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Open access publications by faculty, postdocs, and graduate students in the Department of Mathematical Sciences
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Browsing Open Access Publications by Author "Cai, Jinfa"
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Item Beyond computation: Assessing in-service mathematics teachers’ conceptual understanding of fraction division through problem posing(Asian Journal for Mathematics Education, 2023-12-15) Yao, Yiling; Jia, Suijun; Cai, JinfaProblem posing has long been recognized as a critically important teaching method and goal in the area of mathematics education. However, few studies have used problem posing to assess in-service teachers’ mathematical understanding. The present study investigated in-service teachers’ mathematical understanding of fraction division, which is often considered challenging content in elementary school, from three angles: computation, drawing, and problem posing. Two studies involving 66 and 193 primary and middle school teachers were conducted to reveal the in-service teachers’ mathematical understanding and whether drawing and problem posing affected each other. Although the in-service teachers rarely had the opportunity to pose mathematical problems in their daily teaching, they were able to pose mathematical problems in this study. In addition, problem-posing tasks were more useful in diagnosing the in-service teachers’ conceptual understanding than were computation or drawing. Thus, problem posing seems to have contributed to their conceptual understanding of fraction division on the drawing task.Item Promoting conceptual replications in educational research(Educational Research and Evaluation, 2022-01-31) Cai, JinfaItem Seeing Algebra in Arithmetic Through Mathematical Problem Posing(The Journal of Educational Research in Mathematics, 2022-08-31) Cai, Jinfa; Hwang, StephenThis paper proceeds from the position that elementary- and middle-school students can learn and should be exposed to algebraic ideas and that a fruitful mechanism for this is to help them to see the algebra in arithmetic. After a brief survey of the literature on helping students see algebra in arithmetic, the main focus of the paper is on the use of mathematical problem posing in the classroom to help students see the algebra in arithmetic. To illustrate this, we present three cases of teaching mathematics through problem posing and discuss the perspectives they offer on developing students’ algebraic thinking. The paper concludes with an examination of how teachers might be supported in using problem posing to help their students see the algebra in arithmetic.