Browsing by Author "Cai, Jinfa"

Now showing 1 - 13 of 13
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    April 9, 2007
    (2007-04) Cai, Jinfa
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    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, Jinfa
    Problem 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.
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    December 4, 2006
    (2006-12) Cai, Jinfa
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    February 5, 2007
    (2007-02) Cai, Jinfa
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    March 5, 2007
    (2007-03) Cai, Jinfa
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    May 7, 2007
    (2007-05) Cai, Jinfa
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    November 6, 2006
    (2006-11) Cai, Jinfa
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    October 9, 2006
    (2006-10) Cai, Jinfa
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    Promoting conceptual replications in educational research
    (Educational Research and Evaluation, 2022-01-31) Cai, Jinfa
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    Seeing Algebra in Arithmetic Through Mathematical Problem Posing
    (The Journal of Educational Research in Mathematics, 2022-08-31) Cai, Jinfa; Hwang, Stephen
    This 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.
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    September 18, 2006
    (2006-09) Cai, Jinfa
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    Teaching Mathematics through Problem Posing: four practices for handling students’ posed problems
    (Revemop, 2024-08-17) Ma, Yue; Cai, Jinfa
    Problem posing is both a learning goal and an effective instructional approach, but what are the details of using this approach to foster students’ learning? In this paper, we use teaching cases to demonstrate a step-by-step instructional model that teachers can use to convert non-problem-posing tasks into problem-posing ones and use the tasks to foster students’ learning. More importantly, we provide a detailed illustration of the four practices that teachers and students can use to handle students’ posed problems. The paper ends with a discussion of future work to validate and improve the model and the challenges that teachers experience teaching through problem posing. Resumen Plantear problemas es tanto un objetivo de aprendizaje como un enfoque didáctico eficaz, pero ¿cuáles son los detalles de la utilización de este enfoque para promover el aprendizaje de los alumnos? En este artículo, utilizamos casos de enseñanza para demostrar un modelo de instrucción paso a paso que los profesores pueden utilizar para convertir tareas que no son de resolución de problemas en tareas de resolución de problemas y utilizarlas para promover el aprendizaje de los alumnos. Y lo que es más importante, ofrecemos una ilustración detallada de las cuatro prácticas que profesores y alumnos pueden utilizar para tratar los problemas propuestos por los estudiantes. El artículo termina con una discusión sobre el trabajo futuro para validar y mejorar el modelo y los retos a los que se enfrentan los profesores cuando enseñan a través del planteamiento de problemas.
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    The Future of Mathematics Education Research: A Discussion Group
    (Proceedings of the 14th International Congress on Mathematical Education, 2024-06) Bakker, Arthur; Cai, Jinfa
    With help of a review study by Inglis and Foster published in Journal for Research in Mathematics Education, Jinfa Cai summarized trends in the past 50 years of mathematics education research. Next, Arthur Bakker presented a recent survey published in Educational Studies in Mathematics about the future of mathematics education research. Anna Sfard compared this survey with an earlier survey for ICMI. The presentations were discussed in the whole group, after which Jill Adler highlighted a few points she considered relevant.