Content Analysis of Student Learning For most people who have ridden the roller coaster of primary education, subtracting twenty-three from seventy is a no-brainer. In fact, we probably solve it so quickly in our heads that we don't consciously recognize the procedures we're using to solve the problem. For us, subtraction seems like something that is ingrained in our thinking from the first day of elementary school. It's no surprise that at one point numbers, subtraction, and "carrying" were new to us, just like everything we know today. For Gretchen, a first-grader trying to solve 70-23, subtraction seems like a no-brainer as she verbalizes her confusion, getting different answers using different methods. After watching Gretchen search for a final solution and find herself uncertain, we can gain a much deeper understanding of how the concept of subtraction develops and the discrepancies that can arise when a child searches for what is correct and what is not. After Gretchen posed the problem, she tackles it with her first method: the standard algorithm. To begin, set up the problem by writing "70" and "- 23" directly below, ending with a line below. This configuration indicates several things about Gretchen's basic mathematical understanding. First, demonstrate that you understand the connection between the words and symbols actually written for each number. Also, since she writes “70,” Gretchen probably knows the numbers up to ninety-nine. Finally, the arrangement of the numbers indicates that he is aware that the minus is a symbol for "take away" and that the second number must be placed below the first. While working out the problem and on... half of the paper... relationship in a problem that does not appear in the others. In all of this, there's such a breadth in how one person might approach a problem versus another, and that's great. The main understanding that seems essential here is how everything is related. Mathematics is about the relationships between numbers, methods and models and how they all work in different ways to ideally arrive at the same solution. ReferencesIMAP, Gretchen, 2nd grade interviewVan de Walle, J., , F., Karp, KS, & Bay -Williams, J.M. (2010). Mathematics for elementary and middle schools, developmental teaching. (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). Mathematics for elementary and middle schools, developmental teaching. (Seventh ed.). New York, New York: Allyn and Bacon.