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Students reinventing the general law of energy conservation
Logman, P.S.W.M.
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Download date: 19 Jun 2017
Chapter 7
Conclusion
Introduction
In the Netherlands the curriculum innovation committees for the exact sciences
have advised a context-based approach (Boersma et al., 2007; Commissie
Vernieuwing Natuurkunde onderwijs havo/vwo, 2006; Driessen & Meinema,
2003). Two unsolved problems in context-based education are the difficulty to
achieve transfer (Parchmann et al., 2006; Schwartz, 2006; Goedhart et al., 2001)
and the difficulty to develop abstract concepts in contexts (Parchmann et al.,
2006; Pilot & Bulte, 2006; Schwartz, 2006). The concept of energy conservation
is an abstract concept which is difficult for students to apply to various situations
(Borsboom et al., 2008; Liu et al., 2002) and to adjust when necessary (Kaper,
1997).
The main question for our research has therefore been stated in Section 1.1 as:
“How do context and concept interact in context-based education that is
suitable to develop a versatile concept of energy?”
To answer this research question we have developed a context-based teachinglearning sequence in which a versatile conception of energy conservation may
be developed. To improve the versatility of students’ conceptions we have
chosen a guided reinvention approach (Freudenthal, 1991). We have chosen to
embed the teaching-learning sequence in authentic practices (Boersma et al.,
2007).
To research the development of the intended teaching-learning sequence and
analyze its results and the learning process within it, we have divided the main
question for our research into four researchable questions in Section 1.3. Based
on the results given in Chapters 2 through 6 we will answer each of these four
questions.
7.1 Research question 1 - Developing a versatile concept of
energy conservation
The first question as posed in Section 1.3 is:
“How can we organize the development of a versatile concept of energy
conservation by students while making use of a teaching-learning sequence set
in authentic practices?”
In Chapter 4 we have described our final educational design partly based on the
results of Chapters 2 and 3. The results of the evaluation of the learning process
of the final educational design have been presented in Chapter 5. A quantitative
analysis of how many students successfully improved the versatility of their
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Chapter 7
conception of energy conservation in the teaching-learning strategy is given in
Chapter 6.
Description of final educational design
In our final educational design we have chosen to make use of guided
reinvention to increase the versatility of resulting conceptions and to
substantiate the general law of energy conservation with evidence. We have
embedded our teaching-learning strategy in contexts to motivate students.
Authentic practices have been used to let them experience the relevance of
what is learned and to get students to understand how this knowledge functions
in society. We have combined this with the problem posing approach to give
students a reason to perform every step in the learning process (see Section 4.1
for a more elaborate background of the choices we made).
The learning process is subdivided into three consecutive learning steps:
reinventing partial laws from measurements, combining those partial laws into
one combined law, and extrapolating that combination process to arrive at the
general law of energy conservation (see Section 4.2.1 for a more elaborate
description and Sections 6.4.1, 6.4.2, and 6.4.3 for expected students’ results).
We have embedded these learning steps in three technological design
assignments (conceptual learning step I) followed by three consecutive scientific
assignments (conceptual learning steps II and III) (see Section 4.2.2). These
assignments have been shaped into work phases which are characteristic for the
authentic practices so they can show how the resulting concepts function in
these practices (see Section 4.4).
We will now discuss the three conceptual learning steps in more detail.
Conceptual learning step I
The results on deriving a partial law from measurements improved from the first
to the last assignment (see Section 5.5).
Because in the scientific assignments the conceptual goal and contextual goal
are almost the same the need for a physical law is more clear in such
assignments than in the technological design assignments where the contextual
goal contains many other aspects (e.g. special safety features) than the
conceptual goal (a partial law of energy conservation) we aimed for. To assure
that the relevance of the partial law that we aimed for in the technological
design assignments was clarified to more students than only those that applied
the law in their advice reports we used classroom discussions based on students’
reports and aimed at finding the optimal solution accepted by all students. In
these discussions it was observed that the students chose the solutions in which
the intended partial law was applied as the best (see Section 5.4.1). Therefore
we conclude that embedding the teaching-learning sequence in technological
design assignments enables students to see the relevance of the reinvented
partial conservation laws.
Difficult steps for students to take were:
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Chapter 7

the transition from merely testing a laboratory scale model of their solution
to investigating a quantitative relationship, and
 the derivation of a relationship from measurements.
To improve the results on these two issues a few extra hints for the teacher and
the addition of certain questions to the educational material are suggested in
Section 5.4.1.
