ABSTRACT
One of the challenges to the idea that a thinking-with-things approach, which uses manipulatives and other materials to teach the embodied learner, can be valuable in higher education comes from the idea that what we are teaching is abstract. This chapter aims to challenge our notions of what the abstract and the concrete are, and to show that they reflect a misunderstanding of how humans think and learn. The idea that college students are abstract thinkers, who can effectively be presented with new material introduced in abstract form, stems in part from a misunderstanding of the influential work of Jean Piaget. His stage theory of child development has been widely understood to mean that by the time students arrive in college they are well into the “formal operations” stage of development and therefore comfortable with abstractions. Instead, learners, especially those learning something new, draw heavily on the cognitive resources developed in earlier stages. Effective instruction should begin with things that are close, tangible, graspable and build up to the abstract as the learner develops experience and expertise. A learner’s progression to abstract thinking is not a development from child to adult, but a development from novice to expert.
