Marianne Wiser

On differentiation: A case study of the development of the concepts of size, weight, and density

Abstract This paper presents a case study of 3- to 9-year-old childrens concepts of size, weight, density, matter, and material kind. Our goal was to examine two claims: (1) that individual concepts undergo differentiation during development; and (2) that young childrens concepts are embedded in theory-like structures. To make progress on the first issue, we needed to specify in representational terms what an undifferentiated concept is like and in what sense this undifferentiated concept is a parent of the more differentiated concepts. Our strategy was to use a model of conceptual differentiation suggested by the history of science to guide our search for evidence. In this model, undifferentiated concepts, like differentiated concepts, can be analyzed in terms of their component properties, features, or dimensions. The key difference is that an undifferentiated concept unites certain components which will subsequently be analyzed as components of distinct concepts, and that the undifferentiated concept is embedded in a different theoretical structure from the differentiated concepts. In our study, the same group of 78 children (18 3-year-olds, 18 4-year-olds, 18 5-year-olds, 12 6–7-year-olds, and 12 8–9-year-olds) were given a range of tasks probing their understanding of size, weight, and density; a subgroup of these children were given additional tasks probing their concepts of matter and material kind. We found that young children had a theoretical system which included distinct concepts of size, weight, and material kind and were beginning to form generalizations relating these concepts (e.g., size is crudely correlated with weight, steel objects are typically heavy). The core of their weight concept was felt weight, with density absent from their conceptual system; material kinds were defined in terms of properties which characterize large scale chunks of stuff. Slightly older children (5–7-year-olds) had made modifications to their concepts of weight and material kind. At these ages, their concept of weight now contained both the properties heavy and heavy for size (which we take as evidence of their having an undifferentiated weight/density concept) and they were coming to see weight differences as important in distinguishing whether large-scale objects were made of the same kind of stuff. However, the core of their weight concept was still felt weight and material kinds were still defined in terms of properties of large scale objects. Finally, still older children (8–9-year-olds) had a theoretical system in which weight and density were articulated as distinct concepts, material kinds were reconceptualized as the fundamental constituents of objects, and weight was seen as a fundamental property of matter. We conclude that childrens concepts of weight and density do differentiate in development and that it does make sense to view childrens concepts in the context of theory-like structures.

Learning Progressions as Tools For Curriculum Development

Cognitively-based curricula may take into account research on students’ difficulties with a particular topic (e.g., weight and density, inertia, the role of environment in natural selection) or domain-general learning principles (e.g., the importance of revisiting basic ideas across grades). Learning progressions (LPs) integrate and enrich those approaches by organizing students’ beliefs around core ideas in that domain, giving a rich characterization of what makes students’ initial ideas profoundly different from those of scientists, and specifying how to revisit those ideas within and across grades so that young children’s ideas can be progressively elaborated on and reconceptualized toward genuine scientific understanding.

Computer-based Interactions for Conceptual Change in Science

Science learning has been characterized as the construction of conceptual structures, as the appreciation of the nature of scientific knowledge, and as participation in scientific practices. Research has primarily been carried out in each of these domains separately. There is a growing body of research that addresses the interaction between these components. In this paper we seek to add to this literature by integrating our ideas with that of other researchers to begin an initial formulation of a multifaceted framework for studying physics learning using computer-based conceptual models. In this framework we distinguish two aspects of conceptual restructuring: understanding computer models and internalizing these models as a way to construe the physical world. We argue that two different types of interaction (symmetric and asymmetric) support these different kinds of restructuring. We conclude that achieving deep changes in conceptualization requires consideration of conceptualization as a component of practice.

Looking Through the Energy Lens: A Proposed Learning Progression for Energy in Grades 3–5

This chapter presents a general framework for thinking about the goals of pre-college energy education and a detailed learning progression for Grades 3–5. This work is based on a review of existing literature on children’s understanding of energy as well as interviews and teaching interventions with elementary students. We propose that energy education focus on how scientists use what we call the “Energy Lens” to examine a broad range of phenomena in terms of energy. We identify a network of four interdependent foundational ideas that are central to a scientific understanding of energy, essential for an informed citizen, and can progressively and meaningfully evolve, with instruction, from their precursors in childhood to principles endorsed by scientists. Our proposed learning progression builds on students’ initial ideas and indicates how students’ understanding of the network of foundational energy ideas and the Energy Lens will broaden and deepen over the course of a 3-year instructional sequence from Grades 3–5. This approach shows promise to help students restructure their ideas about energy and prepare them for further instruction and learning in middle school. In pilot classroom activities, 3rd and 5th grade students began to develop language, representations, and habits of mind that enabled them to adopt a model of energy as something that manifests itself in different forms and to associate energy increases with energy decreases, paving the way to understanding energy transfer and, eventually, energy conservation.

At the Beginning Was Amount of Material: A Learning Progression for Matter for Early Elementary Grades

A learning progression for matter is a hypothesis about how knowledge about matter could evolve, with proper instruction, from young children’s ideas about objects and liquids to the atomic-molecular theory taught in high school. It involves a series of deep reconceptualizations consisting of mutually constraining changes in a large network of interrelated domain-specific, epistemological, and mathematical knowledge. Each reconceptualization results in a stepping stone—a coherent state of knowledge about matter that is conceptually closer to scientific understanding and helps students keep moving forward. Reconceptualizing matter at the macroscopic level in elementary school is crucial to understanding the atomic-molecular theory in later grades. In this chapter, we elaborate the K-2 section of a learning progression for matter; we describe how preschoolers’ knowledge about matter could be progressively reconceptualized to include concepts of material, amount of material, and weight that are compatible with a scientific theory of matter at the macroscopic level (2nd grade stepping stone). We present a classroom intervention with kindergartners based on this learning progression. Students’ significant progress (compared to a control group) supports the validity of learning progression as a theoretical construct and as an approach to science education.

REJOINDER: Response to Commentaries

In responding to the thoughtful commentaries on our article, we focus on two important issues raised by most of the reviewers: (a) the curricular dependence of the proposed learning progression and the daunting (twin) challenges of bringing about changes in curriculum and assessment and consolidating and validating the proposed learning progression, and (b) the need for further research and development of a wide variety of sorts. We agree they are major challenges but see them as opportunities as well: opportunities to use research on children’s learning to inform curriculum and assessment much more than is currently the case.