High school students' attitudes toward mathematics.

Abstract

Longitudinal data from four high schools over two school years indicate that students did not want a job using mathematics, even when they viewed mathematics as important. About half were willing to work a long time to understand new ideas or obtain a solution to a problem; slightly more than 50 percent viewed mathematics as mostly memorizing. Teachers must help students develop perseverance and broaden their view of mathematics.

Introduction

In its 1989 Curriculum and Evaluation Standards for School Mathematics, the National Council of Teachers of Mathematics (NCTM) established two goals related to affective issues: learning to value mathematics and developing confidence in one's own mathematical ability. Other documents from the same era, such as Everybody Counts, also focused on the need to change the public's attitudes and beliefs about mathematics, recognizing that too many people do not believe they can be successful at mathematics (National Research Council, 1989). In the revised Principles and Standards for School Mathematics (2000), NCTM again discussed mathematical disposition, highlighting the importance of students' confidence, interest, perseverance, and curiosity in learning mathematics. The recommendations encourage teachers to replace classrooms emphasizing low-level computation with active classrooms focusing on higher-level thinking.

Indeed, how students view mathematics as well as their attitudes toward mathematics can impact their success. Several researchers over the last two decades have found that positive attitudes can increase the tendency of individuals to select mathematics courses and consider careers in mathematics related fields (Haladyna, Shaughnessy, and Shaughnessy, 1983; Maple and Stage, 1991; Trusty, 2002). In analysis of data from the Third International Mathematics and Science Study (TIMSS) for students from Canada, Norway, and the United States, Ercikan, McCreith, and Lapointe (2005) found that the strongest predictor of participation in advanced mathematics courses was students' attitudes toward mathematics. Thus, mathematics educators need to consider these results as they try to encourage more students to consider further study in mathematics related fields.

Schoenfeld (1992) compiled a list of beliefs that many students hold, such as there is only one way to solve a mathematical problem, most students can simply memorize mathematics rather than be expected to understand it, and if a problem cannot be solved quickly then it cannot be solved. These views run counter to those that NCTM is trying to encourage. Yet, the beliefs Schoenfeld identified seem to be reinforced in studies conducted more recently. Signer, Beasley, and Bauer (1996) conducted in-depth interviews with 100 high school students about their beliefs of themselves as mathematics learners. They found that low-achieving students often believe their ability level is fixed and is the cause of their failures; hence, they avoid challenges and do not believe they can solve difficult problems. Higgins (1997) studied middle school students' mathematical beliefs; even among students who had completed a yearlong course utilizing problem-solving instruction, many still equated mathematical problem solving with learning problem-solving skills or rules. Likewise, Olson (1998) surveyed high school geometry students and found that one-third did not enjoy mathematics and close to 40 percent found their experiences with word problems to be frustrating. Perhaps this is not unexpected because word problems are not typically solved quickly. More recently, Schommer-Aikens, Duell, and Hutter (2005) studied middle school students' epistemological and mathematical problem-solving beliefs. They found that many students viewed learning as fast and instinctual. The authors pointed out that such beliefs are likely to influence students' problem-solving strategies and amount of time spent on solving problems.

The National Assessment of Educational Progress (NAEP) has included some attitude items on its regular assessments. At grade 12, the percentage of students who indicate they like mathematics has dropped from 51 percent in 1992 to 47 percent in 2000. However, the percent indicating they are good at mathematics has increased slightly from 50 percent in 1992 to 53 percent in 2000 (Strutchens, Lubienski, McGraw, and Westbrook, 2004). In analysis of TIMSS data, Kifer (2002) reported that 57 percent of twelfth-grade students in the U.S. taking advanced mathematics reported needing lots of natural ability to do well in mathematics and 89 percent reported needing lots of hard work studying at home.

The study reported here differs from NAEP and other studies in that the current study is longitudinal in nature, with attitudinal data having been collected from the same students at three points in time over two school years. Hence, the data reported here provide a measure of the robustness of students' attitudes at the high school level over time. In addition, the items from which the data derive focus on aspects of the importance of mathematics, the desire to use mathematics in a career, and perseverance in learning mathematics and solving problems; these aspects of attitude are somewhat different from those assessed in other studies cited here. Thus, data on the attitudes discussed here are important to understand as teachers work to encourage students to achieve at the levels recommended by NCTM.

