High school mathematics teachers' perception of students with math anxiety
TABLE OF CONTENTS CHAPTER I. INTRODUCTION 1 Statement of the Problem 4 Purpose of the Study 5 Significance of the Study 6 Limitations of the Study 8 Research Questions 8 Definitions of Terms 9 II. REVIEW OF LITERATURE 10 Background 10 Mathematics Anxiety 13 Causes and Effects of Math Anxiety 15 Math Anxiety and Achievement 20 Brief History of Gender Differences and Math Anxiety 32 Current Studies of Gender Debate and Math Anxiety 37 Effective Math Instruction Strategies 41 Summary 44 viii
III. METHODOLOGY 47 Research Design 47 Population and Sample 48 Procedure for Data Collection 50 Instrumentation 50 Hypotheses 52 Data Analyses 53 IV. FINDINGS 54 V. SUMMARY, CONCLUSIONS, & RECOMMENDATIONS 69 Summary 69 Conclusions 71 Recommendations for Future Research 72 Recommendations for the Profession 73 REFERENCES 74 APPENDICES 82 A. Descriptive Data 82 B. Cover Letter Seeking Permission to do Survey 84 C. Letters of Approval 91 D. Survey 95 E. Survey Comments 19 F. NIH Certificate 112 G. IRB Approval 114 ix
LIST OF TABLES
TABLE PAGE T1 Participants Years of Teaching Experience 55 T2 Participants Demographic Information 56 T3 Overall perception of math anxious students in math classes 57 T4 Comparing differences in level of participation 59 T5 Perceptions of math achievement and math anxiety 60 T6 Paired Sample T-Test comparing experience 62 T7 One-Way Anova Descriptive Data comparing teaching experience 63 T8 Test of Between Subjects Effects 64 T9 Perceptions of math anxiety and gender 65 x
Mathematics anxiety and student achievement have been a major focus of many research studies. Math achievement is a very crucial issue that high school students face today. For over two decades, math anxiety has been a serious issue for the educational system and its educators. The problem of anxiety among students has become progressively worse. Kazelskis (2000) asserts that “Not even highly able students are immune to this problem. While there is considerable interest in the treatment of math anxiety, the nature of this mathematics anxiety, its origins, and methods to alleviate it continues to be somewhat elusive” (p 140). Mathematics is more than a simple subject; it is a language that helps us describe ideas and relationships drawn from our environment. Mathematics is a tool of science and technology that enables people to explore concepts with idealized models before trying them in the real world (Clark and Fulton, 2003). Despite the curricular reforms of the 1980s, the “algebra for all” movement of the 1990s, and the arrival of No Child Left Behind in the 2000s, there is still great variety in teaching mathematics in schools across the United States. Teachers’ perceptions of their students and what those students are capable of learning, curriculum, instruction, and the assessment that teachers offer is on the front burner of education policy (Walker, 2006). Students in mathematics classes should be taught the fundamental skills they need, and be exposed to interesting mathematics problems linked to life experiences. All students
should be taught creatively and critically to solve problems. There should be rigorous topics of exploration of how mathematics relates to other subjects to expand students’ understanding of what mathematics really is (Walker, 2006). In today’s society, according to Battista (2003), for a lot of students, school mathematics is a never ending sequence of memorizing and forgetting facts and procedures that make little or no sense to them. Battista (2003) points out that numerous studies have shown that teaching mathematics the traditional way is ineffective, and it also stunts the growth of mathematical reasoning and problem solving in students. Yet traditional teaching continues, taking its toll on the nation and individuals. In spite of the shortcomings of American students in mathematics, educators have been slow to embrace the rapid change that has engulfed other areas of our life. Enter most classrooms today and very little difference from a classroom of a hundred years ago would be observed in the methods of instruction. Even though a sum of money that has been spent of technology, today’s teachers still primarily convey information to students in the form of lecture. Several billion dollars has been spent in the United States to ensure access to technology for all students (Johnson, 2000). Mathematics instruction is too important to not utilize all available resources to their full potential. The belief of many educators is that effective mathematics instruction will hinder the development of mathematics anxiety. Effective math instruction according to Pogrow (2004) is to teach Higher Order Thinking Skills (HOTS). HOTS is an alternative approach to increasing math performance through the use of technology. The math problems would be authentic and tied to the real world. Some inclusions are games, 2
