Musings on Mathematics
Posted on Tuesday, September 17, 2019
A post for Math educators!
What’s love got to do with it? Sister Cecilia Anne Wanner, O.P. offers some essential points for new math teachers and veterans alike. This post summarizes two recently published articles for further reading. Sister Cecilia Anne joined the School of Education in 2019 as Instructor of Education and is working toward her Ph.D. in Mathematics Education at Middle Tennessee State University in Murfreesboro, TN.
By Sister Cecilia Anne Wanner, O.P.
Why do math teachers do what they do?
A good math teacher must have love at the center of his or her teaching. This love must encompass both content and students: A good math teacher must love mathematics, and a good math teacher must love his or her students.
In “Because We Love” (Mathematics Teacher, May 2019, Vol. 112, Issue 7) I explore with co-authors Sarah Bleiler-Baxter and Jeremy Strayer what it means to balance love for mathematics with love for students. The article provides a concrete description of how these two aspects can be balanced, to show what a mathematics classroom can look like when love is at the heart of teaching.
Helping Pre-Service Teachers
On to some practical considerations. If two shapes have the same area, must they also have the same perimeter?
This question is included in the third grade mathematics curriculum – yet many adults themselves struggle with the relationship between area and perimeter of shapes.
One way that we can teach students—and future teachers—about the relationship between area and perimeter is through hands-on mathematical tasks involving pentominoes, which are figures constructed of five joined squares.
Here’s a pentomino with an area of 5 square units and a perimeter of 10 units:
Here’s a pentomino, again with an area of 5 square units, but a perimeter of 12 units.
In the article, “Mitigating Misconceptions of Preservice Teachers: The Relationship between Area and Perimeter” (Ohio Journal of School Mathematics, Summer 2019) I provide a series of instructional tasks, using pentominoes, that can be implemented in a classroom to help students grow in their conceptual understanding of the non-constant relationship between area and perimeter.
The article is focused toward teaching teacher candidates to better understand this concept, so that they can be more effective in teaching it to their future students, although the tasks can also be used with K-12 students.