=Paper=
{{Paper
|id=Vol-2128/scitech2
|storemode=property
|title=Supporting Sophisticated Modeling Practices in Secondary Science
|pdfUrl=https://ceur-ws.org/Vol-2128/scitech2.pdf
|volume=Vol-2128
|authors=Ashlyn Pierson,Doug Clark,Max Sherard
}}
==Supporting Sophisticated Modeling Practices in Secondary Science==
https://ceur-ws.org/Vol-2128/scitech2.pdf
Supporting Sophisticated Modeling Practices in Secondary Science
Ashlyn Pierson, Vanderbilt University, ashlyn.pierson@vanderbilt.edu
Doug Clark, University of Calgary, douglas.clark@ucalgary.ca
Max Sherard, University of Texas-Austin, mksherard@utexas.edu
Abstract: Schwarz and colleagues proposed a learning progression for modeling that provides
a valuable template for envisioning increasingly sophisticated levels of modeling practice
(Fortus, Shwartz, & Rosenfeld, 2016; Schwarz et al., 2009; Schwarz, Reiser, Archer, Kenyon,
& Fortus, 2012). Thinking about learning progressions for modeling, however, involves
challenges in coordinating between aggregate curricular arcs and supporting individuals’
learning. First, students’ purposes for modeling and the nature of the context shape individual
student performances. Second, approaches for longitudinally supporting students in modeling
is a relatively nascent endeavor. Third, research on the highest levels of the progression is
often hypothetical, because few students demonstrate high-level practices in classrooms. In
response to these challenges, we partnered with an eighth grade teacher in a semester-long
design-based study. In this paper, we explore conceptual and representational contexts
designed to support sophisticated modeling practices and beliefs and analyze the nature of
high-level performances achieved through these contexts.
Introduction
Internationally, researchers and practitioners recommend increasing K–12 students’ engagement in authentic
scientific practices such as modeling (e.g. Louca & Zacharia, 2012; National Research Council [NRC], 2012;
Östman & Wickman, 2014). In service of these goals, Schwarz and colleagues have proposed and refined a
learning progression for modeling to support students in developing modeling epistemologies and practices
(Fortus, Shwartz, & Rosenfeld, 2016; Schwarz et al., 2009; Schwarz, Reiser, Archer, Kenyon, & Fortus, 2012).
Thinking about learning progressions for modeling, however, involves challenges in coordinating between over-
arching aggregate arcs in the curriculum and individual student learning trajectories within the curriculum. In
response to these challenges, we conducted a semester-long design-based study of eighth graders engaging in
multi-modal modeling. In this paper, we explore contexts designed to support increasingly sophisticated
modeling practices and beliefs. Specifically, we explore conceptual contexts (the phenomena students were
studying) and representational contexts (the types of models students were encouraged to construct) that support
increasingly sophisticated modeling practices and beliefs by typical students in a low-SES, high-diversity public
charter school and analyze the nature of high levels of performance achieved through the designed curriculum.
Learning progression for modeling
For this paper, we focus our design and analyses around Schwarz and colleagues’ (2012) articulation of a
learning progression for modeling (see Table 1) (Fortus et al., 2016; Schwarz et al., 2009, 2012). During the
development of the learning progression, however, Schwarz and colleagues found few students engaging in
Level 3 practices and no empirical evidence of students performing Level 4 practices (Schwarz et al., 2009,
2012). It is therefore important to continue exploring conceptual and representational contexts that support
middle school students in engaging with high-level modeling performances. Our research explores conceptual
and representational contexts designed to support sophisticated modeling practices and beliefs.
