tensions between conceptual and metaconceptual learning with models

Tensions between conceptual and metaconceptual learning with models

Michele J Mann, Cesar Delgado, Walter M Stroup, & Anthony J Petrosino

[email protected]

ABSTRACT Models and modeling are prominent in the new US science education standards, being present as both a crosscutting concept and a science and engineering practice. Yet, there is a gap between the way scientists use models and how models are used in the science classrooms. Models have been shown to be very useful in achieving student gains in conceptual understanding of phenomena yet models may inadvertently foster inaccurate metaconceptual or epistemological understandings about the phenomenon. An evaluation of two ecosystem models was done to illustrate how these linked models could be used in the classroom to foster both conceptual and metaconceptual learning. Teachers need to be aware when using models of the conceptual outcomes as well as the metaconceptual outcomes; these are often in tension and must be navigated carefully. Students need to be exposed to multiple models during a unit that emphasize different aspects of the phenomena, supporting different conceptual understandings but also illustrating the nature of science and the limitations and strengths of modeling. As the science education community moves towards implementing the vision of the Next Generation Science Standards, metaconceptually aware teaching practices around modeling must come into place.


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Models and modeling are prominent in the new US science education standards, being present as both a crosscutting concept and a science and engineering practice (NRC, 2012, 2013). Yet, there is a gap between the way scientists use models and how models are used in the science classrooms. Models are typically used in the classroom to teach about a process in a static sense (Grosslight, Unger, Jay, & Smith, 1991). Often the student is learning about what happened or happens but not looking at what could happen or emergent properties. Scientists however often use models more dynamically, to determine what can possibly happen. For instance, every year, meteorologists combine models from many different sources to predict the number of hurricanes that will develop in the Northern hemisphere (Chen, Zhao, Donelan, Price, & Walsh, 2007). Students need exposure and experience using models as scientists, i.e., using models for more than learning about a phenomenon. In addition, models by their very nature are not complete representations of the target phenomenon, and the strengths and limitations of the models need to be noted and understood. According to the Framework for K-12 Science Education (NRC, 2012), children in grades K-2 should be drawing and diagramming to help them develop an understanding of a model; as children develop, their models should also progress by no longer just representing what is physically seen in a model but also other features of a system. By high school students should be able to integrate data into a model and be able to discuss the models precision and accuracy (National Research Council, 2012). Through the use of models, students simultaneously develop their own mental models (Sutton, 1992). Modeling as a skill needs to be systematically developed by students by having experiences with many different forms of models (Petrosino, 2003). Models are essentially metaphors (Petrosino, 2003; Sutton, 1992) where a better-known or more concrete phenomenon represents features of the target phenomenon, e.g., sticks and balls represent compounds or beads on pipe cleaners represents nitrogenous bases. There is a natural development in instructional modeling from literal resemblances to relational structure and function (Gentner, 1983; Gentner & Toupin, 1986). The use of models as a tool requires both scientific and mathematical reasoning (Cullin & Crawford, 2002) that is developed through practice.

Models have been shown to be very useful in achieving student gains in conceptual understanding of phenomena (Coll, France, & Taylor, 2005). Yet models may inadvertently foster inaccurate metaconceptual or epistemological understandings about the phenomenon. Recent literature has explored the tensions between conceptual and metaconceptual learning with models (Delgado, in press), and proposed a series of instructional and curricular measures to keep students from coming away with nature of science (NOS) or epistemological misunderstandings at the metaconceptual level. Comparing models may be a useful way of fostering both conceptual and metaconceptual understanding (Delgado, in press; Hodson, 2008; Snir, Smith, & Grosslight, 1993). In this theoretical paper, we present two models of an ecosystem with different affordances and constraints: a three dimensional, real-time living model of an ecosystem that is itself a simplified ecosystem, and the other a stock and flow computer model of the gas chemical reactions in an ecosystem. By simultaneously considering two models of the same target phenomenon, we posit that students may develop a richer understanding of both ecosystems and modeling. This theoretical paper proposes the use of linked models and specific classroom activities that should lead to enhanced conceptual and metaconceptual learning by students.

