On students' understanding of volumes of solids of revolution: An APOS analysis |
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Institution: | 1. Department of Mathematics Education, Faculty of Mathematics and Physics, Charles University, Czech Republic;2. University of Puerto Rico at Mayagüez, Mayagüez, PR, USA |
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Abstract: | We apply Action-Process-Object-Schema theory (APOS) to (1) examine the textbook used by students in the study to infer mental constructions the book proposes that students could do to understand solids of revolution, (2) use semi-structured interviews with nine students to find out which of the textbook’s proposed constructions students actually do, and what unconjectured or unexpected constructions students do, and (3) use the results of the interviews and the research literature to inform and set forth an alternative proposal for constructing volumes of revolution. Results suggest that many students have not constructed processes to visualize solids of revolution and to relate Riemann sums to the corresponding definite integrals. Implications for curriculum and instruction are discussed. |
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Keywords: | Volumes of solids of revolution Riemann sums Visualization APOS Textbook Integral |
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