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How Students Learn: History, Mathematics, and Science in the Classroom 12 Developing Understanding Through Model-Based Inquiry James Stewart, Jennifer L. Cartier, and Cynthia M. Passmore A classroom of students need only look at each other to see remarkable variation in height, hair color and texture, skin tone, and eye color, as well as in behaviors. Some differences, such as gender, are discrete: students are male or female. Others, such as hair color or height, vary continuously within a certain range. Some characteristics—10 fingers, 10 toes, and one head—do not vary at all except in the rarest of cases. There are easily observed similarities between children and their parents or among siblings, yet there are many differences as well. How can we understand the patterns we observe? Students need only look through the classroom window to take these questions a next step. Birds have feathers and wings—characteristics on which they vary somewhat from each other but on which they are completely distinct from humans. Dogs, cats, and squirrels have four legs. Why do we have only two? As with much of science, students can begin the study of genetics and evolution by questioning the familiar. The questions mark a port of entry into more than a century of fascinating discovery that has changed our understanding of our similarities, our differences, and our diseases and how to cure them. That inquiry has never been more vital than it is today. It is likely that people observed and wondered about similarities of offspring and their parents, and about how species of animals are similar and distinct, long before the tools to record those musings were available. But major progress in understanding these phenomena has come only relatively recently through scientific inquiry. At the heart of that inquiry is the careful collection of data, the observation of patterns in the data, and the generation of causal models to construct and test explanations for those
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How Students Learn: History, Mathematics, and Science in the Classroom patterns. Our goal in teaching genetics and evolution is to introduce students to the conceptual models and the wealth of knowledge that have been generated by that scientific enterprise. Equally important, however, we want to build students’ understanding of scientific modeling processes more generally—how scientific knowledge is generated and justified. We want to foster students’ abilities not only to understand, but also to use such understandings to engage in inquiry. For nearly two decades, we have developed science curricula in which the student learning outcomes comprise both disciplinary knowledge and knowledge about the nature of science. Such learning outcomes are realized in classrooms where students learn by “doing science” in ways that are similar to the work scientists do in their intellectual communities. We have created classrooms in which students are engaged in discipline-specific inquiry as they learn and employ the causal models and reasoning patterns of the discipline. The topics of genetics and evolution illustrate two different discipline-specific approaches to inquiry. While causal models are central in both disciplines, different reasoning patterns are involved in the use or construction of such models. The major difference is that the reconstruction of past events, a primary activity in the practice of evolutionary biology, is not common in the practice of genetics. The first section of this chapter focuses on genetics and the second on evolution. The third describes our approach to designing classroom environments, with reference to both units. Our approach to curriculum development emerged as a result of collaborative work with high school teachers and their students (our collaborative group is known as MUSE, or Modeling for Understanding in Science Education).1 As part of that collaboration, we have conducted research on student learning, problem solving, and reasoning. This research has led to refinements to the instruction, which in turn have led to improved student understanding. GENETICS An important step in course design is to clarify what we want students to know and be able to do.2 Our goal for the course in genetics is for students to come away with a meaningful understanding of the concepts introduced above—that they will become adept at identifying patterns in the variations and similarities in observable traits (phenotypes) found within family lines. We expect students will do this using realistic data that they generate themselves or, in some cases, that is provided. However, while simply being familiar with data patterns may allow students to predict the outcomes of future genetic crosses, it provides a very incomplete understanding of genetics because it does not have explanatory power. Explanatory power comes from understanding that there is a physical basis for those
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How Students Learn: History, Mathematics, and Science in the Classroom patterns in the transmission of genetic material (i.e., that there are genes, and those genes are “carried” on chromosomes from mother and father to offspring as a result of the highly specialized process of cell division known as meiosis) and as a result of fertilization. To achieve this understanding, students must learn to explain the patterns they see in their data using several models in a consistent fashion. Genetics models (or inheritance pattern models) explain how genes interact to produce variations in traits. These models include Mendel’s simple dominance model, codominance, and multiple alleles. But to understand how the observed pairings of genes (the genotype) came about in the first place, students must also understand models of chromosome behavior, particularly the process of segregation and independent assortment during meiosis (the meiotic model). We have one additional learning outcome for students—that they will couple their understanding of the transmission of the genetic material and their rudimentary understanding of how alleles interact to influence phenotype with an understanding of the relationship of DNA to genes and the role played by DNA products (proteins) in the formation of an organism’s phenotype (biomolecular models). DNA provides the key to understanding why there are different models of gene interaction and introduces students to the frontier of genetic inquiry today. These three models (genetic, meiotic, and biomolecular) and the relationships among them form the basic conceptual framework for understanding genetics. We have designed our instruction to support students in putting this complex framework in place. Attending to Students’ Existing Knowledge While knowledge of the discipline of genetics has shaped our instructional goals, students’ knowledge—the preconceptions they bring to the classroom and the difficulties they encounter in understanding the new material—have played a major role in our instructional design as well. The genetics course is centered around a set of scientific models. However, in our study of student learning we have found, as have others,3 that students have misunderstandings about the origin, the function, and the very nature of causal models (see Box 12-1). They view models in a “naïve realistic” manner rather than as conceptual structures that scientists use to explain data and ask questions about the natural world.4 Following our study of student thinking about models, we altered the instruction in the genetics unit to take into consideration students’ prior knowledge about models and particular vocabulary for describing model attributes. Most important, we recognized the powerful prior ideas students had brought with them about models as representational entities and explic-
