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IES Grant

Title: Fostering Reliance on Visuospatial Representations to Enhance High School Students' Success in Pre-Calculus Trigonometry
Center: NCER Year: 2015
Principal Investigator: McClelland, James Awardee: Stanford University
Program: Cognition and Student Learning      [Program Details]
Award Period: 4 years (7/1/2015-6/30/2019) Award Amount: $1,543,138
Goal: Exploration Award Number: R305A150453
Description:

Purpose: This project will explore whether encouraging high school and community college students to use visuospatial representations and providing them with support to enhance familiarity with these representations will contribute to success in trigonometry, a difficult subject that sits at the gateway to entry into university-level science, technology, engineering, and mathematics (STEM) coursework and ultimately into careers in these disciplines. It is common to view mathematics as a formal system of abstract symbols and rules, but an alternate view is that mathematical and scientific reasoning operates on idealized objects humans can manipulate in their minds, similar to the ways humans manipulate real objects. A visuospatial representation may provide the type of grounded conceptual framework necessary to support such manipulations. In this project, the research team seeks to identify ways to enhance students' use of visuospatial representations (specifically the unit circle) in solving pre-calculus trigonometry problems, establish whether teaching students using visuospatially-oriented training improves students' ability to master trigonometry relationships, and identify moderators of the relationship between the use of visuospatial representations and performance in trigonometry.

Project Activities: The research team will conduct three studies with community college students who have not had prior exposure to material covered in pre-calculus trigonometry, and with high school students who are enrolled in pre-calculus courses. In Year 1, the research team will conduct a study to examine whether grounding pre-calculus trigonometry instruction in a meaningful visuospatial representation (i.e., the unit circle) improves student learning of sine and cosine functions. In Year 2, researchers will ask the same research question with additional trigonometry concepts. In Year 3, the research team will determine if the visuospatially-oriented training approach improves high school students' classroom performance relative to a more traditional rule-based approach.

Products: This project will provide preliminary evidence of potentially promising practices for improving student learning in trigonometry. The researchers intend to publish their findings in peer-reviewed publications.

Structured Abstract

Setting: The research will be carried out at a community college and at multiple high schools in urban and suburban areas of California.

Sample: Across all three studies, participants will include approximately 450 students (150, 180, and 120 in Studies 1, 2, and 3 respectively). Studies 1 and 2 will consist of a mix of community college students without prior exposure to material covered in pre-calculus trigonometry classes and 11th and 12th grade high school students enrolled in pre-calculus courses. Study 3 will consist of 11th and 12th grade high school students enrolled in pre-calculus courses. Across all studies, participants will be of diverse ethnic and socio-economic backgrounds that are typical of the region.

Intervention: Due to the exploratory nature of this research, there is not an intervention. The goal of these studies is to identify malleable factors of instruction that will improve student learning in trigonometry. However, in order to conduct these studies, the research team will develop a visuospatially-oriented training program, which could be used as the basis for the development of interventions for pre-calculus trigonometry courses. The training program will engage student participants in grounding symbolic trigonometric expressions such as cos (?–90) in a concrete spatial construct (the unit circle).

Research Design and Methods: Researchers will conduct three studies. In each study, students will be randomly assigned to conditions in which they complete pre-tests, training (dependent on condition), and post-tests. The research team will conduct Study 1 to examine whether grounding pre-calculus trigonometry instruction in a meaningful visuospatial representation (i.e., the unit circle) improves student learning of sine and cosine functions relative to a rule-based instructional approach. Study 2 will address the same question with additional trigonometry concepts. In Study 3, researchers will determine if the visuospatially-oriented training approach improves high school students' classroom performance relative to a more traditional rule-based approach.

Control Condition: The comparison conditions vary across studies. Study 1 will include a no lesson control condition as well as a rule-based training condition as a comparison; Studies 2 and 3 will include a rule-based training condition as a comparison.

Key Measures: The primary outcome measure for this study is participants' change scores from pre- to post-test on researcher-developed tests of trigonometric concepts. Researchers will measure students' visuospatial abilities during pre-testing using a mental rotations test and the Impossible Figures Task.

Data Analytic Strategy: Researchers will analyze data using planned t-tests and logistic regression (to explore for effects of gender, spatial ability, and prior knowledge).

Publications

Book chapter

Mickey, K. and McClelland, J.L. (2017). The unit circle as a grounded conceptual structure in pre-calculus trigonometry. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts.

Journal article, monograph, or newsletter

Lampinen, A.K. and McClelland, J.L. (in press). Different presentations of a mathematical concept can support learning in complementary ways. Journal of Educational Psychology.


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