Cheryl A. Cohen

Spatial Thinking and STEM Education: When, Why, and How?

Abstract We explore the relation between spatial thinking and performance and attainment in science, technology, engineering and mathematics (STEM) domains. Spatial skills strongly predict who will go into STEM fields. But why is this true? We argue that spatial skills serve as a gateway or barrier for entry into STEM fields. We review literature that indicates that psychometrically-assessed spatial abilities predict performance early in STEM learning, but become less predicative as students advance toward expertise. Experts often have mental representations that allow them to solve problems without having to use spatial thinking. For example, an expert chemist who knows a great deal about the structure and behavior of a particular molecule may not need to mentally rotate a representation of this molecule in order to make a decision about it. Novices who have low levels of spatial skills may not be able to advance to the point at which spatial skills become less important. Thus, a program of spatial training might help to increase the number of people who go into STEM fields. We review and give examples of work on spatial training, which show that spatial abilities are quite malleable. Our chapter helps to constrain and specify when and how spatial abilities do (or do not) matter in STEM thinking and learning.

Spatial reasoning with external visualizations: what matters is what you see, not whether you interact.

Three experiments examined the effects of interactive visualizations and spatial abilities on a task requiring participants to infer and draw cross sections of a three-dimensional (3D) object. The experiments manipulated whether participants could interactively control a virtual 3D visualization of the object while performing the task, and compared participants who were allowed interactive control of the visualization to those who were not allowed control. In Experiment 1, interactivity produced better performance than passive viewing, but the advantage of interactivity disappeared in Experiment 2 when visual input for the two conditions in a yoked design was equalized. In Experiments 2 and 3, differences in how interactive participants manipulated the visualization were large and related to performance. In Experiment 3, non-interactive participants who watched optimal movements of the display performed as well as interactive participants who manipulated the visualization effectively and better than interactive participants who manipulated the visualization ineffectively. Spatial ability made an independent contribution to performance on the spatial reasoning task, but did not predict patterns of interactive behavior. These experiments indicate that providing participants with active control of a computer visualization does not necessarily enhance task performance, whereas seeing the most task-relevant information does, and this is true regardless of whether the task-relevant information is obtained actively or passively.

Chapter Four – Spatial Thinking and STEM Education: When, Why, and How?

Abstract We explore the relation between spatial thinking and performance and attainment in science, technology, engineering and mathematics (STEM) domains. Spatial skills strongly predict who will go into STEM fields. But why is this true? We argue that spatial skills serve as a gateway or barrier for entry into STEM fields. We review literature that indicates that psychometrically-assessed spatial abilities predict performance early in STEM learning, but become less predicative as students advance toward expertise. Experts often have mental representations that allow them to solve problems without having to use spatial thinking. For example, an expert chemist who knows a great deal about the structure and behavior of a particular molecule may not need to mentally rotate a representation of this molecule in order to make a decision about it. Novices who have low levels of spatial skills may not be able to advance to the point at which spatial skills become less important. Thus, a program of spatial training might help to increase the number of people who go into STEM fields. We review and give examples of work on spatial training, which show that spatial abilities are quite malleable. Our chapter helps to constrain and specify when and how spatial abilities do (or do not) matter in STEM thinking and learning.

It Works Both Ways: Transfer Difficulties between Manipulatives and Written Subtraction Solutions

Three experiments compared performance and transfer among children aged 83–94 months after written or manipulatives instruction on two-digit subtraction. In Experiment 1a, children learned with manipulatives or with traditional written numerals. All children then completed a written posttest. Experiment 1b investigated whether salient or perceptually attractive manipulatives affected transfer. Experiment 2 investigated whether instruction with writing would transfer to a manipulatives-based posttest. Children demonstrated performance gains when the posttest format was identical to the instructed format but failed to demonstrate transfer from the instructed format to an incongruent posttest. The results indicate that the problem in transferring from manipulatives instruction to written assessments stems from a general difficulty in using knowledge gained in one format (e.g., manipulatives) in another format (e.g., writing). Taken together, the results have important implications for research and teaching in early mathematics. Teachers should consider making specific links and alignments between written and manipulatives-based representations of the same problems.

Spatial Thinking and STEM Education

Abstract We explore the relation between spatial thinking and performance and attainment in science, technology, engineering and mathematics (STEM) domains. Spatial skills strongly predict who will go into STEM fields. But why is this true? We argue that spatial skills serve as a gateway or barrier for entry into STEM fields. We review literature that indicates that psychometrically-assessed spatial abilities predict performance early in STEM learning, but become less predicative as students advance toward expertise. Experts often have mental representations that allow them to solve problems without having to use spatial thinking. For example, an expert chemist who knows a great deal about the structure and behavior of a particular molecule may not need to mentally rotate a representation of this molecule in order to make a decision about it. Novices who have low levels of spatial skills may not be able to advance to the point at which spatial skills become less important. Thus, a program of spatial training might help to increase the number of people who go into STEM fields. We review and give examples of work on spatial training, which show that spatial abilities are quite malleable. Our chapter helps to constrain and specify when and how spatial abilities do (or do not) matter in STEM thinking and learning.

Benefits of Constrained Interactivity in Using a Three-Dimensional Diagram

In four experiments participants were allowed to manipulate a virtual 3-D object in order to infer and draw 2-D cross sections of it. Key differences between the experiments were the interface and degree of interactivity available. Two experiments used a three degrees-of-freedom inertia tracking device allowing unconstrained interactions and the other two experiments used a slider bar that allowed only one degree-of-freedom movement at a time. Somewhat counter-intuitively, we found that the constrained interface allowed people to access task-relevant information more effectively and resulted in better performance on the task.