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How Students Learn: History, Mathematics, and Science in the Classroom BOX 12-1 Student Conceptions of Models One early study of student learning in the genetics unit focused on identifying the criteria students used when assessing their models for inheritance phenomena.5 The study was predicated on a commitment to developing with students early in the course the idea of consistency as a basis for model assessment. Students read a mystery scenario involving a car accident and evaluated several explanations of the cause of the accident. Each explanation was problematic because it was either (1) inconsistent with some of the information the students had been given, (2) inconsistent with their prior knowledge about the world, or (3) unable to account for all of the information mentioned in the original scenario. Students discussed these explanations and their shortcomings, and the teacher provided the language for talking about model assessment criteria: she instructed them to seek explanatory power, predictive power (which was discussed but not applied to the accident scenario), internal consistency (among elements within the model), and external consistency (between a model and one’s prior knowledge or other models). Throughout the genetics unit, students were prompted to use these criteria to evaluate their own inheritance models. Despite the explicit emphasis on consistency as a criterion for model assessment, however, we found that very few students actually judged their models this way. Instead, students valued explanatory adequacy, visual simplicity, and “understandability” more strongly. A closer look at the work of students in this study showed that most of them viewed models not as conceptual structures but as physical replicas, instructional tools, or visual representations. In fact, the common use of the term to describe small replicas—as in model airplanes—sometimes interferes with students’ grasp of a causal model as a representation of a set of relationships. Similarly, when attempting to apply model assessment criteria to their explanations for data patterns in liquid poured from a box, several students treated “internal consistency” and “external consistency” literally: they evaluated the box’s proposed internal components and the external phenomena (observations) separately. This confusion stemmed from students’ prior understanding of concepts associated with the vocabulary we provided: clearly “internal” and “external” were already meaningful to the students, and their prior knowledge took precedence over the new meanings with which we attempted to imbue these terms. Given this misunderstanding of models, it was not surprising that our genetics students neither applied nor discussed the criterion of conceptual consistency within and among models.
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How Students Learn: History, Mathematics, and Science in the Classroom itly addressed these ideas at the outset of the unit. In the genetics unit, teachers employ tasks early on that solicit students’ ideas about scientific models and explicitly define the term “model” as it will be used in the science unit. Frequently, teachers present sample models that purport to explain the phenomena at hand and ask students to evaluate these models. Teachers create models that have particular shortcomings in order to prompt discussion by students. Most commonly, students will describe the need for a model to explain all the data, predict new experimental outcomes, and be realistic (their term for conceptual consistency). Throughout the course, teachers return to these assessment criteria in each discussion about students’ own inheritance models. A subsequent study has shown that these instructional modifications (along with other curricular changes in the genetics unit) help students understand the conceptual nature of scientific models and learn how to evaluate them for consistency with other ideas.6 We now provide an example of an initial instructional activity—the black box—designed to focus students’ attention on scientific modeling. As Chapter 1 suggests, children begin at a very young age to develop informal models of how things work in the world around them. Scientific modeling, however, is more demanding. Students must articulate their model as a set of propositions and consider how those propositions can be confirmed or disconfirmed. Because this more disciplined modeling is different from what students do in their daily lives, we begin the course with an activity that focuses only on the process of modeling. No new scientific content is introduced. The complexity of the task itself is controlled to focus students on the “modeling game” and introduce them to scientific norms of argumentation concerning data, explanations, causal models, and their relationships. This initial activity prepares students for similar modeling pursuits in the context of sophisticated disciplinary content. During the first few days of the genetics course, the teacher presents the students with a black box—either an actual box or a diagram and description of a hypothetical box—and demonstrates or describes the phenomenon associated with it. For example, one box is a cardboard detergent container that dispenses a set amount of detergent each time it is tipped, while another is a large wooden box with a funnel on top and an outlet tube at the bottom that dispenses water in varying amounts, shown in Figure 12-1. Once the students have had an opportunity to establish the data pattern associated with the particular box in question, the teacher explains that the students’ task is to determine what mechanisms might give rise to this observable pattern. During this activity (which can take anywhere from 3 to 11 class periods, depending on the black box that is used and the extent to which students can collect their own data), the students work in small teams. At the conclusion of the task, each team creates a poster representing its explana-
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How Students Learn: History, Mathematics, and Science in the Classroom FIGURE 12-1 One black box used in the MUSE science curriculum and typical data patterns associated with the box. tion for the box mechanism and presents it to the class. Classmates offer criticism and seek clarification during these presentations. As the dialogue below suggests, the exercise begins with students engaged in a central activity of scientists—making observations. Teacher Making observations is important in science. I want you to observe this carton. Just call out what you notice and I will write it on the board. The students respond with a variety of observations: Ian The box is white with blue lettering. Delia The contents slosh around and it looks like liquid soap when we pour it. Sarah Hey, it stopped coming out! Try to pour it again so we can see what happens. Owen It always pours about the same amount then stops.
