UNLV Theses, Dissertations, Professional Papers, and Capstones 12-15-2018 Novice versus Expert Algebraic Problem-Solving Strategies: An Eye Tracking Approach Krystal Kamekona-Mendoza Follow this and additional works at: https://digitalscholarship.unlv.edu/thesesdissertations Part of the Cognitive Psychology Commons Repository Citation Kamekona-Mendoza, Krystal, "Novice versus Expert Algebraic Problem-Solving Strategies: An Eye Tracking Approach" (2018). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3501. http://dx.doi.org/10.34917/14279645 This Thesis is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. 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NOVICE VERSUS EXPERT ALGEBRAIC PROBLEM-SOLVING STRATEGIES: AN EYE TRACKING APPROACH By Krystal Kamekona-Mendoza Bachelor of Arts – Psychology University of Nevada, Las Vegas 2012 A thesis submitted in partial fulfillment of the requirements for the Master of Arts – Psychology Department of Psychology College of Liberal Arts The Graduate College University of Nevada, Las Vegas December 2018 Thesis Approval The Graduate College The University of Nevada, Las Vegas November 9, 2018 This thesis prepared by Krystal Kamekona-Mendoza entitled Novice Versus Expert Algebraic Problem-Solving Strategies: An Eye Tracking Approach is approved in partial fulfillment of the requirements for the degree of Master of Arts – Psychology Department of Psychology Mark Ashcraft, Ph.D. Kathryn Hausbeck Korgan, Ph.D. Examination Committee Chair Graduate College Interim Dean David Copeland, Ph.D. Examination Committee Member Colleen Parks, Ph.D. Examination Committee Member Carryn Warren, Ph.D. Graduate College Faculty Representative ii Abstract Algebra continues to be an important point along the educational spectrum. It is often the point at which we see a deviation of educational trajectories for those who are interested in pursuing additional math and science courses and those who are not. Understanding how college algebra students perform is a crucial step in further understanding the difficulties that students often encounter, as well as understanding other potential factors that may contribute to their performance. The novice/expert paradigm is one way to examine performance differences. While existing literature indicates that novices and experts perceive, sort, and solve problems differently across a variety of domains, this paradigm has yet to be applied to algebra. It has also been shown that cognitive processing can guide an individual’s eye movements. Evidence is lacking in this domain with regard to what performance differences look like in terms of these eye movements (e.g., number of fixations, length of fixations) during more complex math tasks. Using an algebraic problem-solving task, this thesis examined performance differences between novices (undergraduate College Algebra students) and experts (graduate students with a substantial background in mathematics). Given the role that working memory plays in mental arithmetic, another purpose of this thesis was to assess how working memory might impact performance when solving algebraic equations and if working memory is a good predictor of performance. iii Table of Contents Abstract ...................................................................................................................... iii Table of Contents ........................................................................................................ iv List of Figures .............................................................................................................. v Chapter 1: Introduction ................................................................................................. 1 Number Sense ................................................................................................... 2 Algebra ............................................................................................................. 3 Working Memory ............................................................................................. 7 Eye Tracking ...................................................................................................10 Novice versus Expert .......................................................................................11 Current Study ..................................................................................................15 Chapter 2: Method .......................................................................................................18 Participants ......................................................................................................18 Materials ..........................................................................................................18 Tasks ...............................................................................................................19 Procedures .......................................................................................................21 Areas of Interest ...............................................................................................22 Chapter 3: Results .......................................................................................................24 Data Analyses ..................................................................................................24 Math Achievement and Effort ..........................................................................25 Baseline Problems............................................................................................25 Behavioral Results ...........................................................................................26 Eye Tracking Results .......................................................................................28 Regression .......................................................................................................34 Chapter 4: Discussion ..................................................................................................36 References ...................................................................................................................41 Curriculum Vitae .........................................................................................................47 iv List of Figures Figure 1: Sample AOIs for Analyses (Easy and Hard Problems) .............................................23 Figure 2: RT Results for Easy and Hard Problems ...................................................................27 Figure 3: Percent Accuracy Results for Hard Problems ...........................................................28 Figure 4: Mean Fixation Duration for Easy and Hard Problems ...............................................30 Figure 5: Number of Fixations for Easy and Hard Problems ....................................................32 Figure 6: Refixations Results for Hard Problems .....................................................................36 v Chapter 1: Introduction Number sense is a topic that has generated research expanding over several disciplines including developmental psychology, neuroscience, educational psychology, and cognitive psychology (Ashcraft & Stazyck, 1981; Jordan, Kaplan, Ramineni & Locuniak, 2009; Petersen & Hyde, 2015; Suarez-Pellicioni, Nunez-Pena, & Colome, 2013). Despite its rich history, much of the existing research has focused on the fundamental concepts of arithmetic (e.g., basic facts; Faust, Ashcraft, & Fleck, 1996). Such studies have examined a variety of ages from early elementary school students to college-aged adults (Hecht, 2002; Moore & Ashcraft, 2015). These studies have built a solid foundation of research defining how basic facts are learned, how performance differs based on different types of problems, and what performance looks like in terms of the common cognitive measures of reaction time (RT) and accuracy. Recently, the study of numerical cognition has grown to include the more in-depth method of measuring eye movements with an eye tracking device (Hartmann & Fischer, 2016; Mock, Huber, Klein, & Moeller, 2016). The use of eye tracking in psychological research has equipped researchers with more accurate measures of the underlying cognitive processes taking place during a given task. Where participants are fixating and the length of a fixation can be an indication of the active processing of that information (Hartmann & Fischer, 2016; Just & Carpenter, 1980), and because of that, such measures provide a more precise depiction of participants’ performance beyond the typical measures of RT and accuracy. Research is still lacking in more advanced mathematical concepts such as algebra. Expanding this research to include this more complex type of math can begin to shed some light on the cognitive processes involved in these more difficult types of problems. It can also begin to unearth some of the problem-solving strategies involved