Douglas B. McLeod

The Role of Affect in Mathematical Problem Solving

When students are given a nonroutine mathematical problem to solve, their reactions often include a lot of emotion. If they work on the problem over an extended period of time, the emotional responses frequently become quite intense. Many students will begin to work on a problem with some enthusiasm, treating it like a puzzle or game. After some time, the reactions become more negative. Students who have a plan to solve the problem may get stuck trying to carry out the plan. They often become quite tense; they may try to implement the same plan repeatedly, getting more frustrated with each unsuccessful attempt. If the students obtain a solution to the problem, they express feelings of satisfaction, even joy. If they do not reach a solution, they may angrily insist on help so that they can reduce their frustration.

Information-processing theories and mathematics learning: the role of affect

Abstract Information-processing theories have been heavily influenced by the development of artificial intelligence and computer technology. This technological orientation has led to the neglect of affective issues in the application of information-processing theories to mathematics learning. This chapter outlines important aspects of the affective domain in the context of mathematics education, and indicates how affective factors can be included in research that uses an information-processing perspective. The affective domain is described in terms of student beliefs, attitudes, and emotions, and research on each of these aspects is summarized. The application of various information-processing concepts (such as short-term memory and automaticity) in research on affect is discussed, and strengths and weaknesses of the approach are indicated.

Locus of Control and Mathematics Instruction: Three Exploratory Studies.

The relationship between locus of control and three dimensions of discovery learning was investigated in a series of studies. Mathematics students were randomly assigned to treatments that differed in level of guidance, inductive or deductive sequencing, or use of small groups. A significant aptitude-treatment interaction occurred between locus of control and small-group instruction on the topic of networks. The other studies did not produce significant interactions, although varying the level of guidance did produce a trend in the predicted direction. Using inductive or deductive sequences of instruction did not appear to interact with locus of control.

The Interaction of Field Independence with Small-Group Instruction in Mathematics

This study tested the hypothesis that the cognitive style of field independence would interact with treatments that dif fered in the use of small groups as opposed to individual in struction. Students (N = 111) were assessed on field inde pendence and general ability and randomly assigned to treatments for a week of instruction. Achievement was measured by an immediate posttest and a delayed retention test, and student ratings of instruction were obtained. There was a significant (p < .05) interaction with measures of field independence when achievement was the dependent variable, but not when student ratings were used. However, the interaction appeared to be due more to general ability than to cognitive style. Also, students gave significantly higher ratings to small-group instruction.