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How Students Learn: History, Mathematics, and Science in the Classroom After several minutes of listening to the students, the teacher stops them and invites them to take a closer look at the carton, prompting them to identify patterns associated with their observations. Their reflection on these patterns leads the students to propose manipulations of the container, which in turn produce more observations. The teacher now interrupts them to guide their attention, saying: Teacher Okay, you’ve made some wonderful observations, ones that you are going to be using in just a few minutes. But, there is more to science than making observations. Scientists also develop ideas of what is not visible in order to explain that which is. These ideas are called models. She goes on to challenge them: Teacher Imagine an invisible “world” inside the container that, if it existed in the way that you imagine, could be used to explain your observations. I want you to make drawings of your imagined world and maybe some groups will have time to develop a three-dimensional representation too. And, one last thing, I want each group to develop at least one test of your model. Ask yourself, “If the world inside the carton is as I imagine it and I do X to the carton, what result would I expect?” Over the next two class periods, the students work in animated groups to develop models that can be used to explain their observations. They describe, draw, and create three-dimensional representations of what they think is in the carton. They argue. They negotiate. They revise. Then they share drawings of their models with one another. Sarah Hey Scott, you have a different idea than ours. How does that flap work? Scott The flap is what stops the detergent from gushing out all at once when you tip it. Delia Yeah, I get that, but does your design allow the same amount of detergent to come out every time? Because we tried a flap, too, but we couldn’t figure out how to get the amount to be the same.
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How Students Learn: History, Mathematics, and Science in the Classroom The students also propose tests of their models: Sarah Well, Scott is saying that the flap is like a trapdoor and it closes to keep the detergent in. But I think that if there is a trapdoor-like thing in there, then we should be able to hear it close if we listen with a stethoscope, right? Delia Hey, Mrs. S., can we get a stethoscope? A visitor to the classroom would notice that Mrs. S. listens attentively to the descriptions that each group gives of its model and the observations the model is designed to explain. She pays special attention to the group’s interactions with other groups and is skillful in how she converses with the students during their presentations. Through her comments she demonstrates how to question the models of others and how to present a scientific argument. To one group she says, “I think I follow your model, but I am not sure how it explains why you get 90 milliliters of liquid each time you tip the box.” To another she comments, “You say that you have used something similar to a toilet bowl valve. But I don’t understand how your valve allows soap to flow in both directions.” And to a third group she asks, “Do you think that Ian’s model explains the data? What question would you ask his group at this point?” By the end of the multiday activity, the students are explicit about how their prior knowledge and experiences influence their observations and their models. They also ask others to explain how a proposed model is consistent with the data and challenge them when a component of a model, designed to explain patterns in observations, does not appear to work as described. This activity creates many opportunities to introduce and reinforce foundational ideas about the nature of scientific inquiry and how one judges scientific models and related explanations. As the class shares early ideas, the teacher leads discussion about the criteria they are using to decide whether and how to modify these initial explanations. Together, the class establishes that causal models must be able to explain the data at hand, accurately predict the results of future experiments, and be consistent with prior knowledge (or be “realistic”) (see the example in Box 12-2). Through discussion and a short reading about scientific inquiry and model assessment, the teacher helps students connect their own work on the black boxes with that of scientists attempting to understand how the natural world works. This framework for thinking about scientific inquiry and determining the validity of knowledge claims is revisited repeatedly throughout the genetics unit. Other modeling problems might serve just as well as the one we introduce here. What is key is for the problem to be complex enough so that students have experiences that allow them to understand the rigors of scien-
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How Students Learn: History, Mathematics, and Science in the Classroom BOX 12-2 Assessing Knowledge Claims in Genetics While working to revise Mendel’s simple dominance model to account for an inheritance pattern in which there are five variations (rather than two), many students propose models in which each individual in the population has three alleles at the locus in question. However, such a model fails to hold up when evaluated according to the criteria established during the black box activity because it is inconsistent with the students’ prior knowledge about meiosis and equal segregation of parental information during gamete formation: Teacher I’m confused. I’m just curious. I’m a newcomer to this research lab and I see you using two alleles in some areas and three in other areas. David We got rid of the three allele model. Michelle Cross that out. It didn’t work. David We didn’t know how two parents who each had three alleles could make kids with three alleles. Michelle When we tried to do the Punnett square and look at what was happening in meiosis, it didn’t make sense. Chee Right. We thought maybe one parent would give the kid two alleles and the other parent would just give one. But we didn’t like that. David We had to stick with only two alleles, so we just made it three different kinds of alleles in the population. Chee But now every person has only two alleles inside their cells. Right? Teacher In other words, you didn’t like this first, three allele, model because it is inconsistent with meiosis? tific modeling. In particular, the activity is designed to give students an opportunity to do the following: Use prior knowledge to pose problems and generate data. When science teaching emphasizes results rather than the process of scientific inquiry, students can easily think about science as truths to be memorized, rather than as understandings that grow out of a creative process of observing, imagining, and reasoning by making connections with what one already knows. This latter view is critical not only because it offers a view of science that is more engaging and inviting, but also because it allows students to