Theoretical Framework


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Models can foster learning about a phenomenon at the conceptual and metaconceptual levels (Delgado, in press). A conceptual level of understanding is knowledge of the facts, concepts, and theories around a phenomenon while metaconceptual is concerned with how the products of science were developed and the characteristics of those products (Delgado, in press). Models are simplified representations of the real world, which means that interpretations, conventions, and limitations of the model need to be considered when using a model. Models can effectively support conceptual learning but at the same time create misinterpretations of metaconceptual understandings. Delgado (in press) explains that there are four characteristics of models and simulations that can be metaconceptually problematic: ahistoricity, teleology, epistemological overreach, and ontological poverty. This framework will be used to evaluate two ecosystem models, and to illustrate how these linked models could be used in the classroom to foster both conceptual and metaconceptual learning.

The Models

Ecosystem in a Bottle. An ecosystem is a community of biotic and abiotic components interacting as a system, e.g., a coral reef ecosystem, which includes the living organisms and nonliving components like sand and water. The largest ecosystem is the Earth as a whole. Biosphere II, a 3.14-acres, domed area that includes an ocean with a coral reef, mangrove wetlands, tropical rainforest savannah grassland and fog desert and a team of eight humans, was an attempt in the nineties to model the Earths biosphere. However, much simpler models can be built even in the elementary classroom, featuring plant and animal life. The first model is an ecosystem in two connected bottles. The bottom bottle is an aquatic system with a few freshwater shrimp, daphnia (a small freshwater crustacean), and snails, along with a sprig of elodea (an aquatic plant). The top part of the system was soil where bean seeds had been planted. Connecting the terrestrial system with the aquatic was a piece of cotton string, allowing the exchange of water and gases across bottles. The system was sealed and placed in a sunny window. This ecosystem in a bottle is a simplified scale model of an aquatic and terrestrial system. This system is dynamic and functioning much like the real system although with limited organisms, space, and interactions outside the enclosed vessel. This model works well to see growth of plants and reproduction of daphnia, shrimp and snails over a long period of time. Over time, the composition of gases changes as the bean plants grow, and with the daily cycle of sunlight.

Computer Simulation. The second model is a participatory aggregate simulation model created on InSight Maker (Foreman-Roe & Bellinger, 2013) to show the daily interactions within an ecosystem. It was designed using data of oxygen and carbon dioxide levels measured in the ecosystem in a bottle. Participatory simulation modeling has been shown to be an effective tool for students to gain understanding of complex systems (W. M. Stroup, Ares, Lesh, & Hurford, 2007; Wilensky & Stroup, 2002, 2013). Stroup and Wilensky (2014) recently found that using aggregate models along with agent-based models effectively increased learning and reasoning. The variables of interest are modeled using a stocks and flows approach. In a stocks and flows model, there are initial levels of the variables that are increased or decreased by different processes. An example is the stock of water in a bathtub, with flows inwards from the faucet and outward from the drain and evaporation. In this model, the stocks are specifically the carbon dioxide, plant food (products of photosynthesis or carbohydrates), and size of the organisms while the flows are photosynthesis, cellular respiration, and rate of growth. This graphically diagramed the dance between


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Figure 1 Carbon dioxide and plant food levels the carbon dioxide and plant food during a daily

cycle. The model transforms the gross physical data into mathematical relationships. Notably, while the data from the ecosystem in a bottle showed stochastic variations, the computer simulation used curve-fitting (Figure 1) to produce exact mathematical relationships across carbon dioxide, plant food, and size of the organisms. Plant food was inferred from measured oxygen levels.

