What is the Purpose of Mathematics?

        In this article in Mathematics Teacher: Learning & Teaching PK-12, Lucy Watson (Belmont University) and Christopher Bonnesen and Jeremy Strayer (Middle Tennessee State University) describe a common dilemma for math teachers: what do you say when students ask, Why do I need to know that? Some teachers point to practical, real-life applications in science, technology, engineering, and math education. Others extoll the beauty and wonder of mathematics. What teachers say might reveal one of three views of the nature of mathematics: 

        - It’s a set of facts, rules, and tools that need to be memorized; 

        - It’s a static body of knowledge bound by discovered truths that never change; 

        - It’s a dynamic, problem-driven discipline defined by creativity, inquiry, and openness to revision. Students taught by a teacher holding each view will learn mathematics quite differently, and will likely be exposed to distinct teaching methods, from rote lectures to discussions and hands-on projects.          

        Watson, Bonnesen, and Strayer believe there hasn’t been enough guidance for math teachers on exactly what the nature of mathematics is, leaving the field wide open to a variety of rationales – and probably some pretty dull teaching. Drawing on several guiding documents in the field, the authors suggest this five-point view of the nature of mathematics: 

        • Mathematics is a product of the exploration of structure and patterns. 

        • Mathematics uses multiple strategies and multiple representations to make claims. 

        • Mathematics is critiqued and verified by people within particular cultures through justification or             proof that is communicated to oneself and others. 

        • Mathematics is refined over time as cultures interact and change. 

        • Mathematics is worthwhile, beautiful, often useful, and can be produced by each and every                         person. 

         The authors believe that as students grapple with high-quality math problems, teachers should get them thinking about this broader view of the nature of mathematics, asking students about purpose before, during, and after solving the problems. Watson, Bonnesen, and Strayer suggest repeating this meaning-seeking activity at intervals through the grades – perhaps with a unit on counting in kindergarten, equivalent fractions in third grade, area relationships in middle school, and absolute value in high school. If this occurs, say the authors, teachers will less frequently hear the question, Why do I need to know that? 

 “The Nature of Mathematics: Let’s Talk About It” by Lucy Watson, Christopher Bonnesen, and Jeremy Strayer in Mathematics Teacher: Learning & Teaching PK-12, May 2021 (Vol. 114, #5, pp. 552-561); the authors can be reached at Lucy.watson@belmont.edu, ctb4d@mtmail.mtsu.edu, and jeremy.strayer@mtsu.edu.

Please Note: This summary is reprinted with permission from issue #888 of The Marshall Memo, an excellent resource for educators.