Method

As part of a longitudinal study of achievement, early high school students in four schools were surveyed about a range of issues at three points in time: fall 1995, spring 1996, and spring 1997. The survey included free-response items, such as the subjects liked the most or the least, the qualities of their best mathematics teacher, their preferred instructional methods (e.g., lecture, small group), and how they used mathematics in everyday life. In addition, there were a series of Likert-scale items regarding attitudes and beliefs about mathematics as a discipline and perseverance in mathematics. Results from only the following items are discussed here:

* It is important for people to learn mathematics.

* Mathematics is harder for me than for most people.

* I will work a long time in order to understand a new idea in mathematics.

* I will work a long time in order to get a solution to a mathematics problem.

* I would like to have a job that lets me use mathematics.

* Learning mathematics is mostly memorizing formulas and rules.

* Mathematics helps me think logically.

* I think mathematics is fun.

At the initial survey administration, participants were typically freshmen or sophomores across a range of mathematics classes (prealgebra, applied mathematics I, applied mathematics II, algebra, geometry, second-year algebra) from one of four schools. School 1 (n=175) is a high school in a rural school district in the southeast; about 60 percent of the student population is Caucasian (not of Hispanic origin), with about 24 percent African American (not of Hispanic origin) and 13 percent Hispanic. School 2 (n=150) is a large high school in an inner city in the southeast with predominantly Hispanic (85 percent) or African American (12 percent) populations. School 3 (n=90) is a medium-sized school in a suburban setting in the southeast; about 80 percent of the students are non-Hispanic white with about 13 percent African American and 5 percent Hispanic. School 4 (n=208) is a large suburban school in the midwest; about 70 percent are non-Hispanic white and 20 percent are Asian. [1]

Several different curricula were used across the four schools. At Schools 1 and 4, the textbooks used were generally those developed by curriculum projects to be aligned with the 1989 NCTM Standards, such as those developed by the University of Chicago School Mathematics Project (e.g., Coxford, Usiskin and Hirschhorn, 1991; McConnell et al., 1990; Senk et al., 1990), the Systemic Initiative for Montana Mathematics and Science (Montana Council of Teachers of Mathematics, 1996a and 1996b), or Computer Intensive Algebra (Fey and Heid, 1991). In contrast, at Schools 2 and 3, the textbooks used were typical textbooks produced for algebra, geometry, and second-year algebra by major commercial publishers prior to the influence of the NCTM Standards (e.g., Dolciani, Brown, Ebos, and Cole, 1984; Dolciani, Sorgenfrey, Brown, and Kane, 1986; Smith et al., 1988). Visits were made to all of the participating schools as part of the study on achievement. Instructional strategies varied across classes, both within and across schools. A variety of instructional approaches were used, including hands-on explorations, lectures, and small group work.

Results

From schools 1, 2, and 3, data are reported only for those students who responded to the survey items at all three points in time. At school 4, the school gave the achievement tests in the fall of the first year but failed to give the survey items; hence, at this school the survey items were given at only the two spring administrations and results are reported only for those students who responded at both times. Therefore, school 4 is not included in the overall results for the fall 1995 administration. The following items are Likert-scale items with five possible responses ranging from strongly agree to strongly disagree. Results for strongly agree and agree have been collapsed together. Results for strongly disagree and disagree are also collapsed in any discussions of those data. Overall percent agreement, calculated as a weighted mean, follows each statement. Because of the problems with the survey administration for fall at school 4, total numbers for the three administrations are 415, 623, and 623, respectively.

It is important for people to learn mathematics. (91, 89, 87) Students at School 2, the inner city school, were slightly more likely to agree that math is important, but students at all four schools overwhelmingly agreed with this statement. Across schools and times, the percentage of students who agreed ranged from 80 percent to 97 percent.

