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Full-Text Articles in Science and Mathematics Education
Strongly And Weakly Directed Approaches To Teaching Multiple Representation Use In Physics, Patrick B. Kohl, David Rosengrant, Noah D. Finkelstein
Strongly And Weakly Directed Approaches To Teaching Multiple Representation Use In Physics, Patrick B. Kohl, David Rosengrant, Noah D. Finkelstein
David Rosengrant
Good use of multiple representations is considered key to learning physics, and so there is considerable motivation both to learn how students use multiple representations when solving problems and to learn how best to teach problem solving using multiple representations. In this study of two large-lecture algebra-based physics courses at the University of Colorado (CU) and Rutgers, the State University of New Jersey, we address both issues. Students in each of the two courses solved five common electrostatics problems of varying difficulty, and we examine their solutions to clarify the relationship between multiple representation use and performance on problems involving …
Riding The Mathematical Merry-Go-Round To Foster Conceptual Understanding Of Angle, Ron Tzur, Matthew Clark
Riding The Mathematical Merry-Go-Round To Foster Conceptual Understanding Of Angle, Ron Tzur, Matthew Clark
Ron Tzur
This article presents playful activities for fostering students' conceptual understanding of angle--a root concept in mathematics--that revolve around the Mathematical Merry-Go-Round game. The authors focus on activities for two reasons. On one hand, NCTM's Principles and Standards for School Mathematics (2000) stresses the central role of student activity in coming to understand mathematics. This emphasis is consistent with a constructivist stance (Piaget 1971) about learning as an active process. On the other hand, typical activities used for teaching angle, in which an introduction of the definition is followed by operations on angles, such as measuring, adding, comparing, and classifying, seem …
Fine Grain Assessment Of Students' Mathematical Understanding: Participatory And Anticipatory Stages In Learning A New Mathematical Conception, Ron Tzur
Ron Tzur
This study addressed a twofold problem--the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinction contributes to fine grain assessment of students' mathematical understandings. As a context for the study served the difficult-to-grasp concept of "inverse" order relationship among unit fractions, that is, the larger the number of parts the smaller the size of each part (e.g., 1/7 greater than 1/10 although 10 greater than 7). I conducted this study as a whole-class teaching experiment in a third grade classroom at a public school in Israel. The qualitative …
From Theory To Practice: Explaining Successful And Unsuccessful Teaching Activities (Case Of Fractions), Ron Tzur
Ron Tzur
In a teaching experiment, I examined a theoretical model of mathematics teaching and learning in practice. In this paper I focus on how the model can guide the teacher's thinking about students' understandings and the generation of activities that foster intended transformations in those understandings. As a research-teacher I taught, twice a week for four months, basic ideas of fractions to 28 third graders, in a public school in Israel. The analysis of both classroom data and researcher's documented reflections indicates how the model can empower the generation and explanation of successful teaching activities, as well as thinking about and …