Can Visual Arts Learning Improve Geometric Reasoning? A Transfer Study

Principal Investigator: 
Project Overview
Background & Purpose: 

The mathematics education field recognizes that both visualization and spatial reasoning are integral to mathematical thinking; geometry is one mathematical strand in which one might particularly expect to see this connection. This research investigates whether intensive study of drawing and painting, disciplines which also require visualization and spatial reasoning and explicitly instruct students in artistic “envisioning,” leads to improvements in geometric reasoning.


The study is being conducted in a large Northeastern city with high school students who attend public schools in a large urban district. This is a naturalistic study, which contrasts the artistic and geometric reasoning of students studying visual arts with students who are not. Students in the “treatment” condition come from two settings: (1) those who attend a public pilot school offering intensive work in visual arts, theater, music, dance, and (2) those who attend an after-school jobs program that trains (and pays) underserved youth to create visual art. Students in the treated control conditions come from two settings: (1) those who study theater in the same public pilot school, (2) those who attend an after-school sports program. A third control group is untreated and consists of students who are friends of students in the treatment condition but who do not participate in intensive training of any kind.

Research Design: 

The research design is quasi-experimental and studies a naturally occurring intervention on a self-selected sample. The intervention is visual arts training (minimum of 9 hours/week). The outcome measure is spatial reasoning in the arts and in geometry.The treated vs. untreated control conditions test for whether any kind of intensive treatment has the same effects. See description of control conditions under Setting.

The study is designed to test the causal hypothesis that instruction in visual arts strengthens spatial reasoning which can then be applied to geometric reasoning. The research design will also includes the identification of associative/correlational relationships within groups. The study also has a qualitative component in that we will be conducting in-depth “loud thinking” interviews with a small sample of students in each testing condition.

The study uses a battery of measures. A geometry visualization measure consists of release items from TIMSS, PISA, NAEP and original items created in conjunction with advisory board members. An art visualization measure, created in conjunction with artist/art educator consultants, assesses aspects of artistic visual/spatial reasoning: identifying the light source, drawing shadows, identifying reflections, imagining new perspectives, completing a scene, identifying the rhythm and shapes underlying compositions, and stretching/compressing compositions. Three standardized spatial reasoning tests provide a validity check for the spatial nature of the art and geometry items: a water level test, a paper folding test, and a mental rotation test. Two control tests are also included: the vocabulary subtest of Kaufman Brief Intelligence test, and the Reading the Mind in the Eyes test. The project also uses a custom-designed self-completion questionnaire for all participants

We will analyze a set of hypotheses about the relative performance of treatment, treated control, and untreated control groups using factor analyses, correlational analyses, analyses of variance, and SEM analyses. We will develop scoring rubrics and coding categories for analyzing the qualitative data that we will obtain from the loud-thinking interviews.

Publications & Presentations: 

Goldsmith, L.T., Hetland, L., & Winner, E. (2009, April). Learning in Visual Arts and Geometry: Designing a Transfer Study. Presented at AERA annual conference, San Diego, CA, in R. Siegesmund (Chair). Reaching out/crossing borders in visual arts research.

Winner, E, Hetland, L., & Goldsmith, L.T. (2009, April). Designing a test of spatial visualization for visual arts. Presented at NAEA annual conference, Minneapolis, MN, in Learning in Visual Arts: What and How.

Hetland, L. (2009). A Trail of Three Studies: How One Research Leads to Another. Cultuur + Educatie (in Dutch).

Other Products: 

Two products will result from this work: a geometric reasoning measure test (built on a compilation of standardized test items) assessing the kind of spatial reasoning used in geometry; this test will require little or no verbal, memorized knowledge of rules, terms, or formulae; and an art visualization test assessing the kind of spatial reasoning used in creating and responding to visual art.