Learning to See: Making Sense of the Mathematics of Change in Middle School

Noble, Tracy; Nemirovsky, Ricardo; DiMattia, Cara; Wright, Tracey

doi:10.1023/b:ijco.0000040891.50250.7e

Cited by 20 publications

(16 citation statements)

References 23 publications

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“…Such an interest can also be found in the growing body of research that investigates students' practical work with graphical representations in science and mathematics education (e.g., Cobb, Yackel, & McClain, 2000;Greeno & Goldman, 1998;Lampert & Blunk, 1998;Nemirovsky, Tierney, & Wright, 1998;Noble, Nemirovsky, Dimattia, & Wright, 2004;Roschelle, 1998;Roth & McGinn, 1997;Roth & Middleton, 2006;Roth, Tobin, & Shaw, 1997). These investigations-which focus on the practices of symbolizing rather than symbols, and graphing rather than graphs-address the social, interactional, and material contexts of, for instance, graphs, and consider their use as an integral part of how mathematics and science education is carried out.…”

Section: Disciplined Perceptionmentioning

confidence: 99%

The Dark Matter of Lab Work: Illuminating the Negotiation of Disciplined Perception in Mechanics

Lindwall

Lymer

2008

Journal of the Learning Sciences

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This study examines the practical work of a pair of students and an instructor using probeware in a mechanics lab. The aim of the study is to describe and discuss a type of interactional sequence that we refer to as dark matter, the ordinary backdrop to the extraordinary sequences that are easily recognizable as clear-cut instances of learning. Although this work is downplayed in the research literature, describing it is critical to properly understanding lab work as an educational practice. With a focus on the negotiation of disciplined perception, we analyze a number of episodes wherein a pair of students and an instructor struggle with the construction and interpretation of a graph depicting a linear relationship between force and acceleration. We demonstrate an intimate interplay between how the students display their problems and understandings and how the instructor tries to make the subject matter content visible and thus learnable. The analyzed episodes are illuminating with regard to the analytical notion of disciplined perception as applied to graph interpretation; the cognitive and practical competencies involved in producing, recognizing, and understanding graphs in mechanics; and the interactive work by which these competencies are made into objects of learning and instruction.This study examines the practical work of two students and an instructor occupied with a mechanics lab assignment. Taking an analytical perspective founded on ethnomethodology (Garfinkel, 1967(Garfinkel, , 2002Livingston, 1986) and conversation analysis (e.g., Sacks, 1992;Schegloff, 2007), this study describes and discusses a type of interactional sequence that we refer to as dark matter. In a discussion of the difference between the findings of conversation analysis and those of classical so-

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Section: Disciplined Perceptionmentioning

confidence: 99%

The Dark Matter of Lab Work: Illuminating the Negotiation of Disciplined Perception in Mechanics

Lindwall

Lymer

2008

Journal of the Learning Sciences

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“…An understanding of graphing, however, involves not only interpretation and translation but also construction. Although technological advances such as graphing calculators and computer programs promote exploration and understanding of functions (e.g., Ainley, Nardi, & Pratt, 2000; Botzer & Yerushalmy, 2008; Hennessy, Fung, & Scanlon, 2001; Kieran, 2001; Levert, 2003; Nicolaou, Nicolaidou, & Zacharia, 2007; Noble, Nemirovsky, Dimattia, & Wright, 2004; Schwartz & Hershkowitz, 1999), they do not always help students gain a full understanding of function (Schoenfeld, Smith, & Arcavi, 1993).…”

mentioning

confidence: 99%

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

Hattikudur

Prather

Asquith

et al. 2012

School Sci & Mathematics

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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.

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“…Students also learn to use mathematical equations and other representations as tools for problem solving (Confrey & Smith, 1991;Presmeg, 1986;Zazkis, Dubinsky, & Dautermann, 1996). As new technologies make increasingly complex mathematical tools of all kinds available to students, they allow students opportunities to experience mathematics in new ways (Kaput, 1998;Noble, Nemirovsky, DiMattia, & Wright, 2004;Noss, Healy, & Hoyles, 1997). In this article, we explore the relationship between developing fluency with tools in the mathematics classroom and learning mathematics, with the goal of better understanding how mathematical tools contribute to mathematics learning.…”

Section: Boston Public Schoolsmentioning

confidence: 99%