Supporting Science Learning
In the preceding chapters we have developed a complex picture of student learning in science. It shows that children come to school with powerful and sophisticated ways of reasoning about the material world that enable them to function effectively in many arenas. It also shows that their reasoning is limited in important ways; it is based on a limited range of experiences, and it lacks the predictive and explanatory power of expert scientific reasoning. Finally, this picture shows that with appropriate instruction children can make significant progress toward more sophisticated scientific reasoning, and we know some key principles that inform the design of that instruction. These results are products of a sustained dialogue among developmental and education researchers.
However, this research dialogue and its results have not significantly influenced science education policy and practice. This is in part because science education policy and practice are legitimately concerned with issues that are peripheral to the research dialogue; for example, by what scientific knowledge is most valued by the American public. In many cases, it is clear that policy and practice could be more effective if they were influenced by the research. Curriculum documents and textbooks fail to recognize the importance of children’s prior experience, underestimating both their capacities for reasoning and the difficulties posed by scientific conceptions. In instruction, knowledge and practice are separated in ways that diminish the power of scientific reasoning. Teachers must often rely on models of instruction that are demonstrably ineffective. Clearly, children in America would benefit if policy makers, curriculum developers, and practitioners made more effective use of research results.
One key reason that policy makers and practitioners fail to do this is the complexity and fragmentation of the research literature. The studies we review in this report, drawn from a range of literatures, were mostly short in duration and limited in scope, focusing on a few students or a few classrooms, learning about some small part of the vast domain of science. These studies are also embedded in a research discourse that is complicated and often inaccessible to nonspecialists. There are reasons for the difficulty of the discourse. Science learning really is complex, and the research on learning cannot be reduced to a few “what works” bullet points without losing much of its value.
In Part III, we begin to take up the challenge of interpreting research on learning so as to inform policy and practice in science education. We begin in Chapter 8 with a proposal for reorganizing the K-8 science curriculum in a way that is more aligned with current understanding of children’s learning in science. The hallmark of this approach is the investigation of a smaller set of core ideas and practices in science over an extended period of time. Instructional sequences that weave together the four strands and thereby coordinate conceptual learning with science practices and discourse require adoption of curriculum and assessment models that function over months, years, and grade bands.
In Chapter 9, we turn to a consideration of instruction and assessment. Our review of the research on learning combined with the four-strand framework has implications for how one thinks about the design of the classroom learning environment. Research on learning shows how important it is to include learning opportunities that develop children’s abilities to obtain and reason with evidence, to develop and evaluate explanations, to develop and evaluate standards of evidence, to represent and communicate scientific data and ideas, and to engage in argumentation practices. Thus, although we argue in Part II that children are very capable learners, this does not preclude the fact that carefully thought out instructional supports and mediation are needed to help develop scientific practices and ways of knowing.
In Chapter 10 we broaden our view to consider the knowledge and tools that teachers need in order to enact high-quality instruction. We analyze the knowledge base of current in-service K-8 science teachers, and we describe what these teachers would need to know about science, teaching, and learning in order to teach science as we have discussed it in this report. We also examine the means of advancing teacher knowledge through a range of opportunities to learn. These include programs of professional development, workplace learning, and use of instructional systems that provide clear instructional guidance for teachers and provide them with timely feedback on their teaching and strategies for improvement.
Main Findings in the Chapter:
Many standards and curricula contain too many disconnected topics that are given equal priority. Too little attention is given to how students’ understanding of a topic can be supported and enhanced from grade to grade. As a result, topics receive repeated, shallow coverage with little consistency, which provides a fragile foundation for further knowledge growth.
Findings from research about children’s learning and development can be used to map learning progressions in science. That is, one can describe the successively more sophisticated ways of thinking about a topic that can follow and build on one another as children learn about and investigate a topic over a broad span of time (e.g., 6 to 8 years).
Steps in these progressions are constrained by children’s knowledge and skill with respect to each of the four strands. Reaching the hypothetical steps described in the progressions is also dependent on teachers’ knowledge and the effectiveness of their instructional practices.
Learning progressions are a promising direction for organizing science instruction and curricula across grades K-8. However, further research and development is needed to identify and elaborate the progressions of learning and instruction that can support students’ understanding of these core ideas across the disciplines of science.
Science learning presents a special challenge to educators because of both the diversity and the complexity of mature scientific knowledge and the fact that it rests on organized conceptual frameworks and sophisticated
knowledge construction and evaluation practices that are fundamentally different from the concepts and meaning-making practices that children bring to school. Although children bring a wealth of resources to the science learning task (see Part II), those resources must be built on, enriched, and transformed if they are to learn science with understanding. One challenge is to understand what is most important to teach (given limited time and resources) at the K-8 level: What might be the most important “core ideas” that both empower students to understand the distinctive value of science and prepare them for further learning in science? Another challenge is to understand the pathways—or learning progressions—by which children can bridge their starting point and the desired end point. Given the complexity and counterintuitive nature of the end point, such learning must necessarily occur over a long period of time, work on multiple fronts, and require explicit instruction. Yet at present, curriculum sequences are not typically guided by such long-term vision or understanding, nor is there clear agreement, given the wealth of scientific knowledge, about what might be truly foundational and most important to teach.
In this chapter we develop the idea of learning progressions as an approach to research synthesis that could serve as the basis for a dialogue that includes researchers, assessment developers, policy makers, and curriculum developers. Learning progressions are descriptions of the successively more sophisticated ways of thinking about a topic that can follow one another as children learn about and investigate a topic over a broad span of time (e.g., 6 to 8 years). They are crucially dependent on instructional practices if they are to occur. In the chapter we (a) discuss key characteristics of learning progressions, contrasting them with current approaches to defining curriculum and assessment and describing some of the challenges in developing them; (b) use current work on a learning progression as an example of both the problems and possibilities in this approach; and (c) discuss implications and further questions.
CURRENT APPROACHES IN POLICY AND PRACTICE
At present, most decisions about instruction and curriculum sequences in science have not been guided by a long-term understanding of learning progressions that are grounded in the findings of contemporary cognitive, developmental, education, and science studies research (much of this research is reviewed in Part II). Two approaches that have influenced policy and practice are (1) approaches characterizing learning in terms of science process skills and (2) approaches to listing important conceptual knowledge in standards documents.
Science Process Skills
Some scope and sequence suggestions that have been influential in the design of elementary science curricula and texts (e.g., the task analyses of the processes of science and of learning done by psychologist Gagne, which led to the sequence of process skills proposed by the curriculum Science: A Process Approach in the 1960s) are based more on rational task analyses than on findings about how children learn meaningful scientific concepts. These proposed “learning hierarchies” focused on building competence with domain-general processes rather than helping children build frameworks of interrelated science concepts. They had an appeal to teachers and curriculum developers because they broke complex tasks down into simpler elements, identified 14 basic process skills that were proposed to develop in a certain sequence and to underlie scientific thinking, and provided many specific exercises for children to practice these skills. But because they ignored the crucial role of meaning, content, and context and treated science instead as a series of disembodied “skills,” they were often carried out as meaningless procedures (Baroody et al., 2004; Mintzes, Wandersee, and Novak, 1997). For example, children practiced making observations of a variety of types or making measurements without a concern for understanding what they were observing or measuring. As we have shown in Chapter 5, knowledge is intimately intertwined with scientific reasoning.
Ultimately, however, children failed to develop meaningful understanding under science-as-process instructional programs, and researchers recognized how little these domain-general “skills” actually generalized. Another criticism of these scope and sequence proposals was that they were based on faulty developmental assumptions about children’s reasoning and learning capacities (e.g., that young children are concrete rather than abstract thinkers and capable only of observation rather than explanation; Metz, 1995; see our discussion in Chapter 3). Consequently, only a small subset of science process skills (e.g., observing, measuring, predicting) were practiced in the early elementary grades, with more advanced skills (e.g., formulating hypotheses, controlling variables, interpreting data) introduced only in the upper elementary and middle school grades, and many other important sense-making practices of science (practices involving modeling, representation, discourse, and argumentation) were omitted entirely. Given that current research has highlighted the interaction between domain-specific knowledge and reasoning, the importance of modeling, representational practices, and discourse in promoting conceptual understanding, and the capacity of young children to engage in a wide range of these meaning-making practices, a very different approach to describing learning sequences is needed, one that that is more centrally grounded in building an understanding of conceptual frameworks (see discussion of this issue in Part II).
Although Gagne’s original formulation of science as a collection of content-free process has largely been rejected by science educators, its legacy persists in both policy and practice. Many textbooks and curriculum documents still have separate sections on scientific inquiry, science processes, or “the scientific method.” Many classroom teachers follow the lead of these resources, teaching skills and inquiry techniques separately from the conceptual content of their courses.
Other approaches to guiding curriculum include writing national, state, and district science standards. These standards are an important start (at codifying values), but they generally were based on values and the personal experiences of their writers rather than research on children’s learning or detailed conceptual analyses of scientific knowledge and practice. Current national, state, and district standards do not provide an adequate basis for designing effective curriculum sequences for several reasons. First, they contain too many topics without providing guidance about which topics may be most central or important. National standards such as the National Science Education Standards (NSES) (National Research Council, 1996) or Benchmarks for Science Literacy (American Association for the Advancement of Science, 1993) do help to pare down the number of science topics to be covered. However, they still retain many more topics than can be covered and do not identify the most central or important topics. For example, a comparison of the NSES with curriculum in high achieving countries that participated in the Third International Mathematics and Science Study (TIMSS) reveals that the NSES call for much broader coverage of topics with little sequencing across grades (Schmidt, Wang, and McKnight, 2005). Second, they typically present the key ideas as simple declarative statements without explaining how those understandings need to be grounded in experience with the material world or in reasoning practices. Third, they are not sequenced in ways that recognize research on the development of children’s understanding. Project 2061’s Atlas of Science Literacy (American Association for the Advancement of Science, 2001) does provide a guide for interconnection between important concepts in science with some sequencing. The analysis is based primarily on the structure of knowledge in the disciplines of science with some attention to what scientific ideas children can understand at a given grade level. We propose a sequencing that is more deeply informed by research on children’s learning such that the sequences are grounded also in what we know about the ideas children bring to the classroom that can form the foundation for developing understanding of scientific ideas. As we explain later in the chapter, these foundational ideas sometimes do not closely resemble the scientific ideas they can support.