simulations, problem-solving activities, challenges and discoveries. Using manipulative and real life mathematical events makes math more meaningful (Pogrow, 2004). Mathematics achievement connects directly to graduation requirements from high school. In addition to requirements for high school graduation, the workforce also requires a basic knowledge in mathematics and reading (Jacob, 2004). Research investigated by Eisenbud (2004) reports that American math education is in trouble. Many students will be ill prepared for the high-paying demanding jobs in the workforce that they will soon enter. The author further stated that the educational system does not produce students that are sufficiently versed in mathematics to fill the demands of the workforce. Eisenbud (2004) argues that in some groups, the results is catastrophic and that 97 percent of African American high school seniors test “not proficient” in algebra, according to the federal Department of Education’s National Assessment of Educational Progress. Eisenbud (2004) also reported that Robert Moses, founder of the Algebra Project, speaks of algebra as a battleground for civil-rights. Students who lack good math skills will not be able to acquire well-paying jobs, and under these circumstances, the American ideal of equal opportunity is lost. The good jobs leave the country for other shores (Eisenbud, 2004). Extensive research on math anxiety, as investigated by Berman and Furner, (2003) has tried to determine why so many people in the United States demonstrate a fear toward math. The National Council of Teachers of Mathematics (NCTM), 2000, recognizes the anxiety of mathematics in daily life and academic situations and has established criteria to help assess student’s mathematical dispositions, (Berman and Furner, 2003). 3
Statement of the Problem
Math anxiety is very real and occurs among thousands of people. Much anxiety happens in the classroom due to the lack of teachers’ consideration of different learning styles among students. A demanding need for mathematics today is a need that society requires (Curtain-Phillips, 1999). This study is intended to examine the effects of mathematics anxiety on student achievement. Literature and research have indicated that teaching students to succeed in mathematics is a national problem. Research indicates that the use of technology, especially computer-assisted instruction is superior to customary methods of instruction. A critical issue for many careers and job opportunities is a strong background in mathematics for today’s technological society (Johnson, 2000). Many students who possess the capability to go in mathematics restrict their educational options early in high school by discontinuing their training in math. High school students must earn a passing grade of 70 or above in three core mathematics courses. The core courses are Algebra I, Geometry, and Algebra II. Students must also take and pass a state mandated test, Algebra I, as one of the criteria for earning a high school diploma. The proficiency level for Algebra I is 30 or above. Reys (2001) commented to The Washington Post, 2001, that “to assume that traditional mathematics programs have shown themselves to be successful is ignoring the data base we have. The evidence indicates that the traditional methods are not serving our students well, and alarmingly only one in five of the nation’s high school seniors are proficient in math, and two in five in reading” ( p 183). 4
The math performance of students is an important aspect of their academic achievement for entering post-secondary schools. Much has been written about the decline of mathematics scores on the Third International Mathematics and Science Study (TIMSS) and Scholastic Aptitude Test (SAT) and a general weakness in mathematics instruction, the practice of setting higher standards, as well as other reform measures. Research about attitudes toward mathematics is important in determining the connection between achievement and math anxiety. The mathematical reform movement in the United States has increasingly shown some educational gain in academic performance. However, teaching students for mathematical understanding is crucial. The thinking behind the current mathematics standards NCTM, 2000, finds that the standards themselves fall short in the guidance they offer to teachers who lack the experience and confidence to teach in a way that they were not taught themselves. The poor performance and earning failing grades in mathematics courses cause many students to wait until their senior year to take the classes they failed. This produces chaos for the school’s curriculum.
