Full metadata
Title
Investigating Student's Systems of Thinking Regarding Graphs of Continuous Functions in Coordinate Planes
Description
Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair of quantities vary. Previous research has shown that different students interpret calculus statements differently depending on their meanings of points in the coordinate plane. As a result, students' widely differing interpretations of graphs presented to them. Researchers studying how students understand graphs of continuous functions and coordinate planes have developed many constructs to explain potential aspects of students' thinking about coordinate points, coordinate planes, variation, covariation, and continuous functions. No current research investigates how the different ways of thinking about graphs correlate. In other words, are there some ways of thinking that tend to either occur together or not occur together? In this research, I investigated student's system of meanings to describe how the different ways of understanding coordinate planes, coordinate points, and graphs of functions in the coordinate planes are related in students’ thinking. I determine a relationship between students' understanding of number lines or coordinate planes containing an infinite collection of numbers and their ability to identify a graph representing a dynamic situation. Additionally, I determined a relationship between students reasoning with values (instead of shapes) and their ability to create a graph to represent a dynamic situation.
Date Created
2023
Contributors
- Villatoro, Barbara (Author)
- Thompson, Patrick (Thesis advisor)
- Carlson, Marilyn (Committee member)
- Moore, Kevin (Committee member)
- Roh, Kyeong Hah (Committee member)
- Draney, Karen (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
185 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.2.N.189254
Level of coding
minimal
Cataloging Standards
Note
Partial requirement for: Ph.D., Arizona State University, 2023
Field of study: Mathematics Education
System Created
- 2023-08-28 04:52:08
System Modified
- 2023-08-28 04:52:13
- 1 year 2 months ago
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