Fourth, while they recognize the central role of involving students in the culture of scientific practice to build scientific knowledge, they do not fully articulate how students’ participation in science practices can be integrated with learning about science concepts. Finally, although many standards documents include at least the first three of the four strands of scientific proficiency that we use to organize this report, these strands are generally described separately, so the crucial issue of how advances in one strand are linked to and support children’s learning in the other strands is not addressed.
Curriculum and Instruction in K-8 Science Classrooms
As currently described and enacted in U.S. K-8 science classrooms, curriculum—the sequence and series of tasks and assignments posed to students—rarely builds cumulatively and in developmentally informed ways, from students’ early knowledge and resources toward scientifically accepted theories and concepts. Although there are some curricular materials that pursue this approach, they tend to cover a limited slice of content and are often restricted in duration to periods spanning a few to several weeks of instruction. It is highly unlikely that brief periods of uncoordinated instruction are going to achieve the goal of helping students generate a scientifically informed epistemology, a deep and well-structured knowledge base, and a firm understanding of the purposes and methods of science.
Analyses of science curricula in the United States indicate that they are generally poorly designed for the purpose of effective knowledge building. Evaluations recently conducted under the leadership of the American Association for the Advancement of Science (AAAS) Project 2061 staff suggest that the major commercial textbook series, which do at least take a multiyear perspective to sequencing instruction, have major flaws of various kinds, including content, motivation, and attention to student prior conceptions (Kesidou and Roseman, 2002). The AAAS analysis indicates that curriculum is rarely framed around the big ideas. Indeed, the big ideas are largely lost in the curriculum. Roseman, Kesidou, Stern, and Caldwell (1999), authors of the AAAS report, concluded (p. 2):
[T]he textbooks covered too many topics and didn’t develop any of them well. In addition, the texts included many classroom activities that either were irrelevant to learning key science ideas or didn’t help students relate what they were doing to the underlying ideas.
Valverde and Schmidt’s (1997) comparison of U.S. science curriculum with the 10 countries performing best on the tests of science achievement in the Trends in International Mathematics and Science Study provide further support for the AAAS conclusions, as well as the results of these curricular
patterns on student learning. They found that U.S. science curricula constitute a relatively extreme case of broad and superficial coverage, with little attention to building links across concepts. The U.S. science texts covered many more topics than the texts of the high-achieving countries. In their words, “breadth of topics is presented in these textbooks at the expense of depth of coverage. Consequently, U.S. textbooks are limited to perfunctory treatment of subject matter” (p. 62). More specifically, Valverde and Schmidt point to the failure of U.S. science curriculum to build connections between the abundant knowledge pieces presented in the curriculum and the resultant epistemic messages this conveys about the structure of the discipline (pp. 62):
The unfocused curriculum of the United States is also a curriculum of very little coherence…. U.S. textbooks and teachers present items one after the other from a laundry list of topics from state and local district guides …. This is done with little or no regard for establishing the relation between various topics or themes on the list. The loss of these relationships between ideas encourages children to regard these disciplines as no more than disjointed notions that they are unable to conceive of as belonging to a disciplinary whole.
An increasingly popular approach to science curriculum in U.S. school districts is the use of science kits. Individual kits may provide students with a 6- or 8-week experience that, in some cases, provides a coherent set of experiences that build logically. While kits can bring some coherence to science curriculum (at least at the level of the unit), the cumulative effect of a kit-based approach to science can be very problematic. In many cases, students receive a series of brief exposures to a collection of unrelated topics (the rainforest, rocks and minerals, weather) presented in modular units or kits. The sequence of presentation hardly matters, as the ideas do not build in any meaningful way. Although we know of no research that has explicitly probed the learning research base of kits, their presentation of science topics as essentially interchangeable and noncumulative raises serious concerns. Kit-based curricula appear to be sensitive to a number of practical concerns, including variability in standards from locale to locale, so that a teacher can never count on a student’s having knowledge prerequisite to a new set of concepts. It also maximizes flexibility, so that teachers with low content knowledge can easily skip over topics that are too unfamiliar. However, it also sacrifices the potential long-term benefits of carefully crafted curricula that strategically build on student skills and their knowledge base.
Curriculum needs restructuring to much more adequately support building robust science knowledge. It is not sufficient to teach lots of pieces of science knowledge. The curricular scaffolding of robust knowledge in the
form of cohort knowledge structures, organized around core ideas, is critical for supporting science proficiency (see Chapter 4 for discussions of conceptual change and building knowledge structures). K-8 science curriculum needs to much more adequately build robust science knowledge of this form.
Deciding how research can guide standards and curriculum has also proved to be a difficult process. Which studies are trustworthy? Should one take evidence that few students have learned a concept at a given age as evidence that few students can learn? Conversely, should one take evidence of successful teaching in a few classrooms as justification for including content in standards?
DEFINING LEARNING PROGRESSIONS
Learning progressions are descriptions of the successively more sophisticated ways of thinking about a topic that can follow one another as children learn about and investigate a topic over a broad span of time (e.g., 6 to 8 years). They are crucially dependent on instructional practices if they are to occur. That is, traditional instruction does not enable most children to attain a good understanding of scientific frameworks or practices, but there is evidence that the proposed learning sequences could occur with appropriate instructional practices.
The more effective instructional practices aim to build understanding through involving students in a variety of practices, including gathering data through observation or experiment, representing data, reasoning—with oneself and others—about what data mean, and applying key ideas to new situations. At the same time, bringing about understanding of scientific frameworks is difficult, so innovative instructional practice is most effective when sustained over a period of time. The timescale of most innovative teaching interventions has typically been relatively short (on the order of 2 or 3 months for a specific topic). Thus, our ideas about longer term learning progressions are conjectural—ideas about how understanding could be developed given sustained and appropriate instructional practices—while at the same time based on research syntheses and open to empirical investigation in future research. That is, they are plausible hypotheses, greatly constrained by the findings of research. More specifically:
Learning progressions are anchored on one end by what is known about the concepts and reasoning of students entering school. There is now a very extensive research base at this end (see Chapter 3), although much of it is not widely known or used by the science education community, which often relies on older (outdated) characterizations of preschool and elementary schoolchildren’s competence from the (earlier) developmental literature.
At the other end, learning progressions are anchored by societal expectations (values) about what society wants middle school students to understand about science. They are also constrained by research-based conceptual and social analyses of the structure of the disciplinary knowledge and practice that is to be learned. Analysis of disciplinary knowledge is important in helping to identify the core ideas in science—those of greatest explanatory power and scope—that it may be most important to teach, because they provide central frameworks for further learning. Examples of such core ideas are the atomic-molecular theory of matter and evolutionary theories of life’s diversity. In addition, analysis of disciplinary knowledge helps identify the network of ideas and practices on which those core ideas rest, and hence what will be important component ideas to develop as part of their construction.
Learning progressions propose the intermediate understandings between these anchor points that are reasonably coherent networks of ideas and practices and that contribute to building a more mature understanding. It is important to note that some of the important precursor ideas may not look like the later ideas, yet they crucially contribute to their construction. For example, realizing that objects are composed of materials and have some properties because they are made of that material is a critical first step toward understanding atomic-molecular theory. By thinking hard about what initial understandings need to be drawn on in developing new understandings, learning progressions highlight important precursor understandings that might otherwise be overlooked by teachers and educators.
The intellectual exercise of constructing learning progressions requires one to synthesize results from disparate (often short-term) studies in ways that begin to address questions of how longer term learning may occur; learning progressions suggest priorities for future research, including the need for engaging in longer term studies based on best bets suggested by these research syntheses; and they present research results in ways that make their implications for policy and practice apparent. Ultimately, well-tested ideas about learning progressions could provide much needed guidance for both the design of instructional sequences and large-scale and classroom-based assessments.
The learning progression approach has four characteristics that are mostly absent from accounts of domain-general developmental sequences and current standards documents.
Use of the current research base: We suggest that learning progressions should make systematic use of current research on children’s learning (reviewed in Part II) to suggest how well-grounded conceptual understanding can develop. For more on how the research can be used, see the example developed below.
Interconnected strands of scientific proficiency: Learning progressions consider the interaction among the strands of scientific proficiency in building understanding (know, use, and interpret scientific explanations of the natural world; generate and evaluate scientific evidence and explanations; understand the nature and development of scientific knowledge; participate productively in scientific practices and discourse) and always involve students with meaningful questions and investigations of the natural world.
Organization of conceptual knowledge around core ideas: Learning progressions recognize that the first strand of scientific proficiency (understanding and using scientific explanations) involves far more than learning lists of facts. Scientific understanding is organized around conceptual frameworks and models that have broad explanatory power. The purpose of concepts is to extend understanding—to allow one to predict, understand, and explain phenomena one experiences in the world—as well as to solve important problems. It is therefore important to explicitly recognize these frameworks and to help children develop them through instruction that involves model building and conceptual change.
Recognizing multiple sequences and web-like growth: Learning progressions recognize that all students will follow not one general sequence, but multiple (often interacting) sequences around important disciplinary-specific core ideas (e.g., atomic-molecular theory, evolutionary theory, cell theory, force and motion). The challenge is to document and describe paths that work as well as to investigate possible trade-offs in choosing different paths.
In the development of learning progressions that are research-based and reflect the variety of ways that children can learn meaningfully about a topic, there are three challenges, none of which can be completely overcome with the existing research base: (1) describing a student’s knowledge and practice at a given point in the learning progression, (2) describing a succession of ways students can understand a topic that show connections between ways and respect constraints on their learning abilities, and (3) describing the variety of possibilities for meaningful learning for students with different personal and cultural resources or different instructional histories. We discuss each of these challenges below.