Conceptual learning step II
Students learn how to include a new variable into the conservation law during
conceptual learning step II. This includes combining a new partial conservation
law with the one established earlier. As a preparation for performing such a
combination by themselves during the final scientific assignment the teacher
showed the students how the combination procedure is performed during the
first two scientific assignments.
The steps from studying the new variable up to performing an experiment to
find a new partial law did not cause major problems (see Section 5.4.2), except
for describing a suitable experiment to find a new partial law, and describing the
procedural steps to perform a combination of such laws. Other steps that are
needed before both laws can be combined and that went well are: describing
phenomena that can connect the new variable with a variable that is already
included in the conservation law, naming the preconditions and domains of
earlier established partial laws, and describing the procedural steps for the
derivation of a new partial law from measurements.
After the teacher had given the results of an appropriate experiment to the
students about two thirds of them derived the partial law of energy
conservation that describes the results of the experiment (see Section 6.5.2)
Most of those students started combining the new partial law with the earlier
established law but only about half the students that derived the new partial law
finished this procedure successfully and met our strict requirements (see
Sections 5.5 and 6.5.2).
The two main issues left are that students had difficulty in applying
preconditions to their proposed experiments and in identifying which procedural
steps were necessary to successfully combine partial laws of energy
conservation (see Section 5.5).
The analysis for conceptual learning step II has shown that it is possible, in
principle, for students to take every substep of conceptual learning step II (see
Section 5.4.2). We have also observed that a classroom discussion can be used
to guide students through the process of combining partial laws (twice) to
enable at least a part of the students to do it themselves a third time (see
Section 5.5). However because only about a third of the students (see Section
6.5.2) were capable of reaching the goal of this conceptual learning step
improvements are needed.
Specific recommendations on expanding the role of preconditions in all
assignments and on making students see the need for each step in the
combination procedure in the scientific assignments are given in Section 5.4.2.
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Chapter 7
Conceptual learning step III
Having chosen a guided reinvention approach we want the students to
substantiate the general validity of the law of energy conservation with
evidence. To do so the students are expected to discuss each step of the
combination procedure to determine whether expanding the conservation law is
always possible when necessary. The procedural reflections in the first two
scientific assignments serve as a preparation for this step but the step itself can
only be taken by the students themselves in the third and final scientific
assignment.
During the preparation for conceptual learning step III about a fifth of the
students described the combination procedure completely.
In answering the question on the general validity of the conservation law about
a third of the students discussed at least one of the seven necessary procedural
steps (see Section 6.5.3). Each of the seven procedural steps was discussed by at
least one of the students but there was no student discussing all procedural
steps (see Section 5.5). A few students discussed six out of the seven procedural
steps. In the end almost two third of the students were explicitly convinced that
it would always be possible to expand the law. None of the students explicitly
stated that this would not be the case (see Section 6.6).
The main issues left concern the recollection and critical understanding of the
procedural steps by the students.
By adding a scientific debate after the students have formulated their evidence
for the general validity of the conservation law the results may improve. The
teacher can make sure that each of the seven procedural steps are discussed at
the end of the first two scientific assignments so the students may see the need
of discussing all the steps to form a substantiated opinion on the general validity
of the law. The discussion will also help them expressing their opinion on the
general validity of the law better (see Section 5.5).
The learning process as a whole
For a new teaching approach a first step is to try out whether the various
substeps in the intended learning process are feasible (Plomp, 2007;
Gravemeijer & Cobb, 2006; Nieveen, 1999). We took on such a challenge by
developing a teaching-learning sequence in which students are to reinvent the
general law of energy conservation and we have shown that it is possible for
each step in the learning path to be taken by at least part of the students.
The interaction between context and concept in the teaching-learning sequence
may be described as follows:
1. the need for a concept stems from a characteristic (the built-in need for an
extrapolation) of a specific problem within a context (see Chapter 2),
2. the concept is subsequently generalized by comparing various situations
within the same context (conceptual learning step I), and
3. the concept is then applied to the original problem within that context to
come up with a specific solution to it.
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There are more aspects to the concept such as its domain, its preconditions, and
the procedure by which it is derived. As for the concept itself also for these
aspects a need must be created for them and these aspects subsequently may
be applied in new assignments. However, the need for these aspects becomes
apparent at different stages in the context than the stages where the need for
the concept shows itself. The same holds for the stage in which they are applied
(see Section 5.5).
