causes of negative attitudes toward mathematics in middle school students

Causes of Negative 1

Introduction

“I’m not good at math”, “I hate math” or “math is too hard” are

common phrases heard by teachers and parents. “One of the curious

aspects of our society is that it is socially acceptable to take pride in not

being good in mathematics” (National Council of Teachers of Mathematics

[NCTM], 1991, ¶16). Where do these attitudes and beliefs come from? Can

they be changed? Through reviewing literature, three main ideas surfaced

as possible reasons students dislike math: math anxiety, lack of motivation

in mathematics, and a negative attitude toward mathematics.

Math Anxiety

Math anxiety is a condition in which students experience negative

reactions to mathematical concepts and evaluation methods (Cates &

Rhymer, 2003). Math anxiety can lead to several consequences. For

example, Suinn and Richardson (1972) found that mathematics anxiety

may prevent students from pursuing higher-level math courses and HO,

Senturk, Lam, Zimmer, Hong, Okamoto, Chui, Nakazawa, & Wang (2000)

stated, “math anxiety has been found to have a negative relationship with

mathematics performance and achievement” (p.362). Anxious individuals

may avoid mathematics classes, may be more likely to have negative

attitudes toward mathematic related activities, or if they become

elementary teachers, may not spend as much time teaching mathematics

as their less anxious colleagues (Ho et al., 2000). Several studies have


proposed that math anxiety has two dimensions: affective (nervousness,

tension, dread, fear) and cognitive (worry) (Meece, Wigfield, & Eccles,

1990; Wigfield & Meece, 1988; Ho et al., 2000).

Ho et al. conducted a study across three nations consisting of 671

sixth grade students from China (211, 92 girls and 119 boys), Taiwan (214,

106 girls and 108 boys), and the United States (246, 111 girls and 135

boys). The focus in this study was to address the differential predictions of

the affective and cognitive factors of math anxiety for mathematics

achievement. For the anxiety measure the MAQ (Math Anxiety

Questionnaire) was used. It contained 11 items using a Likert scale and

contained items in the cognitive and affective dimensions. For the math

achievement dimension, two similar tests were given 4 to 6 weeks apart

with reliability coefficient of .82. One third of the items were from

textbooks, one-third from another cross-national study, and the other third

developed by the researchers. The relationship between the affective

math anxiety factor and achievement showed a strong negative effect

(p<.05). Cognitive anxiety was inconsistent across the samples. China and

U.S. samples were not significant, whereas, Taiwan had significant and

positive effects (p<.05) from cognitive anxiety. Analysis of the gender

interaction showed only Taiwan had significant effect with girls having

higher affective anxiety (p<.05). Taiwanese and U.S. girls had higher

cognitive anxiety (p<.05) than Taiwanese and U.S. boys. Gender

differences in China were not significant. In mathematics achievement


only the main effect for nation was significant (p<.05). Gender and

interaction of gender by nation were not significant. The results suggest

that the affective factors of math anxiety are consistently related to

mathematics achievement, while the cognitive factors yield inconsistent

results. Ho et al. (2000) conclusion is that the affective dimension of math

anxiety correlates more strongly with negative performance than does the

cognitive dimension.

Meece, Wigfield, & Eccles (1990) conducted a 2-year long

longitudinal study that focuses on the influence of math anxiety on

students' course enrollment plans and performance in math. The study

had two goals; to identify important predictors of math anxiety and assess

the predictive influence math anxiety has on enrollment plans. The sample

included 250 students in 7th through 9th grade at predominantly white

middle-class suburban communities. The 7th and 8th grade students were

enrolled in classes of approximately equal difficulty. Ninth grade students

were enrolled in regular algebra or advanced algebra. Seven students

were enrolled in a slow-paced algebra class. Questionnaires were

administered in the spring of year one and two. The Student Attitude

Survey (SAQ) was used which contains items to assess students

expectancies for success, perceived values, perceived ability, perceived

effort, perceived task difficulty in both math and English, and several other

items. Most items were assessed using two or more 7 point Likert scale

items. Predictor variables were divided into three factors. The perceived


math ability measure consists of three items tapping students' sense of

their math ability and how well they were doing in math. The expectancies

measure consists of two items asking students how well they expected to

do in their current math class. The importance measure consists of items

asking students to rate how important it is for them to do well at math and

to get good grades. The SAQ also includes an item asking students to

indicate whether they would take more math classes in the future if they

were not required. A measure of math anxiety was included in the second

year of the study. It contained 11 items to assess cognitive (concern about

doing well in math) and negative affective dimensions of math anxiety.

