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doi:10.7282/t3-8jgz-rg05

This analytic shows the different mathematics understanding of 4th grade students. They stated different arguments about what rod would have the number name one half when the blue rod is called one. There are some different assumptions and structures of the students’ arguments that offer different forms of reasoning. Their arguments contain very important elements, which students have to practice. According to several publications, argumentation is an important mathematical practice for the K-12 mathematics classroom. (NCTM 1991; CCSS, 2010). Understanding students’ argumentation is important for teachers because argumentation is evident in many disciplines (See, for example, Douek, 1999 for examples of argumentation in science). According to Conner et al. (2014), argumentation has a common usage that means persuasion (convincing), negotiation, and disagreement. Students need to use clear mathematics language to communicate their reasoning. This is a process that can best represent students’ mathematical understanding. So an important component of teacher knowledge is understanding and recognizing student mathematical argumentation. Van Ness (2017) suggests the creation and use of VMCAnalytics for preservice teachers’ studying of argumentation.
Cuisenaire rod was support tool to help students build models and refer to components of the model in order to express their reasoning. In the discussion, David first proposed that when the blue rod is called 1, no rod could be called one half. But Erik countered this and suggested another definition of half, which is that two halves can be different lengths. Then Jessica, David, Andrew and Alan came up with a retort to Erik’s suggestion; they claim that the two halves must be equal in length. Andrew revealed the contradictions in Erik’s argument that he should get a quarter rather than half. Finally, David offered another reason to justify his solution, grouping rods according to odd and even number names.

References:
Common Core State Standards Initiative. (2010). National Governors Association Center for Best Practices and Council of Chief State School Officers. Retrieved from http://www.corestandards.org/.

Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16(3), 181-200.

Douek, N. (1999). Argumentation and conceptualization in context: a case study on sunshadows in primary school. Educational Studies in Mathematics, 39(1-3), 89-110.

National Council of Teachers of Mathematics. Commission on Teaching Standards for School Mathematics. (1991). Professional standards for teaching mathematics. National Council of Teachers of Mathematics.

Van Ness, C. K. (2017). Creating and Using VMCAnalytics for Preservice Teachers’ Studying of Argumentation. Retrieved from https://doi.org/doi:10.7282/T34X5B7T

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