Elementary teachers' attitudes and beliefs about spatial thinking and mathematics.

Considering how spatial thinking connects to Science, Technology, Engineering and Mathematics (STEM) outcomes, recent studies have evaluated how spatial interventions impact elementary students' math learning. While promising, these interventions tend to overlook other factors affecting math learning; perceptions of math abilities, beliefs about math, and math anxiety can also impact math performance. Additionally, perceptions of spatial skill and spatial anxiety impact spatial performance. This study investigated how elementary teachers' perceptions of spatial thinking connects with math perceptions. Specifically, we focused on teachers' attitudes and beliefs around three topics: teaching and learning math, spatial abilities, and spatial thinking in mathematics. We found that lower spatial anxiety related to lower anxiety about teaching math, greater alignment between math beliefs and math standards, and greater efficacy in teaching and learning math. Further, a factor analysis showed one factor that connected stereotypical math thinking with both math and spatial anxiety, and another that connected spatial competencies, teaching and learning math, and spatial thinking within math. To further evaluate spatial thinking in math, we introduced a math categorization and verified it using teachers' ratings of teaching difficulty, visualization helpfulness, and spatial-thinking involvement. Structural equation models revealed that the level of spatial-thinking categorization was the best model of all three of the teachers' ratings. Overall, results showed numerous connections between teachers' attitudes and beliefs about mathematics and spatial thinking. Future intervention studies should consider teachers who are spatial and/or math-anxious, and future research should investigate the role of stereotypical thinking in spatial and math anxiety.

Make-A-Dice Test: Assessing the intersection of mathematical and spatial thinking.

Individuals with better spatial thinking have increased interest and greater achievement in science, technology, engineering, and mathematics (STEM) disciplines (Wai, Lubinski, & Benbow in Journal of Educational Psychology, 101, 817-835, 2009). This relationship means that STEM education may benefit from leveraging spatial thinking, but measures of spatial thinking as they relate to specific STEM disciplines are needed. The present work presents an assessment of spatial and mathematical reasoning, called Make-A-Dice. In Make-A-Dice, individuals are presented with a cube net (i.e., a flattened cube) with numbers on two sides. Their goal is to "make a dice" by filling in the blank sides using two rules: opposite sides add to 7, and the numbers 1 through 6 should be used once each. Make-A-Dice was given to adults (Study 1) and elementary students (Studies 2 and 3) along with math, spatial, and other measures, across two sessions in all studies. Make-A-Dice had both internal and test-retest reliability, with items ordered by difficulty. Furthermore, performance was related to spatial and mathematical reasoning. In Study 1, adults reported a range of strategies used to complete Make-A-Dice, and one strategy predicted performance. Studies 2 and 3 showed that Make-A-Dice is age-appropriate for elementary students. Make-A-Dice shows promise as an individual-difference measure linking spatial and mathematical thinking and has the potential to identify elementary-aged children who may benefit from spatial training.

Think3d!: Improving mathematics learning through embodied spatial training.

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students' spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains - specifically for problem types expected to show gains from spatial training - and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.