For example the need to generalize the domain of the concept shows itself in
describing as many future problems as possible. This is used to guide the
students in the classroom discussion at the end of each technological design
assignment. The application of the domain does not occur until an experiment is
to be proposed to solve a subsequent technological design or scientific problem.
7.2 Research question 2 - Characteristics of authentic
practices
The second question as posed in Section 1.3 is:
“Which characteristics does an authentic practice have that is suitable for
developing a versatile concept of energy conservation?”
The discussion in Section 7.1 shows that it appears possible to develop an
abstract concept such as energy conservation while embedding the learning
process in authentic practices.
Based on the results from various chapters we can now identify characteristics
of authentic practices that contribute to the learning process. In Chapter 2 we
discussed the first design and try-out of our material and as a result identified a
characteristic of technological design practices in which students can reinvent
partial laws of energy conservation. Chapter 3 discussed the second design and
try-out which added a characteristic to that first result and made us choose to
use scientific practices for the learning step of combining partial laws and
extrapolating the combination procedure to reinvent the general law of energy
conservation. In Chapter 4 we have mentioned these characteristics and
explained how they are applied in our final educational design. In Chapter 5 the
try-out of this final design is described from which one more characteristic was
drawn for a scientific practice in which combining partial laws and the
extrapolation of that procedure is encouraged.
The identified characteristics are summarized in the following paragraphs.
In Chapter 3 we noticed that some students did not see the need for
experimenting when a ready-made solution was available to the context (e.g.
electric lifting apparatus).
A characteristic for technological design practices that makes students see the
need for an experiment turned out to be the following:
1. the problem needs to be set in a time or place in which a ready-made
solution is not available (see Section 3.4).
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In our educational design we experienced that we could use the same
characteristic for scientific practices to prevent students from coming up with
combined laws from other sources without knowing how to combine partial
laws themselves.
In Chapter 2 we noticed that in descriptions for technological design problems in
which the solution could be tested on a realistic scale students logically did not
see the need for a physical law to translate their laboratory scale results to the
real solution. The following characteristic has been tried out to solve this:
2. the problem needs a solution that cannot be tested on a realistic scale but
can be tested only on laboratory scale to make students see the need for a
physical law to extrapolate the laboratory-scale solution to the real solution
(see Section 2.6).
Dierdorp (2011) found a similar characteristic for using authentic practices in
mathematics.
To prepare students for combining partial laws by themselves we needed
students to find specific preconditions of the partial laws of energy conservation.
In the second try-out of the assignment of designing a rollercoaster we noticed
that for students the absence of friction was more essential to the problem in
designing an uphill rollercoaster than in designing a downhill rollercoaster (see
Section 4.3). The precondition of having no friction is necessary to derive the
specific partial laws we aimed at but also later on in the learning process for
taking conceptual learning step II in which students are to combine partial laws
with specific preconditions.
Thus, for technological design practices in which students are to combine partial
laws of energy conservation we identified the following characteristic:
3. the technological problem should be such that any solution to it requires an
insulated system, e.g. friction is undesirable for an uphill rollercoaster (see
Section 4.3).
In trying to take the final conceptual learning step III we wanted students to
discuss all seven procedural steps for combining partial laws (see Table 5.12) in
order to form a substantiated opinion on the general validity of the law of
energy conservation. More than half the students did not discuss any procedural
step and only a few discussed six out of seven (see Section 6.6). We propose to
organize a scientific debate among the students to improve these results.
Therefore we formulate the following characteristic for a scientific practice:
4. the practice needs to lead to a scientific debate on the validity of the
generalization of a procedure in a natural way to make students see the
need of discussing procedural steps before validating a generalization of a
procedure like combining partial laws (see substep 22 in Section 5.4.2).
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7.3 Research question 3 - Resulting versatility of students’
conceptions
The third question as posed in Section 1.3 is:
“To which extent can students develop a versatile conception of energy
conservation in context-based education making use of authentic practices?”
In Chapter 6 we presented the results of our summative evaluation. These will
be discussed together with the recommendations we formulated in Chapter 5.
In Chapter 1 we subdivided versatility into applicability and revisability. The first
is described by the domain in which the students are able to apply their
conception of energy conservation, the second describes students’ capability of
revising their conception of energy conservation. For the latter we have
described various levels (see Section 1.2.3):
Revisability level 1.1: students are able to generalize a partial law from specific
situations.
