High school students' math beliefs and society.

Abstract

Research has pointed to schools and society as environmental influences on student beliefs about mathematics. This article highlights findings from two activities designed to elicit high school students' beliefs, particularly those related to gender. As a result of the activities, females in upper level classes rated themselves as having less confidence than males. In addition, viewing a movie clip was sufficient for some students to modify their descriptions of someone who is good at mathematics.

Introduction

My prior experiences with public perceptions about what it means to be good at mathematics have led me to investigate the role that society and the media play in high school students' confidence and beliefs. It seems as though some sort of justification or clarification is necessary when a female appearing to be "normal" can do mathematics. Evidently those who succeed in mathematics are males who lack social skills. I am interested in what these stereotypes are saying about those of us who enjoy mathematics. Additionally, I am concerned that similar situations may prohibit both male and female students from pursuing their interests in mathematics.

Background

As a female and former classroom teacher who has found success in mathematics, I have witnessed the wide range of beliefs about mathematics. Prior research on beliefs about mathematics has mainly focused on students' previous experience with mathematics (Bandura, 1986; Pajares, 1996; Weiner, 1986). Like Mcleod (1992) I will consider confidence as a belief about one's competence in mathematics. There is considerable anecdotal and research evidence that girls and women generally express less confidence about their mathematical capabilities than boys and men (Dweck, 1986; Willis, 2000). The subject of mathematics is unique because failure often does not lead to embarrassment. Instead students have been known to refer to their inabilities with a sort of pride (Damarin, 2000). On the other hand, those who succeed or hold some confidence in their mathematics abilities are viewed as outcasts. Research on the mathematically able has described them as a marked category in the form of deviance from the larger society (Damarin, 2000). It appears the understanding of mathematics has been placed out of the reach of most students.

To find out more about student beliefs and mathematics, it is worthwhile to consider what might contribute to them. Some prior research has pointed to schools as influencing or even promoting these beliefs. Several sources of educational influences on students' beliefs about mathematics have been identified. Valerie Walkerdine (1998) examined the stereotypes placed on girls within mathematics classrooms. In another article Walkerdine (1989) attempted to tell a stow of female classroom success by explaining that it is necessary to avoid being caught in the empiricist trap of proving the mathematical equivalence of girls. Sue Willis (1995) explained a social typification of girls' success in mathematics as due to hard work and rule-following which can play a role in teacher behaviors. Leedy, Lalonde, and Runk (2003) discovered that even in a mathematically talented group of students, girls demonstrated a lack of confidence in their abilities. Other authors have discussed how society might play a role in students' mathematical beliefs. Suzanne Damarin (2000) described how mathematicians are portrayed in the media and how this influences the mindset of teenagers and young professionals. Similarly, Jo Boaler (2002) criticized researchers and popular media for their explanation of differences in the mathematical abilities of boys and girls. Dorothy Nelkin (1986) found that Nobel Prize scientists are portrayed as 'socially removed, apart from and above most human occupations.' In addition, Tapia and Marsh (2004) explained that children's peer cultures may assist in determining their choices.

The relationship between student beliefs and societal influences is significant, especially as students consider future courses and careers. The purpose of this study was to answer several questions concerning high school students' beliefs and what influences those beliefs. In particular, I was interested in determining the beliefs about mathematics of students enrolled in a mid-size, small town high school as well as the extent to which beliefs differ by gender and/or level of mathematics being studied. I was also interested in how society influences students' beliefs and whether those influences differ according to the student's gender and/or level of mathematics studied.

Method

This study took place over a period of five weeks in the fall of 2004 in a mid-size Midwestern high school. During this time period, I visited pre-algebra, algebra II, advanced geometry, and pre-calculus classrooms once a week and administered activities designed to elicit students' beliefs about mathematics as well as the source of those beliefs. To simplify the analyses, I categorized the pre-algebra and algebra II classes as lower-level and the advanced geometry and pre-calculus as upper-level. Students at this high school take algebra and algebra II before geometry and other higher level courses.

I went to the school on four Fridays and one Monday, visiting each classroom at the beginning of the period or at the end of the period, depending on the classroom teacher's preference. All activities lasted between 15 and 30 minutes. I used the same five activities with each class of students. However, on my final visit I was not able to complete the activity with one class because they were taking final exams. In order to keep track of each student's thinking throughout the project, some class discussions were videotape recorded and all student work was collected. Fifty-five students returned signed consent forms to participate in the study, so the results are based on their responses.

Within this article, I will share activity results from the first and third week in the classrooms. The first activity, based on suggestions by Wilson and Hart (2001), students were asked to rate their confidence in mathematics on a scale of one to ten and explain what it is about mathematics that caused them to rate themselves this way. Students were also asked to describe someone who is good at mathematics by using words or drawing a picture and to explain what they think about someone who is good at mathematics verses what they think about someone who has confidence in mathematics (see figure 1, website http://rapidintellect.com/AEQweb/fal2005.htm). The data collected from this activity consisted of individual student papers.