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How Students Learn: History, Mathematics, and Science in the Classroom grasp that what we understand today can be changed, sometimes radically, by tomorrow’s new observations, insights, and tools. By carrying out a modeling activity they see as separate from the academic content they are studying in the unit, students are more likely to engage in understanding how models are generated rather than in learning about a particular model. Search for patterns in data. Often the point of departure between science and everyday observation and reasoning is the collection of data and close attention to its patterns. To appreciate this, students must take part in a modeling activity that produces data showing an interesting pattern in need of explanation. Develop causal models to account for patterns.7 The data produced by the activity need to be difficult enough so that the students see the modeling activity as posing a challenge. If an obvious model is apparent, the desired discourse regarding model testing and consideration of the features of alternative models will not be realized. Use patterns in data and models to make predictions. A model that is adequate to explain a pattern in data provides relatively little power if it cannot also be used for predictive purposes. The activity is used to call students’ attention to predictive power as a critical feature of a model. Make ideas public, and revise initial models in light of anomalous data and in response to critiques of others. Much of the schoolwork in which students engage ends with a completed assignment that is graded by a teacher. Progress in science is supported by a culture in which even the best work is scrutinized by others, in which one’s observations are complemented by those of others, and in which one’s reasoning is continually critiqued. For some students, making ideas public and open to critique is highly uncomfortable. A low-stakes activity like this introductory modeling exercise can create a relatively comfortable setting for familiarizing students with the culture of science and its expectations. A teacher might both acknowledge the discomfort of public exposure and the benefits of the discussion and the revised thinking that results in progress in the modeling effort. Students have ample opportunity to see that scientific ideas, even those that are at the root of our most profound advances, are initially critiqued harshly and often rejected for a period before they are embraced. Learning Genetics Content Having provided this initial exposure to a modeling exercise, we turn to instruction focused specifically on genetics. While the core set of causal models, assumptions, and argument structures generated the content and learning outcomes for our genetics unit, our study of student understanding and reasoning influenced both the design and the sequencing of instructional activities. For example, many high school students do not understand
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How Students Learn: History, Mathematics, and Science in the Classroom the interrelationships among genetic, meiotic, and biomolecular models, relationships that are key to a deep understanding of inheritance phenomena.8 To deal with this problem, we identified learning outcomes that address the conceptual connections among these families of models, and the models are introduced in a sequence that emphasizes their relatedness. Initially, for example, we introduced genetic models, beginning with Mendel’s model of simple dominance, first. This is typical of many genetics courses. In our early studies (as well as in similar studies on problem solving in genetics9), students often did not examine their inheritance models to see whether they were consistent with meiosis. In fact, students proposed models whereby offspring received unequal amounts of genetic information from their two parents or had fewer alleles at a particular locus than did their parents.10 Because of their struggles and the fact that meiosis is central to any model of inheritance, we placed this model first in the revised curricular sequence. Students now begin their exploration of Mendelian inheritance with a firm understanding of a basic meiotic model and continue to refer to this model as they examine increasingly complex inheritance patterns. A solid integration of the models does not come easily, however. In early versions of the course, it became apparent that students were solving problems, even sophisticated ones, without adequately drawing on an integrated understanding of meiotic and genetic models.11 In response, we designed a set of data analysis activities and related homework that required students to integrate across models (cytology, genetics, and molecular biology) when conducting their genetic investigations and when presenting model-based explanations to account for patterns in their data. By providing tasks that require students to attend to knowledge across domains and by structuring classrooms so that students must make their thinking about such integration public, we have seen improvements in their understanding of genetics.12 We then focus on inheritance models, beginning with Mendel’s model of simple dominance. Mendel, a nineteenth-century monk, grew generation after generation of pea plants in an attempt to understand how traits were passed from parent plants to their offspring. As Chapter 9 indicates, Mendel’s work represented a major breakthrough in understanding inheritance, achieved in large part by selecting a subject for study—peas—that had discontinuous trait variations. The peas were yellow or green, smooth or wrinkled. Peas can be self-fertilized, allowing Mendel to observe that some offspring from a single genetic source have the same phenotype as the parent plants and some have a different phenotype. Mendel’s work confirmed that individuals can carry alleles that are recessive—not expressed in the phenotype. By performing many such crosses, Mendel was able to deduce that the distribution of alleles follows the laws of probability when the pairing of alleles is random. These insights are fundamental to all the work
