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IES Grant

Title: Spatial Ability as a Malleable Factor for Math Learning
Center: NCER Year: 2012
Principal Investigator: Mix, Kelly Awardee: University of Maryland, College Park
Program: Cognition and Student Learning      [Program Details]
Award Period: 4 years (7/1/2012-6/30/2016) Award Amount: $1,531,180
Type: Exploration Award Number: R305A150588

Previous Affiliation: Michigan State
Previous grant number: R305A120416

Co-Principal Investigator: Susan Levine (University of Chicago)

Purpose: Previous research shows that children and adults who perform better on spatial tasks also perform better on tests of mathematical ability. However, the relation between spatial and math ability is not yet well understood. This grant will conduct studies to clarify which aspects of spatial ability relate to different aspects of math performance, and gather evidence regarding whether training to improve spatial ability also improves math performance. Results will lay the groundwork for the development of future interventions for mathematics that are based on specific kinds of spatial training.

Project Activities: The three studies in this grant will study the relationship between several measures of spatial ability and mathematical ability, and then investigate the effect of improving specific types of spatial ability on mathematical ability. In Year 1, researchers will collect and analyze the first wave of data for an exploratory factor analysis that will relate specific spatial abilities to a set of math tasks. In Year 2, researchers will gather data for the second wave of data in this study and conduct a confirmatory factor analysis based on the results from Year 1. In Years 2 and 3, researchers will complete two studies that test whether spatial training within a factor leads to improvement in math abilities within the same factor.

Products: The products of this project will be preliminary evidence of the relationships between spatial and mathematics ability that can be used to guide the development of interventions to improve spatial and math ability. Peer reviewed publications will also be produced.

Structured Abstract

Setting: These studies will draw from students attending schools in rural, suburban, and urban areas serving ethnically and socioeconomically diverse communities in the Midwest.

Sample: Study 1 will include two samples of 660 children (220 per grade in Kindergarten, Grade 2, and Grade 4). Study 2 will include 315 kindergarten, second-, and fourth-grade children (105 children per grade). Study 3 will include 150 second-grade students. All children will be typically developing and speak English as their primary language.

Intervention: This grant investigates how spatial ability relates to math ability, and the mechanisms through which this connection may operate. Pilot research found significant improvement in certain types of mathematics problems (i.e., those missing addends or subtrahends) after training in mental rotation of objects. In this grant, researchers will carry out training experiments to study the effect of varying the length of training and the amount of movement observed in student performance. The team will also examine other potential training relations that emerge from the factor analyses in Years 1 and 2. This information will inform the future development of spatial training interventions.

Research Design and Methods: Researchers will carry out three studies. In Study 1, the team will explore the specific ways that spatial ability and math are related. The research team will collect cross-sectional data from two waves of students in Kindergarten through Grade 4. Students will complete measures of general intelligence, six different spatial tasks, and four math tasks. Researchers will carry out exploratory and confirmatory factor analyses to study the pattern of relationships among these measures in order to construct hypotheses to guide spatial training in Studies 2 and 3.

In Study 2, the team will investigate what parameters mediate the effects of mental rotation training by varying the amount of training offered and the inclusion of different motor components. Students will complete two brief training sessions (20 minutes) each week for 6 weeks. Students will also complete a pretest battery of math and spatial tasks at the beginning and end of the study. The math test will also be given at weeks 2, 4, and 6 to measure the effect of various amounts of training. Students will be randomly assigned to a control group or one of two training conditions. In one training condition, students will see two halves of a shape presented on separate cards and then choose a picture that shows the whole shape from among four choices. Children will then be provided with the correct choice. In the second training condition, students will complete the same training trials but will physically move the cards together to form the correct matching shape.

In Study 3, the researchers will contrast the effects of mental rotation training with other spatial training tasks to determine whether spatial training effects apply generally to all math skills or whether they increase some math skills more than others. Students will be randomly assigned to a control group or one of four training conditions: (1) the same mental rotation task used in Study 2, using the feedback option that was shown to be most efficacious; (2) a mental rotation task in which children match a form to a picture of the same form in a different orientation; (3) a task in which children are shown a black and white grid for 3 seconds, and then fill in an empty grid to indicate which squares were black in the model; or (4) training on copying line drawings of increasingly complex figures.