Conceptual and Metaconceptual Learning: An Analysis Ecosystem in a Bottle The strengths of this model for conceptual learning are that students can observe all or part of the life cycles of the bean plants, elodea, daphnia, snails and fresh water shrimp. The prescriptive instructions for building the model are such that a successful system will most likely occur. The students can also observe the water cycle when condensation forms inside the bottles. The plants growing and the animals thriving is evidence that the carbon, nitrogen and phosphorus cycles are functioning in the ecosystem. To further understand the cycles, measurements of atmospheric oxygen and carbon dioxide can be taken and soil and water can be tested. However, a weakness of this model for conceptual learning is that students cannot directly observe the gas cycles. The products of photosynthesis and cellular respiration can be inferred but not directly observed in the process. Students are also not able to measure the amount of plant food or carbohydrates the plants are producing. The prescriptive model set-up does not lead to a better understanding of how ecosystems interact to reach sustainability. Lastly this model has fewer trophic levels than are commonly observed in nature. Metaconceptual strengths of this ecosystem are that in the lesson plans accompanying instructions it is explicitly stated that this is simpler ecosystem than found in nature, building an understanding of the nature of the modeling process. However, there are also weaknesses at the metaconceptual level. Ontological poverty is an issue because the models robustness (while helpful for conceptual learning) conceals the possibility of unstable equilibria or sudden outside shocks to the system that can occur in real ecosystems. This model does not have all the factors present in a natural ecosystem, and there are fewer trophic levels with fewer organisms. Epistemological overreach is a problem as well, as the students might get the impression that balanced sustainable ecosystems are easily built, well known, and are more the rule than the exception. In fact, there are components of the ecosystem (e.g., microbes in the soil) that are essential but not fully studied by science and not explicitly mentioned in the simulation. Computer Simulation Due to space constraints only the part of the simulation dealing with amount of carbon dioxide and plant food is discussed in this paper (the rest will be analyzed in the full paper distributed at the conference). The strength of this model for conceptual learning is that it effectively shows the interaction between carbon dioxide and plant food, demonstrating the reactants and products of photosynthesis and cellular respiration. The simulation allows for multiple, quick cycles of experimentation. It makes explicit important cycles that are not obvious at the macrolevel. A weakness for conceptual learning is that the nature of the relationship between carbon dioxide levels and plant growth is not clear. Students might assume that as more carbon


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dioxide is produced, that causes more plant food to be produced. While the carbohydrates cannot be produced without carbon dioxide, it is not causing the carbohydrates to be produced. At the metaconceptual level, this part of the simulation produced a specific graph that, while helpful in understanding the concept of the relationship between photosynthesis and carbon dioxide, may be problematic. The model is ontologically impoverished because it does not account for all of the fluctuation in the concentration of the carbon dioxide and oxygen. There could be gases sequestered in the soil or dissolved in the water that are not accounted for in the simulation. Epistemological overreach is also an issue because the graphs (e.g., Fig. 1) feature smooth curves with perfect inverse relationships rather than the scattered data points and imperfect relationships of real data. The continuous lines imply continuous measurement of data (which is actually at discrete points in time). Plant food levels are inferred from O2 levels rather than measured directly, again implying to the user a greater degree of certainty than actually exists.

Navigating the Tensions Between Conceptual and Metaconceptual Learning

Van Driel and Verloop (2002) found that teachers showed an awareness of the value of using models to teach science concepts but not the value of using models to learn about science. There needs to be more emphasis in professional development on how to use models in science to not only teach the conceptual understanding but also the metaconceptual understandings. Teachers need to be aware when using models of the conceptual outcomes as well as the metaconceptual outcomes; these are often in tension and must be navigated carefully (Delgado, in press). In the case of our two linked models, the simpler the model the more conceptual learning is supported. For instance, a perfect inverse relationship between carbon dioxide and plant food levels is easier to detect and understand than one that is more realistic, but the idealization of the curves are an example of epistemological overreach. Engaging students in plotting real, messy data and deriving that the relationship is approximately inverse can help navigate the tension between conceptual and metaconceptual learning. After doing this, the perfect curves of the simulation are more likely to be understood as an idealized model. The stability of the ecosystem in a bottle is very useful for classroom implementation and conceptual understanding, but is ontologically impoverished relative to real ecosystems with many additional factors and components. While standard lesson plans for the ecosystem in a bottle prescribe the number and types of organisms, experimenting with proportions and components across a classrooms ecosystems may provide a more realistic vision of ecosystem stability. Students need to be exposed to multiple models during a unit that emphasize different aspects of the phenomena, supporting different conceptual understandings but also illustrating the nature of science and the limitations and strengths of modeling. As students are exposed to different models during a unit of study, there is the opportunity for them to develop tools to critique a model. Teachers can teach students to be critical by having them answer questions about a model for instance: What phenomena does this model represent? What are the strengths of this model? What are the weaknesses of this model? and How could you improve this model? Using models in the science classroom can be effective at teaching concepts, facts and theories; however, for students to learn at both the conceptual and metaconceptual level they will need to be exposed to several different models of a phenomena and be taught how to be critical of models. As the science education community moves towards implementing the vision of the Next Generation Science Standards, metaconceptually aware teaching practices around modeling must come into place. Thus, we feel that this paper will be of interest to the NARST community.


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