’ understanding. ISBN 978-91-7063-205-1 (Doctoral Dissertation) Karlstad
University
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28. Per Högström (2009): Laborativt arbete i grundskolans senare år - lärares mål och hur
de implementeras. ISBN 978-91-7264-755-8 (Doctoral Dissertation) Umeå University
29. Annette Johnsson (2009): Dialogues on the Net. Power structures in asynchronous
discussions in the context of a web based teacher training course. ISBN 978-91977100-9-1 (Doctoral Dissertation) Malmö University
30. Elisabet M. Nilsson (2010): Simulated ”real” worlds: Actions mediated through
computer game play in science education. ISBN 978-91-86295-02-8 (Doctoral
Dissertation) Malmö University
31. Lise-Lotte Österlund (2010): Redox models in chemistry: A depiction of the
conceptions held by upper secondary school students of redox reactions. ISBN 97891-7459-053-1 (Doctoral Dissertation) Umeå University
32. Claes Klasander (2010): Talet om tekniska system – förväntningar, traditioner och
skolverkligheter. ISBN 978-91-7393-332-2 (Doctoral Dissertation) Linköping
University
33. Maria Svensson (2011): Att urskilja tekniska system – didaktiska dimensioner i
grundskolan. ISBN 978-91-7393-250-9 (Doctoral Dissertation) Linköping University
34. Nina Christenson (2011): Knowledge, Value and Personal experience – Upper
secondary students’ use of supporting reasons when arguing socioscientific issues.
ISBN 978-91-7063-340-9 (Licentiate thesis) Karlstad University
35. Tor Nilsson (2011): Kemistudenters föreställningar om entalpi och relaterade begrepp.
ISBN 978-91-7485-002-4 (Doctoral Dissertation) Mälardalen University
36. Kristina Andersson (2011): Lärare för förändring – att synliggöra och utmana
föreställningar om naturvetenskap och genus. ISBN 978-91-7393-222-6 (Doctoral
Dissertation) Linköping University
37. Peter Frejd (2011): Mathematical modelling in upper secondary school in Sweden An
exploratory study. ISBN: 978-91-7393-223-3 (Licentiate thesis) Linköping University
38. Daniel Dufåker (2011): Spectroscopy studies of few particle effects in pyramidal
quantum dots. ISBN 978-91-7393-179-3 (Licentiate thesis) Linköping University
39. Auli Arvola Orlander (2011): Med kroppen som insats: Diskursiva spänningsfält i
biologiundervisningen på högstadiet. ISBN 978-91-7447-258-5 (Doctoral
Dissertation) Stockholm University
40. Karin Stolpe (2011): Att uppmärksamma det väsentliga. Lärares ämnesdidaktiska
förmågor ur ett interaktionskognitivt perspektiv. ISBN 978-91-7393-169-4 (Doctoral
Dissertation) Linköping University
41. Anna-Karin Westman (2011) Samtal om begreppskartor – en väg till ökad förståelse.
ISBN 978-91-86694-43-2 (Licentiate thesis) Mid Sweden University
42. Susanne Engström (2011) Att vördsamt värdesätta eller tryggt trotsa.
Gymnasiefysiken, undervisningstraditioner och fysiklärares olika strategier för
energiundervisning. ISBN 978-91-7485-011-6 (Doctoral Dissertation) Mälardalen
University
43. Lena Adolfsson (2011) Attityder till naturvetenskap. Förändringar av flickors och
pojkars attityder till biologi, fysik och kemi 1995 till 2007. ISBN 978-91-7459-233-7
(Licentiate thesis) Umeå University
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44. Anna Lundberg (2011) Proportionalitetsbegreppet i den svenska gymnasiematematiken – en studie om läromedel och nationella prov. ISBN 978-91-7393-132-8
(Licentiate thesis) Linköping University
45. Sanela Mehanovic (2011) The potential and challenges of the use of dynamic software
in upper secondary Mathematics. Students’ and teachers’ work with integrals in
GeoGebra based environments. ISBN 978-91-7393-127-4 (Licentiate thesis)
Linköping University
46. Semir Becevic (2011) Klassrumsbedömning i matematik på gymnasieskolans nivå.
ISBN 978-91-7393-091-8 (Licentiate thesis) Linköping University
47. Veronica Flodin (2011) Epistemisk drift - genbegreppets variationer i några av
forskningens och undervisningens texter i biologi. ISBN 978-91-9795-161-6
(Licentiate thesis) Stockholm University
48. Carola Borg (2011) Utbildning för hållbar utveckling ur ett lärarperspektiv –
Ämnesbundna skillnader i gymnasieskolan. ISBN 978-91-7063-377-5 (Licentiate
thesis) Karlstad University
49. Mats Lundström (2011) Decision-making in health issues: Teenagers’ use of science
and other discourses. ISBN 978-91-86295-15-8 (Doctoral Dissertation) Malmö
University
50. Magnus Oscarsson (2012) Viktigt, men inget för mig. Ungdomars identitetsbygge och
attityd till naturvetenskap. ISBN: 978-91-7519-988-7 (Doctoral Dissertation)
Linköping University
51. Pernilla Granklint Enochson (2012) Om organisation och funktion av människokroppens organsystem – analys av elevsvar från Sverige och Sydafrika.
ISBN 978-91-7519-960-3 (Doctoral Dissertation) Linköping University
52. Mari Stadig Degerman (2012) Att hantera cellmetabolismens komplexitet –
Meningsskapande genom visualisering och metaforer. ISBN 978-01-7519-954-2
(Doctoral Dissertation) Linköping University
53. Anna-Lena Göransson (2012) The Alzheimer A! peptide: Identification of Properties
Distinctive for Toxic Prefibrillar Species. ISBN 978-91-7519-930-6 (Licentiate thesis)
Linköping University
54. Madelen Bodin (2012) Computational problem solving in university physics education
- Students’ beliefs, knowledge, and motivation. ISBN 978-91-7459-398-3 (Doctoral
Dissertation) Umeå University