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Elementary Students’ Self-Generated Models of Small, Unseen Particles
Brenda J. Gustafson, Peter Mahaffy*, and Brian Martin*
University of Alberta, *The King’s University College, Edmonton, Alberta
Roundtable presented at the annual conference of the Canadian Society for the
Study of Education (CSSE), Fredericton, New Brunswick, June 2011.
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Elementary Students’ Self-Generated Models of Small, Unseen Particles
Introduction
What is a Model?
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A model is a physical, visual, or mental representation of objects, phenomena
or processes.
A model is a simplified representation that concentrates attention on salient
features of the real thing (Gobert & Buckley, 2000).
A model represents another perceptual pathway to understanding
(Mathewson, 1999).
What is a Self-Generated Model?
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
A physical expression (verbal, pictures, diagrams, writing, etc.) of ideas that
reveals the private, internal, personal, mental models being used to make
sense of some real thing.
A self-generated model is an expressed model that is shared in order to
demonstrate understanding and/or to support sense-making (Schwarz et al.,
2008)
Why Should Students be Encouraged to Self-Generate Models?
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It is a way for students to learn how to do science through expressing and
revising their ideas in light of new understandings; modeling is a core
component of scientific practice (Acher, Arca, & Sanmarti, 2007; Baek,
Schwarz, Chen, Hokayem, & Zhan, 2009; Justi & Gilbert, 2002; Schwarz et al.,
2008, 2009; Windschitl, Thompson, & Braaten, 2008).
It provides a way to: a) draw inferences into students’ thinking, b) gain
information needed to scaffold understanding, c) show how ideas change
over time, and, d) show how ideas are organized and connected to other
(Buckley & Boulter, 2000; Ergazaki, Zogza, & Komis, 2007; Gobert & Buckley,
2000; Sharp & Kuerbis, 2005).
What Should We Also Consider When Encouraging Self-Generated Models?
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Some self-generated models may be poor conceptual matches for the target
concept (the real thing) (Yerrick et al., 2003)
Sometimes self-generated models are given such personal authority that they
can lead to misconceptions. Self-generated models (like all models) can act
as a barrier to further understanding (Gobert, 2000).
Students need guidance to support and avert conceptual detours (Yerrick et
al., 2003).
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Study Questions
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What are the helpful and unhelpful ideas portrayed in Grade 5 students’ selfgenerated (expressed) pictorial models of particles comprising a solid?
What is the nature of Grade 5 students’ self-generated (expressed) written
models of the movement and arrangement of small, unseen particles?
Study Methods
Study Participants
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One Grade 5 (ages 10-11) class (13 males, 9 females) attending a rural
elementary school.
Classroom teacher was completing a MEd in Elementary Mathematics and
Science.
Study Context
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Teacher was asked to teach her five-week Classroom Chemistry unit as
planned and to integrate at her discretion the six digital learning objects
(DLOs) created by the researchers.
The DLOs provided the students with an introduction to: a) the nature of
models (e.g., models are not exactly like the real thing, all models have
strengths and limitations, models can help to understand what we cannot
see), b) the particle nature of matter (e.g., particles are too small to see,
particles make up all matter, particles can help to explain the properties of
matter, the movement and arrangement of particles can help explain the
properties of solids, liquids, and gases, there is empty space between
particles, it can be difficult to believe that particles exist), c) physical change
(e.g., changes among solids, liquids, and gases), and d) chemical change (e.g.,
particles splitting apart and joining together in new ways to make new
substances).
DLOs were created at the King’s Centre for Visualization in Science and can
be viewed at: http://www.kcvs.ca/site/projects/elementary.html
Study Data
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Students completed surveys and worksheets before, during, and after
viewing the DLOs.
Teacher sent feedback by e-mail throughout the teaching of the chemistry
unit.
Although the study emphasis was not on self-generating, evaluating, and
revising models we did include a Module 2 worksheet question where
students were able to demonstrate their understanding of DLO concepts by
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working with a partner to draw and explain a picture of the small, unseen
particles that comprise a table.
Further, we were able to gain some understanding of mental images and
ideas they were using to make sense of particles by including a Module 3
worksheet question that asked them to talk with another student and write
down the mental models they were using to think about small, unseen
particles (see Figure 1).
Figure 1: Screen capture from Module 3 asking students to express their mental
models of particles.
Results and Discussion
Drawing a Model to Demonstrate Understanding of Particles
Comprising a Table
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In the Module 2 worksheet, students were asked to work with a partner to
respond to the following: “Draw a picture of the small, unseen particles that
make up a table. My explanation of my picture is …”.
