Of particular interest for teachers, curriculum designers, and other educators

As part of the Energy in the Human Body curriculum,¹ a middle school class spent several days investigating how glucose travels through the bloodstream and gets to the cells in the body. In prior chapters in the curriculum, the students had already learned that cells need oxygen and glucose to get energy from ATP through a process called cellular respiration. They had also learned about mitochondria and about certain characteristics of the blood and blood vessels, as well as about the circulatory system as a whole.

One of the investigations undertaken by that class will serve as our example throughout this tour (adapted from Nunez-Oviedo & Clement, 2017). The focus was on how glucose moves from the intestines into the blood. The arc followed by this investigation is typical of that followed by other lessons in modeling curricula we have investigated. Major components of these investigations usually include:

• Setting the Stage (including constructing an initial model)
• Improving the Model
• Model Consolidation and Application

An additional Model Competition component may or may not occur.

Level IV of the Modeling Framework

Setting the Stage Identifying the Pattern to Be Explained. For this investigation, the pattern to be explained was how glucose moves into the blood. To get students focused on this question, the teacher first showed them a drawing of the villi in the intestine and asked them to create individual drawings to show a small portion of the intestine and to draw ideas about the position of the capillaries with respect to the villi. How should they be situated in order for the body to provide maximum absorption of nutrients? Generating an Initial Model. In order to engage in iterative cycles of model revision and improvement, there must be a starting point, an initial model that can be evaluated and revised. In this class, after the students were clear on what it was they were trying to explain, the teacher led them through several steps to produce useful initial models. First, the students shared their individual drawings in small groups and each group produced a group drawing, then these group drawings were shared with the whole class. Then the teacher used an overhead projector as she drew an outline of villi in the small intestine (Figure 1). She asked students to come up and add their ideas about the position of the capillaries with respect to the villi. As they drew on the overhead in red, the class could see the drawings take shape. The result was three ideas for initial models (all shown in Figure 2).	Figure 1. How are capillaries arranged with respect to villi in the intestine? Wavy lines are the villi lining the intestine. The students' job was to add the capillaries.
Engaging in Model Competition Normally at this point, the teacher would support students in a gradual process of evaluating and modifying the initial model to bring it increasingly in alignment with the scientifically accepted model of a phenomenon. But an optional approach when more than one initial model has active support in the class is to engage the class in evaluating each model and then deciding which ones they will discard and which one they will keep for later modification. Evaluating the Models. To begin evaluating the models using Model Competition, the teacher asked the students, “What is the least efficient model, A, B, or C?” (Figure 2). The students agreed that A was the least efficient. This reduced the models under consideration to B and C. She then asked, “What is the most efficient model?” Most students thought B was, which was problematic, because C is actually closest to the target model. The teacher had to come up with a different question with which to compare the two. She asked the students to think about the environment the capillaries were in. For B, was the environment friendly or hostile? The students decided that it was hostile because there are acids in the stomach. This eliminated B, and Model C was the one taken forward into the next classroom discussion mode.	Figure 2. Three initial models
Improving the Model Evaluating the Model. In order to improve the remaining model, the teacher led the class through a series of questions about Model C. For instance, she asked them what the main function of the capillaries was, and one student replied, “Exchange?” The teacher confirmed, “It is a site of exchange...but these capillaries look like dead ends.” Eventually, the students realized that in order for the capillaries to do their work, they needed to form loops in the villi, but the loops they made were of a single color. Modifying the Model. The teacher sent them back to their small groups with the challenge to improve their drawings. She reminded them that they had used two colors in capillaries before and said: “I want to see that loop and find a colorful way to distinguish the difference in this loop.” Most students redrew villi as shown in Figure 3. Evaluation and Modification can occur as distinct classroom phases or they can alternate rapidly. Especially in small group work, we have observed students engaging in numerous and occasionally rapid cycles of evaluation and modification. These work together in Improving the Model.	Figure 3. Student capillary loop model
Model Consolidation and Application The last component of any lesson may be the one that gets dropped due to time. However, this component is crucial in order for students to integrate and retain their new knowledge. This teacher allowed substantial time to help the class converge on a final instructional model and to integrate their new understandings with other concepts they had gained. First, she showed them a transparency of the target model, which all the small group models were now near enough that the difference constituted only a small conceptual jump (Figure 4). Later, when the class investigated what happens in the lungs, the teacher brought back their villi model to compare with their new alveoli model. The capillary arrangement is different, but a commonality is that both maximize the surface area to get maximum exchange. In this way, their final villi model was brought back to their attention and integrated into their larger understanding of bodily systems.	Figure 4. Target Model on Transparency

Level IV Overview

Figure 5. Progression through Level IV in the Modeling Framework

We call these broad divisions in investigations Classroom Modeling Modes. Each of these modes takes some time. This teacher had planned distinct activities for Setting the Stage, Improving the Model, and helping students Consolidate their understandings about the target model. However, the opportunity for Model Competition arose during class and was not planned ahead of time. Fortunately, this teacher knew several strategies that could help her do this. Below, we will use this same example to illustrate how the teacher used strategies of different sizes, from large, planned activities to small, spontaneous strategies to help students visualize the system and to keep the discussion moving in a constructive path. On this page, we will focus on several strategies that supported the first lesson component, Setting the Stage, to show what we mean by Levels. (Strategies that support or contribute to the other lesson components are illustrated with examples in the Catalog.)