Mathematics is harder for me than for most people. (21, 22, 24) In general, less than a fourth of the students agreed with the statement; slightly more than half disagreed. Agreement across schools and times ranged from 18 percent to 27 percent. Results were generally consistent at the school level.

I will work a long time in order to understand a new idea in mathematics. (49, 52, 45) This item and the following one address perseverance. Across schools and times, the percentage of students who indicated a willingness to work a long time to learn a concept in mathematics ranged from 36 percent to 57 percent. Slightly more than 20 percent of the students disagreed with the statement. Percent agreement at school 3 was somewhat lower than at the other schools.

I will work a long time in order to get a solution to a mathematics problem. (54, 54, 54) Many mathematics problems cannot be solved quickly but require sustained time to solve. From 40 to 62 percent of the students at the schools agreed that they would work a long time to obtain a solution to a mathematics problem; overall, slightly more than 20 percent disagreed. At the school level, results were relatively consistent; variability occurred across schools, with a smaller percentage of students agreeing at school 3 than at the other schools.

I would like to have a job that lets me use mathematics. (34, 34, 33) Overall, about a third of the students were interested in a job that used mathematics; about an equal number disagreed.

Learning mathematics is mostly memorizing formulas and rules. (57, 60, 56) This item addresses a view of mathematics and provides a contrast with the view of mathematics that NCTM is attempting to implement. Overall, slightly more than half of the students agreed with a view of mathematics that is contrary to a classroom focus on higher-order thinking. Across schools and time, the percentage agreement ranged from 47 percent to 65 percent.

Mathematics helps me think logically. (69, 72, 69) From 57 percent to 82 percent of the students agreed with the statement. Results were generally consistent across times within a school. At schools 2 and 4, the percentage of agreement was over 70 percent; at schools 1 and 3, agreement was in the neighborhood of 60 percent.

I think mathematics is fun. (48, 47, 46) Overall, close to half of the students agreed with the statement, with the agreement percentage ranging from 38 percent to 56 percent; slightly more than a fifth disagreed. Results were generally consistent at the school level. These responses provide another perspective on students' views of mathematics, and provide a contrast to views about the importance of mathematics. Students may view mathematics as important but may not be as likely to view mathematics as fun. This is the pattern that occurred.

Discussion

Research has shown that students' attitudes toward mathematics tend to become less positive as they get older (McLeod, 1992; Strutchens et al., 2004). However, unlike most studies dealing with attitudes toward mathematics, these data were collected from the same students over three points in time and from four schools with different environments. Results from these survey items were relatively consistent across the four schools and across time. This is true regardless of the curricular materials or the instructional strategies in use. Although care must be taken in generalizing to the entire nation from these four schools, these schools are representative of the types of schooling environments in the country. [2]

Mathematics is essential to such fields as engineering, science, and technology, as well as economics, business, anthropology, sociology, and many more. Thus, students need to study more mathematics than they currently do. It is commonly believed that students who view mathematics as unimportant and who find mathematics difficult are likely to avoid studying it. However, these results indicate that even when students overwhelmingly viewed mathematics as important, only about half of them were willing to work a long time in order to understand a new idea in mathematics or to get a solution to a mathematics problem. Perhaps even more surprising, although about 88 percent viewed mathematics as important to learn, only about one-third of these high school students wanted to have a job that lets them use mathematics, even when they did not view mathematics as harder for them than for most people. These students were evidently unaware that most jobs do assume some mathematics knowledge, such as the ability to understand and use algebraic thinking and the ability to solve problems in the work place.

Roughly comparable numbers of students thought mathematics helped them think logically and that mathematics was mostly memorizing formulas and rules. These responses would seem to be in conflict with each other. How does memorization contribute to the development of logical thought? Are students equating a set of steps in completing an algorithm with logical thought? Perhaps students have been told by teachers that math helps them think logically, but they may not really understand what this means. Although they know that math is logical, all they understand of math is the memorization. In either case, teachers need to engage students in non-routine problem-solving experiences in which they need to reason their way to a solution.