On the third Friday at the school I showed a brief and edited clip of Good Will Hunting. I selected this clip because of Damarin's (2000) mention of how mathematicians are portrayed in the movie. She claims Will is portrayed as "having more humanity and as heroic" but Professor Lambeau is "a driven character, vein in his accomplishments, disdainful of his college friend who did not realize his mathematical potential, and manipulative in his efforts to draw Will into a mathematics profession" (p. 77). The clip I used consisted of the first ten minutes of the movie where Will seems to be a regular guy by hanging out with his friends and getting into trouble. Behind the scenes he has the ability to solve challenging mathematics problems. After viewing this clip, the students answered questions about what the movie told them about people who are good at math, whether this matched their feelings about mathematics, how the clip affected their feelings about mathematics, and whether they hope to be good at mathematics (see figure 2). These responses were individually written out so that they would remain confidential. Beliefs were used as a framework to analyze the multiple data sources. Notes from the class discussion as well as written responses to each activity were examined to better understand the students' beliefs. Student opinions and perceptions were considered in relation to prior statements throughout the analysis. This approach allowed me to highlight common themes and identify any shifts in student beliefs in order to address my initial research questions and interests.

Results

Based on my initial reading of the results, I found three patterns of student responses as critical to the study. Because this article highlights two activities, I will focus on the two aspects that play a fundamental role in the activities. In particular, the students' indications of confidence and reactions to the media influences revealed a lot about their beliefs and what might influence them. I discovered some different student opinions based on gender and level of mathematics course being taken.

Confidence

Students rated their confidence in mathematics by placing a mark on a number line that extended from 0 to 10 during the first activity. The results of this self rating were fairly consistent with prior research (Leder, 1992; Leedy et al., 2003). In the two lower level mathematics classes (pre-algebra and algebra II) the female students rated themselves as being more confident than the males. The female confidence averages were 7.2 and 7.41 and the male confidence averages were 6.5 and 5.25 respectively. On the other hand, the results were reversed in the two upper-level mathematics classes (advanced geometry and pre-calculus). In this case, the male average confidence ratings were 8.33 and 8.05 while the female confidence averages were 8.31 and 6.31. It is interesting to consider what might lead to this confidence reversal in the higher level mathematics classes. Perhaps the girls begin to feel as though they do not belong in the upper level mathematics courses. When explaining why they rated themselves the way that they did 11 out of 23 students in the lower level classes explained that they were "OK" at math, or that they fall somewhere in between because they understand some things and not others. Ten of these students were females. One female student in the pre-algebra class stated "because I am good at some math, like I'm halfway. I don't know everything, but I know some ... well most." A male student in the algebra 11 class offered the explanation, "Because I can do some things but not others ..."

Students in the upper level classes offered an assortment of reasons for their self-ratings. But, nine out of 31 students offered the same explanation as the lower level students. Six females and 3 males claimed that they were "OK" at math and better at some things than at others. Eleven out of the 31 upper level students explained that they have always been good at math. Interestingly enough, seven of these students were female. Finally, 6 of the 31 students (3 male and 3 female) stated that they like mathematics. In fact, one female in the advanced geometry class said "I've always liked mathematics problems that are hard but I can still solve it in the end because I like the challenge and I love to know that I accomplished something ..." These results reveal that even though the female students in the upper level classes rate themselves as having less confidence than the males, some claim to be good at mathematics and like it.

When the students were asked to describe someone who is good at mathematics using words or pictures, they presented some interesting representations. A majority of students offered a description of this person's behaviors. Other students mentioned physical characteristics. The most common word used to describe someone who is good at mathematics was "smart", with 19 out of 55 students using this word somewhere within their explanation. However, the pre-algebra students often described this person as also studying and doing their homework. Four pre-algebra students said that this person was female and one student said the person was male. In the algebra 11 class, this person was described as someone who studies, does their homework, and helps others understand. Interestingly enough, some students in this class described this person as being female and wearing glasses; no one claimed it was male. The advanced geometry students described this person as someone who likes numbers and helps others understand. In addition, they claimed that this person is male and wears glasses. Lastly, the pre-calculus students described a person who studies, does their homework, and helps others understand. Two pre-calculus students claimed this person was female and four claimed the person was male. They also indicated that this person wears glasses. Throughout most classes, there was an indication that this person does their homework and should be able to help others understand. Perhaps the students felt as though they needed someone to bring the mathematics down to their level. Overall, more students described this person as male than female, but this was not an obvious difference. It seemed as though most students described someone that they knew was good at math, such as their math teacher. The descriptions of this person as female may be related to the fact that most mathematics teachers at their school were female.