Math achievement information was collected on each student for both

years from school records. The final grade for each year was used. The

study suggests those students' current performance expectancies in

mathematics (highly significant at p<.01) and to a lesser extent perceived

importance of mathematics have the strongest direct effect on their

anxiety and are stronger predictors of performance and course enrollment

than math anxiety. Their findings also support the idea that it is the

students’ interpretations of their achievement outcomes and not the

outcomes themselves that have the strongest effects on students'

affective reactions to achievement.

Other studies have focused on the effect anxiety has on

achievement. In one such study, Ma (1999) conducted a meta-analysis

consisting of 26 individual studies that investigated the relationship


between math anxiety and achievement in math. The population

correlation for the relationship between math anxiety and math

achievement between the studies was significant (p<.01). The U3 statistic

corresponding to the population correlation is .71. This indicates that “the

measures (or treatments) that resulted in movement of a typical student

in the group of high anxiety into the group of low anxiety would be

associated with improvement of the typical students level of achievement

from the 50th percentile to the 71st percentile” (Ma, 1999, p. 528). This

study suggests that there is a significant relationship between anxiety and

achievement. It also quantified the potential improvement when anxiety is

reduced. Most studies have emphasized addressing affective factors, but

the significance of the relationship indicates the value of addressing

cognitive based treatments such as skill development (Ma, 1999).

Cates & Rymer (2003) conducted a study that builds on MA’s (1999)

meta-analysis study, by connecting it to the learning hierarchy. The

learning hierarchy suggests that there are four stages of learning:

acquisition, fluency, generalization, and adaptation. Their purpose was to

investigate the extent to which level of math anxiety may be related to a

more advanced stage of the learning Hierarchy than to the initial

acquisition stage by assessing fluency as opposed to overall accuracy. The

study involved fifty-two college students taking an introductory

psychology. They were given the FSMAS (a mathematics anxiety test) and

divided into a low anxiety group and a high anxiety group. These groups


were then given a timed math probe with multiple operations including

addition, subtraction, multiplication, division, and linear equations. The

results showed a significant difference (p<.05) on fluency between high

and low anxiety groups. “Students with lower anxiety completed more

digits correct per minute an all probes. There was no significant difference

in error rates between high and low anxiety groups. Both groups were

equally accurate on basic mathematics operations” (Cates & Rymer, 2003,

p 30). These results suggest that fluency in math may be more related to

math anxiety than overall performance. In other words, math anxiety may

increase with problem complexity. One implication is that as students

progress through high school and classes become more complex their

anxiety level will increase.

Motivation

Motivation can be divided into two categories: extrinsic and intrinsic.

Extrinsic motivation is desire to obtain rewards for academic tasks, such as

grades, or avoid punishments. "Academic intrinsic motivation is the drive

or desire of the student to engage in learning ‘for its own sake’”

(Middleton & Spanias, 1999, p. 66).

Schiefele & Csikszentmihalyi (1995) conducted a study to answer

questions related to motivation. First, is quality of experience when doing

mathematics more dependent on ability or motivational characteristics?

Second, are subject-matter-specific measures of motivation more

predictive of quality of experience and achievement than general


measures of motivation? Third, do motivational characteristics and quality

of experience when doing mathematics predict achievement in

mathematics independently of ability? The study included 108 freshman

and sophomores from two suburban high schools. From the 108 students,

teachers nominated students they thought were talented in one or more

subject matters. Students were given a questionnaire to gauge interest in

mathematics and achievement motivation. Ability was measured by scores

on the PSAT (Preliminary Scholastic Aptitude Test). Quality of experience

was measured using the Experience Sampling Method (ESM). This method

provides the subject a pager and throughout the day whenever the subject

is signaled they fill out the questionnaire. Semester grades were used as

an indicator of mathematics achievement. Students who were talented in

mathematics had significantly higher (p<.001) values for mathematic

ability, better grades for the first four years, and a higher course level than

those talented in other subjects. The results clearly indicate that interest

was the strongest predictor of quality of experience in the mathematics

class (Schiefele & Csikszentmihalyi, 1995). Specifically, interest showed

significant relations to potency (p<.01), intrinsic motivation (p<.05), self-

esteem (p<.01), and perception of skill (p<.001). “Surprisingly, level of

mathematic ability was not related to experience at all” (Schiefele &

Csikszentmihalyi, 1995, p. 173). This study suggests that teachers should

create more interest in order to improve motivation. Wiess (cited in

Schiefele & Csikszentmihalyi, 1995), for example, found that teachers tend


to emphasize learning facts and principles and to develop a systematic

approach to problem solving. Their methods were lecture, discussion, and

seatwork. These approaches however, may not create much interest in

mathematics.

Anderson (2007) conducted a qualitative study to address “the notion of

identity, drawn from the social theories of learning as a way to view

students as they develop as mathematics learners” (p. 7). The students in

this study were participants in a larger study of students’ enrollment in

advanced mathematics classes. Fourteen students were selected from one

high school for semi-structured interviews. Two groups were formed:

students enrolled in Precalculus or Calculus and students not taking a

mathematics course that year. All of the students had taken the two

required and any elective high school mathematics in the same high

school. “One teacher taught most of these courses. When interviewed, this

teacher indicated the ‘traditional’ nature of the curriculum and pedagogy:

‘We’ve always stayed pretty traditional… We haven’t really changed it to

the really ‘out there’ hands-on type of programs.’” (Anderson, 2007, p. 7-

8) Anderson (2007) describes the four faces of mathematics identity (how

we define ourselves and how others define us as mathematics learners) as

engagement (direct experiences in the classroom), imagination

(envisioning how activities fit into the big picture), alignment (how the

curriculum fits with future plans), and nature (abilities we’re born with).

From the interviews, the social learning theory, and previous studies


conclusions are drawn about how the four faces impact a students’

mathematic identity. “Some students may not identify themselves as

being a ‘math person.’ Students may mistakenly believe that they are

unable to learn mathematics or they weren’t born with the genetics

needed to be good at math, but scientific evidence does not support these

ideas” (Anderson, 2007, p. 8).

While all four faces contribute to the formation of students’ identities

as mathematics learners, the nature face provides the most unsound

and unfounded explanations for students’ participation in the

mathematics community. To allow for the development of all

students to identify as mathematics learners, students and teachers

must discount the nature face and build on the other three faces of

identity (Anderson, 2007, p. 11).

“Mathematical tasks that engage students in doing mathematics,

making meaning of mathematics, and generating their own solutions to

complex mathematical problems can be beneficial in engaging students

and supporting their identity as mathematics learners” (NCTM as cited in

Anderson, 2007, p.12). Anderson (2007) suggests that to increase interest,

instruction should involve more active and student-centered activities.

“Teachers can reinforce the idea that mathematics is an interesting

subject, used in other disciplines, and is an admission ticket for colleges

and careers. Teachers could have working professionals to visit the classes


and share how they use mathematics in their profession” (Anderson, 2007

p. 12).

Stipek, Salmon, Givvin, & Kazemi (1998) ask the question: What are

the associations between teaching practices, student motivation and

mathematics learning? In their study, twenty-four 4th through 6th grade

teachers were selected from schools in a large urban ethnically diverse

area. Three groups were formed. Two groups had expressed a

commitment to implementing reforms and agreed to teach using a reform-

oriented unit on fractions. One of those groups was given training on

implementing reforms. The third group taught using standard methods

and textbooks and expressed no interest in reforms. Six hundred ninety

four (694) students of diverse ethnic backgrounds participated. Each

teacher was videotaped for at least two periods and evaluated for teaching

practices and a questionnaire was given asking teachers about their

assessment practices. Students completed a questionnaire twice: once

before the intervention and once after the unit on fractions related to

motivational dimensions. Students were also evaluated from the

videotapes of the classroom. Students were assessed on fractions from

routine to conceptually challenging. Tests were given at the beginning of

the year and after the fractions unit. The effects on student motivation

based on teacher practices were significant between help seeking

(p<.001) and enjoyment (p<.05) with the positive affective practices of

the teacher. The effects were also significant for positive emotions


(p<.05), enjoyment (p<.05) and learning conceptual items (p<.05) with

the learning orientation practices of the teacher. The learning orientation

of the teacher refers to the teacher giving timely and substantive feedback

and focuses on improvement and mastery over grades. The study

suggests that the affective climate is a strong predictor of students’

motivation and fosters mastery orientation in students.

“Students’ feeling of relatedness to their teachers was strong

predictors of their cognitive, behavioral, and emotional engagement in

classroom activities” (Stipek et al., 1998, p. 483). Davis, Maher, and

Noddings (1990) gave this example:

Jaime Escalante, the real-life hero of the film Stand and Deliver,

insists that he must teach his students for three years if they are to

succeed in AP calculus. He conscientiously builds relations of care

and trust with each student. He shows steady concern for the

integral development of his students – how they are doing in English,

how their home lives are going, what jobs and sports they

participate in. This attitude and effort that accompanies it are part of

teaching mathematics. As we build such relations, our students learn

to trust us. When the work is not as exciting as we’d like it to be or

when they have low moments (as we all do), students will often

persist in mathematical endeavors for their teacher. “Okay, if you

say so. I’ll do it - just for you” (p. 191).


Middleton & Spanias (1999) conducted a review of literature to

“describe theoretical orientations guiding research in mathematics

motivation and to discuss findings in terms of how they facilitate or inhibit

achievement" (Middleton & Spanias, 1999, p. 65). The conclusions are as

follows: “students' perception of success in mathematics are highly

influential in forming their motivational attitudes” (Middleton & Spanias,

1999, p. 79); “motivations towards mathematics are developed early, are

highly stable over time, and are influenced greatly by teacher actions and

attitudes" (Middleton & Spanias, 1999, p. 80); “providing opportunities for

students to develop intrinsic motivation in mathematics is generally

superior to providing extrinsic incentives for achievement” (Middleton &

Spanias, 1999, p. 81); and “Last, and most important, achievement

motivation in mathematics, though stable, can be affected through careful

instructional design” (Middleton & Spanias, 1999, p. 82).

Attitude toward Mathematics

“Attitude toward mathematics is defined as a general emotional

disposition toward the school subject of mathematics” (Haladnya et al.,

1983, p. 20). Maple and Stage (as cited in Schiefele & Csikszentmihalyi,

1995) found that “attitude toward mathematics significantly influenced

choice of mathematics major. “One of the most important reasons for

nurturing a positive attitude in mathematics is that it may increase one’s


tendency to elect mathematics courses in high school and college and

possibly to elect careers in a math related field” (Schiefele &

Csikszentmihalyi, 1995, p. 177). One of the most important factors in

students’ attitude toward mathematics is the teacher and classroom

environment.

Haladnya et al. (1983) conducted a study designed to examine

teacher and learning environment variables that were believed to be the

most powerful causal determinants of attitude toward mathematics. Over

2,000 students in grades 4, 7, and 9 participated in the study. The

students were given the Inventory of Affective Aspects of Schooling (IAAS)

that addressed student motivation, teacher quality, social-psychological

class climate, management-organization class climate and attitude toward

math. The correlations of each independent variable with attitude and

motivation were all significant (p<.05) using a one-tailed test. A path

analysis was also conducted to determine causal relationships. The

findings suggest that teacher quality (enthusiasm, respect, commitment to

help students learn, fairness, praise and reinforcement) seems to be

consistently related to attitude toward mathematics.

Wilkins & Ma (2003) conducted a study to answer questions about

how student attitudes changed from middle school to high school. Data

came from Longitudinal Study of American Youth (LSAY), a national study,

which tracked over 3,000 seventh-grade students for six years.

Information about student affect was collected (via questionnaires) and


three measures created: attitude toward mathematics, social importance

of mathematics (usefulness of math in daily lives and on the job), and

nature of mathematics (whether changes in science theory over time

cause more good than harm). The findings show that mathematical beliefs

and attitudes change gradually. “However, the important trend highlighted

in this study is that students in secondary school become increasingly less

positive with regard to their attitude toward mathematics and their beliefs

in the social importance on mathematics” (Wilkins & Ma, 2003 p. 58).

Students’ notions of the nature of science showed little change. In regard

to middle school changes, attitude and social importance of mathematics

declined at a significantly slower rate (p<.001) for students with positive

teacher push and positive peer influence. Parental push was also a

significant (p<.05) influence. In high school, positive peer influence

(p<.001), positive teacher push (p<.05), and curriculum (students taking

higher math) (p<.001) were related to slower rates of decline in attitude

and social importance. Wilkins and Ma (2003) make several observations

and suggestions such as: “If teachers hold high expectations and present

students with challenging mathematics, then students may be more likely

to enjoy mathematics and recognize it usefulness” (p. 59) and “teachers’

choice of activities and mathematics problems can have a strong impact

on the values that are portrayed in the classroom and on how students

view mathematics and its usefulness” (Wilkins and Ma, 2003, p. 59).

Supporting positive peer networks and involving parents in school


activities involving mathematics can help slow decline of students’

negative attitude toward mathematics (Wilkins & Ma, 2003).

Ma & Kishor (1997) conducted a meta-analysis of 113 studies to

examine the relationship between attitude toward math and achievement

in math. Although the study produced no significant results, there was an

indication that junior high may be the most important period for students

to understand and shape their attitude as it relates to their achievement in

math. Therefore, the junior high years may provide teachers an

opportunity to treat negative attitudes toward math and foster high

achievement.

Summary

It is clear from the research reviewed that math anxiety, motivation,

and attitude all play important roles in whether or not students will pursue

advanced mathematics courses and careers in math related fields. As the

National Council of Teachers of Mathematics (1991) suggests, it has not

only become acceptable to not be good at mathematics, but acceptable to

be proud of not being good in mathematics. Many suggestions have been

offered to address the problem, for example: change teaching methods,

get students actively involved in learning mathematics, show students the

relevance of mathematics in their lives, build relationships with the

students, promote a positive affective environment, and create interest in

the mathematics field are just a few. In any case, the affective

environment can play a large role in reversing the trend of negative


attitudes about mathematics, lack of motivation, and the adverse effect of

math anxiety on our students.


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causes of negative attitudes toward mathematics in middle school students

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