CONCEPT IMAGE OF SLOPE: UNDERSTANDING MIDDLE SCHOOL MATHEMATICS TEACHERS’ PERSPECTIVE THROUGH TASK BASED INTERVIEWS

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Hoffman, T. (2015). CONCEPT IMAGE OF SLOPE: UNDERSTANDING MIDDLE SCHOOL MATHEMATICS TEACHERS’ PERSPECTIVE THROUGH TASK BASED INTERVIEWS. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

The mathematical concept of slope has traditionally been a critical topic in the high school mathematics curriculum. However, current educational trends in the United States introduce this concept in middle school. This trend shifted the responsibility of teaching slope from high school teachers to those at the middle school level; specifically, eighth grade teachers. This qualitative study fills a void in the field of mathematics education by exploring middle school mathematics teachers’ understanding of slope. Ten middle school mathematics teachers (Grades 6-8) participated in two task-based interviews, three to five weeks apart, in which they answered questions and engaged in tasks that revolved around the mathematical concept of slope. The data was analyzed using an integrated framework of concept image and concept definition (Tall & Vinner, 1981) and eleven conceptualizations of slope (Stump, 1999; Moore-Russo, Conner & Rugg, 2010). The teachers’ concept image was defined as the total number of conceptualizations that each evoked during their problem solving. The results indicate that the middle school teachers focused heavily on the steepness of the line to define slope and evoked real-world examples when they were tasked with explaining slope. The teachers drew heavily on geometric and algebraic ratios to calculate the slope and were challenged when slope was presented in a form that diverged from procedure-based tasks. Within their concept image, the number of conceptualizations varied among the teachers with some teachers drawing on up to eight conceptualizations as they engaged with the interview tasks. The results also indicate teachers with experience teaching Algebra 1 or more advanced mathematics courses had a more robust concept image of slope. Further, teachers with a more robust concept image had greater success in explaining their thinking, as they could draw on the flexibility of their knowledge and adapt it to the task at hand.

Details
Author

Hoffman, Timothy

Title

CONCEPT IMAGE OF SLOPE: UNDERSTANDING MIDDLE SCHOOL MATHEMATICS TEACHERS’ PERSPECTIVE THROUGH TASK BASED INTERVIEWS

Physical Description

1 online resource (328 pages) : PDF

Date

2015

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

The mathematical concept of slope has traditionally been a critical topic in the high school mathematics curriculum. However, current educational trends in the United States introduce this concept in middle school. This trend shifted the responsibility of teaching slope from high school teachers to those at the middle school level; specifically, eighth grade teachers. This qualitative study fills a void in the field of mathematics education by exploring middle school mathematics teachers’ understanding of slope. Ten middle school mathematics teachers (Grades 6-8) participated in two task-based interviews, three to five weeks apart, in which they answered questions and engaged in tasks that revolved around the mathematical concept of slope. The data was analyzed using an integrated framework of concept image and concept definition (Tall & Vinner, 1981) and eleven conceptualizations of slope (Stump, 1999; Moore-Russo, Conner & Rugg, 2010). The teachers’ concept image was defined as the total number of conceptualizations that each evoked during their problem solving. The results indicate that the middle school teachers focused heavily on the steepness of the line to define slope and evoked real-world examples when they were tasked with explaining slope. The teachers drew heavily on geometric and algebraic ratios to calculate the slope and were challenged when slope was presented in a form that diverged from procedure-based tasks. Within their concept image, the number of conceptualizations varied among the teachers with some teachers drawing on up to eight conceptualizations as they engaged with the interview tasks. The results also indicate teachers with experience teaching Algebra 1 or more advanced mathematics courses had a more robust concept image of slope. Further, teachers with a more robust concept image had greater success in explaining their thinking, as they could draw on the flexibility of their knowledge and adapt it to the task at hand.

Genre

doctoral dissertations

Subjects--Topics

Mathematics--Study and teaching

Degree

Ph.D.

Keywords

Concept Definition
Concept Image
Conceptualizations
Middle School Teachers
Slope

Subject Area

Curriculum & Instruction

Advisor(s)

Fernandes, Anthony
Stephan, Michelle

Committee Members

Mraz, Maryann
Stump, Sheryl

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2015.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Hoffman_uncc_0694D_10973

Permalink

http://hdl.handle.net/20.500.13093/etd:1784