can be drawn upon to tackle the new problem. Thus, it might be necessary to develop expertise in particular contexts before one can see the connections to some more general spatial skill (e.g., one might become expert at seeing things in three dimensions in biology, but still need considerable practice to learn to apply the skill to seeing new kinds of forms, shapes, and positions in chemistry or geology).

The benefits of practicing spatial thinking initially tend to be domain specific, and as is the case for other forms of expertise, learning to think spatially is best conducted in the context of the types of materials one is seeking to learn and understand. Thus, practicing spatial skills is most effective if it is contextualized within a domain of knowledge.

Structured, systematic practice greatly improves the speed and accuracy with which people can generate spatial representations and transform spatial information. Thus, it is important to identify the types and forms of spatial representations and transformations that are critical for different learning goals and encourage students to practice them (see Appendix D).

Spatial representations can help students in learning and problem solving. The evidence suggests that we should (1) have students generate their own spatial representations; (2) use spatial representations to provide multiple and, where possible, interlocking and complementary representations of situations, especially where the phenomena are not readily available to direct sensory perception; (3) use a wide variety of spatial representations; (4) use spatial representations to convey a variety of kinds of thinking (e.g., data about how something is structured now, how it could or should appear in the future or did appear in the past); and (5) learn where—and which types of—spatial representations can be useful. The evidence also suggests that we should not (1) force students to use a spatial approach to a problem when another approach is equally or better suited; (2) overload students’ cognitive capabilities by exposing then to a novel spatial representation while simultaneously asking them to reason about a complex situation; or (3) assume that animations are necessarily better than sequences of static representations (see Appendix D).

Expertise in spatial thinking varies among different groups. There are different average levels of skills or expertise associated with different groups (e.g., younger and older children). There is also, however, significant variation within any given group on any given spatial skill. This means that one cannot automatically infer what any given learner brings to the task. Thus, from an instructional standpoint, it will be necessary to have tasks with multiple levels of achievement and multiple strategies for achieving them.

The distributions of performance on spatial tasks shows a great deal of overlap for boys and girls and some average differences too. Boys and girls show differences on average performance of some spatial skills, where boys outperform girls on some skills and girls outperform boys on others. Thus, it is important not to “discount” the spatial learning capabilities of either boys or girls—practice and learning significantly boost the performance of both boys and girls (see Appendix C).

People vary in how rapidly they can create and transform spatial representations, and their levels of spatial thinking skill can help or hinder their learning across the broad range of sciences. Students with higher levels of initial skill will find learning that involves spatial thinking easier than those with lower levels of initial skill. For students with critically low levels of skill in spatial thinking, the use of tools for spatial thinking, such as graphics and figures, may actually interfere with, not facilitate, learning.

Effective learning depends on having sufficient levels of general and particular spatial thinking skills. Thus, it is important to assess the strengths and limitations that individual learners bring to their learning goals.



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