LEARNING THEORY

Adult Learning Theory



Adult Learning Theory

A Theoretical Framework

Our theory begins with an hypothesis on the nature of mathematical knowledge and how it develops. An individual's mathematical knowledge is her or his tendency to respond to perceived mathematical problem situations by reflecting on them in a social context and constructing or reconstructing mathematical actions, processes and objects and organizing these in schemas to use in dealing with the situations. There are a number of important issues raised by this statement, many relating to assessment.

For example, the fact that one only has a "tendency" rather than a certainty to respond in various ways brings into question the meaning of written answers in a timed exam(Caffarella, Merriam, 2007). Another issue is that often the student perceives a very different problem from what the test-maker intended and it is unclear how we should evaluate a thoughtful solution to a different problem. The position that learning occurs in response to situations leaves very much open the sequence of topics which a student will learn.

In fact, different students learn different pieces of the material at different times, so the timing of specific assessments becomes important. Finally, the position that learning takes place in a social context raises questions about how to assess individual knowledge.

The last part of our hypothesis relates directly to how the learning might actually take place(Daley, 2006 ). It is the role of our research to try to develop theoretical and operational understandings of the complex constructions we call actions, processes, objects and schemas (these technical terms are fully described in our publications) and then to relate those understandings to specific mathematical topics.

Given our understandings of the mental constructions involved in learning mathematics, it is the role of pedagogy to develop strategies for getting students to make them and apply them to the problem situations. Following is a list of the major strategies used in courses that we develop. * Students construct mathematical concepts on the computer to foster direct mental constructions and provide an experiential base for reflection.

* Students work in cooperative groups that are not changed for the entire course.

* Lectures are de-emphasized in favor of small-group problem solving to help students reflect on their computer constructions and convert them to mental constructions of mathematical concepts.

* Students are repeatedly confronted with the entire panorama of the material of the course and have various experiences that help different students learn different portions of this material at different times. We refer to this arrangement as an holistic spray.

An approach to assessment

In our courses, students are assigned to permanent groups (of 3 or 4) very early in the course and they do most of their work in these groups, including some of the tests. We use the following assessment items(Huitt, 2007). Because the first of these, computer assignments, are designed to stimulate mental constructions and often ask students to do things that are new and different for them, the grading is relatively lenient and tries to measure mental ...