Societal Influences and Reactions

After establishing an understanding of how these students felt about mathematics, I attempted to interpret how the popular media might influence these feelings. The clip from Good Will Hunting painted a much different picture of someone who is good at mathematics. The male character, Will is portrayed as being more normal than most mathematicians in the movies. He is un-schooled, but finds math problems to solve on chalkboards of MIT classrooms that he cleans as a janitor. Although he stops his work to solve problems and prove theorems, he is not tied to the world of mathematics (Damarin, 2000). When the students were asked what this clip told them about people who were good at mathematics, most replied that he is a "normal" guy and "'not your typical math student." Other students explained that people who are good at math can do anything and be anybody, but they are sometimes quiet. Some upper level students claimed that people who are good at math are interested in it and like it, but they are also sometimes quiet about it. Perhaps the students believed it was important to hide any sort of success in mathematics for fear of criticism. This interpretation was made because Will conceals his mathematical abilities in the movie. This is reasonable when considered in relation to Leder's (1992, p. 615) "fear of success."

The opinions of some students appear to have been transformed after viewing the clip from Good Will Hunting. In fact, 19 out of 49 students offered different descriptions of someone who is good at math than what they reported in the first activity. One male student originally described someone who is good at math as having "long hair, a beard, glasses, a mustache, and thin." In this activity he altered his description to claim "I see many people who are good at math." One female student had originally described someone who is good at math as "smart and good with numbers." She drew a picture of a male with thick glasses and pens in his front shirt pocket to support this description. However, after viewing the movie clip she claimed that "people who are good in math come in all shapes and sizes." It is interesting that most students did not mention that the changes in their opinions were associated with viewing the movie clip. The one student who did refer to the movie clip explained that she "expected mathematicians to dress nicely, behave well, and look nice." This matched her original description, but she obviously found a mismatch with the way Will was depicted in the movie. The remaining students used their responses to the question whether the movie matched their feelings or experiences with mathematics as a support or justification for their prior beliefs that were revealed in the first activity.

Discussion

These activities shed quite a bit of light on students' beliefs about mathematics. Mathematical confidence and media resources played a role in the understanding of student beliefs about mathematics. The two areas made it easier to distinguish how and why student beliefs might differ. In the beginning, most students revealed some sort of confidence in mathematics. Like the findings of Lampert (1990) and Weiner (1986), this confidence was mainly supported by their prior achievements and understanding of mathematics. However, females and males in lower-level and upper-level mathematics courses rated themselves differently on a measure of confidence. Female students in the higher level courses rated themselves as less confident than males enrolled in these courses. Leedy et al. (2003) also discovered a lack of confidence in higher achieving females. This lower rating could be a result of feeling uncomfortable or out of place in higher level mathematics courses.

The students also offered some interesting descriptions of someone who is good at mathematics. Several descriptions were linked by the common adjective "smart" while others varied by gender and level of mathematics being studied. The students pointed to several resources for their ratings and descriptions. They often described someone resembling their mathematics teacher. Damarin (2000) discussed students' views of teachers as being competent in mathematics, but she described it as a negative view point. Several students in this study described someone who is good at math as female which might serve as a positive influence.

Nonetheless, there is more that goes on in the lives of these students than attending school. The media resources utilized in the third activity had enough of an influence on the students to alter some of their prior descriptions. However, some students were not capable of recognizing or identifying these changes. Like the work of Damarin (2000), it is unfortunate the students did not see a problem with hiding success in mathematics. In some cases there was a mismatch between the students' descriptions of someone who is good at mathematics and the clip from Good Will Hunting. I was able to recognize this mismatch when reading through the data, but the students did not notice it within their own explanations and descriptions offered from week to week. Because most students did not realize they had changed their descriptions, they also were not able to identify what led them to make these changes. Although these students did not directly blame the media for influencing their beliefs about mathematics, its effect is evident in their responses.

As has been found in prior research, the beliefs that high school students hold about someone who is good at mathematics are impacted by outside influences (Boaler, 2002; Damarin, 2000; Leedy et al., 2003; Tapia & Marsh, 2004; Walkerdine, 1989, 1998). Students do not have to be a certain gender or have a certain personality to do well in mathematics. As long as they have the desire and ambition, they can find success. As some of these students have stated, regular, females can excel in the field of mathematics if given the opportunity. When students second-guess their abilities, they fall into society's stereotypical trap.

The activities described within this article encouraged high school students to think about their mathematical beliefs and how these beliefs might be influenced by society. Students participating in these activities revealed their feelings and confidence about mathematics, which is something they may never have considered. Classroom activities similar to those described here will initiate student thinking and encourage their confidence in mathematics. Breaking down the stereotypes and obstacles that exist within schools and society provides all students with opportunities to pursue their interests in mathematics.

Author Note

I thank Peter Kloostennan for providing feedback as I completed the study and editing suggestions as I organized the results.

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Shelby Morge, Indiana University in Bloomington

Shelby Morse, MS, is a Ph.D. student in Mathematics Education at Indiana University in Bloomington.