and third components of the expertise acquisition model. Expertise consists of domain-specific knowledge; therefore, this is also true for areas of expertise specifically involving spatial thinking to greater and lesser degrees. If you want to think fluently and well about particular types of patterns, you have to put in time studying those patterns. Practice at constructing spatial representations reduces the drain on working memory when constructing spatial representations of objects and situations like others in the domain of study, but practice at spatial representations in one domain transfers minimally to representations in other domains. Practice at mental spatial operations shows a similar degree of domain specificity. However, there is limited “near transfer,” and practice discriminating or mentally rotating one set of shapes does benefit discriminating and mentally rotating highly similar shapes. Unfortunately, we do not know the metric that defines degrees of similarity.
The other approach builds on the second and fourth components of the expertise acquisition model and is based on the concept of “learning to learn.” With expertise comes the ability to “know what it takes to learn.” Students can learn that practice at spatial thinking really helps—it helps them to call spatial patterns to mind more rapidly and accurately, and it helps them to imagine transformations in those patterns more rapidly and accurately. They can also understand that the benefits of pattern learning are specific to the types of pattern learned and that the benefits of practicing mental transformation are specific to the types of patterns involved in the practice.
Expertise in spatial thinking is strongly linked to a particular knowledge domain. Through practice and experience, experts build the domain knowledge base and skills that allow them to think fluently and deeply. Central to expertise is pattern learning; skill in creating representations, especially spatial representations; and the ability to transform information. Although much of expertise is internal or cognitive, it also draws on external supports in the form of tools and representations (especially spatial representations).
Learners who have had more versus less experience in a domain, in using certain kinds of representations, or in reasoning about domain-specific problems approach new spatial learning tasks differently. Differences in domain-specific expertise are, however, not the only way of characterizing distinctions among learners. Appendix C addresses other ways in which differences among learners are relevant for spatial thinking. It discusses the notion of learner differences in general and then considers the links between three learner characteristics—chronological age, developmental level, and biological sex and cultural gender—and the process of spatial thinking.
As with all cognitive competencies, there are significant differences among people as to how, how quickly, and how well they can do something. Spatial thinking is no exception. Within domains of knowledge, there are experts and novices (see Section 3.6). Differences between experts and novices can be accounted for by training and experience (see Section 5.6). Across domains of knowledge, there are disciplines, such as geoscience, within which spatial thinking is emphasized and taught, and those, such as philosophy, within which it plays a hidden and relatively minor role. Across groups, there are also significant variations in how people approach spatial thinking. Across age, for example, children and adults do not think spatially in the same way. These differences can be accounted for by maturation, education, and experience (see Appendix C).
If, for the moment, we ignore the effects of domain, we can use the expert-novice distinction to understand some of the major differences in the ways in which people think spatially. A key goal, especially in science, is to learn to extract functional information from spatial structures and to understand how and why something works. In learning to do this, we must master three component tasks of spatial thinking.