Nurturing Structural Thinking through Teacher-Facilitated Problem Solving

Authors

  • Xiangquan [James] Yao Pennsylvania State University

Keywords:

Problem solving, rich tasks, structural thinking

Abstract

One essential goal of mathematics teaching is to develop the habit of mind and the ability to look for and recognize structures, to probe into and act upon structures, and to reason and justify in terms of general structures. Framed by the five practices for orchestrating productive mathematics discussions (Smith & Stein, 2011), this paper uses the Horse Rider problem as an example to illustrate how teachers can nurture student structural thinking through careful sequencing of mathematical tasks. 

Author Biography

Xiangquan [James] Yao, Pennsylvania State University

Dr. Xiangquan [James] Yao is an Assistant Professor of Education within the Department of Curriculum and Instruction at Pennsylvania State University. His research interest considers the nature of mathematics thinking with technology and mathematics understandings for teaching with technology. Dr. Yao’s current work focuses on learners’ engagement in mathematical generalizing when using technological tools that are capable of performing mathematical procedures.

References

Bass, H. (2017). Designing opportunities to learn mathematics theory-building practices. Educational Studies in Mathematics, 95(3), 229-244. https://doi.org/10.1007/s10649-016-9747-y

Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10-32. https://doi.org/10.1007/BF03217543

Mason, J. (2003). On the structure of attention in the learning of mathematics. Australian Mathematics Teacher, The, 59(4), 17-25.

National Governors Association Center for Best Practices (NGA Center) and Council of Chief State School Officers (CCSSO). 2010. Common Core State Standards for Mathematics. Washington, DC: NGA Center and CCSSO.

Smith, M. & Stein, M. (2011). Five practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.

Usiskin, Z. (1968). Six nontrivial equivalent problems. The Mathematics Teacher, 61(4), 388-390. https://www.jstor.org/stable/27957852

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Published

2023-02-20

How to Cite

Yao, X. (2023). Nurturing Structural Thinking through Teacher-Facilitated Problem Solving . hio ournal of chool athematics, 93(1), 27–33. etrieved from http://voyager.janeway.systems:9999/index.php/OJSM/article/view/9333

Issue

Vol. 93: Spring 2023

Section

Articles

License

By submitting this agreement, the author hereby grants to The Ohio State University, on behalf of its University Libraries