Revisability level 1.2: students are able to combine various partial laws into one
combined law.
Revisability level 1.3: students are able to extrapolate the combination procedure
for partial laws to establish the general law of energy conservation.
These levels coincide with the expected results of learning steps I, II, and III so
quantitative results for these levels are reported in Chapter 6 and summarized in
Section 7.1. For all types of versatility (applicability and revisability) except
revisability level 1.3 we have shown that part of the students are capable of
attaining them (see Section 6.6). For improving the results for revisability level
1.3 we have given recommendations to also make this revisability level
attainable for students.
The applicability results for sixteen- or seventeen-year-olds answering the
Energy Concept Inventory (Swackhamer & Hestenes, 2005)(see Section 6.5.4)
were comparable to the results for eighteen-year-olds given in preliminary
research by Borsboom (Borsboom et al., 2008). We have divided the various
situations in which students were to apply their conception of energy into very
near transfer, near transfer, and far transfer. Very near transfer meant that
students were to apply their conception in the situation from which they had
derived a partial law of energy conservation. Near transfer meant that students
were to apply their conception of energy conservation to other situations from
the same domain but not the one they derived the law from. Far transfer meant
that students had to apply their conception to uninvestigated domain parts of a
combined law. Dividing the Energy Concept Inventory questions according to
these categories again showed similar results for sixteen- or seventeen-year-olds
that had followed our teaching-learning sequence as those for eighteen-yearolds in preliminary research (see Section 6.5.4). Furthermore about three
quarters of the students were capable of answering questions comparable to
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those of the Dutch exam without making conceptual mistakes (see Section
6.5.4). Overall the applicability results are comparable to traditional approaches.
Of our student couples 64.7% (n=34) were able to reinvent a partial law from
measurements and thereby showed that they attained revisability level 1.1 (see
Section 6.5.1). By combining partial laws of energy conservation correctly 32.4%
of our student couples showed that they attained the accompanying revisability
level 1.2 (see Section 6.5.2). Most of our recommendations concern this
revisability level. Generalizing the combination procedure in order to end up
with the general law of energy conservation was only tried out once. None of
our students showed a complete discussion of the combination procedure but
38.2% discussed at least one of the procedural steps to substantiate their
opinion that the law of energy conservation is generally valid (see Section 6.5.3).
About two thirds of all the couples concluded by themselves in assignment 6
that it is always possible to expand the conservation law when necessary and
none of the couples stated that this would not be possible. The procedural
reflection functioned for only just over a third of the students. The question
whether such a procedural reflection is attainable for students at this level is
difficult to answer.
The recommendations we have for future try-outs include giving more attention
to the development of the domains during the combination procedure to clarify
each step in it and to expand the role of preconditions in selecting experiments
suitable for the research at hand (see Section 5.5).
7.4 Research question 4 - Achieved competencies as a
physicist
The fourth question as posed in Section 1.3 is:
“Can a teaching-learning sequence that is aiming at the general law of energy
conservation also enhance the competencies of a student as a physicist?”
This question is seen as a part of our evaluation of the learning process given in
Chapter 5. It is also discussed together with the given recommendations in that
chapter.
For the technological design skills we were able to analyze possible
improvement by tracking students’ skills from the first assignment to either the
second or the third which were done in parallel.
Students clearly showed progress in skills such as formulating uncertainties
containing the essence of a technological design problem, proposing
experiments that fit the research at hand, performing measurements, and
deriving physical laws from them (see Section 5.5).
It was harder to analyze students’ progress on the scientific skills because in the
first two scientific assignments the teacher was allowed to show the students in
a classroom discussion how to apply the most important of the scientific skills:
combining partial laws. For that skill we therefore only had one measurement
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during the final scientific assignment. Several of the scientific skills for which we
could track progress already showed 60% to 80% of the students capable of it
from the start. The scientific skills for which we were able to identify
improvement were describing the procedure to derive laws from measurements
and actually deriving such laws (see Section 5.4.2).
In traditional teaching the concept of energy conservation, technological
designing and the scientific method are normally treated separately. We have
shown that a separate treatment is not necessary.
By embedding the learning process in authentic practices, besides making
progress towards the conceptual goal of our teaching-learning sequence, it also
proved possible to improve students’ skills as a physicist in technological design
practices and scientific practices.
7.5 Reflection
To conclude, all our answers and recommendations are discussed in the light of
future teaching of the subject of energy, possible variations of our educational
design, social acceptability of our approach, the relation between our research
and the current Dutch curriculum innovation, and the contributions to
educational research.