Table 1: Schwarz and colleagues’ progression (adapted from Schwarz et al. (2012) and Fortus et al. (2016))
Category Levels
A. Salience- 1. Models are literal illustrations of a single phenomena
generality 2. Models consider things that are inaccessible to the senses and can represent
multiple similar phenomena
3. Multiple models can represent the same phenomena, and one model can represent
multiple phenomena
4. Models can represent unknown phenomena or ideas
B. 1. Models are made for the teacher
Audience/user 2. (A) Models are made to show what I think
(B) Models are made to help others understand
3. Models are made to communicate with others
4. Models are made to help me think
C. Evidence 1. No justification needed
2. (A) Content knowledge
(B) Authority
(C) Evidence in a specific case
3. Evidence in general with a justification for how evidence supports claims
D. Mechanistic- 1. Descriptive only
generative 2. Illustrate with a vague sense of explaining and predicting
3. Represent a mechanism to explain a predicted phenomena
4. Predict and generate questions about possible new phenomena
E. Revision 1. Models are not revised; they are either right or wrong
2. Revised to better fit information from authorities
3. Revised to better fit evidence obtained
4. Revised to enhance explanatory and predictive power
Design conjectures
The high-level conjecture guiding our work was that Level 4 modeling practices could be supported by
engaging students in several representational contexts by encouraging them to construct and coordinate across
three types of models: diagrammatic models (drawings that communicate explanatory mechanisms), physical
models (material objects created to test mechanisms), and computational models (runnable simulations created
by programming explicit rules for groups of actors in a system). We conjectured that creating and interrelating
multiple types of models would serve to support students in using models as tools because shifting between
models would position the models as resources rather than as final products. We further conjectured that shifting
among models would support students in revising their models to increase their explanatory power or empirical
accuracy, because each model they constructed would provide a new perspective of the phenomenon that they
were studying. We situated these models within a complex and tangible conceptual context, which we
conjectured would provide opportunities for creating abstract, generative models by encouraging students to
highlight aspects of phenomena and by enabling students to root their models in evidence they collected. We
embodied this conjecture by grounding the students’ work in the ecological relationships in the school's garden,
which has proved a powerful context in prior research (e.g., Manz, 2012).
Participants and intervention design
This semester-long study was conducted in a public charter school located in a large metropolitan school district
in the southeastern United States in partnership with Max, the third author, and his three eighth grade science
classes (91 students). At this school, 85% of the students qualify for free and reduced lunch. The school is
culturally and linguistically diverse; 53% of students identify as Black or African American, 31% as Hispanic or
Latino, 15% as White, and 1% as Asian. Students with disabilities make up 11% of the school, and 8% of
students are English Learners. Max and the first author, Ashlyn, codesigned and cotaught the lessons. Lessons
took place twice a week during students’ 55-minute science class periods over the course of 5 months (33 days
total).
This project consisted of three cycles. During each cycle, students chose to focus on a new research
question. Students developed their Cycle 1 research question as a class during their first encounters with the
garden as they observed that some parts of the garden were more moist than others. Then, they worked in small
groups of three to five students to construct models to investigate the relationship between soil moisture and a
variable of the group's choice, such as depth of soil, roots, or shade. The students began by observing the garden
and drawing diagrammatic models that highlighted patterns they noticed. Then, they tested the relationships
within their models in their classroom with physical microcosms and computational models. Though most
groups’ findings were straightforward, groups that investigated roots presented inconclusive findings.
Therefore, in Cycle 2, Max and Ashlyn encouraged students to investigate roots. Each group
constructed models to explore the relationship between roots and their surrounding environment in terms of a
variable of their group's choice, such as symbiotic relationships with bacteria and fungi, transpiration, hydrogen
pumps, and root growth through mitosis and elongation. In this cycle, students began by using online research to
draw diagrammatic models of their predictions about these mechanisms. They tested these relationships with
both physical and computational models and used data collected from the physical and computational models to
revise their diagrammatic models to improve the models’ accuracy and explanatory power.
This work increased students’ awareness of ecosystem services provided by plants, and several
students suggested researching phenomena in which plants performed services that could benefit their school
community for Cycle 3, such as phytoremediation of heavy metals in soil, carbon sequestration, and the
absorption of airborne toxic chemicals. During this cycle, students did not have time to engage with physical
and computational models; however, they created diagrammatic models based on their predictions and online
research, presented their models to younger students, and selected species to grow at the school.
