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How to Keep Students from Falling Off the Slope

Dawn D. Hakkenberg & Diana Fisher

and she asks her students to explain what the sign represents. In addition, she discusses the units of measure, their placement in the slope ratio, and the significance of this information (Teuscher and Reys, 2010). In the first two activities, equations are used to describe how a function behaves over time, within the context. The last activity uses line ar regression to give the students the opportunity to see how the past behavior of a function can be used to predict future behavior. Samples of her stu dents ’ work are shown below. Algebra students learn more deeply when they are actively engaged in problem solving activities through predicting, investigating, and drawing con clusions. In this way, they “ see and touch ” the math. In addition, group activities support students ’ development of mathematical language as they dis cuss their ideas and solutions with each other (Wolbert, 2017). For Ms. Hakkenberg, this repre sented a shift toward student - centered learning, which is preferred to traditional learning and pro vide students with the opportunity to develop their intuitive insights, which in turns helps them devel op a firm mathematical foundation (Kaput, 2018).

Introduction

The purpose of this paper is to introduce readers to a set of three hands - on, technology - based Algebra activities that use multiple representations that fo cus on slope - based mathematical content. The au thors used the Online Desmos Graphing calculator to provide students with a visual representation of function behavior over time. In addition, they pro vided repeated experiences with multiple represen tations for linear functions in a real - world context. The first activity provides an introduction to Vir ginia SOL A.7 (Virginia Department of Education, 2017) material using a real - world problem provid ed by Dan Meyer ’ s Water Tank task (Meyer, 2011). The students explore four ways the linear function can be represented. In the second activity, the students ’ focus is on A.6 concepts as they use walking patterns and a motion detector to create various distance vs. time graphs. In the third activ ity, the students toss a ball, make a people vs. time table, find a line of best fit and make predictions for outputs with given inputs, SOL A.9. Through out these three activities, the teacher (Ms. Hakken berg) frequently asks about the sign of the slope

Virginia Mathematics Teacher vol. 46, no. 2

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