What I’ve Learned About Math Operations

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As a student, I always enjoyed math. In high school I took all math classes offered, including Calculus. The first math class I took in college was a breeze, and I thought that this one would be no different. What could I learn about elementary school math that I didn’t already know? The first day of class showed me what a ridiculous question that was and I went on to learn things about math that had never before been brought to my attention. This paper will discuss what I’ve learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.

Cardinality and Subitizing

Cardinality and subitizing are not topics encountered in everyday life, unless you happen to be a math education specialist. Both were labels I had not heard before for concepts that hadn’t previously occurred to me. They were the beginning of my math vocabulary—an important asset when expected to talk freely about math. Van de Walle, Karp, and Bay-Williams explain that understanding the concept of cardinality means knowing that “the last count word indicates the amount of the set” (p. 127). Those who understand this concept—that the last number counted has value—“are said to have the cardinality principle” (Van de Walle, et. al, 2010, p. 127). The concept of cardinality initially perplexed me—I took for granted that counting had meaning. However, putting a name to the concept helped to solidify my understanding of numbers and provided me with a vital piece of vocabulary when discussing mathematics. The same was true for subitizing. Clements describes subitizing as “the direct perceptual apprehension of the numberosity of a group” or “instantly seeing how many” (1999, p. 400). I ...

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...nship between addition. The difference between kindergarten and fifth grade is only the numbers within which these computations should be done.

Works Cited

Van De Walle, J. A., Karp, K.S., Bay-Williams, J.M., (2010). Elementary and Middle School Mathematics. Boston: Allyn & Bacon.

Smith, S. S., & Stein, M. K., (1998). Selecting and Creating Mathematical Tasks: From Research to Practice. Mathematics Teaching in the Middle School, 3(4), 268-275.

Battista, Michael T., (1999, February). The Mathematical Miseducation of America’s Youth: Ignoring Research and Scientific Study in Education. Phi Delta Kappan.

Clements, D. H., (1999, March). Subitizing: What Is It? Why Teach It?. Teaching Children Mathematics.

Taylor, A. R., Breck, S. E., Aljets, C. M., (2004, October). What Nathan Teaches Us about Transitional Thinking. Teaching Children Mathematics.

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