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How Students Learn: History, Mathematics, and Science in the Classroom and the extent to which students’ knowledge is integrated). We have seen, time and again, teachers becoming aware of students’ common struggles and beginning to “hear” their own students differently. Thus, an important feature of instructional activities that give students opportunities to make their thinking and knowledge public and therefore visible to teachers is that they make assessment and instruction seamless. This becomes possible when students articulate the process of arriving at a solution and not simply the solution itself. Because students struggle with conceptual problems in the genetics unit, for example, we incorporate a number of assessments that require them to describe the relationships between models or ideas that they have learned (see Box 12-7). Whenever possible, we design formal assessments as well as written classroom tasks that reflect the structure of students’ work in the classroom. Our students spend a great deal of their class time working in groups, pouring over data, and talking with one another about their ideas. Thus, assessments also require them to look at data, propose explanations, and describe the thinking that led to particular conclusions. In the evolution course, students are required during instruction to use the natural selection model to develop Darwinian explanations that account for rich data sets. To then ask them about data or the components of natural selection in a multiple-choice format that would require them to draw on only bits and pieces of knowledge for any one question appears incomplete at best. Instead, we provide them with novel data and ask them to describe their reasoning about those data using the natural selection model—a task analogous to what they have been doing in class. An instance of this type of assessment on the final exam asks students to write a Darwinian explanation for the color of polar bear fur using information about ancestral populations. In this way, during assessment we draw on students’ ideas and skills as they were developed in class rather than asking students to simply recall bits of information in contrived testing situations. While assessments provide teachers with information about student understanding, students also benefit from assessments that give them opportunities to see how their understanding has changed during a unit of study. One method we have used is to require each student to critique her or his own early work based on what she or he knows at the conclusion of a course. Not only does this approach give teachers insights into students’ knowledge, but it also allows students to glimpse how much their knowledge and their ability to critique arguments have changed. Students’ consideration of their own ideas has been incorporated into the assessment tasks in both units. On several occasions and in different ways, students examine their own ideas and explicitly discuss how those ideas have changed. For example, one of the questions on the final exam in evolution requires students to read and critique a Darwinian explanation they created on the first
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How Students Learn: History, Mathematics, and Science in the Classroom BOX 12-7 Sample Exam Question: Consistency Between Models This exam question is one of several tasks designed to produce evidence of students’ understandings about the need for models to be consistent with one another and with the data they purport to explain. Below is a concept map that represents the relationships among specific models, models in general, and data. Use the map to respond to the tasks below. Remember that a line in a concept map represents a relationship between two terms (concepts, ideas, etc.) in the map. Write a few sentences that describe the numbered relationships between the terms given. Be as specific as you can: use the appropriate vocabulary of genetics to make your point as clearly as possible. Draw a line (not necessarily a straight one) to separate the world of ideas from that of observations on this map. Please label both sides. Justify your placement of that line. day of class (see Box 12-8). We have found this to be one of the most powerful moments for many students, as they recognize how much their own ideas have changed. Many students are critical of the need-based language that was present in their original explanation, or they find that they described evolutionary change as having happened at the individual rather than the population level.
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How Students Learn: History, Mathematics, and Science in the Classroom BOX 12-8 Examples of Students’ Critiques of Their Own Darwinian Explanations On the first day of class, students were asked to explain how the carapace of Galapagos tortoises may have changed from the dome shape to the saddleback shape. As part of the final exam for the class, students were asked to critique the explanation they had given on the first day. Below are the original explanation and critique offered by one student. Original Answer The saddleback carapace came into being due to the need of migrating tortoises to adjust to a new environment. On Albermarle Island the domed shaped carapaces served well for shedding rain and eating ground vegetation. However, when the tortoises began to migrate to a smaller, drier island with less ground vegetation, they had to adapt in order to survive. The majority of the food was now higher up and the domed shell served as a hindrance. Over time, the saddleback carapace developed to allow the neck to extend further, thereby allowing the tortoises to reach the fleshy green parts of the prickly pear cactus. This evolutionary process created a new species of giant tortoise that could live successfully in a new environment. Critique on Final Exam In my original answer, I used an almost exclusive Lamarckian definition of evolution. In my introductory statement I stated that the saddleback carapace came into being due to the need of the tortoise to fit its environment. I needed to acknowledge the existence of variation within the tortoise population of the shape of the shell. My original explanation makes the evolutionary process sound like a physical change taking place during the life of the tortoise and then being passed on to the offspring. I now know that variations that are advantageous give animals a better chance of survival (survival of the fittest!) and allow them a better chance of passing on their advantageous trait to their offspring. In my original explanation I also touched on ideas of use and disuse to explain how the saddleback carapace came to be, this is a Lamarkian model of evolution which is incorrect. I did explain how the saddleback carapace was an advantage because it allowed the tortoise to eat higher vegetation. Since I didn’t understand evolution through the generations, I wasn’t able to describe how the species changed over time. Overall, I would say I had a basic but flawed understanding of evolution but I lacked the tools to explain evolution from a scientific and Darwinian perspective, until now.