The results reported here have implications for all mathematics educators. Clearly, encouraging students to view mathematics as important is not enough. These students already recognized the importance of mathematics, yet they still did not want a job that used mathematics. Perhaps this is a reflection on how mathematics is taught in this country. Approximately 58 percent of students viewed learning mathematics as mostly memorizing formulas and rules; less than half of them viewed mathematics as fun. If this is how these students viewed mathematics, is it really a surprise that they did not want a job that used mathematics? Mathematics educators must do a better job of instilling a love of mathematics in their students. These students viewed mathematics as valuable and important, but not as fun or something they would like to use in a job.

Teachers must provide students with learning opportunities in which they experience the excitement that comes from making sense of mathematics instead of memorizing formulas and rules. This focus on making sense of mathematics is an essential component of the reform movement in mathematics education. It is also important for teachers to help students understand the role mathematics plays in fields that they might find interesting or challenging, such as engineering, science, and technology. Helping students realize these types of connections between the mathematics they are learning in school and its applications in the outside world is strongly encouraged by the reform movement.

The vast majority of high school students participating in this study said that mathematics was important. However, about half of these students reported that they lacked the persistence and perseverance to stick with mathematics in order to understand a new concept or solve a problem. Teachers need to help students understand and value extended work on mathematics tasks. Perseverance is a critical element of inquiry-based classrooms as students work together to understand mathematics.

Conclusion

The NCTM has established affective goals for all mathematics students. These include learning to value mathematics and developing confidence, interest, perseverance, and curiosity in learning mathematics. Students' beliefs about and attitudes toward mathematics have been shown to impact their participation in advanced mathematics courses and their choice of a mathematics-related career.

Unlike most studies dealing with affective issues related to mathematics, this study examined high school students' attitudes toward mathematics at three points in time over two years and from four schools with different environments and curricula. Results were relatively consistent across the four schools and across time. Students overwhelmingly viewed mathematics as important, but only about half were willing to work a long time to understand a new idea or to get a solution to a mathematics problem. They did not view mathematics as harder for them than for most people, but only about one-third wanted a mathematics-related job. They thought that mathematics helped them think logically, but they viewed mathematics as mostly memorizing formulas and rules.

These results suggest that teachers must help their students understand and value the need for perseverance in solving mathematics problems. They must help students realize the connections between the mathematics they learn in school and the mathematics-related fields that might interest them. Instead of focusing on formulas and rules, mathematics teachers should help their students make sense of the mathematics they are learning.

In addition, these results suggest that teachers should be focused not only on the mathematics content they are teaching, but also on their students' attitudes toward mathematics. Making affective goals a priority is essential if we want more of our students to choose higher-level mathematics courses and mathematics-related careers. Educators need to survey students' attitudes periodically to determine trends and/or shifts in attitudes as a result of changes in curricula or instruction. Rather than snapshot surveys of different groups of students at different points in time, more longitudinal work with the same students, as begun in this study, needs to be done. [3]

References

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Endnotes

[1] The U.S. Census 2000 (http://www.census.gov/prod/2001 pubs/c2kbr01-1.pdf) lists race and Hispanic origin as two separate items. The school questionnaire asked for the ethnic makeup of the school using the following categories: Caucasian (not of Hispanic or Latino origin), African American (not of Hispanic or Latino origin), Hispanic or Latino, Asian or Pacific Islander, American Indian or Alaska Native, or Other.

[2] Students were not asked on the survey to provide their ethnicity. Thus, we cannot provide data by ethnic group. However, students were surveyed in a range of classes from low-level courses (prealgebra or applied math) to more advanced courses (geometry and second-year algebra). Results were generally consistent across courses within a school. In visiting the classes, we have anecdotal information that we obtained data across the ethnic background of each school.

[3] Although the researchers have not followed up on this particular research, their current research related to revisions of the University of Chicago School Mathematics Project curriculum may provide an opportunity to determine the extent to which high school students' attitudes have changed since the data reported here were collected.

Joy B. Schackow, University of South Florida 

Denisse R. Thompson, University of South Florida

Joy B. Schackow, Doctoral Candidate in Mathematics Education, is interested in attitudes of preservice teachers. Denisse R. Thompson, Professor of Mathematics Education, is interested in curriculum development.