Control Condition: Due to the nature of the research design of Study 1, there is no control condition. In both Studies 2 and 3, children in the control group will complete crossword puzzles.

Key Measures: The first study will use a battery of 11 measures including the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) Vocabulary subtest; 6 spatial tasks, and 4 math tasks. Spatial tasks include the Neuberger et al. Mental Rotation task, the WISC-IV Block Design subtest, the Visual Patterns Test, the Motor-Free Visual Perception Test, and a researcher-developed map reading measure. Measures of math will include the Test of Early Mathematics Ability-Third Edition, and researcher-developed measures of number line estimation, flexible use of equal sign, and magnitude judgments.

Data Analytic Strategy: Exploratory factor analysis will be used to analyze data from the first wave of data collection in Study 1. Confirmatory factory analysis will be used to analyze data from the second wave of data collection in Study 1 in order to contrast the factorial model suggested by the exploratory factor analysis with reasonable alternatives. This will allow researchers to verify that the exploratory analysis model provides the best fit. Data from the training studies will be analyzed using analysis of covariance with pretest scores as the covariate, training condition as a between subjects factor, and posttest scores as the dependent measure. Paired sample t-tests also will be used to make post-hoc comparisons and to determine which groups improved significantly from pre- to posttest.


Journal article, monograph, or newsletter

Mix, K. S. & Cheng, Y. L. (2012). The relation between space and math: Developmental and educational implications. In J. B. Benson (Ed.) Advances in Child Development and Behavior, Volume 42 (pp. 197-243). New York: Elsevier.

Newcombe, N., Levine, S.C. & Mix, K.S. (2015/11). Thinking about quantity: The intertwined development of spatial and numerical cognition. WIREs Cognitive Science, 6 (6), 491-505. doi: 10.1002/wcs.1369

Mix, K. S., Levine, S. C., Cheng, Y., Young, C., Hambrick, D. Z., Ping, R. & Konstantopolous, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145 (9), 1206-1227. doi: 10.1037/xge0000182

Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C. J., Hambrick, D. Z., & Konstantopoulos, S. (2017). The latent structure of spatial skills and mathematics: Further evidence from Wave 2. Journal of Cognition and Development, 18 (4), 465-492. doi: 10.1080/15248372.2017.1346658

Young, C. J., Levine, S. C., & Mix, K. S. (2018) The connection between spatial and mathematical ability across development. In H.-C. Nuerk, K. Cipora, F. Domahs, & M. Haman (Eds.) Special Issue: On the Development of Space-Number Relations: Linguistic and Cognitive Determinants, Influences, and Associations. Frontiers in Psychology, 9 (1). doi.: 10.3389/fpsyg.2018.00755

Mix, K. S., Hambrick, D. Z., Satyam, V. R., Burgoyne, A., & Levine, S. C. (2018). The latent structure of spatial skill: A test of the 2x2 typology. Cognition, 268-278. doi: 10.1016/j.cognition.2018.07.012

Mix, K. S. & Battista, M. (2018) Spatial Visualization in Mathematics. Springer.

Young, C.J., Levine, S. C., & Mix, K. S. (2018). The connections between spatial skill and mathematics ability across development. In H.-C. Nuerk, K. Cipora, F. Domahs & M. Haman (Eds.) On the Development of Space-Number Relations: Linguistic and Cognitive Determinants, Influences, and Associations (pp. 122-128). Lausanne: Frontiers Media SA. doi: 10.3389/978-2-88963-588-7

Young, C.J., Levine, S. C., & Mix, K. S. (2018). What processes underlie the relation between spatial skill and mathematics? In K.S. Mix & M. Battista (Eds.) Spatial Visualization in Mathematics (pp. 117-148). Cham, Switzerland: Springer.

Mix, K. S. (2019). Why are spatial skill and mathematics related? Child Development Perspectives, 13 (2), 121-126. doi: 10.1111/cdep.12323

Mix, K. S., Levine, S. C., Cheng, Y.-L. & Stockton, J. D. (2020). Does spatial training improve mathematics performance? A comparison of training type, age, and mathematics outcome. Journal of Educational Psychology.

Johnson, T., Burgoyne, A., Mix, K. S., Levine, S. C., & Young, C. J. (under review). Individual differences in the relation between spatial skill and mathematics.