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Level III of the Modeling Framework

Within the section for each Classroom Modeling Mode above are subsections that describe Modeling Phases. These are at Level III in our framework and there are four of them: Identifying the Pattern to Be Explained, Generating an Initial Model, Evaluating the Model, and Modifying the Model. Now we will look more deeply into one of these phases, Generate an Initial Model. It contributed to the Setting the Stage classroom mode (Figure 6). In turn, there are smaller, more detailed strategies that can support or contribute to it, as examples from the villi lesson will show.

Figure 6. Digging down beneath the Setting the Stage lesson component

Level II of the Modeling Framework

This level of the framework comprises both a large number of creative reasoning processes used by students and strategies teachers use to support those processes. For purposes of this Tour, we will look at two strategies that were used in the villi lesson to support the Generate Initial Model modeling phase.

In the villi lesson, when asking students to go to their small groups and generate their initial models, the teacher Provided a Partial Model (a drawing of the villi) to get the students started. (Figure 1) This supporting strategy is described in the Strategy Catalog Level II: Creative Reasoning Processes to Support Model Generation.

She also Asked the Students to Provide Model Elements, in this case, capillaries.

There are a large number of such strategies at Level II that can be used to support creative reasoning, including familiar ones such as using analogies and extreme cases.

Figure 7. Asking students to provide model elements is one strategy teachers use to support their students in generating an initial model. Other support strategies are described at Level II in the catalog.

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Level I of the Modeling Framework

In the villi lesson, in order to help the students Provide Model Elements for an initial model, the teacher had them draw their own individual models, then combine those into small group drawings, and then she had them add their ideas to a drawing on an overhead transparency (Figure 1). This use of Scientific Drawings is an example of a Level I Visualization Strategy. (See Figure 8.) These are a large collection of strategies for helping students use their own mental imagery as a thinking tool. Any of these strategies can be used at any point in classroom discussion -- probably the more the better, as it has been shown (Lowe, 1995, 2004)² that educators have tended to underestimate the information students are able to reap from images.

In addition, there is a set of important Level I Participation Strategies provided in our Strategy Catalog.³ Some of the many participation strategies this teacher used were Establishing a Safe Environment and Withholding Answers During Open Discussions. These are general strategies for initiating and sustaining any whole class discussion. They support important discussion processes that are prerequisites for using the other more specific cognitive strategies on this site.

Figure 8. Both Visualization Strategies and Participation Strategies are at Level I in our framework; they underlie all of the other classroom modeling levels and enable those levels to function. This diagram shows examples of strategies at each level and how they supported Setting the Stage in the villi lesson. Thus, this is an example of how one part of the framework might look for one particular lesson.

The strategies in Figure 8 were used almost simultaneously and this helps us understand the idea of levels of strategies that support each other. It illustrates how part of the framework could look to support one part of a lesson. The entire framework is shown in the Full Theory section, but most useful for pre- and in-service teachers is probably the core of the framework, shown in the Core of this Teaching Approach.

Comment About the Importance of Mental Imagery

Our own research, as well as that of others, provides evidence that the use of mental imagery is an important part of creative reasoning processes such as analogical thinking, extreme case reasoning, and thought experimentation.^4,5 This appears to be true for students as well as scientists. While some teachers intuitively use frequent supports for imagery (gestures, drawings), we find that it is common to underestimate how much support students need in order to leverage their imagistic abilities as an effective support for scientific reasoning. The Visualization Strategies are at Level I. This does not mean that they are less important, but that on the contrary, they provide crucial support to everything above them in the list. Many teachers are aware that discussion-participation strategies are crucial and use them frequently. We see effective teachers of model-based lessons doing something similar with imagery support strategies, using them almost constantly during model-based lessons.

Where to Go Next

• We suggest that you look at the Core of this Approach page if you have not done so already.

• The Catalog of Strategies section lists all strategies organized by levels

• The Course Syllabus Ideas section contains suggestions for using this site as a resource for a graduate course. It includes ideas arising from experience teaching aspects of this material in courses for pre- and in-service teachers. Teachers who want to self-instruct can also use the exercises and videos accessed from the Syllabus Ideas section to gain a more in-depth undesrstanding of strategies that support modeling.

• An Introduction to the Full Theory provides a fuller rationale for the organization of the framework and a graphical map of the Strategy Catalog.

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¹ Rea-Ramirez, Núñez-Oviedo, & Clement, 2004

² Lowe, R. K. (1995). Selectivity in diagrams: Reading beyond the lines. Educational Psychology, 14(4), pp. 4667-4692.
Lowe, R. (2004). Interrogation of a dynamic visualization during learning. Learning and Instruction 14(3), 257-274.

³ For participation strategies on other sites, see https://ambitiousscienceteaching.org/ and https://inquiryproject.terc.edu/prof_dev/Goals_and_Moves.cfm.html.

⁴ Stephens & Clement, 2009

⁵ Clement, 2009, 2018