We wish to develop descriptions of students’ knowledge and practice that will ultimately include all four strands of scientific proficiency (see Box 2-1) and that recognize the complex organization of meaningful scientific knowledge and practice. Furthermore, we would like to describe children’s knowledge and practice in ways that help us to see the continuities—and the discontinuities—between the reasoning of children of different ages. Inevitably, these descriptions must fail in some way; no organizational scheme can fully capture the organization of a child’s knowledge or its connections with her practices, with systems and phenomena in the material world, and with developmental changes over time. The various approaches to describing core ideas and strands in children’s reasoning discussed in this book represent various compromises that emphasize some aspects of the organization of their reasoning while obscuring others.
In addition to describing children’s knowledge and practice at a given age, learning progressions aspire to describe how that knowledge and practice could change over time, with successive understandings representing an achievable advance from earlier ones. This presents multiple challenges. We wish to describe both continuities and discontinuities in children’s thinking, as well as successional trends over time. The choices we make will inevitably emphasize some of those continuities and discontinuities while obscuring others. In addition, each phase must represent an achievable advance from the one before. The strongest evidence for a suggested advance comes in the form of teaching experiments that demonstrate how students can move from one set of understandings to the next or longitudinal studies showing systematic progressions in students’ understanding. When this kind of empirical evidence is not available, we can suggest stages that represent reasonable advances across all four strands of scientific proficiency.
Finally, no single learning progression will be ideal for all children, since they have different instructional histories, bring different personal and cultural resources to the process of learning science, and learn in different social and material environments. The best learning progressions are those that make effective use of the resources available to different children and in different environments. This is the challenge that we are farthest from responding to effectively with the current research base.
INITIAL WORK ON LEARNING PROGRESSIONS
What might such long-term learning progressions look like? Recently, two design teams that were composed of scientists, science educators, and experts on children’s learning were asked to use existing research to construct possible learning progressions for two important theories in natural science: the atomic-molecular theory (Smith et al., 2004) and evolution (Lehrer, Catley, and Reiser, 2004). These two theories are unquestionably core ideas
in modern science for many reasons. Each is well tested, validated, and absolutely central to its discipline. Each integrates many different findings and has exceptionally broad explanatory scope. Each is the source of coherence for many key concepts, principles, and even other theories in the discipline. Each provides insight into the development of the field, guides new research, and can be understood in progressively more complicated ways. Each enables creative links to be made between disciplines. For example, atomic-molecular analyses are important in physics, chemistry, biology, and geology. In that way, understanding and describing matter at an atomic-molecular level is truly foundational for later learning in any science. Evolutionary theory is also integrative of many disciplines, ranging from genetics to ecology and geology, and foundational to all aspects of modern biology, geology, and psychology.
Significantly, there were important similarities in the approaches taken by the two design teams that resonate with findings from current research and that might prove valuable to other (future) design efforts. First, the learning progressions were organized around big ideas of disciplinary importance—major theoretical frameworks in modern science—rather than very abstract or domain-general core ideas, such as systems, interactions, model, and measurement, that are considered important cross-cutting themes in the science standards documents. This disciplinary approach fits with the increasing recognition of the importance of specific content and context in thinking and learning and the power of theories to define and organize understandings of particular domains, something that domain-general ideas by their nature don’t have the power to do (see Chapters 3, 4, and 5 for discussions of conceptual knowledge and its role in scientific thinking).
Second, both design teams identified a number of high-level (abstract) ideas that go into building these disciplinary core ideas, but which, unlike the scientific theories themselves, were more accessible at the start of schooling. These foundational ideas, although not elaborated or well-tested theories themselves, can nonetheless be a source of coherence, providing a framework for organizing children’s learning of new facts, inquiry, and explanation. Thus, both the atomic-molecular theory and the theory of evolution were seen as emergent core ideas, creative syntheses that required the progressive elaboration and transformation of these foundational ideas as they were increasingly grounded in empirical data, integrated, and intercoordinated with each other. In these ways, both design teams acknowledged that even young children have important domain-specific ideas that serve as a foundation for their learning and that the development of complex scientific ideas involved both continuities and discontinuities in children’s thinking (two themes discussed in Chapters 3 and 4).
For example, although the idea of evolution via natural selection is a complex emergent idea, it builds on and integrates a wide variety of ideas that
are accessible to investigation even by young children, including ideas about:
Biodiversity: The existence of different kinds of living things (i.e., the diversity of species);
Structure/function (adaptation): Living things have structures that serve important biological functions (and hence can promote adaptation);
Ecology/interrelationships: Living things populate a habitat and interact with other things in that habitat (e.g., predator/prey relationships);
Variation: Individuals (within a species) vary in their properties;
Change in living things can occur at different scales of time and organization (e.g., growth is change in individuals over the life cycle; populations may also change in characters across multiple generations); and
Geologic processes: The earth has changed in regular ways over time (e.g., mountain formation, erosion, layering of sediments, volcanic eruptions; fossils found trapped in different layers of the earth provide clues about the earth’s past).
In the case of the atomic-molecular theory, although the very notions of atoms, molecules, chemical substance, and chemical and physical change are complex emergent ideas, even children entering school make a distinction between objects and the materials they are made of, are elaborating on their knowledge of the properties of objects and materials, and thus have resources for beginning to explain why objects have the characteristics they do and for beginning to track some underlying constancies and changes in objects and materials across various transformations (e.g., dividing into pieces, reshaping).
Third, in keeping with the science-as-practice models discussed earlier, both design teams recognized that understanding an idea involves engaging in a wide range of practices that support using and developing that idea. Hence it was important to specify the nature of those practices, both in order to support the design of effective learning environments and appropriate assessments of student learning. These practices are of a wide variety of sorts, including being able to use ideas to question, describe, classify, identify, predict, measure/compare, explain, represent (or symbolize) ideas and data using a variety of cultural tools, design studies, evaluate ideas/make arguments, etc. Furthermore, although it was recognized that practices would become more complex and intercoordinated in the course of learning, even young children were seen as able to engage with a rich set of practices right from the start (see Chapter 3). Thus, in contrast to the skill progressions outlined in Science: A Process Approach, the focus was on meaning-making
(knowledge construction) practices enacted and supported in a cultural context (not isolated, disembodied skills), with explanation, evaluation, and symbolization recognized as central practices right from the start.
Finally, both design teams assumed that understanding of the core ideas of science also involves understanding their epistemology (i.e., the data patterns and knowledge construction and evaluation practices that serve to give rise to those core ideas) and that even young children would have some initial epistemological ideas that could be built on, enriched, and transformed in the course of science learning (see Chapters 3 and 6). Hence the foundational ideas used to structure the learning progressions included foundational epistemological ideas as well as the foundational domain-specific ideas previously discussed. In the case of the learning progression for evolution, those epistemological ideas were characterized as of two broad sorts: (1) ideas about forms of argument (which would be elaborated over the learning progression to include understanding of both model-based and historical arguments) and (2) knowledge of specific mathematical and representational tools that can be used to enrich one’s descriptions of nature (which would be elaborated to include the tools of measurement, data creation, representations of distributions, Venn diagrams, cladograms, etc.). In the case of the learning progression for the atomic-molecular theory, the designers focused on the elaboration of the core epistemological ideas of measurement, models, and evaluation of ideas using data and argument.
Including important foundational ideas about epistemology (to be built on and elaborated in the course of the learning progressions) is in keeping with current research findings that children have a capacity for metacognitive reflection: that is, they can ask themselves not only “What do I know?” or “What should I do?” but “How do I know?” “Why should I do it?” Furthermore, there is increasing evidence that flexible and adaptive use of practices is greatly aided by explicit understanding of the reasons for those practices. Current research also makes clear that these deeper epistemological understandings do not come for free with the mere use of practices (Roth, 2002). Rather, they require explicit reflection and discussion of these issues. Significantly, recognizing the importance of engaging students with these issues has led to changes in how the practices themselves are taught.
This work on constructing learning progressions is new, still partial and incomplete, and has not had a chance to be discussed and critiqued by the larger community. We present one example in greater detail here—work on a learning progression for matter and atomic-molecular theory—because of the somewhat larger research base in this area for K-8 students and to illustrate what such an approach might look like and how it is different from current practice. Also, this example shows how core ideas permit cross-domain integration (in this case, spanning domains as different as the physi-
cal and life sciences) and has implications for developing an informed citizenry able to understand current practical issues and policy debates (environmental issues and problems). Currently, other design teams are working on learning progressions for other core ideas (genetics, matter cycling). We think more work on describing such large-scale learning progressions is going to be crucially important to the improvement of science education in the United States.
A LEARNING PROGRESSION FOR THE ATOMIC-MOLECULAR THEORY OF MATTER
As mentioned above, research on children’s learning is currently fragmentary, falling well short of suggesting a complete sequence of steps in learning about matter or any other topic. We therefore need to make principled use of the research to suggest the general nature of a learning progression that would lead to understanding and to fill in the gaps when research is not available. In developing a learning progression for the atomic-molecular theory of matter, we suggest reasonable steps that are constrained by three of the four strands of scientific proficiency: (a) students’ existing concepts, (b) their knowledge construction and evaluation abilities, and (c) their understandings of science as a way of knowing. (Research focusing on the fourth strand, productive participation in science, currently is not easily integrated with research focusing on the first three within a learning progression focused on matter.)
Thus, in describing the learning progression, we discuss how it reflects the interactions among these three kinds of constraints and how competence in the first three strands of scientific proficiency can develop interactively. We also discuss some of the research base for the steps in the progression, the way it challenges some aspects of existing practice and provides guidance for ways of elaborating the science standards, as well as important limitations in the existing progression and questions raised for future work.
Developing an Understanding of Materials and Measurement
The learning progression developed by Smith et al. (2004) identifies several ideas (concepts, resources, abilities) that children have at the start of elementary school that enable them to begin their initial exploration of three basic questions. The learning progression is described in part as the progressively more sophisticated answers that children can give to these questions (the overview table in Appendix A describes the learning progression in these terms):
What are things made of and how can one explain their properties?