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How Students Learn: History, Mathematics, and Science in the Classroom Community-Centered As Chapter 1 suggests, the knowledge-centered, learner-centered, and assessment-centered classrooms come together in the context of a classroom community. The culture of successful scientific communities includes both collaboration and questioning among colleagues. It involves norms for making and justifying claims. At the source of the productivity of such a community is an understanding of central causal models, the ability to use such models to conduct inquiry, and the ability to engage in the assessment of causal models and related explanations. We have found that these outcomes can be realized in classrooms where students are full participants in a scientific community.34 Interestingly, one unexpected outcome of structuring classrooms so that students are expected to participate in the intellectual work of science has been increased involvement and achievement by students not previously identified as successful in science. In addition to establishing expectations for class participation and a shared framework for knowledge assessment, MUSE curricula promote metacognitive reflection on the part of students by incorporating tasks that require discourse (formal and informal) at all stages of student work. While working in groups and presenting results to the class as a whole, students are required to share their ideas even when those ideas may not be fully formed. Moreover, recall that the context for idea sharing is one in which discipline-specific criteria for assessment of ideas have been established. Thus, discourse is anchored in norms of argumentation that reflect scientific practice to the extent possible. Learning with Understanding While the four features of classroom environments can be described individually, in practice they must interact if students are to deeply engage in learning for understanding. High school students have had more than 9 years of practice at playing the “game of school.” Most have become quite adept at memorizing and reiterating information, seeking answers to questions or problems, and moving quickly from one topic to another. Typically during the game of school, students win when they present the correct answer. The process by which one determines the answer is irrelevant or, at best, undervalued. The students described here are quite typical in this regard: they enter our genetics and evolution classes anticipating that they will be called upon to provide answers and are prepared to do so. In fact, seeking an end product is so ingrained that even when we design tasks that involve multiple iterations of modeling and testing ideas, such as within the genetics course, students frequently reduce the work to seeking algorithms that have predictive power instead of engaging in the much more difficult
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How Students Learn: History, Mathematics, and Science in the Classroom task of evaluating models on the basis of their conceptual consistency within a family of related ideas.35 After studying how people solved problems in a variety of situations, Klayman and Ha36 noted the frequent use of what they call a “positive test strategy.” That is, solvers would propose a model (or solution) and test it by attempting to apply it to the situation most likely to fit the model in the first place. If the idea had explanatory or predictive power, the solver remained satisfied with it; if not, the solver would quickly test another idea. The positive test strategy was frequently applied by students in early versions of our genetics course.37 This method of problem solving does not map well to scientific practice in most cases, however: it is the absence of disproving evidence, and not the presence of confirming evidence that is more commonly persuasive to scientists. Moreover, testing a model in limited situations in which one expects a data–model match would be considered “confirmation bias” within scientific communities. Nevertheless, Klayman and Ha point out that this positive test strategy is often quite useful in real-life situations. Given our students’ facility with the game of school and the general tendency to apply less scientific model-testing strategies when problem solving, we were forced to create tasks that not only afford the opportunity for reflection, but actually require students to think more deeply about the ways in which they have come to understand science concepts, as well as what is involved in scientific argumentation. We want students to realize that the models and explanations they propose are likely to be challenged and that the conflicts surrounding such challenges are the lifeblood of science. Thus, we explicitly discuss with our students the expectations for their participation in the course. Teachers state that the students’ task is not simply to produce an “answer” (a model in genetics or a Darwinian explanation in evolutionary biology), but also to be able to defend and critique ideas according to the norms of a particular scientific discipline. In other words, we ask the students to abandon the game of school and begin to play the game of science. Examination of ideas requires more than simply providing space for reflection to occur; it also involves working with students to develop systematic ways of critiquing their own ideas and those of others. This is why we begin each course with an activity whose focus is the introduction of discipline-specific ways of generating and critiquing knowledge claims. These activities do not require that students will come to understand any particular scientific concepts upon their completion. Rather, they will have learned about the process of constructing and evaluating arguments in genetics or evolutionary biology. Specific criteria for weighing scientific explanations are revisited throughout each course as students engage in extended inquiries within these biological disciplines.
