Mathematics reforms and motivation research converge

Diverse Elementary ClassResearch on motivation has proved that classroom practices can be designed to nurture motivation.  In the present study, researchers examined whether reforms in mathematics education nurture motivation to learn, and whether this leads to increased achievement.

Deborah Stipek, Julie M. Salmon, Karen B. Givvin, and Elham Kazemi, University of California/Los Angeles; Geoffrey Saxe, University of California/Berkeley; and Valanne L. MacGyvers, University of Southwestern Louisiana, assessed the links between instructional practices, motivation, and the learning of fractions with 624 fourth-through-sixth-graders.

Increasing motivation

Reformers share several objectives for improving motivation and, subsequently, learning. These include:

1. a focus on understanding mathematics concepts as well as getting the right answers,

2. self-confidence as mathematics learners,

3. willingness to take risks and approach challenging tasks,

4. enjoyment in doing mathematical activities and positive feelings about math in general.

This study makes a distinction between a learning orientation, defined as a focus on developing skills, increasing understanding, or achieving mastery, and a performance orientation, a focus on looking smart or avoiding looking incompetent. Mathematics reformers have recommended instructional practices that include giving students opportunities to discuss mathematical problems and solutions, incorporating students’ inadequate solutions into instruction (conveying that mistakes are a natural, helpful part of the learning process) and giving substantive feedback rather than scores or grades. In this study, Stipek et al. examined, in regular classroom settings, how these instructional practices affected student motivation and how they related to the learning of fractions.

This study involved students in 24 classes in several school districts in a large, ethnically diverse urban area. Fourth-, fifth- and sixth-graders were assessed at the beginning of the year and again after they had completed a unit on fractions. All the schools served predominantly low-income children, with 25 percent of the students having limited English proficiency. Classes averaged 32 students.

To ensure a broad range of instructional practices, three groups of teachers were selected. Two of the groups had expressed a commitment to implementing reform-oriented mathematics; they had attended workshops and had previously taught the fractions unit aligned with reform objectives. One of these two groups had been involved in a year-long intensive intervention designed to help them implement instructional reforms. Teachers in a third group (matched by grade level and experience) used textbooks, followed traditional teaching methods and expressed no interest in reform-oriented math practices.

The researchers made two videotapes in each teacher’s classroom and, in addition, observed each teacher giving at least two fractions lessons. They coded teachers’ practices along nine dimensions:

1. the degree to which the teacher emphasized student effort and conveyed the message that effort will eventually pay off ;

2. the degree to which the teacher encouraged students to focus on learning, understanding and mastery by encouraging them to try new strategies, to explain their strategies, and to apply new concepts;

3. the degree to which the teacher emphasized performance (getting answers right, high grades) by praising or criticizing their performance;

4. the degree to which the teacher encouraged and gave opportunities for students to work autonomously by pointing out resources in the room, encouraging students to evaluate their own performance, giving them choices in how to solve problems, and refraining from offering unnecessary help;

5. the frequency with which teachers made social comparisons such as commenting about children’s performance relative to others’, displaying a chart of performance or asking for a show of hands to see who got the right answer;

6. the kind of affect teachers displayed, whether generally negative (anger, sarcasm, dissatisfaction, aloofness) or positive (sensitivity, respect, interest);

7. the level of teachers’ enthusiasm for and interest in mathematics;

8. the type of environment the teacher fostered, whether threatening (ignoring wrong answers, using tests as threats, tolerating put-downs among students) or risk-supportive (conveying that mistakes are O.K., providing scaffolding for a child having difficulty, refusing to tolerate students’ putting one another down);

9. the degree to which teachers emphasized speed in completing tasks.

Teachers also completed a questionnaire about the kinds of evaluation they used. And students answered a questionnaire about motivation in the beginning of the year, and again when they finished the fractions unit.

Encouraging risk-taking

Data from this study suggest that it is possible to reliably describe teachers’ typical instructional practices from a small number of observations. Teachers were consistent in their teaching practices. Teachers who scored high on a learning orientation were able to convey to students that effort and persistence pay off. In addition, teachers who held a learning versus a performance orientation were more likely to exhibit a positive manner in class and were less likely to treat students differently based on their perceived ability or achievement. These teachers appeared to enjoy mathematics more and to try to make it interesting
for students.

Results also revealed a fair amount of consistency between students’ reports of their motivation at the beginning of the year and after completing the fractions unit. Students bring a level of motivation to academic tasks that tends to be consistent over time. Perceptions of their own ability greatly affect their motivation to perform a task. Despite that, there was a clear connection between teachers’ behavior and students’ motivation. Results of this study show that the more positive teachers provided a context that encouraged risk-taking, and that their students sought help when they needed it, were focused on learning and understanding and felt generally positive about studying fractions. Teachers’ who emphasized students’ learning, mastery, effort and autonomy made learning fractions more enjoyable.

This same set of instructional practices appeared to have positive effects on students’ learning as well as their motivation. In classes where teachers emphasized effort and learning, de-emphasized performance and encouraged autonomy, students made substantially greater gains on conceptual understanding. Such practices, however, do not necessarily enhance procedural skills. It appears that orienting students toward learning rather than performance engenders more active learning strategies such as reviewing poorly understood material, asking questions, planning, setting goals and monitoring comprehension.

The results of this study demonstrate the value of instructional practices recommended both by researchers who study motivation and by the National Council of Teachers of Mathematics Standards.

“The Value (and Convergence) of Practices Suggested by Motivation Research and Promoted by Mathematics Education Reformers” Journal for Research in Mathematics Education, Volume 29, Number 4, October 1998, pp. 465-488.

Published in ERN October 1998 Volume 11 Number 7

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