What changes and what stays the same when things are transformed?
How do we know?
For starters, even preschool children make some distinction between material and object levels of description and have learned words to label things at both levels: kinds of objects (e.g., boats, cars, beds, balls, kites) and kinds of materials (e.g., water, milk, play dough, wood, plastic). Children also have rich vocabulary for describing the properties of things based on commonsense impressions—for example, size (big/small), weight (heavy/ light),1 texture (soft/hard, rough/smooth), color (red/blue), shape (round/ square), taste (sweet/salty), smell—and have some initial ideas about which properties may pattern at object or material kind levels. They not only are fluent language speakers (which allows them to use language to form and express ideas in symbolic form) but they also have some facility at counting, drawing, and building or making things (which extends the resources they have for symbolizing things). Thus, they can use their existing ideas to engage in a variety of practices, including asking questions, describing and representing their observations, identifying and classifying things, making arguments, and proposing explanations (see the chapters in Part II for a review of research that supports these claims).
At the same time, the proposed learning progression acknowledges the extensive research that shows young children’s initial conceptual knowledge of materials, of physical quantities such as weight and volume, and of the knowledge construction practices of science are still quite limited. For example, although young children are learning names for some kinds of materials, descriptions at the level of objects is much more salient and important in their everyday life, and their knowledge of and experience with different materials is still quite limited (Krnel, Watson, and Glazar, 1998; Krnel, Glazar, and Watson, 2003).
Furthermore, although young children may implicitly treat materials as homogeneous constituents of objects in some circumstances, this understanding is still fragile and unarticulated. Indeed, there are many situations in which they deny that an entity broken into tiny pieces is still the same kind of stuff in part because it no longer looks like the same stuff (Dickinson, 1987; Krnel, Glazar, and Watson, 2003). Their knowledge of object properties is limited to those accessible to commonsense impressions, so many of
the most enduring and essential characteristics of materials (density, boiling and melting points, thermal and electrical conductivity, solubility, etc.) are not yet known to them (Johnson, 1996; Smith, Carey, and Wiser, 1985; Wilkening and Huber, 2002). Related to this, their knowledge construction and evaluation practices are based on casual everyday observations using their commonsense impressions, not on careful measurement, modeling, and extended argument. At the outset of school, they have had limited experiences using instruments to measure things, and they have even less understanding of the deeper reasons for using instruments or of explicit criteria for judging what makes a good measurement (Lehrer, Jenkins, and Osana, 1998).
Hence, the overall goal at the K-2 level is to have children clarify, extend, systematize, and even begin to problematize their understandings of common materials and important physical quantities (especially weight and measures of spatial extent). Curriculum developers need to be mindful that children are ready to tackle these issues, while at the same time realizing that they are still conceptually difficult for them. They need to realize that central to helping students make progress with these issues is not just providing them with new facts or experiences, but also introducing them to cultural tools and practices that enable them to extend and restructure their understandings.
One specific goal is to extend children’s knowledge of materials and help create a richer notion of material kind as a dense causal nexus: that is, to realize that objects are constituted of materials and have some properties because they are made of that material. For example, children can be presented with objects made of a range of different materials (or containers with a range of different liquids). They can be asked to organize, describe, and classify the things by the kind of material they think they are made of and to defend their classifications. They can be asked to describe the properties of the objects and compare them in their properties, using new tools for organizing their descriptions, such as Venn diagrams and attribute/value charts.
In addition, they can consider why objects behave as they do in situations that implicate the materials they are made from. For example, they can compare the properties of two cups (one made of plastic and the other glass) and consider how each will respond when dropped and why. Or they might compare the properties of two balls (one made of metal and another of rubber) and consider how they respond when dropped and why. They can be introduced to common names for certain materials and asked how they could tell if something else was made of that material. They can predict how the observable properties of things might change or stay the same if an object is reshaped, divided into little pieces, or heated until melted, and whether they think it will still be the same kind of material. They then carry out those transformations and record and interpret what happens. For ex-
ample, they might melt a chocolate bunny and be asked to describe how it has changed. They can also be asked whether they think it is still chocolate, whether it still has the same amount of stuff, whether it has the same weight, and to make arguments about how they can tell.
In the course of these activities, not only will they be learning about how to form meaningful classifications, to carry out simple investigations, and to represent and record data in useful ways, but also they will deepen their understanding of materials. They will learn that not all properties of chunks stay the same when cut into pieces and that there are at least two ways of trying to trace (or track) the identity of different materials over time—by historical continuity (i.e., by following where it came from, or what was done to it, such as grinding) or by consideration of its observable properties.2 Originally, children might be more inclined to use commonsense properties than historical tracing. Historical tracing is important (especially across decompositions, such as grinding into smaller pieces) because it helps build an explicit idea of a material as an underlying constituent. By engaging children with considerations of what happens to materials with decomposition, they come to identify materials not just by their common perceptual features, but as constituents that can maintain their identity (and certain properties) even when they become arbitrarily small. They also begin to realize that not all large-scale properties of materials are preserved during that decomposition (i.e., some emerge when there is enough stuff or under certain conditions).
Another (related) goal identified for this period is to extend children’s descriptions beyond commonsense perceptions—especially for important physical magnitudes like weight and volume—by engaging them with the problem of constructing measures for a variety of quantities so that they can develop an explicit theory of measure that underlies the practice of measurement. Measurement is an important scientific practice that contrasts with everyday practice and grows out of concern with having data that can be described in precise objectively reproducible (or verifiable) ways and made amenable to mathematical representation and manipulation. It also greatly aids in finding lawful patterns in data—patterns that would be totally obscured if one relied on commonsense impressions. Yet many aspects of the underlying logic of measurement are not initially obvious to students and can be hidden by simply teaching them how to use preexisting or standard measuring procedures or instruments. Thus, learning to measure should in-
volve much more than developing procedural competence; it should also involve developing a conceptual understanding of measurement (Lehrer, Jenkins, and Osana, 1998).
Even infants and preschoolers make judgments about how big or heavy something is, but these judgments are grounded in their commonsense impressions, not yet informed by explicit measurement procedures. Furthermore, although these commonsense impressions are useful in everyday life, they provide a poor basis for scientific practice. For example, felt weight is influenced by a host of physical variables and hence is not a very precise, reliable, or valid measure of the objective weight of objects. For these reasons, scientists have developed a wide range of measuring instruments that enable them to measure important physical variables. These measures also enable them to potentially deal with entities that are not on a scale that is accessible to commonsense impressions—both the very large and the very small.
As mentioned above, devising measuring instruments and figuring out how to use or apply mathematical ideas to one’s physical concepts is by no means a trivial undertaking for students for multiple reasons. First, one needs to identify a physical situation that responds to the physical variable in question—for example, balance scales respond to weight, and alcohol in thermometers responds to temperature. Second, one needs to create a unit for that quantity of fixed size that one can use to “cover” the measurement space, which one then can count. Third, one needs to consider how to deal with fractional units. In cases in which no direct indicator for the quantity in question exists, one may need to derive a unit by mathematical combination of other units. Thus, some measurements are simpler to devise than others and may be foundational in the sense that one uses one measurement in deriving others. They also may be useful entry points for considering the basic issues that arise in measurement (i.e., constructing a theory of measurement that can inform one’s understanding of the issues faced in constructing measures).
All of these possibilities occur in the learning progression for matter and constrain its proposed sequences. Thus, the proposed learning progression builds on the research of Lehrer, Schauble, and their colleagues who have investigated instructional sequences for building an understanding of the measurement of important physical quantities. In their work, learning to measure length and area provides an important foundation that aids in children’s later construction of measures of volume and weight. Their classroom studies (replicated many times in different classrooms) have shown that not only are K-2 children capable of inventing initial measures of length and area (e.g., see Lehrer, Jenkins, and Osana, 1998), but also that doing so enables them to engage with basic epistemological issues about measurement (understanding the 0 point, equal partition, fractional units, the need to cover the measurement space, etc.). These are issues that even much
older children often fail to understand if they are taught merely to use measurement systems developed by others. Furthermore, children who have developed these epistemological understandings of measure are able to build on these understandings in tackling the more difficult problems of measuring weight and volume (Lehrer, Jaslow, and Curtis, 2003). For these (and other) reasons, engaging K-2 children with these epistemological issues is made central to the proposed learning progression.
Because the measurement of weight and volume is more complex, students should not work on measuring those quantities (quantitatively) until the appropriate foundation has been laid. However, one problem that K-2 children are ready for working on involves figuring out that balance scales are responsive to weight (rather than, say, the size of objects, number of objects, or kind of material an object is made of), although the task is by no means trivial for children at this age (Metz, 1993). Working on this problem enables them to have two ways of making judgments: felt weight judgments (using their hands) and weight comparisons (using pan balances). It also allows children to confront an important epistemological issue: Which is a more reliable and valid (qualitative) measure of the weight of two objects, their hands or a balance scale? They can explore this question in a variety of ways: for example, by making repeated comparisons of the same objects under different conditions to see if they get the same outcome (e.g., after they have hefted a heavy object), or considering cases in which their felt weight judgments are at odds with those of the balance scale because of size/weight illusions, etc. By debating and engaging with this issue, they may come to more deeply value and trust pan balance measurements and begin to restructure their understanding of weight as an objectively defined (rather than subjectively assessed) physical magnitude. (They can also consider these issues for length and area—for example, by exploring the Muller-Lyer optical illusions.)
How This Differs from Current Practice
Very little if anything is expected to be accomplished in science during the K-2 years in most U.S. elementary school classrooms, where the overwhelming focus is on developing early literacy and numeracy. Most science activities are short (one lesson long) rather than coherent units. There is frequent shifting from topic to topic rather than a coherent building. In fact, the shift between topics may be confusing to students. For example, students might do an activity involving identification of materials one day; on another, they might identify or describe solids, liquids, and gases—both as part of their matter unit. This is potentially confusing to students at this age because, lacking a clear concept of matter (or forms of matter), they may mistakenly think of solids, liquids, and gases as kinds of materials. Phenom-
ena are often selected—such as sinking or floating or evaporation—more by their surprise or attention-getting value than with a thought about what students will conceptually understand by exploring them. In fact, students are often presented with phenomena that they have no real means of understanding at this grade. Finally, students are often simply introduced to standard measurement procedures, without engaging them in trying to understand the underlying logic of those procedures.
