Area of a Changing Triangle: Piecing It Together

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Blake Peterson recently published an article titled “Area of a Changing Triangle: Piecing It Together” in the Mathematics Teacher: Teaching and Learning PK-12. Blake has answered a few questions about this article below: 

Who would you say is the target audience for this article?

High school teachers

What is the big problem you hoped to address with this article?

Piecewise functions are usually taught in a very abstract way and void of context. I saw this problem in Japan and was fascinated to see a context for piecewise functions and even more interesting was that some of the pieces were not linear. I think the context can make piecewise functions more accessible for students.

What are some of the key ideas in the article?

With some careful scaffolding and board organization, students can make some great connections about equations, graphs and function behavior without the teacher having to tell them what connections to make. However, if the problem shared in this paper is given to students without some scaffolding and good board organization, they can be overwhelmed.

What are some of the main ideas you hope your audience will take from this article?

As mathematics teachers we typically have been successful in learning to generate equations by just looking at tables of data. However, such abstract thinking is very difficult for many students. Thus connecting the behavior of a function to some kind of geometric situation makes writing the equations for these functions more accessible to students. I think the problem shared in this article along with some careful scaffolding will put more students in a position to generate equations by connecting the geometric quantities to values in the equation.