1. Spatial ability and gender as predictors of mathematics problem solving skills Martha Carr, Pat Janes, Sara Woodruff University of Georgia The research was supported by funds from the National Science Foundation GSE/RES program #0114945 and #0429088.

2. Objectives To determine the impact of three-dimensional spatial skill on  Fluency  Use of place value  Ability to represent complex word problems  Cognitive strategy use  Mathematics subtest performance To determine whether gender influenced these factors when three-dimensional spatial ability was included in the model.

3. Mental Number Line Math facts thought to be stored in a mental number line/network (Ashcraft, 1983). Development of mental number line linked to more abstract,semantic representation of number. Emerging research indicates a spatial representation for number, likely in combination with a semantic representation (Dehaene, Dupoux & Mehler, 1993) &

4. Place Value Mathematics educators report spatial-like strategies in working with place value (Fuson & Kwon, 1992). Neural modeling indicates both spatial and semantic representations of place value (Grossberg & Repin, 2003).  What is it? Where is it?

5. Problem Representation Work by Hegarty and Kozhevnikov (1999) indicates that the ability to schematically represent relations in the problem predicted good performance. Booth and Thomas (1999) found that students with good visuo-spatial skills were good at setting up and solving word problems

6. Questions Does three dimensional-spatial ability influence math competency through  Fluency for basic math facts  Problem representation  Use of place value  Cognitive strategy use Does gender predict when three-dimensional spatial skills are in the model. How do spatial and math skills impact performance on geometry, number sense, computation, word problem solving subtests?

7. Methods, Data Sources Complete longitudinal data on 189 fourth grade children (102 girls, 87 boys). Assessed In fall  fluency for basic math facts  three-dimensional spatial ability (Vandenberg & Kuse, 1978)  Correct cognitive strategies (22 double and triple digit computation and word problems).  Use of place value on strategy problems  Correct represent word representation on 6 strategy problems.  (e.g., Jesse writes two pages on a computer. He writes 234 words on page 1 and 188 words on page 2. How many more words does he need for a 500- word story?). Spring assessment- mathematics competency

9. Overview of Direct Effects The models for all four subtests indicated a good fit of the model to the data. Three-dimensional spatial ability predicted place value (.18) and problem representation (.24) directly. Place value (.47) and problem representation (.66) predicted correct cognitive strategy use. Place value and problem representation also predicted subtest performance.  Computation model exception Path from correct cognitive strategy use to subtest performance was found only for the computation and word problem subtests.

10. Overview of Gender Effects Gender had no direct effects in any model other than in the computation model where it predicted subtest performance.  This path, however, became non-significant when indirect effects were taken into consideration. Gender had no indirect effects, what existed tended by be negative.

11. Total Effects Total effects include direct effects and indirect effects through mediating variables  The standardized total effects of three-dimensional spatial ability were significant for  place value (.18),  problem representation (.24),  correct cognitive strategy use (.19).  and for the subtests  number sense (.16),  problem solving (.22),  geometry (.18),  computation (.10).

17. Conclusions Three-dimensional spatial ability has largest impact through problem representation. Also evident in children’s ability to use place value. Three-dimensional spatial skill did not predict fluency  Need to work with younger children to see if relationship there. Influences a range of subtest through problem representation and place value

18. Limitations Only looked at three dimensional spatial skill. We need to look at other forms of visual and spatial representation. Only looked at problem representation, place value and fluency. We need to better explore exactly how spatial skills influence mathematics learning. What are the underlying skills for each mathematical task?

19. Thank You!