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Self-Generated Model #1
Analysis: Model was likely influenced by depictions outside of project
experiences (orbitals). Therefore, an indication of what St (Student) has
seen, remembered, and thinks is applicable to this drawing task.
Helpful Ideas: Particles distributed throughout table. Everything made of
particles.
Unhelpful Ideas: No movement, wide spaces, scale?
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Self-Generated Model #2
Analysis: Possibly influenced by spherical models used in the DLOs.
Helpful Ideas: particles distributed throughout table, packed close together,
vibrating
Unhelpful ideas: Scale?
Explanation:
Helpful ideas: Small, unseen particles are small, close together but still some space,
and vibrating.
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Self-Generated Model #3
Analysis: Does the student think that the particle level mirrors the
observable level?
Helpful Ideas: Particles are packed close.
Unhelpful Ideas: No movement, not distributed throughout table, scale. Are
visible blocks of wood the small, unseen particles?
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Self-Generated Model #4
Analysis: Model was influenced by depictions outside of project experiences
(molecules that show atoms joined by lines). Therefore, an indication of
what St has seen, remembered, and thinks is applicable to this drawing task.
Helpful Ideas: Particles distributed throughout table, particles close together
with some space between them
Unhelpful Ideas: No movement, scale?
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Self-Generated Model #5
Analysis: Used a model that bore great resemblance to those used in the
DLOs.
Helpful Ideas: Particles throughout table, tightly packed with small spaces
between, movement suggested in written explanation.
Unhelpful Ideas: Particles are round.
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Self-Generated Model #6
Analysis: Particles are overlapping and sticking together in some way.
Helpful Ideas: Particles distributed throughout the table, particles attracted
in some way
Unhelpful Ideas: No movement, scale?
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Table 1
Summary of Helpful and Unhelpful Ideas Portrayed in Self-Generated Models
Student Ideas
Helpful Ideas
Number of Students* (N=22)
-
Particles are throughout the table
17
-
Particles are closely packed
11
- Particles move
Unhelpful Ideas
7
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Particles are not throughout the table
1
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Particles are not closely packed
4
Particles do not move
13
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Particles are joined by bonds to make molecules.
4
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Particles have orbitals
-
Particles look like blocks of wood
-
Metal and particles are not the same
Other
2
1
1
*Each student could fit more than one idea category.
Discussion Questions
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What was most difficult for the students to portray in their self-generated
models? why was this so?
How would you describe the students’ understanding of particles that
comprise a table?
What would be worthwhile next steps?
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Expressing Their Mental Models to Reveal Ideas Used to Make Sense of
Particle Arrangement and Movement
In the Module 3 worksheet, students were asked to work with a partner to respond
to the following: Scientists think we can explain the properties of solids, liquids, and
gases if we believe that all matter is made up of small, unseen particles. Talk with
another student about what could be used to model the arrangement and movement
of these small, unseen particles. Record your ideas.
Table 2
Summary of Expressed Models Used to Make Sense of Particle Arrangement and Movement
Expressed Sense-Making Model
Student Rationale
People, balls, cats, wheels, dancing leprechauns
They can move and not
move. They can go
further apart and
closer together. They
can bounce off each
other. You can use
different numbers of
moving balls to show
solids, liquids, and
gases.
Solids vibrate.
Birds and gases can
move freely.
Liquids are close
together but can go
through each other.
Particles are small and
round. The DLO shows
round balls.
N/A
They are good enough
models.
Vibrating phones
Bird in a cage.
Ghosts running into each other.
Beads, rocks, and balls shaken in a container.
Hummingbird
Molymod® kit materials
No answer
*Each student could have more than one idea.
Number of Students*
(N=22)
8
3
3
3
8
3
2
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Discussion Questions
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Were the students using helpful mental models to understand particle
behavior in solids, liquids, and gases?
What would be helpful next steps?
Summary
Data collected during the entire study showed that the idea that everything was
made of small, unseen particles appeared easy to accommodate into the students’
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existing knowledge. Opportunities to discuss the particle nature of knowledge with
each other and their teacher, participate in a variety of classroom experiences,
interact with the digital learning objects, and express their own models all likely
contributed to this understanding. Responses to select worksheet questions
showed they worked to relate the observable and particle levels of thinking about
chemistry with some providing clear connections and others still in need of more
work.
The study provided some insight into the intellectual challenge of learning
about particles while relying on models. Inevitably there are trade-offs – an
emphasis on ‘good enough’ spherical DLO models to reduce complexity may end up
contributing to conceptions that particles are spherical or colored.
With respect to self-generated models, our findings suggest that it may be
valuable to address at least two additional questions: a) to what degree do students’
self-generated models foreshadow students’ final ideas about particles, and b) how
can self-generated models designed to demonstrate understanding be used to
support sense-making?
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