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Teaching Dilemmas: Understanding the Concept of "Slope" Through Graphs and Storytelling Denise Wilkinson

NCTM’s Principles to Actions: Ensuring Mathematical Success for All stresses the im- portance of teaching mathematical topics to stu- dents in relatable ways that help clarify concepts and promote mathematical reasoning through stu- dent engagement and collaboration (NTCM, 2014.) Mathematics teachers additionally recognize the value of incorporating real world problems or prob- lems that are experientially real and familiar to students into our algebra classes to enhance the learning process ( Gravemeijer, 1999). I have strug- gled with recognizing whether or not students truly understand mathematical concepts through the introduction to a topic, examples and problems. By connecting the concepts to relatable and applicable examples as supported by these views, I have found that students tend to gain a stronger and deeper understanding and have a better chance of retaining that understanding. A specific algebra topic that my students have found conceptually challenging is slope as a rate of change. When teaching this topic using more traditional teaching practices, I have found that students are often able to memorize the formu- la to find the slope of a line by calculating the change in “Y” divided by the change in “X.” Addi- tionally, they seem to understand that the formula represents “Rise over Run.” I have also observed that students appear to recognize that slope tells us the steepness of a line. However, many students seem to have difficulty wrapping their brains around the concept of the slope as the rate of change of two measurements in an application- based problem. A while back, I became inspired by a series of examples in an algebra workbook that included graphs that told stories (The Consortium for Foundation Mathematics, 2012). In hopes of achieving success with a new teaching approach, I reflected on the “story” concept and implemented a “Stories and Slopes” group work activity in my

algebra class on the day that I first introduce the topic of slope. The activity presents a relatable example of a student, named Joe, who is travelling from his dorm room to his math class. Students are instructed to find the rate of the change of the dis- tance Joe travelled (feet) over the change in time lapsed (minutes) during each leg of Joe’s journey from his dorm room to his math class. Joe’s jour- ney is presented as a graph of various connected line segments in the first quadrant of a coordinate system. The graph is shown below.

I organize the students into groups of three and give each group a copy of the graph. Students are initially asked to discuss their interpretation of the graph and the meaning of the line segments on the graph. This introduction provides me with a base line of comprehension. Students tend to un- derstand that the graph is a relationship between distance and time and that, in some context, Joe is travelling from his dorm room to his math class. However, when interpreting the meaning of the line

Virginia Mathematics Teacher vol. 44, no. 1

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