Research on Motivation and Learning

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Research on Motivation

In summarizing 20 years of research in the area of motivation in mathematics education, James A. Middleton and Photini A. Spanian (2002) found five main factors that influence motivation:

First, motivation or lack of motivation is learned. In primary grades many children report that mathematics is their favorite subject. However, educators follow grouping practices, which convince students in the middle grades that only the fast students can succeed and success is an innate ability. These poor attitudes extend to high school and college with students attempting to avoid the subject where they feel they are poor learners.

Second, motivation hinges on students' perception of their abilities to succeed or fail. Researchers have found that if students are successful about 70% of the time they will continue to be engaged.

Third, intrinsic motivation is better than a reward. Thus mathematics teachers must find strategies that interest the student in significant, rich mathematical thinking.

Fourth, inequities are influenced by how different groups are taught to view mathematics. Past studies have indicated that teachers expect greater success from boys studying mathematics and expect more boys to study higher level mathematics. The gender gap on national assessments has been closing, and the trend is for more girls to take more advanced mathematics courses in high school, but a gap still exists. The same can be said about differences across racial and ethnic groups.

Fifth, teachers do matter. "Students in inquiry-based classrooms are less likely to believe that the teacher's way ... leads to success" (Middleton & Spanian, 2002). Instead they come to believe that success comes from working hard to understand the mathematics. Teaching concepts within a context has the advantages of (1) piquing students' interest, (2) stimulating their imaginations, and (3) giving functional mathematics knowledge useful in applications.

The good news from this set of studies is that you can influence students to do, learn, and enjoy mathematics. Your best practice is to know your students-their interests and how to challenge and encourage them.

Additional Research on Learning

Kloosterman (1996) reports on a study in which he taught two classes of youngsters to solve nonroutine problems. To encourage the students to think for themselves, he refused to tell them whether their answers were correct. Soon some students refused to work, presumably because he was not doing what a teacher should do. However, after a while the students adapted and began to work very diligently to double-check their problems to ensure correctness. Kloosterman (pp. 135-137) lists the following beliefs about learning mathematics that are necessary to consider and debate:

• "Mathematics is computation." For students to be willing to persist on nonroutine problems, they must not believe that the hallmark of a good mathematician is to perform computations quickly, but rather appreciate the benefit of the ability to attack and solve problems new to their experience, even when it takes time to work one problem.
• "Mathematics requires proof." For students to become comfortable with making conjectures, they must go beyond the concept of mathematics as simply structured, deductive proof and instead perceive it as requiring mathematical justification.
• "Mathematics is useful." For students to recognize the application of mathematical procedures in solving real-world problems, they must perceive numerical operations as tools, not as goals in themselves.
• "Mathematics topics are integrated." For students to try a variety of approaches to problem solving, they must envision an integration of mathematical concepts and processes instead of a series of unrelated topics, each with its own solution method.
• "Mathematics consists of clearly defined problems." For students to learn to estimate and make reasonable assumptions, they cannot expect all mathematical problems to include only exactly what is needed in the problem.

A group of exemplary high school teachers conducted action research by alternatively teaching units with either direct instruction or guided discovery methodology to examine students' preferences and beliefs about learning mathematics. The teachers had been trained in constructivist techniques in an extensive 3-year professional development program. Three of the teachers primarily taught the innovative curriculum, Interactive Mathematics Program (IMP). A fourth teacher who had previously taught this curriculum began a new position in a very traditional school with a traditional mathematics curriculum. The teachers collaborated to rewrite the IMP materials into direct instruction format and the traditional curriculum into discovery lessons. They varied the order of presentation methods of several units of coursework and surveyed the students to find their preferences in modes of instruction. Half of the students had a strong preference for guided discovery, one-fourth had no preference, and one-fourth preferred direct instruction. The statistically significant results showed that students were more likely to feel positive about their mathematics class and more likely to rate themselves highly on their mathematics ability when taught by guided discovery. These results held when gender, grade level, course grade, or previous curriculum experience were considered. A majority of students enjoyed some teaching and learning with each pedagogy, that is, they liked variety. The students had remarkably mature thoughts on the research. One said, "The teachers should decide which method to use based on the concepts in the curriculum" (Callis, 1997, p. 57).