Purpose of the Study
The purpose of this study is to examine the math anxious attitudes of high school students enrolled in math classes as perceived by high school mathematics teachers. The intent of the study is to determine if math anxiety contributes to poor mathematics performance. Poor mathematics achievement has been linked to environment, family structure, and background, lack of motivation to learn, teaching methods and gender. Educational researchers must be aware of those factors that cannot be controlled by 5
teachers and administrators that influence student’s achievement (Ferguson, 2000). However, they must also be aware of the factors they can control, which involves student’s self-esteem as they learn mathematics.
Significance of the Study
In a country such as the United States, where many jobs demand some level of mathematical sophistication, knowledge of mathematics is needed to obtain a desired position in the work force. In addition to its necessity in scientific and technical fields, knowledge of mathematics is increasingly important in business, social sciences, and the humanities. Many intellectually capable students avoid taking math courses in high school and in college, in spite of the importance of mathematics (Jacob, 2004). Mathematics provides students with a uniquely potent set of tools to understand and change the world. These tools include problem-solving skills, logical reasoning, and the ability to think in abstract ways. Mathematics is important in everyday life, in many forms of employment, in the medical field, the economy, the environment, in science and technology, and in public decision-making (Clark and Fulton, 2003). The special emphasis on mathematical achievement reflects the fact that competencies in mathematics have important economic consequences for individuals and for the United States. For the individual, strong mathematics competencies improve the likelihood of employment, result in higher wages once employed, and improves job productivity. The overall productivity of society’s citizens, has an important influence on the standard of living of members of the society (Clark & Fulton, 2003). 6
Well-educated and economically productive citizens normally enjoy good living conditions. Given the important link between competencies in mathematics and economic outcomes, it is in the best interest of the United States to develop a world-class educational system in mathematics (Geary and Hamson, 2004). Poor mathematical competencies restrict college major and later career choices for individuals pursuing post- secondary education. However, the more math-intensive the occupation, the higher the entry-level and subsequent wages will be. These relatively high-paying occupations include math-intensive physical sciences and engineering (Geary and Hamson, 2004). The rank of American students is disturbingly low in mathematics, but the real significance is found in the enormous gap between mathematical competencies of America’s students and their counter-parts in most other nations. The mathematical competencies of the typical American student are below international standards and even the best of educated mathematics students in the United States are, by most comparisons, no match for the best educated students in many other industrialized nations (Geary and Hamson, 2004). This research is seeking to explore the relationship between mathematics anxiety and mathematics achievement. It addresses the mathematical anxiety of high school math students. It is the intent that this study will provide some reasons for this anxiety as well as a much better understanding of students who are perceived to display attitudes of mathematics anxiety.
Limitations of the Study
The study is limited to the teachers in Wilson County and Rutherford County Public Schools. It is also limited to high school mathematics teachers in Wilson County and Rutherford County Public Schools who respond to participate in the study. It is further limited to the 2007-2008 school year.
The following research questions were designed to guide the researcher in . the study: 1. Does a statistically significant difference exist in the overall perceptions of teachers about math anxious students in calculus and trigonometry classes and the perceptions of teachers about math anxious students in Math Foundations and Algebra I classes? 2. Does a statistically significant difference exist in the perception of teachers about the level of classroom participation of math anxious students and the level of classroom participation in students who are not math anxious? 3. Does a statistically significant difference exist in the teachers’ perception of the math achievement of math anxious students and the teachers’ perception of the math achievement of students who are not math anxious? 4. Does a statistically significant difference exist in the perceptions of teachers who have taught less than five years compared to teachers who have taught six to ten years? 8
5. Does a statistically significant difference exist in the perceptions of teachers about math anxiety who have taught 11-15 years compared to teachers who taught 16 or more years? 6. Do math teachers perceive that more female students are math anxious compared to male students?
