Prospective Secondary Mathematics Teachers' Understanding and Cognitive Difficulties in Making Connections among Representations

Moon K.; Brenner M.E.; Jacob B.; Okamoto Y.

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Prospective Secondary Mathematics Teachers' Understanding and Cognitive Difficulties in Making Connections among Representations

机译：未来中学数学教师在表征之间建立联系的理解和认知困难

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This study investigates prospective secondary teachers' cognitive difficulties and mathematical ideas involved in making connections among representations. We implemented a three-week teaching unit to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to formulating connections among representations, in the context of conic curves. Qualitative analysis of data showed that most undergraduate mathematics majors and minors in this study struggled with variation, the Cartesian Connection, and other affiliated ideas such as graph as a locus of points. Furthermore, they were unable to identify basic metric relations encoded in algebraic expressions such as the distance between points, which further compounded their difficulties in making connections among representations. We argue that mathematics teacher education needs more focus on these ideas so that their graduates can successfully teach these big ideas in their future instruction.

机译：本研究调查了未来中学教师在表征之间建立联系所涉及的认知困难和数学思想。我们实施了为期三周的教学单元，以帮助未来的中学数学教师在圆锥曲线的背景下，理解对于构想表示之间的联系至关重要的重要思想。数据的定性分析表明，本研究中大多数本科数学专业和未成年人都在与变异，笛卡尔连接和其他附属概念（例如图形作为点的位置）作斗争。此外，他们无法识别代数表达式中编码的基本度量关系，例如点之间的距离，这进一步加剧了他们在表示之间建立联系的困难。我们认为，数学老师的教育需要更多地关注这些思想，以便他们的毕业生能够在未来的教学中成功地教授这些重要思想。

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《Mathematical thinking and learning》 |2013年第3期|共27页
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Moon K.; Brenner M.E.; Jacob B.; Okamoto Y.;
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Prospective Secondary; Mathematics Teachers'; Cognitive Difficulties;

机译：中学;数学教师;认知困难;

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1. Prospective Secondary Mathematics Teachers' Understanding and Cognitive Difficulties in Making Connections among Representations [J] . Moon K., Brenner M.E., Jacob B., Mathematical thinking and learning . 2013,第3期

机译：未来中学数学教师在表征之间建立联系的理解和认知困难
2. Prospective and current secondary mathematics teachers' criteria for evaluating mathematical cognitive technologies [J] . Ryan C. Smith, Dongjo Shin, Somin Kim International Journal of Mathematical Education in Science and Technology . 2017,第5a6期

机译：未来和当前中学数学教师评估数学认知技术的标准
3. Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-Nspire in Scottish secondary schools [J] . Allan Graham Duncan ZDM . 2010,第7期

机译：苏格兰中学对教师使用TI-Nspire动态链接多种表示形式，教学实践和学生对数学的理解的观点
4. Lecture Design for Strengthening Concepts Understanding of School Mathematics for Prospective Teachers [C] . Zainal Abidin, Kurnia Noviartati International Conference on Progressive Education . 2019

机译：加强概念对潜在教师学校数学理解的讲义设计
5. Understanding of function, proof and mathematical modelling in the presence of mathematical computing tools: Prospective secondary school mathematics teachers and their strategies and connections. [D] . Zbiek, Rose Mary. 1992

机译：在使用数学计算工具的情况下了解功能，证明和数学建模：中学数学教师及其策略和联系。
6. Investigating the Associations of Constructivist Beliefs and Classroom Climate on Teachers Self-Efficacy Among Australian Secondary Mathematics Teachers [O] . Fang Guangbao, Teo Timothy 2021

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Prospective Secondary Mathematics Teachers' Understanding and Cognitive Difficulties in Making Connections among Representations

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