In contrast, the proposed learning progression outlines a set of conceptual goals that can be investigated in a more sustained, mutually reinforcing manner, based on a principled interpretation of research on children’s interpretations of matter and materials. In particular, we note that the research enables us to identify phenomena and topics for discussion that will help students make progress with respect to each of the first three strands of scientific proficiency:
Understanding and using scientific explanations of the natural world. Children can learn to make the critical distinction between objects and the materials of which the objects are made. They can begin using observable properties to describe materials and transformations in materials and consider what properties of objects may depend on (and thus be explained by) the kind of materials they are made of.
Generating and evaluating scientific evidence and explanations. Children can begin the process of building the measurement skills and understandings that will be essential to developing scientific concepts of material kind and of such properties as mass, volume, and density. They can actively investigate properties of materials and transformations in materials and being to understand that some transformations (e.g., grinding into little pieces, melting) lead to changes in some perceptible properties of materials without fundamentally changing the identity of the material or the amount of material.
Understanding how personal and scientific knowledge are constructed. Children can develop important epistemological understandings of measurement and of transformations of materials. They can consider how reliable measurements can be generated and the circumstances in which measurements are more useful or trustworthy than personal impressions. They can also consider ways in which both history and observation are used to understand transformations that destroy objects (e.g., breaking, dividing, melting) but may leave the materials of which the objects are made intact.
Thus the strands of scientific proficiency can be used in conjunction with the research to identify serious work that can enable K-2 students to lay a foundation, especially in their early work on measurement, and their exploration of materials that will continue to have payoff in the later grades. The design of the approach to measurement, which emphasizes modeling
and epistemological understandings rather than mere computations, has implications for the design of early mathematics instruction as well. The approach emphasizes the importance of developing important domain-specific concepts and foundational epistemological ideas as a base from which to build in later grades.
Developing an Explicit Macroscopic Understanding of Matter
Work in grades K-2 to elaborate children’s understanding of specific materials prepares them to move up a level of abstraction and develop an initial macroscopic understanding of matter at this next age band. Students now can consider not just the salient properties that distinguish different kinds of materials, but ask the question of whether there are some properties that all material entities have in common. In this way, they can be led (with relevant instructional practices) to articulate a general concept of matter that was initially implicit in their notion of material kind. In so doing, a new causal nexus—matter—is developed as students come to realize that objects made of different materials “have weight and occupy space because they are made of something (pieces of stuff) that continues to exist, take up space, and have weight across a broad range of transformations” (Smith et al., 2004, p. 46). Some core ideas important to develop at this age band include understanding that:
Objects are made of matter that takes up space and has weight.
Solids, liquids, and air are forms of matter and share these general properties.
There can be invisible pieces of matter (i.e., too small to see with the naked eye).
Matter continues to exist when broken into pieces too tiny to be visible.
Amount of matter and weight are conserved across a range of transformations, including melting, freezing, and dissolving (Smith et al., 2004, p. 45).
Research has shown that elementary schoolchildren are beginning to develop an intuitive (abstract) notion that there is “an amount of stuff” in objects that can remain constant across changes in surface appearance. For example, in their classic conservation studies, which have been replicated many times by others, Piaget and Inhelder (1974) poured liquid from a short, fat container into a tall, thin one and asked children if there was the same amount of liquid in both containers or if one had more. Similarly, they
took a ball of clay and rolled it out into a thin sausage shape or divided it into several smaller pieces and asked if there was still the same amount of clay in the ball, the sausage, and the set of pieces. They found that young elementary schoolchildren were developing the idea that the amount of stuff remained the same despite the striking changes in surface appearances, changes that typically led younger preschool children to deny that the amounts could be the same. In this way, they showed that elementary schoolchildren were increasingly capable not only of thinking about the particular qualities (or characteristics) of a material, but also of its underlying amount.
At the same time, research also provides extensive evidence that children’s notion of “amount of stuff” is still inchoate in many ways—not yet based on a clearly articulated notion of matter that is tightly interrelated with their notions of taking up space and having weight nor clearly (explicitly) understood as an additive quantity itself (Carey, 1991; Smith, Solomon, and Carey, 2005; Smith, Carey, and Wiser, 1985). So, for example, children often judge that some material objects (such as a piece of Styrofoam, a small piece of clay) weigh nothing at all, a difficulty that for many students persists well into the middle school years (Smith et al., 1997; Smith, 2005). In addition, they also often judge that when an object is repeatedly divided into littler pieces (so tiny that they are no longer visible) that the matter itself has disappeared (Smith et al., 2004; Yair and Yair, 2004). Further evidence that having weight is not criterial in their conceptions of matter stem from analysis of the instances they judge as being made of matter as well as from their explicit definitions of matter. In fact, elementary schoolchildren often fail to include many instances as matter that clearly have weight (e.g., liquids or biological entities such as a flower, dog, or meat) as well as overextend to include entities that are associated with matter but are not matter itself (e.g., fire, electricity) (Carey, 1991; Stavy, 1991). Consistent with their noncanonical classifications, their explicit definitions of matter fail to identify taking up space or having weight (mass) as criterial for being matter. Instead, they either simply list examples, focus on commonsense perceptual properties (it is something that one can see, feel, or touch) or on its having some physical effect, or noninformatively say it is something that one can use or make things from (Carey, 1991; Stavy, 1991).
These difficulties mutually support each other. Part of the problem is with children’s conception of weight. To the extent that children rely on feeling objects to determine weight differences—hence the core of their weight concept is felt weight, rather than being an objective measurable quantity—it is not obvious that all material objects do have weight or that weight itself is an additive quantity. In fact, many light objects feel like they weigh nothing at all. In addition, felt weight judgments are affected by both absolute weight differences and pressure differences in one’s hand (a small object made of a dense material can feel much heavier than a large object
made of a less dense material), further obscuring their understanding of weight as an extensive quantity. Part of the problem may stem from the limitations in their conception of matter itself. To the extent that it is defined only in terms of limited particular examples, or in terms of properties of large-scale chunks, rather than as a constituent that continues to exist, take up space, and have weight with decomposition, children cannot conceptualize “amount of matter” as an underlying additive quantity. Furthermore, without knowing that all matter has weight, they will have no way of precisely measuring amount of matter or telling whether the amount of matter has really changed across some transformations (e.g., when an ice cube is melted, when a sugar cube dissolves in water).
The preceding analysis, however, suggests that these difficulties are by no means insuperable for elementary schoolchildren. Instead, it highlights the very practices that they can engage in that will help them restructure their conceptions of weight and taking up space as measurable objective quantities and allow them to build a sound macroscopic conception of matter at this time. It also highlights why building such an understanding is truly foundational, in that it opens up new avenues for tracing the existence of matter over time and different transformations. Given the importance of these understandings for further scientific investigations, as well as the evidence that elementary schoolchildren are very capable of developing them with appropriate instruction, it seems critical to make it a goal for curricula at this time.
One set of practices that will support their reconceptualization of weight and taking up space is learning to measure weight and volume, especially if children engage with learning to measure as a form of modeling and explicitly confront key epistemological issues. That is, students are not taught measurement as a set of disembodied procedures (e.g., being told the volume of a rectangular cube is the length × width × height, or the weight of an object is a digital read from a scale). Instead, students are involved in the active construction of mathematical models of those quantities as additive magnitudes, and they have to think through problems of identifying a relevant unit, iterating that unit, covering the measurement space, etc. As previously discussed, children’s initial work in K-2—learning about materials, learning to measure length and area, learning that balance scales can measure weight—prepares them for taking this next step. The research of Lehrer, Jaslow, and Curtis (2003) has documented that with this kind of instruction in earlier grades, even third graders can develop robust understanding of the measurement of weight and volume. Significantly, the researchers found that children use many of the explicit ideas they have developed about measure from their earlier work on length and area (e.g., ideas about the need to identify a fixed unit, equal partition, and fractional unit, as well as constructing two-dimensional arrays) in their new investigations. They note
that although children must still work through these (and other) issues for the new quantities in question, they work through these issues more quickly than they did for the earlier quantities. Hence, they suggest meaningful transfer has occurred by allowing children a speed-up in working through new problems, not a side-stepping of the problems themselves. (For example, in constructing a measure of volume, students need to confront the new problem of imagining a three-dimensional array. Work with multiple forms of representation and coordinating among these different representations is crucial to this process.)
Having developed these tools, children can use them to deepen their exploration of the characteristics of matter and measurements. For example, they can use a scale to measure the weight of an object (e.g., a clay ball), and then be asked how much the object would weigh if it were half its size or one-quarter its size. Then they could carry out investigations to check their predictions. In carrying out these investigations, different groups of children need to measure the weight of the ball and its volume (to confirm they have made it half or a quarter its size) multiple times. In the process, they will have to decide how to handle variability in their data and wrestle with the idea of measurement error. They can also be asked to extrapolate to a much smaller piece—say a piece 1/100th the size. If the initial piece weighed 1 gram, what would a piece 1/100th that size weigh? If the scale didn’t tip down, does that mean it weighs nothing at all? How could they investigate it further? This kind of thought experiment allows students to use mathematical reasoning and conceptual arguments to go from what they know to what they think should be. For example, they might argue that, as long as there is some amount of stuff, it must weigh something, although it may be only a tiny, tiny bit; one cannot take a string of nothings and get something. In this way, they can add features to their conceptual representation that follow inferentially rather than through direct observation. It also allows them to confront important issues about precision of measurement. After students have had a chance to discuss these issues, they might be challenged to think of ways of constructing more sensitive scales.
