Content Analysis of Student Learning

Content Analysis of Student Learning

For most people who have ridden the roller coaster of primary education, subtracting twenty-three from seventy is a piece of cake. In fact, we probably work it out so quickly in our heads that we don’t consciously recognize the procedures that we are using to solve the problem. For us, subtraction seems like something that has been ingrained in our thinking since the first day of elementary school. Not surprisingly, numbers and subtraction and “carry over” were new to us at some point, just like everything else that we know today. For Gretchen, a first-grader trying to solve 70-23, subtraction doesn’t seem like a piece of cake as she verbalizes her confusion, getting different answers using different methods. After watching Gretchen pry for a final solution and coming up uncertain, we can gain a much deeper understanding for how the concept of subtraction first develops and the discrepancies that can arise as a child searches for what is correct way and what is not.

After Gretchen is given the problem, she approaches it with her first method: the standard algorithm. To start off, she sets up the problem by writing out “70” and writing “- 23” directly below it, finishing out with a line underneath. This setup indicates several things about Gretchen’s basic mathematical understanding. First, it shows that she understands a connection between the words and the actual written symbols for each number. Also, since she writes “70,” Gretchen probably has knowledge of numbers up to ninety-nine. Last, her arrangement of the numbers indicates that she has knowledge of the minus being a symbol for “take away” and the second number be placed underneath the first. As she works the problem and su...

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... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.

References

IMAP, Gretchen, 2nd grade interview

Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.

References

IMAP, Gretchen, 2nd grade interview

Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.