Mathematics in Today's Schools (page 3)
What about the mathematics dispositions of students? There is quite a bit of research on the strong relationship between attitudes and achievement in general. Research on the student’s view of his or her own learning and success (Weiner, 1985) indicates that students who have self-perceptions of low ability or make “I can’t” statements usually debilitate their own success. An early study by Collins (1982) of children with high or low efficacy beliefs related to mathematics ability found that children who had the stronger belief in their efficacy, regardless of ability, solved more problems, chose to rework unsuccessful problems, and eventually solved more problems successfully. Other studies have confirmed the power of belief in one’s abilities. Bouffard-Bouchard (1990) found that regardless of ability level, students with higher efficacy beliefs showed greater strategic flexibility in searching for solutions, achieved higher performances, and were more accurate in self-evaluations. Schunk (1989) studied children with severe deficits in mathematics in a program of self-directed learning. Children’s learning was influenced by cognitive modeling, strategy instruction, performance feedback, and learning goals. Again, children with similar ability differed in performance on the strength of their perceived efficacy.
A student’s perceived self-efficacy is the “belief in one’s capabilities to organize and execute the courses of action required to produce given attainments” (Bandura, 1997, p. 3). Perceived self-efficacy may influence motivation, thought processes, course of action, level of effort, perseverance, and, ultimately, level of accomplishment. High self-efficacy and improved performance result when students set short-range goals, apply specific learning strategies, and receive performance-contingent rewards (Pintrich & De Groot, 1990). Self-assurance from efficacy beliefs may be the key factor that combines with capability to enable students to manage difficult tasks. The opposite disposition, learned helplessness, results when students view their failures as insurmountable and out of their control. Helplessness is accompanied by passivity, loss of motivation, depression, and declining performance.
The most influential sources of efficacy information are experience, vicarious experience, and verbal persuasion (Bandura, 1997). Students who experience success begin building positive beliefs in their abilities. However, easy successes are not helpful; experience with success in challenging tasks that require perseverance and even involve setbacks along the way lead to stronger efficacy beliefs. Vicarious experiences, or viewing models by which to compare one’s capabilities, can positively or negatively influence self-efficacy beliefs. Teachers should be cautious in using comparative models so that students focus on the instructive elements for self-improvement and not simply make an evaluative comparison. Finally, verbal persuasion, more frequently termed performance feedback, can also promote or undermine self-efficacy beliefs, depending on its use. Good persuaders must cultivate students’ beliefs in their capabilities, structure activities for success, and encourage students to engage in self-evaluation, not merely voice positive encouragers.
A critical goal for teachers providing mathematics instruction is to foster positive student dispositions toward mathematics learning. Desirable student dispositions include:
- seeing the world mathematically
- willingness to take risks and explore multiple problem solutions
- persistence with challenging problems
- taking responsibility for reflecting on one’s own work
- an appreciation for the communicative power of mathematical language
- willingness to question and probe one another’s thinking about ideas
- willingness to try different tools for exploring mathematical concepts
- having confidence in one’s abilities
- perceiving problems as challenges (NCTM, 2000; Martinez & Martinez, 1996)
Teachers know that students’ attitudes toward math can range from enthusiasm, interest, and confidence to dislike, rigidity of thought, avoidance, anxiety, and even phobia. What makes the difference? In addition to success with difficult tasks and positive performance feedback, as described previously, there is evidence that teachers’ beliefs about their instructional efficacy predicts levels of academic achievement, regardless of level of student ability (Ashton & Webb, 1986). Teachers with a high sense of instructional efficacy tend to view all students as teachable, believe they can overcome negating community influences through effective teaching, devote more classroom time to academics, maintain an orderly classroom, encourage struggling students, hold high expectations, and encourage student self-direction (Bandura, 1997). Teachers working with students with mathematics learning problems should choose significant and interesting topics, focus on understanding, have high but reasonable expectations, help students set and monitor learning goals, and acknowledge student achievements.
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