Children can also use explicit modeling to interrelate notions of volume and weight and construct a distinct notion of density as they pursue the question of why objects made of different materials weigh what they do. In this case, they can work with families of objects of different size made of different materials. There are a variety of ways in which instruction can successfully proceed.
Lehrer et al. (2001) had fifth grade students construct graphical representations of measured weights and volumes of objects made of different materials, interpolate a “best fit” line, and interpret the slope of the line; these investigations built on prior mathematical investigations in which students investigated similarity of form in families of rectangles of different
proportions and drew graphical models of them. Smith and colleagues (1992, 1997) involved students in constructing visual dots-per-box models of materials, exploiting visual analogies with quantitative potential.
Central to each approach is engaging students with model-based reasoning. For example, students construct representations (visual or graphical) that show the relation between two quantities, derive new implications from these representations, and evaluate them against further data. Significantly, Lehrer et al. (2001) have found that the notion of density itself, notoriously a difficult notion for even much older children, becomes accessible to fifth grade elementary school students when taught this way.
Indeed, their work has documented sophisticated model-based reasoning in a variety of domains (e.g., modeling the growth of plants, the workings of an elbow) among third to fifth grade elementary school students who have had prior experience with modeling (Lehrer and Schauble, 2000). In each of these cases, students are not simply using models to depict some feature they have observed (the approach taken more often by younger children), but to investigate phenomena and derive new inferences. Note too that by differentiating weight from density, students enrich their understanding of a distinguishing property of materials, as well as enhance their ability to explain the weight of an object as a joint function of its volume and density.
Finally, students can also investigate more precisely whether the weight of objects changes or stays the same with melting, freezing, and dissolving. They can be asked to make arguments from these investigations about whether they think matter has been added or lost across these transformations. They can engage in further exploration and design investigations to determine if air is matter (e.g., weighing a basketball before and after air has been pumped into or out of it). They can use their emerging understanding of matter to identify and classify a range of entities as either matter or not matter.
How This Contrasts with Current Practice
Too often curricula rush to tell students about atoms and molecules in the elementary grades before a sound (embodied) macroscopic understanding of matter is in place. In addition, curricula often do not recognize that conceptual restructuring is needed to build this macroscopic understanding of matter—they assume it is obvious or already in place—and hence do not use teaching practices that make it more likely that restructuring will occur. For example, almost totally absent from science classrooms is any systematic use of modeling or model-building activities that call for students to use new representational tools (including relevant mathematical tools and understandings) to make predictions that are tested against observations and iteratively revised.
Instead, most elementary science classrooms simply present new ideas in science in declarative form—as definitions that should be memorized and learned—and teach students about measurement as a set of simple procedures. Thus, they teach students that solids, liquids, and gases are matter without considering whether they have a notion of matter that allows this grouping to make sense. They teach them some procedures for making weight and volume measurements, without considering whether children have a conceptual understanding of what they are doing when they make measurements or alternative ideas about weight and volume that need restructuring. They move from one set of topics to another, which are not deeply connected to each other (thinking this will maintain interest), rather than pursue topics or investigations that mutually reinforce each other.
In contrast, the proposed learning progression suggests ways that children can continue to develop the conceptual and procedural knowledge that will enable them to reason flexibly about matter. The research on children’s learning is used to suggest logical progressions that connect the first three strands of scientific proficiency:
Understanding and using scientific explanations of the natural world. Children can build on their understanding of materials to develop a generalized conception of matter, recognizing weight and volume as key properties that all materials have in common and density as a distinguishing characteristic of material kinds. In order to do this, they must develop more robust conceptions of weight and volume, based on measurement rather than sense impressions, and they must recognize these characteristics as essential to the definition of matter. They must also reason in principled ways about transformations in materials and amounts of materials that are too small for direct measurement of their properties. As they consider these problems, they can provide deeper explanations of why objects weigh what they do (in terms of the density of the kind of material and the volume of the material). They are also laying the groundwork for tracing matter through physical and chemical changes and for a robust understanding of atomic-molecular theory.
Generating and evaluating scientific evidence and explanations. Children can engage in measurements of weight and volume not merely as procedures, but as ways of actively modeling matter and its properties. As they use their measurements of weight and volume to compare related objects and materials and to trace materials through such transformations as dividing and melting, they develop both improved measurement skills and a robust evidence-based understanding of matter and its properties.
Understanding how personal and scientific knowledge are constructed. A key characteristic of the activities suggested in this learning progression is that they engage students in developing scientific arguments from evidence. Their developing understanding is based neither on the authority of teacher
and text nor on unmediated personal experience. Instead, they engage in systematic data collection and principled reasoning to construct new understandings both of matter and of the foundations of scientific knowledge.
Thus the strands of scientific proficiency can be used in conjunction with the research to develop understandings in upper elementary school students that build on their learning in grades K-2 and that lay the foundations for reasoning about matter using atomic-molecular models in middle school.
Developing an Initial Understanding of the Atomic-Molecular Theory
Children’s macroscopic understandings of matter (now grounded in a well-articulated set of measurable quantities) provide a framework from which they can ask still deeper explanatory questions and, in response to these questions, construct another layer of explanation (i.e., in terms of atoms and molecules). For example, what is the nature of matter and the properties of matter on a very small scale? Is there some fundamental set of materials from which other materials are composed? How can the macroscopically observable properties of objects and materials be explained in terms of these assumptions? These deeper questions arise only as puzzles requiring further explanation if students have a rich, embodied, and sound macroscopic understanding of matter on which to build (Snir, Smith, and Raz, 2003). But given such macroscopic understandings and prior experience with model-based reasoning, students are ready to take on the challenge of investigating, describing, and explaining a host of new phenomena as well as reexplaining and more deeply understanding phenomena with which they are already familiar. In addition, armed with new insights provided by knowledge of the existence of atoms and molecules, they can conceptually distinguish between elements (substances composed of just one kind of atom) and compounds (substances composed of clusters of different atoms bonded together in molecules). They can also begin to imagine more possibilities that need to be considered in tracking the identity of materials over time, including the possibility of chemical change.
One set of puzzling phenomena for students to explain is how the volume of something can change in situations in which its mass or weight has been conserved. Of course, to even describe these situations, students need to not only clearly distinguish the quantities of weight and volume, but also have ways of accurately measuring them to be sure that one has clearly changed without the other. In addition, to be puzzled by this state of affairs,
students have to have developed some clear expectations about materials and how they should behave. These are exactly the kinds of expectations that they have been developing in grades 3-5, as they are learning to measure both weight and volume and coming to understand that matter has weight and takes up space.
There are a large number of situations in which this basic data pattern (of volume change but weight conservation) can be readily observed by students. Some involve solids, some involve liquids, some involve gases, and still others involve a change of state. In the course of teaching, students should be exposed to all these situations. For starters, however, consider one phenomenon that research has shown to be especially intriguing and puzzling for middle school students and how it can be used to invite initial debate and discussion about whether matter is fundamentally particulate or continuous (Snir, Smith, and Raz, 2003).
The phenomenon involves mixing two equal volumes of water and alcohol, which are both colorless liquids. If you mix a given volume of water (say 50 ml) with a given volume of alcohol (also 50 ml), the resultant mixture of water and alcohol is only about 96 ml, not 100 ml, which is what students would have expected. Students immediately suspect that some liquid has been lost in the transfer. To rule out this possibility, it can be shown that there has been no loss of material: the weight of the mixture is equal to the weight of the two component parts. In addition, to allow students to more fully study the mixing itself, the two liquids can each be colored (with different food coloring) so students can watch more clearly what happens as they mix. Just as before, they can collect data showing that the total weight, but not the total volume of the system has been conserved. They can also see that if the (blue) colored water is mixed with the (red) colored alcohol, the two liquids intermingle and intermix, turning a uniform purple throughout. A number of provocative questions can be raised about this simple demonstration, including:
How can two (continuous) liquids intermix?
Why is the volume of the mixture less than the sum of the volumes of its parts?
Why is the weight of the mixture equal to the sum of the weights of its parts?
Students are very intrigued (and surprised) by this demonstration, and in searching for possible explanations, they can be asked: What might matter be like at a very tiny scale (much too small to directly observe), in order for this to be? Students can consider a number of alternative models of the situation, based on different assumptions about what matter is like at such a small scale. For example: Would it be continuous all the way down (i.e., no
gaps or breaks)? Would there be discrete but tightly packed particles (i.e., no spaces between the particles)? Would there be discretely spaced particles of different sizes? For each alternative, they can then work through the consequences of those assumptions—what would be predicted to happen in this situation—on each set of assumptions. They can then consider how well each imagined alternative can actually explain the three main facts.
Note that, to even engage with this issue, students have to be able to imagine that if matter were repeatedly divided in half until it was in a piece too small to see, some matter would still be there—it wouldn’t simply disappear if it were no longer visible. Research has shown that as students move from thinking about matter in terms of commonsense perceptual properties (something one can see, feel, or touch) to defining it as a constituent, that takes up space and has weight, they are increasingly comfortable with making this assumption. In this way, the framework they are developing in grades 3-5 is preparing them for theorizing at this level. In addition, they need to engage in “hypothetico-deductive” model-based reasoning: they must conjecture about (and represent) what matter is like at a level that they can’t see, make inferences about what follows from different assumptions, and evaluate the conjecture based on its fit with a pattern of results. Significantly, two small-scale research studies have shown that middle school students are able to (enthusiastically) discuss these issues, especially when different models (for several puzzling phenomena) are implemented on a computer and they are put in the position of judging which models can account for the facts (Snir, Smith, and Raz, 2003). Indeed, this approach led students who had relevant macroscopic understandings of matter to see the discretely spaced particle model as a better explanation than alternatives (e.g., continuous models and tightly packed particle models). Furthermore, class discussions allowed students to make an important ground rule for evaluating models more explicitly: models were evaluated on the basis of their consistency with an entire pattern of results and their capacity to explain how the results occurred rather than on the basis of a match in surface appearance. In this way, discussions of these simulations were used to help them build important metacognitive understanding of an explanatory model.