Definitions of Terms
Math Anxiety – Math anxiety is defined as a fear of math, a panic that conjures up fear of some type when faced with solving a problem in mathematics. It’s a feeling of frustration and helplessness that often stems from having a shortage of confidence to do a mathematical problem correctly (Russell, 2008). Perceive – perceive is defined as recognition and interpretation of sensory stimuli based on memory. It is defined as a means to achieve an understanding, discernment, insight, notice, observation, and judgment (Webster’s Thesaurus, 2006). 9
CHAPTER II REVIEW OF LITERATURE Background The review of literature focused on mathematics anxiety; the causes and effects of mathematics anxiety; how mathematics anxiety affects achievement; and how mathematics anxiety affects gender. It also embraced research on effective mathematics instruction strategies. “In our schools, children of today and tomorrow will need more math than our parents did. They will need to be taught in a much better way. The problem is that along with change comes conflict according to history. We are now in an information age, and need an extensive math base to support this age. Ambitious standards are required in order to achieve a society that has all the possibilities of being able to think and reason mathematically” (Marshall, 2003 p, 194) For so many people, mathematics as a discipline seems to have very negative connotations. This would not be such a dilemma if mathematics were an avoidable part of everyday life. However, this is not the case and mathematics is a part of every person’s life. It is an inescapable reality, because we are charged with learning to manage mathematical problems starting in elementary school and continue throughout the rest of our pre and post-secondary schooling (Rahim & Koeslag, 2005). In a world that is driven by technology, it is very common to see individuals that are capable of operating computers and using complex software either for work or for
play. People in the 21st Century carry pocket computers that are multi-task oriented and are capable of complex operations with the mere touch of a button. Students in today’s schools are either provided with or required to have an advanced calculator that can perform mathematical computations on demand (Ashcraft, 2002). With such powerful tools, as calculators and computers, one might be expected to perform the basic mathematical computations with ease. Unfortunately, this does not seem to be the case; void of these electronic gadgets, people exhibit feeling of anxiety when working with numbers. Students lack the elementary skills to perform these technological operations. Teachers are reverting to teaching the basic concepts of math explaining why these operations are necessary (Davis, 1999). Ashcraft (2002) found that mathematics anxiety tends to have the most dramatic impact on students when they are working on certain types of mathematical problems, especially those with large numbers or those that require several steps. Ashcraft (2002) discovered that students with high levels of mathematics anxiety manage to rush through problems making them prone to errors. When students become this math-anxious they experience greater difficulty with problems that require methods of “carrying” numbers than with problems where this method is not needed. In a historical study done by Paulos (1988), it was stated “the lack of or the inability to deal comfortable with the fundamental notions of number and chance is innumeracy, a mathematical equivalent to illiteracy”. Paulos (1988) further stated that innumeracy “plagues far too many otherwise knowledgeable citizens” (p. 3). Most of the time in mathematics, people are not embarrassed to admit their weakness, but in other subjects, they feel a need to hid this weakness or feeling of embarrassment” (p 4). 11
Since mathematics is an essential and fundamental part of life, it seems very important for people not to be afraid of math and not to shy away from the discomfort of mathematics as a subject. It does not have to be an avoidable stress (Rahim & Koeslag, 2005). There’s an immense amount of literature regarding mathematics anxiety. Carmen (2004) remarked “Research of mathematics anxiety has prospered, spurred by increasing perceptions that the construct threatens both achievements and participation in mathematics” (p. 34). North Central Regional Laboratory (2004) reported that because of the high importance of academic achievement in mathematics, any method used to teach mathematics that is successful should be encouraged. One of the first studies researched about mathematics anxiety was done by Richardson and Suinn (1972). The work done by these researchers sparked a fire and drew attention to the age old problem of learning mathematics. In today’s world, students are perplexed at the idea of doing math and why it can’t be fun. Learning basic math need not be boring and uninteresting. Students become very anxious and get confused because of their inability to comprehend basic math concepts (Jacob, 2004). The most significant factors in predicting the performance of basic mathematics were math anxiety (Bichel & Miller, 2003). Research has shown relationships between mathematics anxiety and achievement and also between mathematics anxiety and gender. A negative relationship between mathematics anxiety and mathematics achievement has been found across all grade levels, K-college through the research of (Betz, 1978; Ma, 1999). 12
In recent years, Cavanagh (2007) explains that researchers and educators alike have dug further and further into the topic of “mathematics anxiety”, or the avenues in which students’ lack of confidence in the subject of mathematics erode their academic achievement. Today, the issue is receiving renewed attention from academic scholars and practitioners who have faith that, by developing a broader understanding of the implications and causes of mathematics anxiety will be the key to improving students’ learning the subject of math.