Future teaching of the subject of energy
Because the research was performed by a teacher-researcher first of all it is
interesting to discuss what it has delivered for future teaching. First, the
teachers involved in the second and third try-outs developed new ideas on
teaching the subject of energy conservation. These ideas can also be applied to
teach other subjects in contexts (e.g. crash test engineers reinventing Newton’s
second law
). The approach consumes about 30% more contact hours
than a traditional introduction to energy conservation but the approach
combines this conceptual goal with learning how to solve technological design
problems and how to employ the scientific method. By embedding the teaching
of energy conservation in authentic practices the students enhance their
competencies as a physicist and get to know how physicists function in
technological design and scientific practices as well.
Possible variations of our educational design
The six assignments were now given sequentially in one course but the
assignments may also be spread over more time and even more school years.
The technological design assignments may be given in any order and also earlier
or in the same grade as we did (sixteen-year-olds). It may be more suitable to
give the scientific assignments a grade later (seventeen-year-olds) because
especially combining partial laws seems to be more demanding. A clear
connection between the assignments however has to be assured.
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Social acceptability
Compared to traditional approaches our educational design seems to fit the new
Dutch exam requirements better. The educational design addresses many exam
requirements in one coherent course that results in similar conceptual results as
for traditional approaches.
Deriving physical laws from measurements embedded in technological design
practice (conceptual learning step I) has proven to be effective. This approach
can be applied for other concepts as well. It is too early to make similar claims
for conceptual learning steps II and III. Further research on these two steps is
necessary in which the given recommendations can be tested on their
effectiveness. For many concepts in physics and other exact sciences these
conceptual learning steps however are not necessary. They are only necessary
for the more abstract concepts in which several generalizations succeed one
another (e.g. conceptual learning step II appears necessary in a guided
reinvention of the ideal gas law
).
Relation between our research and the current Dutch curriculum innovation
At the start of this research project we decided not to test our ideas using the
new materials that were created at that time in preparation for the new Dutch
exam program. Even though those materials are based on contexts they are still
traditional in handing the students the general law of energy conservation as an
indisputable fact. At that stage of the research we did not have strong enough
arguments to convince the authors responsible for those materials to try a
different approach. At the end of the research we think we now have stronger
arguments to make the writers consider a different approach. This implies that
even though the innovation committees took ample time to try out new
materials to test the new exam program it is advisable to have educational
research on a new approach precede the development of new material.
Contributions to educational research
First of all we have expanded the theory on versatility (Dekker, 1993; Van
Parreren, 1974) by subdividing it into applicability and revisability. We have
subdivided the latter further into several revisability levels using the ideas of
assimilation and accommodation.
We have given evidence that it is possible to develop abstract concepts in
contexts and have given characteristics for authentic practices suitable to
develop such abstract concepts.
Last but not least we have shown that a new phenomenological approach to
teaching the concept of energy conservation is feasible. Because of the lack of
data from other approaches it is difficult to compare this approach to other
approaches. More data and more research on the various approaches to teach
the concept of energy are needed to be able to decide in the future which
approach is most suitable for which aspect of energy and for which type of
students.
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Teacher and researcher in one
Being both a teacher and a researcher has had advantages and disadvantages.
At the beginning of the research I first had to develop all sorts of educational
research skills. Having come from a technical background this broadened my
view on scientific research. It also made me respect social research more
because of the tough analysis phase it contains. Now, at the end of this research,
I think this has made me what I set out for: a broader developed person.
My limited knowledge of the physics educational research knowledge database
was a disadvantage. As a teacher it is difficult to obtain access to educational
research articles. If one wants to bridge the gap between teachers and
educational research it would be my first advice to give interested teachers free
access to the most important educational research material.
Being an experienced teacher it made me dare to take more chances in
developing the teaching-learning sequence than educational researchers might
have done. This has made the teaching-learning sequence more suitable to
research our ideas on versatility and context-based education.
It has also given me an intermediary role between teachers and researchers
which helps to bridge the gap between them. Besides that I got to see some
excellent teachers and laboratory assistants at work in their own environment
sparking a great exchange of ideas between us.
In the end this research made me a better teacher in many ways although I have
to admit that at busy stages in the research I had to reduce my attention to my
school tasks to a minimum. It has been a trying period of my life but in the end it
1
was worth it. “There are no shortcuts to any place worth going.”
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