Describing and explaining the behavior of air or other gases—for example, understanding that (macroscopically) they compress and expand and searching for underlying (more microscopic) explanations of how that happens—provides another fertile ground for appreciating the explanatory power of assuming that matter is fundamentally particulate rather than continuous (Lee et al., 1993; Nussbaum, 1998). Of course, these investigations bear on students’ emerging ideas about the nature of matter only if they understand that gases are material, something the proposed learning progression recommends that students begin to investigate at the previous age band. At the same time, coming to understand the behavior of gases in particulate terms
should help consolidate student understanding that gases are matter and enable them to visualize their (unseen) behavior. In other words, developing macroscopic and atomic-molecular conceptions can be mutually supportive. Direct support for this assumption was provided in a large-scale teaching study with urban sixth grade students that compared the effectiveness of two curriculum units. One unit focused more exclusively on teaching core elements of the atomic-molecular theory, without addressing student misconceptions about matter at a macroscopic level. The other included more direct teaching of relevant macroscopic and microscopic concepts and talked more thoroughly about how properties of invisible molecules are associated with properties of observable substances and physical changes. The latter unit led to much greater change in understanding phenomena at both macroscopic and molecular levels (Lee et al., 1993).
Furthermore, as the extensive research of Nussbaum and colleagues with seventh and eighth grade students attests, such instruction is especially effective if students are involved in classroom debates and discussion about essential (metaphysical) ideas, alternative theories, and larger epistemological issues (Nussbaum, 1998). For example, how could a vacuum exist? Why wouldn’t matter be automatically sucked into empty space? If there are discretely spaced particles, what holds them together? How do particles move and interact (e.g., do they obey laws of mechanical causality)? Such classroom debate and discussion allow classroom experiments to become more meaningful and informative to students. In addition, thought experiments are used to help students contrast descriptions at the particulate and macro level. For example, students are asked to imagine that a small dwarf (tinier than the smallest particle of matter) stuck a needle into a particle of water or a particle of gas. Would water leak out? Would the gas burst out and make a hissing sound? In this way, they can contrast the behavior of an individual particle of water (or gas) and a macroscopic fluid. One sequence of activities (involving debates, analogies, experiments, and thought experiments) is used to lead students to explain the compressibility of air in terms of a model of vacuum and particles. Another sequence is designed to help them explain the elasticity of air in terms of the continual and random movement of particles. This model in turn helps them to understand air pressure and the diffusion of gases. Thus, central to building an understanding of the atomic-molecular theory is engaging students in cycles of model building while developing their appreciation of the deeper metaphysical and epistemological commitments of atomic-molecular theory. A 3-year longitudinal study showed the much greater effectiveness of this curricular approach in helping students internalize and use the atomic-molecular theory than more traditional didactic instruction (Margel, Eylon, and Scherzo, 2006).
Still other phenomena that have been effectively used to initiate discussions of the particulate nature of matter with middle school students concern
explaining the different properties of solids, liquids, and gases (Driver et al., 1995; Lee et al., 1993); thermal expansion of solids, liquids, or gases (Snir, Smith, and Raz, 2003; Lee et al., 1993); changes of state (Lee et al., 1993); dissolving (Lee et al., 1993); the transmission of smells (Nussbaum, 1998); and why materials cannot (chemically) combine in any proportion (Snir, Smith, and Raz, 2003). Based on the findings of this research, the learning progression proposes that during this age band, students can be meaningfully introduced to the following core tenets of atomic molecular theory:
Existence of discretely space particles (atoms).
There are empty spaces between atoms (idea of vacuum).
Each atom takes up space, has mass, and is in constant motion.
The existence of over 100 different kinds of atoms; each kind has distinctive properties including its mass and the way it combines with other atoms or molecules.
Atoms can be joined (in different proportions) to form molecules or networks—a process that involves forming chemical bonds between atoms.
Molecules have different characteristic properties from the atoms of which they are composed.
The learning progression also proposes that students should practice using these tenets in cycles of building, testing, and revising models of a wide range of particular situations.
This same body of research indicates that it takes considerable time and effort to introduce students to these tenets in a meaningful manner. For example, Nussbaum’s teaching units on the behavior of gases involved over 30 (45-minute) lessons; Lee et al.’s teaching for a broad range of phenomena spanned 10 weeks of sixth grade. However, it may be important to take that time at the middle school level for several reasons. First, understanding the atomic-molecular theory opens up many productive new avenues of investigation about matter. For example, it opens up the whole topic of chemical change, which research suggests is not really accessible to students with only macroscopic criteria for identifying substances (Johnson, 2002). It also helps students much more clearly understand what stays the same and what changes in the water cycle (Lee et al., 1993). Second, many important topics that are discussed elsewhere in the science curriculum, including biology and earth science, depend on these understandings: topics like osmosis and diffusion, photosynthesis, digestion, decay, ecological matter cycling, the water cycle, and the rock cycle, to name just a few. Finally, it provides an opportunity for students to begin to develop an understanding of and respect for the tremendous intellectual work and experimentation that underlies developing a well-tested, successful scientific theory.
How This Contrasts with Current Practice
Current texts often have separate chapters for “Properties of Matter,” “Changes in Matter,” and “Atomic-Molecular Theory.” Atomic-molecular theory is often presented as a set of facts (declarative knowledge) about atoms and molecules, disconnected from any concrete everyday experiences that it may help explain. There is often no attempt made to acknowledge the counterintuitive nature of the claims or to show the usefulness of the theory. As a result, as research on student misconceptions makes abundantly clear, the majority of students fail to internalize the core assumptions of the theory, and they have little understanding of such important ideas as chemical change (see Driver et al., 1995, for reviews). As Schwab and others have argued, science is typically taught as “rhetoric conclusions” rather than as a complex process for making sense of the world (in the words of Niels Bohr, a way of “extending our experience and reducing it to order”) that rests on certain metaphysical and epistemological assumptions. Because of this, students do not appreciate what a tremendous intellectual construction a scientific theory really is, why it deserves great respect, and why it cannot be challenged by another idea that does not attempt to meet those epistemological standards. In an important sense, without constructing an understanding of those epistemological standards, students will not know the grounds on which they should believe important scientific theories.
In contrast, the proposed learning progression outlines a set of conceptual goals that can be investigated in a more sustained, mutually reinforcing manner, based on a principled interpretation of research on children’s interpretations of matter and materials. In particular, we note that the research enables one to identify phenomena and topics for discussion that will help students make progress with respect to each of the first three strands of scientific proficiency:
Understanding and using scientific explanations of the natural world. The learning progression develops atomic-molecular theory as a useful set of conceptual tools that resolve a wide variety of puzzles concerning properties of matter and changes in matter. Description at this level can explain conservation of matter and weight, the composition of materials (elements, compounds), the appearance and disappearance of specific materials, the constancy of materials across change of state, etc. These puzzles are real puzzles for children only if they already have a robust macroscopic understanding of matter and its measured properties. Furthermore, students must master several basic tenets of atomic-molecular theory and use them successfully before the power of atomic-molecular models is apparent.
Generating and evaluating scientific evidence and explanations. The arguments from evidence that support atomic-molecular theory depend on children’s abilities to measure such properties of matter as mass and volume consistently and accurately, as well as their commitment to ideas about the nature of these properties (for example, that mass/weight is a reliable indicator of the amount of matter). Furthermore, they must use these measurements in the context of arguments that require a commitment to logical consistency in predictions and explanations and that involve the coordinated use of model-based reasoning, analogies, and thought experiments.
Understanding how personal and scientific knowledge are constructed. In developing an understanding of the atomic-molecular theory of matter, students need to appreciate that the epistemological standards that are central to science and that are used in deciding between competing views (e.g., explanatory scope, rigor, and precision, ability to integrate large patterns of data, generativity of new testable predictions) are actually different from those typically used in everyday life (e.g., consistency with immediate perceptual experience or initial intuitive ideas—standards less dependent on long chains of reasoning and that have a closer match with surface reality or appearance). Thus, mature scientific theories will often embrace core tenets that on the surface seem implausible or even unintelligible to the novice as long as these assumptions are needed to explain a large pattern of data, are supported by a logical chain of reasoning, and can provide detailed explanations of why surface appearances are misleading. The atomic-molecular theory is a clear case in point. The reason scientists believe in the existence of discrete tiny particles in different arrangements and constant motion (i.e., atoms and molecules) is not because of simple, direct perceptual evidence for such a theoretical analysis; rather it is because of the theory’s tremendous explanatory power and scope and detailed experimental support.
Thus the strands of scientific proficiency can be used in conjunction with the research to develop understandings in middle school students that build on their learning in elementary school and that lay the foundations for reasoning about matter using atomic-molecular models in many different contexts in the life, earth, and physical sciences. With appropriate preparation and teaching, students can engage in true model-based scientific reasoning. They can come to appreciate both the power of scientific models to predict and explain a diversity of phenomena, and how those models are grounded in careful collection and evaluation of scientific evidence.
The proposed learning progression is in several ways incomplete or speculative. Limitations stem from the fact that this is a relatively new way of thinking about organizing learning experiences, from questions that have not been examined in research, and from the kind of research available to us.
In our extended example at grades 6-8, we assume some instructional history with understanding force and motion that would feed into constructing some elements of the atomic-molecular theory. Yet the nature of that earlier work is not specified. In addition, some prior introduction to ideas about energy, its role in change, and discussion of heat would be important but, again, is not explicitly treated. The case of energy is interesting, because it points to a need for key ideas to be introduced, but perhaps not explicitly defined as they serve as important placeholder ideas. Another issue that was not addressed, in part due to the limited research base, is whether it would be productive to have earlier exploration of the formation and separation of mixtures. Thus, the heavy dependence of this learning progression on ideas about material, matter, weight, volume, density, atom, and molecule should by no means imply that these are the only important notions to be addressed. They are a subset of ideas that are important, and they exist within a broader array of ideas that are not merely related linearly, but also within a web interconnecting learning among multiple learning progressions.
