Students’ Application of Concavity and Inflection Points to Real-world Contexts

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In mathematics education, much of what is taught connects to the outside world. However, there are often disconnects between how students learn math in math courses and how they use or apply that math in the real world or in science courses. Past research has shown that this is especially true of calculus content. Dr. Steven Jones chose to study this disconnect from application to other fields by examining the calculus concepts of concavity and inflection points and how they are reasoned qualitatively and quantitatively by students.

Dr. Jones conducted his research by giving students currently enrolled in calculus courses particular tasks which dealt with these concepts. Some tasks were ones that would be typically seen in their calculus classes and others dealt with examining these concepts in real world contexts. Dr. Jones found this exercise to be important, as “science and engineering instructors often assume students already know how to do these types of tasks from having taken calculus. Instructors [in either of the fields] might not realize that we are asking students to make the same types of jumps going from calculus to science/engineering that I’m asking them to do in these interviews.” 

From this study, Dr. Jones was able to understand the importance of both qualitative and quantitative meaning in fully understanding concepts like these. He also gathered that “there is a gap in how [these concepts are] typically presented and understood in math classes versus how they might be used in science/engineering classes. This study helps us understand that disconnect better in a way that could help bring coherence across the math/science divide.”

Dr. Jones suggests that students can apply his findings by regularly and proactively asking about the quantitative meanings of concepts in class to improve their overall understanding. In doing so, the gap in understanding begins to shrink.