A student’s attitude toward mathematics is not a one-dimensional construct. Just as there are different types of mathematics, there potentially are a variety of attitudes towards each type of mathematics (Leder, 1987).
Despite inconsistent definitions of attitude relative to mathematics, Fennema (1977) suggests that research supports these “tentative conclusions”:
1. A significant positive correlation exists between student attitudes and mathematics achievement—this relationship increases as students proceed through the grades.
2. Student attitudes toward mathematics are quite stable, especially in Grades 7–12.
3. The middle grades are the most critical time period in the development of student attitudes toward mathematics.
4. Extremely positive or negative attitudes tend to predict mathematics achievement better than more neutral attitudes.
5. Gender-related differences in attitudes towards mathematics exist, perhaps related to similar gender-related differences in confidence or anxiety measures relative to learning mathematics.
Students develop positive attitudes toward mathematics when they perceive mathematics as useful and interesting. Similarly, students develop negative attitudes towards mathematics when they do not do well or view mathematics as uninteresting (Callahan, 1971; Selkirk, 1975). Furthermore, high school students’ perceptions about the usefulness of mathematics affect their decisions to continue to take elective mathematics courses (Fennema and Sherman, 1978). High levels of positive feeling toward mathematics and intrinsic motivation are important prerequisites for student creativity, student use of diverse problem solving strategies, and deep understanding of mathematics (McLeod and Adams, 1989; Schiefele and Csikszentmihalyi, 1995). • Elementary students think that mathematics is difficult. In fact, if something is easy, they conclude that it cannot involve mathematics. As they get older and the once difficult mathematics now seems easy, students adjust their view of mathematics to ensure that it is difficult and unfamiliar (Kouba and McDonald, 1987).
Research on student locus-of-control has revealed a growing amount of “fatalism” in middle school mathematics classrooms that seems to persist through high school. Students state that they are “not in control” when they try to solve a mathematics problem, as “something or somebody else pulls all the strings.”
Furthermore, the attitude can develop into a belief that they cannot solve mathematics problems (Haladyna et al., 1983). The development of positive mathematical attitudes is linked to the direct involvement of students in activities that involve both quality mathematics and communication with significant others within a clearly defined community such as a classroom (van Oers, 1996). One out of every two students thinks that learning mathematics is primarily memorization (Kenny and Silver, 1997). Students rapidly lose or ignore meaning in mathematics when in middle school, a time when symbols take on “a life of their own” with few connections being made to conceptual representations. The result is an overuse of rote rules or procedures with no effort on the students’ part to evaluate the reasonableness of any answers they obtain (Wearne and Hiebert, 1988b).
Students believe that mathematics is important, difficult, and based on rules (Brown et al. (1988). Similarly, students associate mathematics with uncertainty, with knowing, and being able to get the right answer quickly (Schoenfeld, 1985b; Stodolsky, 1988). In turn, Lampert (1991) suggests that “these cultural assumptions are shaped by school experience, in which doing mathematics means remembering and applying the correct rule when the teacher asks a question, and mathematical truth is determined when the answer is ratified by the teacher” (p. 124). • Students exhibit four basic “dysfunctional” mathematical beliefs (Borasi, 1990; based on a review of Buerk, 1981, 1985; Oaks, 1987; Schoenfeld, 1985a):
1. The goal of mathematical activity is to provide the correct answer to given problems, which always are well defined and have predetermined, exact solutions.
2. The nature of mathematical activity is to recall and apply algorithmic procedures appropriate to the solution of the given problems.
3. The nature of mathematical knowledge is that everything (facts, concepts, and procedures) is either right or wrong with no allowance for a gray area.
4. The origin of mathematical knowledge is irrelevant—mathematics has always existed as a finished product which students need to absorb as transmitted by teachers.
Students’ beliefs about mathematics can weaken their ability to solve nonstandard problems in mathematics. For example, if students believe that they should be able to complete every mathematics problem in five minutes or less, they will not persevere when trying to solve a problem that requires more than five minutes. The problem is that these beliefs are built from their perceptions of mathematics that is experienced continually in classroom situations (Schoenfeld, 1985a; Silver, 1985). Teachers confront “critical moments” in their mathematics classroom by making decisions that reflect their personal beliefs about mathematics and how it should be taught (Shroyer, 1978). Student attitudes toward mathematics correlate strongly with their mathematics teacher’s clarity (e.g., careful use of vocabulary and discussion of both the why and how during problem solving) and ability to generate a sense of continuity between the mathematics topics in the curriculum (Campbell and Schoen, 1977).
The attitude of the mathematics teacher is a critical ingredient in the building of an environment that promotes problem solving and makes students feel comfortable to talk about their mathematics (Yackel et al., 1990). Many students respond intensely and negatively when they confront word problems that involve multiplying or dividing by decimals less than one. This negative reaction is triggered by the students’ solution process (though possibly correct) because it contradicts their expectations that in mathematics “multiplication makes bigger, division makes smaller” (L. Sowder, 1989). Students who attribute their success in mathematics to high ability or effort will be motivated to learn mathematics. In contrast, students who attribute their lack of success in mathematics to low ability or the material’s difficulty will not be motivated to study mathematics and expect not to be able to learn mathematics. Mathematics teachers need to intervene to help the unmotivated students realize that success in learning mathematics is related to effort (Weiner, 1984). Teaching children to both set personal learning goals and take responsibility for their own learning of mathematics leads to increased motivation and higher achievement in mathematics (DeCharms, 1984).
Teacher feedback to students is an important factor in a student’s learning of mathematics. Students who perceive the teacher’s feedback as being “controlling and stressing goals that are external to them” will decrease their intrinsic motivation to learn mathematics. However, students who perceive the teacher’s feedback as being “informational” and that it can be used to increase their competence will increase their intrinsic motivation to learn mathematics (Holmes, 1990). Mathematics teachers have little understanding of the actual beliefs of students relative to their intrinsic motivation in mathematics classrooms. Thus, teachers build mathematics lessons based on their personal conceptions of intrinsic motivation, which may not be appropriate in every situation. When given techniques for both giving attention to and being able to predict student beliefs, mathematics teachers are able to “fine-tune their instruction to turn kids on to mathematics” (Middleton, 1995).
Mathematics teachers need to focus their students’ motivation and persistence on both “deriving meaning from the mathematics task rather than just getting the task done” and “developing independent thinking skills and strategies for solving mathematics problems rather than on obtaining the one right answer to the mathematics problem” (p. 12) Peterson (1988). Students “learn” to believe that mathematical processes are “foreign to their thinking.” This learned belief causes them subsequently to forgo common sense and not use the wealth of their personal knowledge when solving mathematical problems (Baroody and Ginsburg, 1990).
Students’ views of mathematical truth and the value they place on the practicality of mathematics often interfere with their conceptual growth in mathematics, especially in regard to their appreciation of the need for formal thinking (Williams, 1991). Confidence scores are good predictors of students’ decisions on enrolling in elective mathematics classes, especially for female students (Sherman and Fennema, 1977).
High-confidence students have more interactions about mathematics with their teachers than low-confidence students and these interactions tend to be on a higher cognitive level. Mathematics teachers perhaps are unconsciously sending a message to the low-confidence students that they also have less ability in mathematics and thus should expect less of themselves mathematically (Reyes, 1980). A meta-analysis of 26 research studies concludes that there is a consistent, negative correlation between mathematics anxiety and achievement in mathematics. This correlation is consistent across all grade levels, both gender groups, and all
ethnic groups (Ma, 1999). The most effective ways to reduce mathematics anxiety are a teacher’s use of systematic desensitization and relaxation techniques (Hembree, 1990).
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