Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Abstract

Middle-school students are expected to understand key components of graphs, such as slope and y-intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and y-intercept. Sixth-graders' responses prior to formal instruction in graphing reveal their intuitions about slope and y-intercept, and seventh-and eighth-graders' performance indicates how instruction shapes understanding. Students' performance in graphing slope and y-intercept from verbally presented linear functions was assessed both for graphs with quantitative features and graphs with qualitative features. Students had more difficulty graphing y-intercept than slope, particularly in graphs with qualitative features. Errors also differed between contexts. The findings suggest that it would be valuable for additional instructional time to be devoted to y-intercept and to qualitative contexts.

Measuring Graph Comprehension, Critique, and Construction in Science

“…Plotting values from a table is unlikely to demonstrate students' scientific understanding. Rather, Hattikudur et al (2012) recommend the use of qualitative graphs that allow students to depict general relationships without specifying all numerical values. By allowing students to depict qualitative relationships, graph construction can be used to evaluate integration of graph and science knowledge from a different perspective than graph comprehension.…”

Linear Functions and Slope: How Do Students Understand These Concepts and How Does Reasoning Support Their Understanding?/Linearne funkcije i nagib pravca: kako učenici shvaćaju te pojmove i kako razmišljanje djeluje na njihovo razumijevanje?

“…This result is consistent with the finding reported by Birgin (2006). In short, as suggested by evidence (Barr, 1981;Hattikudur, Prather, Asquith, Alibali, Knuth, & Nathan, 2012;Lobato & Siebert, 2002;Lobato & Thanheiser, 2002;Planinic et al, 2012;Stump, 2001b;Teuscher & Reys, 2010), some of the students in our study were not aware of the constancy of the slope on any point in a line and the equality of the constant rate between the slope's vertical and horizontal lengths, and they were misguided by the idea that "as points change on the axis, different lines will occur and, therefore, the slopes of the lines will also change". Nevertheless, we also observed in our study that those students who were aware of the relationship between the slope and rate of change were able to make the necessary confirmations, and they supported their confirmations by using multiple representations in this process.…”

Taking advantage of automated assessment of student‐constructed graphs in science

“…While graph construction activities can be designed to address conceptual knowledge (Hattikudur et al, ), most research studies that incorporate graph construction focus on procedural aspects of plotting points from given data (Berg & Smith, 1994; Clement, ; Kerslake, ; Wavering, ; Yerushalmy & Schwartz, 1993) or feature simple constructions with limited features (Mevarech & Kramarski, 1997; Ploetzner, Lippitsch, Galmbacher, Heuer, & Scherrer, ). Although a number of studies leverage technology during instruction to focus students on complex features of graphs representing scientific content (e.g., Jackson, Edwards, & Berger, ), the role of automation on science graph assessment has not been featured in prior literature.…”

“…For assessment purposes, these errors provide greater insight into student thinking. As such, Hattikudur et al () suggest that students construct qualitative graphs, which depict specified relationships with limited (or no) reference to specific numerical values. For example, Linn and Hsi () asked students to construct cooling curves given initial and final temperatures, while Hattikudur et al () asked students to draw graphs depicting the relationship between items sold and dollars earned in alternative narratives.…”

“…As such, Hattikudur et al () suggest that students construct qualitative graphs, which depict specified relationships with limited (or no) reference to specific numerical values. For example, Linn and Hsi () asked students to construct cooling curves given initial and final temperatures, while Hattikudur et al () asked students to draw graphs depicting the relationship between items sold and dollars earned in alternative narratives. Although correct responses to qualitative construction items may differ in terms of specific values, general spatial features or patterns will be consistent (Nemirovsky & Rubin, 1991; Noble & Nemirovsky, 1995; Stylianou, Smith, & Kaput, ), thereby permitting reliable evaluation.…”