The Basics Interview Analysis

EDC 365C - Understanding “The Basics” Interview

On a cold Sunday morning, I conducted a short clinical interview with my friend Matt who enthusiastically agreed to be my test subject. Matt is a third-year advertising major here at UT-Austin. Because he is enrolled in the Moody College of Communication, he has only taken basic science and mathematics classes for non-majors. The last math class he took was Calculus 408L (integral calculus) during his first year of college. I chose to give him the question that divides a fraction by a fraction (1/5 divided by 2/3) because I personally had a hard time justifying why dividing by a fraction meant multiplying by the reciprocal. Therefore I wanted to see how someone with a different mathematics
Knowing that I probably had to end the interview soon, I concluded with an open-ended question – “How do you think your elementary school teachers could have taught the concept better?” Without hesitation, he replied “it would help a lot if they explained the actual conceptual reasoning behind the math rather than just teaching us the formula for dividing by a fraction.” I then thanked him for his time and ended the clinical
However, when he tried to get behind the reasoning of dividing by a fraction, he was increasingly lost. If he was asked to show another person how to answer the question, he would have no problem since he knows the rule by heart. However, if he was asked to explain why the rule works, then he would probably have a much harder time. This shows that Matt is reliant on procedure rather than understanding in this situation. Because I’m taking Knowing & Learning, I question what balance there lies between procedural knowledge of mathematics and actually knowing and understanding the background. I recognize that understanding concepts are essential to knowing but different situations require different practicalities. For example, in the real world, knowledge of the quadratic formula is essential for most math classes and many engineering jobs. However, knowing the reasoning and proof behind the quadratic formula isn’t very applicable to many situations. Furthermore, especially in mathematics, proofs (which stress conceptual understanding) are difficult to derive – some seemingly easy formulas require high -level physics knowledge. Before conducting this interview, I believed that “knowing mathematics” meant that a person understands everything conceptually “behind the scenes.” However, I realize that not a lot of people can achieve this knowledge and that time could be better spent on knowing