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How Students Learn: History, Mathematics, and Science in the Classroom SUMMARY For students to develop understanding in any scientific discipline, teachers and curriculum developers must attend to a set of complex and interrelated components, including the nature of practice in particular scientific disciplines, students’ prior knowledge, and the establishment of a collaborative environment that engages students in reflective scientific practice. These design components allow educators to create curricula and instructional materials that help students learn about science both as and by inquiry. The students in the biology classrooms described in this chapter have developed sophisticated understandings of some of the most central explanatory frameworks in genetics and evolutionary biology. In addition, they have, unlike many high school students, shown great maturity in their abilities to reason about realistic biological data and phenomena using these models. Moreover, they have accomplished this in classrooms that are structured along the lines of scientific communities. This has all been made possible by a concerted collaboration involving high school teachers and their students, university science educators, and university biologists. That MUSE combined this collaboration with a research program on student learning and reasoning was essential. With the knowledge thus gained, we believe it is possible to help others realize the expectations for improving science education that are set forth in reform documents such as the National Science Education Standards.38 In particular, there has been a call for curricular reforms that allow students to be “engaged in inquiry” that involves “combin[ing] processes and scientific knowledge as they use scientific reasoning and critical thinking to develop their understanding of science.”39 Recommendations for improved teaching of science are solidly rooted in a commitment to teaching both through and about inquiry. Furthermore, the National Science Education Standards do not simply suggest that science teachers incorporate inquiry in classrooms; rather, they demand that teachers embrace inquiry in order to: Plan an inquiry-based science program for their students. Focus and support inquiries while interacting with students. Create a setting for student work that is flexible and supportive of science inquiry. Model and emphasize the skills, attitudes, and values of scientific inquiry. It is just these opportunities that have been described in this chapter.
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How Students Learn: History, Mathematics, and Science in the Classroom NOTES 1. We encourage readers to visit our website (www.wcer.wisc.edu/ncusla/muse/). The site includes discussions of student knowledge and reasoning, intended learning outcomes, instructional activities, instructional notes, assessments, examples of student work, teachers’ reflections, and connections to the National Science Education Standards and Benchmarks for Science Literacy. 2. Wiggins and McTighe, 1998, Chapter 1. 3. Grosslight et al., 1991. 4. Grosslight et al., 1991; Harrison and Treagust, 1998. 5. Cartier, 2000a. 6. Cartier, 2000b. 7. We consider a causal model to be an idea or set of ideas that can be used to explain particular natural phenomena. Models are complex constructions that consist of conceptual objects (e.g., alleles, populations) and processes (e.g., selection, independent assortment) in which the objects participate or interact. 8. Cartier, 2000a; Kindfield, 1994; Wynne et al., 2001. 9. Kindfield, 1994. 10. Cartier, 2000a. 11. Cartier, 2000a; Wynne et al., 2001. 12. Cartier, 2000b. 13. Darden, 1991. 14. Meiosis is the process by which sperm and egg cells are formed. During meiosis, chromosomal replication is followed by two rounds of cell division. Thus, one cell undergoing meiosis produces four new cells, each of which contains half the number of chromosomes of the original parent cell. 15. Kitcher, 1984, 1993. 16. Kitcher, 1984, p. 356. 17. Kitcher, 1984, p. 356. 18. Mendel, 1959. 19. Discontinuous traits are those for which two or more distinct categories of phenotypes (or variants) are identified. For example, Mendel studied the trait of height in pea plants. He noted that the pea plants were either short (18 in.) or tall (84 in.). In contrast, height is not a discontinuous trait in humans: human height is best characterized as continuously variable, or nondiscrete, because humans are not simply either 18 or 84 in. tall. Thus, the phenotype categories for height in humans are not clear-cut. 20. Calley and Jungck, 2002. 21. Achondroplasia is inherited in a codominant fashion. Individuals with two disease alleles (2,2) are severely dwarfed and seldom survive. Individuals who are heterozygous (1,2) are achondroplastic dwarfs, having disproportionately short arm and leg bones relative to their torsos. Thus while these two phenotypes differ from normal stature, they are distinct from one another. 22. In the past, our students have developed the following explanations for protein action in traits inherited in a codominant fashion:
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How Students Learn: History, Mathematics, and Science in the Classroom • One allele (designated 1) codes for an active protein. The other allele codes for an inactive protein. Thus, individuals with genotype (1,1) have the greatest amount (or dose) of active protein and the associated phenotype at the organismal level. Individuals who are (2,2) have little or no measurable protein activity, and this is reflected in the phenotype. Heterozygous individuals (1,2) have an intermediate level of protein activity and a phenotype that is also intermediate. For example, in the case of achondroplasia, (1,1) individuals would have two alleles for a growth receptor and a phenotype of normal stature; (2,2) individuals would have few or no functional receptors and suffer from severe growth retardation; and heterozygotes (1,2) would have half as much growth receptor activity as the (1,1) individuals and consequently be short-statured achondroplastic dwarves without the additional health problems of the (2,2) individuals. This example of codominance is admittedly simplified, as students do not study the systemic effects of achondroplasia. However, this model is applied widely in genetics and sometimes referred to as the “dosage” model. • Both alleles code for active proteins, giving rise to observable phenotypes at the macroscopic level. Heterozygotes display the phenotypes associated with both alleles. For example, in human blood types, individuals carrying alleles for protein A and protein B have both of these proteins on their blood cells. The phenotype is not blended or dosage dependent as in the achondroplasia example above. Instead, both proteins are detected intact in heterozygous individuals. 23. Cartier, 2000a, 2000b. 24. White and Frederiksen, 1998, p. 25. 25. Cartier 2000a, 2000b. 26. Mayr, 1982, p. 481. 27. Kitcher, 1993, pp. 20-21. 28. Richards, 1992, p. 23. 29. O’Hara, 1988. 30. Mayr, 1997, p. 64. 31. Bishop and Anderson, 1990; Demastes et al., 1992, 1995, 1996. 32. Bishop and Anderson, 1990. 33. Cartier, 2000a, 2000b; Passmore and Stewart, 2002. 34. Cartier, 2000b; Passmore and Stewart, 2000. 35. Cartier, 2000a. 36. Klayman and Ha, 1987. 37. Cartier, 2000a. 38. National Research Council, 1996. 39. National Research Council, 1996, p. 105. REFERENCES Bishop, B.A., and Anderson, C.W. (1990). Student conceptions of natural selection and its role in evolution. Journal of Research in Science Teaching, 27(5), 415-427.