The research base itself also necessarily limits the quality of our conceptualization of learning progressions. We have relied on many short-term studies and assembled these in an effort to depict learning across longer periods of time. Furthermore, these studies are primarily studies of knowledge—snapshots of students’ capabilities at a given time—not depictions of learning or the change in capability over time. While our learning progression highlights the ways in which one could be doing more in elementary school to provide a productive foundation for later learning, there is little research to guide in identifying key early experiences. What are the ideas and practices that, if learned early on, would provide greater cognitive payoffs down the road?
We can see implications of learning progressions like the one described above for several areas of policy and practice, including curriculum and standards, assessment, and classroom instruction.
Curriculum and standards. This learning progression suggests several ways in which current curricula and standards are problematic and
could be improved. This learning progression suggests ways in which students of different ages could learn age-appropriate versions of core ideas with understanding, rather than addressing them in current haphazard ways. This learning progression also suggests priorities in the curriculum, helping to identify the conceptual tools and practices that are the foundation for critical learning.
Suggesting appropriate ages for introduction of key ideas. For example, many textbooks and state curricula introduce atomic-molecular stories (not functional as models) as early as third or fourth grade, while the national science education standards delay atomic-molecular models until high school. This research suggests why middle school students could benefit from learning to use atomic-molecular models and what the key elements of those models might be.
Large-scale and classroom assessment. This learning progression suggests the most important conceptual tools and practices to be assessed, common alternatives or misconceptions, and specific questions or tasks that could be used (for an extensive discussion of assessment in the learning progressions framework, see Smith et al., 2006).
Classroom instruction. What is known about mechanisms of learning can be useful for guiding classroom instructions: key questions to address with children of different ages, important experiences that may move the process of succession forward, and key conceptual tools and practices that can be introduced and mastered.
Taken together, these literatures (on preschool understanding, mature scientific understanding, the response of children to sustained good instruction) along with societal expectations and values could form a powerful set of constraints on the development of a set of plausible learning progressions. Clearly, though, there could be more than one way to make choices about what core ideas should be the focus for learning progression analysis. Undertaking the intellectual task of thinking through detailed learning progressions for different end-state core ideas, however, might be one step in thinking through possible advantages and disadvantages of different approaches. In addition, even if we agree on focal core ideas that are the target of instruction and a learning progression that connects the two end points, it would not fully prescribe the instructional sequence. In much the same way as there are constraints on how a complex structure such as a house can be built from its starting components—for example, certain things such as the foundation and then walls must come first to provide structural support for the windows and roof—yet within those constraints there is some flexibility as well and multiple ways to build a house.
American Association for the Advancement of Science. (1993). Benchmarks for science literacy. New York: Oxford University Press.
American Association for the Advancement of Science. (2001). Atlas of science literacy: Mapping K-12 learning goals. Washington, DC: Author.
Baroody, A.J., Cibulskis, M., Lai, M-l, and Li, X. (2004). Comments on the use of learning trajectories in curriculum development and research. Mathematical Thinking and Learning, 6(2), 227-260.
Carey, S. (1991). Knowledge acquisition: Enrichment or conceptual change? In S. Carey and R. Gelman (Eds.), The epigenesist of mind: Essays on biology and cognition (pp. 257-291). Hillsdale, NJ: Lawrence Erlbaum Associates.
Dickinson, D.K. (1987). The development of material kind. Science Education, 71, 615-628.
Driver, R., Leach, J., Millar, R., and Scott, P. (1995). Young people’s images of science. Buckingham, England: Open University Press.
Johnson, P. (1996). What is a substance? Education in Chemistry, March, 41-45.
Johnson, P. (2002). Children’s understanding of substances, part 2: Explaining chemical change. International Journal of Science Education, 24(10), 1037-1054.
Kesidou, S., and Roseman, J.E. (2002). How well do middle school science programs measure up? Findings from Project 2061’s curriculum review. Journal of Research in Science Teaching, 39(6), 522-549.
Krnel, D., Glazar, S.A., and Watson, R. (2003). The development of the concept of “matter”: A cross-age study of how children classify materials. Science Education, 87, 621-639.
Krnel, D., Watson, R., and Glazar, S.A. (1998). Survey of research related to the development of the concept of “matter.” International Journal of Science Education, 20(3), 257-289.
Lee, O., Eichinger, D.C., Anderson, C.W., Berkheimer, G.D., and Blakeslee, T.D. (1993). Changing middle school students’ conceptions of matter and molecules. Journal of Research in Science Teaching, 30(3), 249-270.
Lehrer, R., Catley, K., and Reiser, B. (2004). Tracing a prospective learning progression for developing understanding of evolution. Commissioned paper for the National Research Council Committee on Test Design for K-12 Science Achievement Workshop, May 6-7, Washington, DC. Available: http://www7.nationalacademies.org/bota/Evolution.pdf [accessed November 2006].
Lehrer, R., Jaslow, K., and Curtis, C. (2003). Developing understanding of measurement in the elementary grades. In D.H. Clements and G. Bright (Eds.), Learning and teaching measurement. 2003 yearbook (pp. 100-121). Reston, VA: National Council of Teachers of Mathematics.
Lehrer, R., Jenkins, M., and Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer and D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Mahwah, NJ: Lawrence Erlbaum Associates.
Lehrer, R., and Schauble, L. (2000). Modeling in mathematics and science. In R. Glaser (Ed.), Advances in instructional psychology: Educational design and cognitive science (vol. 5, pp. 101-159). Mahwah, NJ: Lawrence Erlbaum Associates.
Lehrer, R., Schauble, L., Strom, D. and Pligge, M. (2001). Similarity of form and substance: Modeling material kind. In S. Carver and D. Klahr (Eds.), Cognition and instruction: Twenty-five years in progress. Mahwah, NJ: Lawrence Erlbaum Associates.
Margel, H., Eylon, B.S., and Scherz, Z. (2006). We actually saw atoms with our own eyes: Conceptions and convictions is using the scanning tunneling microscope in junior high school. Journal of Chemical Education, 81(4), 558-566.
Metz, K.E. (1993). Preschoolers’ developing knowledge of the pan balance: From new representation to transformed problem solving. Cognition and Instruction, 11, 31-93.
Metz, K.E. (1995). Reassessment of developmental constraints on children’s science instruction. Review of Educational Research, 65, 93-127.
Mintzes, J.J., Wandersee, J.H., and Novak, J.D. (1997). Meaningful learning in science: The human constructivist perspective. In G.D. Phye (Ed.), Handbook of academic learning (pp. 405-447). San Diego, CA: Academic Press.
National Research Council. (1996). National science education standards. National Committee on Science Education Standards and Assessment. Washington, DC: National Academy Press.
Nussbaum, J. (1998). History and philosophy of science and the preparation for constructivist teaching: The case for particle theory. In J.J. Mintzes, J.H. Wandersee, and J.D. Novak (Eds.), Teaching science for understanding (pp. 165-194). New York: Academic Press.
Piaget, J., and Inhelder, B. (1974). The child’s construction of physical quantities. London, England: Routledge and Kegan Paul.
Roseman, J.E., Kesidou, S., Stern, L., and Caldwell, A. (1999 November/December). Heavy books light on learning: AAAS Project 2061 evaluates middle grades science textbooks. Science Books & Films, 35(6), 243-247.
Roth, K.J. (2002). Talking to understand science. In J. Brophy (Ed.), Social constructivist teaching: Affordances and constraints (Advances in Research on Teaching, vol. 9, pp. 197-262). New York: JAI Press.
Schmidt, W., Wang, H.C., and McKnight, C. (2005). Curriculum coherence: An examination of U.S. mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37, 525-559.
Smith, C. (2005). Bootstrapping processes in the development of students’ commonsense matter theories: The role of analogical mapping, though experiments, and learning to measure. Submitted to Cognitive Psychology.
Smith, C., Carey, S., and Wiser, M. (1985). On differentiation: A case study of the development of the concepts of size, weight, and density. Cognition, 21, 177-237.
Smith, C., Maclin, D., Grosslight, L., and Davis, H. (1997). Teaching for understanding: A study of students’ preinstruction theories of matter and a comparison of the effectiveness of two approaches to teaching students about matter and density. Cognition and Instruction, 15, 317-393.
Smith, C., Snir, J., and Grosslight, L. (1992). Using conceptual models to facilitate conceptual change: The case of weight/density differentiation. Cognition and Instruction, 9(3), 221-283.
Smith, C.L., Solomon, G.E.A., and Carey, S. (2005). Never getting to zero: Elementary school students’ understanding of the infinite divisibility of number and matter. Cognitive Psychology, 51(2), 101-140.
Smith, C., Wiser, M., Anderson, C.A., and Krajick, J. (2006). Implications of research on children’s learning for standards and assessment: A proposed learning progression for matter and atomic molecular theory. Measurement: Interdisciplinary Research and Perspectives, 4.
Smith, C., Wiser, M., Anderson, C.A., Krajick, J., and Coppola, B. (2004). Implications of research on children’s learning for assessment: Matter and atomic molecular theory. Commissioned paper for the National Research Council Committee on Test Design for K-12 Science Achievement Workshop, May 6-7, Washington, DC. Available: http://www7.nationalacademies.org/bota/Big%20Idea%20Team_%20AMT.pdf [accessed November 2006].
Snir, J., Smith, C.L., and Raz, G. (2003). Linking phenomena with competing underlying models: A software tool for introducing students to the particulate model of matter. Science Education, 87, 794-830.
Stavy, E. (1991). Children’s ideas about matter. School Science and Curriculum, 91, 240-244.
Valverde, G.A., and Schmidt, W.H. (1997). Refocusing U.S. math and science education. Issues in Science and Technology, 14(2), 60-66.
Wilkening, F., and Huber, S. (2002). Children’s intuitive physics. In U. Goswami (Ed.), Blackwell handbook of childhood cognitive development (pp. 349-370). Malden, MA: Blackwell.
Yair, Y., and Yair, Y. (2004). Everything comes to an end: An intuitive rule in physics and mathematics. Science Education, 88(4), 594-609.