Data collection and analysis
During each class period, we collected video recordings of the classroom, audio recordings of Ashlyn's
conversations with students during group and individual work, student artifacts such as models and written
reflections, and Ashlyn's field notes from each class period. In addition to this detailed longitudinal data
collection, we also collected baseline and summative data at the beginning and end of the project to provide
benchmarks for student progress over the course of the semester. Data analysis necessarily unfolded in relation
to students’ participation in our design. Our ongoing analysis was critical to informing the evolution of the
curriculum and supports for students. We focused our analysis on evaluating and revising our conjectures about
how to support students in engaging more frequently in Level 3 and 4 modeling conceptions and practices.
Challenges and opportunities
We present the challenges and opportunities identified in our work by category of the learning progression. For
each category, we describe our initial conjectures about supporting students in higher levels of modeling. Then,
we analyze of the nature of high-level performances to operationalize Level 4 modeling practices achieved in
these conceptual and representational contexts.
A. Salience-generality
Initially, we conjectured that interaction with diagrammatic models would support high-level practices in the
salience-generality category because students would be encouraged to consider the inclusion and exclusion of
different aspects of phenomena in the representational context of static, two-dimensional representations.
However, on Day 2 when students created their first diagrammatic models of the garden, 65% of students
created literal representations (Level 1). We conjectured that most students created literal models because the
students had not yet established criteria for determining what was relevant or irrelevant in their models.
Therefore, on Day 4 of Cycle 1, we encouraged students to use their models to represent a pattern that they
noticed in the garden and to propose an explanation for their pattern. About 50% of the students represented
unseen phenomena in their models and about 75% of the students created abstract models. Our current
conjecture about this activity is that the goal of representing a mechanism is one way to support students in
representing abstract and unseen phenomena (Level 2) rather than creating literal models (Level 1) because
focusing on a mechanism provided students with a lens for what was important to include in their models.
In terms of high-level practices, the Schwarz and colleagues’ progression proposes that Level 4
performances in the salience-generality category involve students viewing and using models as tools for
representing ideas and unknown phenomena. This interpretation of a Level 4 performance was easily identified
in students’ reflections about modeling. For example, Kingston defined a model as, “a picture of what you are
thinking about a topic,” and Jack wrote, “models don't need to actually look like the real thing they only need to
explain the idea or nature of it as much as possible.” We noticed that students tended to demonstrate this
performance when they used models to reason about unknown phenomena.
We coded students’ modeling performances as Level 4 when they used their models as a way to make
sense of the relationship between different factors of their phenomena. For example, when one student was
presented with anomalous data, she used her model as a resource to generate ideas that could explain the data,
revising her conception of the original phenomenon. We currently conjecture that shifting among models was
critical in supporting this practice. Students were able to generate new ideas because they were able to critique
their initial diagrammatic and computational representations with data collected from their physical models. We
found few examples of this level of practice; only about 25% of the students demonstrated Level 4
performances by the end of the project in either reflection or as they were constructing models, and no student
demonstrated Level 4 performances across all conceptual and representational contexts. These data demonstrate,
however, that middle school students are able to engage with Level 4 practices and epistemologies.
B. Audience
Initially, we conjectured that shifting among model types would support students in seeing models as tools. We
assumed that students would intuitively recognize models as communicative, and we did not explicitly design to
support this performance. During the project, we found that the collaborative nature of students’ tasks supported
them in using models for communication. Throughout the semester, students shifted between perceptions of
models as tools for communication and for constructing knowledge, sometimes voicing both perspectives
simultaneously. For example, Dylan's initial description of models indicated that she saw models as tools for
teaching (Level 2). This perspective was typical for our students; in their Day 1 definitions of models, over 50%
of the students wrote that models could be used to “show information” or “teach.” Similarly, when prompted to
describe the purpose of the diagrammatic models they constructed on Day 2, about 20% of students wrote that
their models were intended to show information to others or teach others. On Day 2, Dylan wrote, “Models can
be used to easily teach others of a certain relationship.” This perspective is likely a result of how students were
using their models. At this point in the project, students were showing their models to their peers, but they had
not yet used their diagrammatic models to design physical models to test their ideas.
At the end of Cycle 1, Dylan described models as tools for constructing knowledge. On Day 13, Dylan
wrote, “Models are used to make predictions about mechanisms and to see the relationship between two
variables. Physical models can also be used to test the relationship between two specific variables to help
understand your mechanism.” In this description, Dylan focused on models as constructive tools and did not
address their utility as communicative tools for teaching or collaboration, engaging at Level 4 of the Schwarz
progression (models as constructive tools). Dylan's development in the audience category was representative of
her peers; by Day 13, 52% of students described models as constructive tools, while only 9% described models
as collaborative tools. These data suggest that physical modeling increased students’ opportunities to perceive
models as tools for constructing knowledge. While diagrammatic modeling had affordances for communicating
with others, physical models were better suited to testing ideas. Overall, the percentage of students who
described their models as collaborative and constructive increased in their written reflections throughout the
semester. By the end of the project, roughly 25% of students expressed a belief that models are both
collaborative and constructive in these reflections, and over 50% of the students identified models as either
collaborative or constructive tools. Similarly, during the end-of-semester interviews, almost all students
described models as a tool for learning and a tool for communication.
It is important to note, however, that when engaged in model construction, students’ sense of purpose
in terms of audience was more tenuous. Even when explicitly prompted to describe choices that they were
making while modeling during Cycle 2, only about 50% of the students connected their choices to constructive
or collaborative purposes. Of these students, roughly 50% described their models as tools for showing others
information (Level 2), and approximately 55% described their models as tools for collaborating or for
constructing knowledge (Level 3 and 4). As in the salience-generality category, no students exhibited Level 4
performances for the audience category across all conceptual and representational contexts. The cause of the gap
between students’ sense of audience in written reflections and their sense of audience during model construction
is unclear. As we suggested in the salience-generality category above, it is possible that the gap was created by
the difference between students’ declarative knowledge and knowledge-in-practice. Students may also have
perceived their own models as different from models in general, affecting their responses to these prompts. It is
also likely that learning activities shaped students’ beliefs and practices; for example, the task of writing may
have provided greater affordances for considering audience and purpose, while the task of physical modeling
encouraged students to focus on the material challenges of constructing knowledge. Exploring the affordances
of these activities for engaging in high-level practice is important because it has implications for how students
construct, use, and perceive their models.
C. Evidence
Initially, we conjectured that providing students with accessible, tangible content would support high-level
practice in the evidence category, because students would have direct access to the phenomena they were
studying rather than relying on external sources. Our data support this conjecture; in our classrooms, from the
beginning of the semester to the end, the majority of the students demonstrated Level 3 conceptions of modeling
in the evidence category. Our students’ first modeling activity encouraged them to justify their models with
general empirical evidence (Level 3). When students created their diagrammatic models on Day 2, they were
asked to create a model based on observations from the garden. This activity discouraged the Level 1
perspective that no justification is needed for models, because students’ models were explicitly grounded in
their observations of the garden. The activity structure also reduced students’ opportunities to adopt Level 2
justifications because (1) few students had prior knowledge about the garden, (2) students had no access to
authority information sources like textbooks (because they were outdoors) or teachers (because Max and Ashlyn
did not provide any content-related information), and (3) students attempted to represent all five garden beds in
one image, discouraging them from creating case-specific representations. As a result, from the beginning of the
project, this activity provided strong opportunities for students to engage with the Level 3 perspective that
models are warranted by general empirical evidence.
D. Mechanistic-generative
Initially, we conjectured that physical and computational models would support students in using and perceiving
their models as mechanistic and generative tools, because these models would emphasize cause-and-effect
relationships and present data that resisted students’ explanations of phenomena. Throughout the semester, we
found that diagrammatic models also supported high-level practice. In this section, we describe the scaffolds
that supported students in engaging with high-level practices in the mechanistic-generative category.
When we collected baseline data for diagrammatic modeling on Day 2, we noticed that while most
students’ models were descriptive, a few students identified patterns within their models. For example, in
Meristem's model, she noted, “the thicker the layer of grass, the wetter the soil underneath.” We conjecture that
identifying such patterns is foundational for developing mechanisms because mechanisms explain why such
patterns occur. We leveraged pattern identification to help students build predicted mechanisms (Level 3) by
encouraging them to identify puzzling patterns and make predictions about causal explanations for those
patterns. For example, prompting Meristem to explain the pattern that she identified led to mechanistic physical
and diagrammatic models. In these models, she investigated mechanisms that regulate soil moisture, such as rate
of evaporation at different depths of soil, rate of water absorption from roots, and differences in evaporation
caused by shade from a variety of dead and alive plants.
We identified evidence of Level 4 beliefs and practices both in students’ reflections about modeling
and in the models that they created. Reflections were classified as Level 4 if they described models as
generative predictive tools. For example, when prompted to describe the purpose of models on Day 32, Dylan
wrote: “People use models to make predictions about a possible solution to a problem, make predictions about
why things happen a certain way, and ask questions about the environment.” Dylan's description was
representative of a majority of the students. By the end of Cycle 3, over 60% of our students described models
as tools for generating predictions and questions. We classified students’ models as Level 4 if they included
predictions or relevant unanswered questions. Approximately 45% of the students enacted this practice in their
models by the end of Cycle 3, though no student engaged in this practice across all contexts.
E. Revision
Initially, we conjectured that thinking across model types would support students in engaging in revision
practices as they encountered data that challenged their previous conceptions of their phenomena. Throughout
the semester, however, we found that the collaborative nature of the project motivated students to engage in
practices of revision for explanatory power as well. We currently conjecture that the structure of our activities
prevented students from adopting Levels 1 and 2 practices in the revision category. Because we provided
students with opportunities to revise their models within the first week of class, they did not believe that models
were unchangeable. Because we did not provide them with access to textbooks and did not act as content
experts, they could not rely on authority sources to revise their models during Cycle 1.
Yet, rather than making revisions rooted in empirical evidence (Level 3), we noticed that our students’
initial revisions were made to increase their models’ explanatory power (Level 4). For our students, revising
models based on evidence was less accessible than improving them as mechanistic and predictive tools.
Therefore, in this section, we explore challenges and supports for Level 3 practice as well as Level 4 practice in
this category. Existing research suggests that responding to anomalous data is particularly challenging for both
students and professional scientists. When faced with data that pushes back on their theories, students typically
reinterpret or reject evidence in a way that does not require them to modify their existing theories (Chinn &
Brewer, 1993; Kuhn, 2010). This response is amplified when students have not considered alternate theories
that could explain their evidence. Our students’ behavior was consistent with Chinn and Brewers’ findings and
with Kuhn's findings. When students’ data contradicted their predicted mechanism, students tended to trust their
reasoning over their evidence; they often assumed bias or errors in the evidence they collected rather than
revising their models. Given that revision based on evidence is characterized as challenging for students in the
literature, we believe that our students’ difficulty with this performance is likely to be observed in other
classrooms as well. Still, with appropriate scaffolds, students can revise models based on evidence, as
demonstrated both by Schwarz and colleagues (2009) and by our students. By the end of the project, a majority
of our students revised their models based on empirical evidence that they had collected and analyzed.
Significance
This paper contributes to ICLS’s goal of helping researchers and practitioners unpack the complexity of learning
and teaching in four ways, which we will explore in the following paragraphs. First, from a perspective of naïve
epistemologies as fine-grained context-sensitive resources, the ideas that students draw on change in response to
the classroom environment and students’ interactions with other students and their teacher (Berland et al., 2015;
Hammer & Elby, 2003). Our findings support this perspective, demonstrating that learning progressions for
complex practices like modeling do not represent fixed linear pathways through which all students learn. Rather,
a student may exhibit practices at multiple points along the progression at any given time across different
conceptual and representational contexts.
Second, we have demonstrated that middle school students are able to engage in high-level modeling
performances across categories of the learning progression. The examples documented for Level 4 performances
provide insight into the nature of students’ thinking, perspectives, capabilities, and limitations while engaging in
high-level modeling practices.
Third, we described our conjectures about conceptual and representational contexts that supported and
boot-strapped high-level performances. These findings align with existing research that proposes that circulating
among mutually referential models encourages students to redefine and re-represent their ideas about the
phenomena they are modeling (Lehrer et al., 2009).
Fourth, although learning progressions have traditionally been conceptualized as tools for designing
aggregate curricular arcs (e.g., Gotwals & Alonzo, 2012), our students’ enactments of modeling practices and
beliefs did not follow the sequential trajectory of the learning progression. Instead, we found that the learning
progression represented a range of modeling practices available to students, a valuable upper anchor for high-
level performance, and an analytic framework for examining students’ modeling beliefs and practices rather
than a set of sequential levels that students move through linearly (Hammer & Sikorski, 2015).
References
Berland, L. K., Schwarz, C. V., Krist, C., Kenyon, L., Lo, A. S., & Reiser, B. J. (2015). Epistemologies in
practice: Making scientific practices meaningful for students. Journal of Research in Science Teaching,
53(7), 1082–1112.
Chinn, C. A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: A theoretical
framework and impli- cations for science instruction. Review of Educational Research, 63(1), 1–49.
Fortus, D., Shwartz, Y., & Rosenfeld, S. (2016). High school students’ meta-modeling knowledge. Research in
Science Education, 46(6), 787–810.
Gotwals, A. W., & Alonzo, A. C. (2012). Learning progressions in science: Current challenges and future
directions. Rotterdam, The Netherlands: Sense Publishers.
Hammer, D., & Elby, A. (2003). Tapping epistemological resources for learning physics. The Journal of the
Learning Sciences, 12(1), 53–90.
Hammer, D., & Sikorski, T. R. (2015). Implications of complexity for research on learning progressions.
Science Education, 99(3), 424–431.
Kuhn, D. (2010). Teaching and learning science as argument. Science Education, 94(5), 810–824.
Lehrer, R. (2009). Designing to develop disciplinary knowledge: Modeling natural systems. American
Psychologist, 64(8), 759– 771.
Louca, L. T., & Zacharia, Z. C. (2012). Modeling-based learning in science education: Cognitive,
metacognitive, social, material and epistemological contributions. Educational Review, 64(4), 471–
492.
Manz, E. (2012). Understanding the codevelopment of modeling practice and ecological knowledge. Science
Education, 96(6), 1071–1105.
National Research Council. (2012). A framework for K-12 science education. A framework for K-12 science
education: Practices, crosscutting concepts, core ideas. Washington, DC: National Academies Press.
Östman, L., & Wickman, P.-O. (2014). A Pragmatic Approach on Epistemology, Teaching, and Learning.
Science Education, 98(3), 375–382.
Schwarz, C., Reiser, B. J., Acher, A., Kenyon, L., & Fortus, D. (2012). MoDeLS: Challenges in defining a
learning progression for scientific modeling. In A. Alonzo & A. W. Gotwals (Eds.), Learning
progressions in science: Current challenges and future directions. The Netherlands: SensePublishers,
Rotterdam.
Schwarz, C. V., Reiser, B. J., Davis, E. A., Kenyon, L., Achér, A., Fortus, D., Krajcik, J. (2009). Developing a
learning progression for scientific modeling: Making scientific modeling accessible and meaningful for
learners. Journal of Research in Science Teaching, 46(6), 632–654.