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How Students Learn: History, Mathematics, and Science in the Classroom Calley, J., and Jungck, J.R. (2002). Genetics construction kit. (The BioQUEST Library IV, version 1.1B3) [Computer software]. New York: Academic Press. Cartier, J.L. (2000a). Assessment of explanatory models in genetics: Insights into students’ conceptions of scientific models. Research report 98-1 for the National Center for Improving Student Learning and Achievement in Mathematics and Science. Available: http://www.wcer.wisc.edu/ncisla/publications/main.html#reports/RR98-1.pdf [accessed February 3, 2003]. Cartier, J.L. (2000b). Using a modeling approach to explore scientific epistemology with high school biology students. Research report 99-1 for the National Center for Improving Student Learning and Achievement in Mathematics and Science. Available: http://www.wcer.wisc.edu/ncisla/publications/reports/RR99-1.pdf [accessed February 3, 2003]. Darden, L. (1991). Theory change in science: Strategies from Mendelian genetics. New York: Oxford University Press. Demastes, S., Good, R., and Peebles, P. (1995). Students’ conceptual ecologies and the process of conceptual change in evolution. Science Education, 79(6), 637-666. Demastes, S., Good, R., and Peebles, P. (1996). Patterns of conceptual change in evolution. Journal of Research in Science Teaching, 33(4), 407-431. Demastes, S.S., Trowbridge, J.E., and Cummins, C.L. (1992). Resource paper on evolution education research. In R.G. Good, J.E. Trowbridge, S.S. Demastes, J.H. Wandersee, M.S. Hafner, and C.L. Cummins (Eds.), Proceedings of the 1992 Evolution Education Conference, Louisiana State University, Baton Rouge, LA. Grosslight, L., Unger, C., Jay, E., and Smith, C.L. (1991). Understanding models and their use in science: Conceptions of middle and high school students and experts. Journal of Research in Science Teaching, 28, 799-822. Harrison, A.G., and Treagust, D.F. (1998). Modeling in science lessons: Are there better ways to learn with models? School Science and Mathematics, 98(8), 420-429. Kindfield, A.C.H. (1994). Understanding a basic biological process: Expert and novice models of meiosis. Science Education, 78(3), 255-283. Kitcher, P. (1984). 1953 and all that: A tale of two sciences. The Philosophical Review, 93, 335-373. Kitcher, P. (1993). The advancement of science: Science without legend, objectivity without illusions. New York: Oxford University Press. Klayman, J., and Ha, Y. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94, 211-228. Mayr, E. (1982). The growth of biological thought: Diversity, evolution, and inheritance. Cambridge, MA: Belknap Press of Harvard University Press. Mayr, E. (1997). This is biology: The science of the living world. Cambridge, MA: Belknap Press of Harvard University Press. Mendel, G. (1959; Original publication date 1865). Experiments on plant hybridization. In J. Peters (Ed.), Classic papers in genetics. Upper Saddle River, NJ: Prentice Hall.
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How Students Learn: History, Mathematics, and Science in the Classroom National Research Council. (1996). National science education standards. National Committee on Science Education Standards and Assessment, Center for Science, Mathematics, and Engineering Education. Washington, DC: National Academy Press. O’Hara, R.J. (1988). Homage to Clio, or, toward a historical philosophy for evolutionary biology. Systematic Zoology, 37, 142-155. Passmore, C.M., and Stewart, J. (2002). A modeling approach to teaching evolutionary biology in high schools. Journal of Research in Science Teaching, 39, 185-204. Richards, R.J. (1992). The structure of narrative explanation in history and biology. In M.H. Nitecki and D.V. Nitecki (Eds.), History and evolution (pp. 19-53). Albany, NY: State University of New York Press. White, B.Y., and Frederiksen, J.R. (1998). Inquiry, modeling, and metacogntion: Making science accessible to all students. Cognition and Instruction, 16, 3-118. Wiggins, G., and McTighe, J. (1998). Understanding by design. Upper Saddle River, NJ: Merrill/Prentice-Hall. Wynne, C., Stewart, J., and Passmore, C. (2001). High school students’ use of meiosis when solving genetics problems. The International Journal of Science Education, 23(5), 501-515.
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Representative terms from entire chapter: