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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
Causes of Negative 2
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
Causes of Negative 3
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
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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
Causes of Negative 5
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
Causes of Negative 6
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
Causes of Negative 7
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
Causes of Negative 8
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
Causes of Negative 9
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
Causes of Negative 10
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
Causes of Negative 11
(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).
Causes of Negative 12
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
Causes of Negative 13
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
Causes of Negative 14
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
Causes of Negative 15
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
Causes of Negative 16
attitudes about mathematics, lack of motivation, and the adverse effect of
math anxiety on our students.
Causes of Negative 17
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Causes of Negative 18
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