Mathematics Anxiety Math anxiety is defined as a fear of math. It is similar to stage fright. Math anxiety conjures up fear of some type. The fear of not being able to do the math or the fear that it’s too hard or the fear of failure which often stems from having a lack of confidence. Math anxiety is the fear about doing the math right, the mind draws a blank and it thinks it’ll fail and of course the more frustrated and anxious the mind becomes, the greater the chance for drawing blanks. Added pressure of having time limits on math tests and exams also cause the levels of anxiety to grow for many students (Russell, 2008) Texas State University Counseling Center (2008) states math anxiety has become so prevalent on college campuses that many schools have designed special counseling programs to help math anxious students. They state that math anxiety is an emotional, rather than intellectual, problem. However, math anxiety can interfere with a person’s ability to learn math and therefore become an intellectual problem. 13
There are numerous definitions of mathematics anxiety. Tobias and Weissbrod (1980), and Fiore (1999) define math anxiety as “the panic, helplessness, paralysis, and mental disorganization that arises among some people when they are required to solve a mathematical problem” (p 403). Even though some anxiety can be motivating or even exciting, too much anxiety can cause “downshifting” in which the brain’s normal processing mechanisms begin to change by limiting perceptions, inhibiting short term memory and behaving in more primal reactions” (McKee, 2002, p. 2). Many people think of mathematics as a punishment or something that induces stress (Zaslavsky, 1999). Arem (2003) equates great amounts of math anxiety with test anxiety, and says it’s three- fold: Poor test-taking strategies, poor test preparation and psychological pressures. Arem (2003) notes that it’s exacerbated by poor health habits especially diet and sleep. Math anxiety is the result of negative experiences while working with teachers, tutors, classmates, parents or siblings (Jacobs, 2004). Jacob (2004) also describes math anxiety as a worry or fear of mathematics or some part of it and is usually caused by previous bad experiences with mathematics. It is a fairly common problem that reinforces math anxiety in many instances. Jacob (2004) points out lower grades in mathematics are considered more socially acceptable because it is tougher than other courses. Math anxiety is more than a psychological problem and the body’s physiological reaction to math anxiety can perpetuate the problem. The body senses the anxiety, which it interprets as fear. Pries & Biggs (2001) describe a cycle of math avoidance: In phase one, the person experiences negative reactions to math situations. These may result from past negative experiences with math, and lead to a second phase in which a person avoids 14
math situations. This avoidance leads to phase three, poor mathematics preparation, which brings them to phase four, poor math performance. This generates more negative experiences with math and brings us back to phase one. This cycle can repeat so often that the math anxious person becomes convinced they cannot do math and the cycle is rarely broken. Ashcraft (2002) a noted expert on math anxiety states that the feeling of fear and dread of math can sap the brain’s limited amount of working memory. A much needed resource to compute difficult math problems. Mathematics anxiety can be defined as an “irrational dread of mathematics that interferes with manipulating numbers and solving mathematical problems within a variety of everyday life and academic situations” (p.172). Highly mathematics anxious individuals have a strong tendency to avoid math. This eventually hurt their math competence and forecloses important career paths (Ashcraft, 2002). Krantz (1999), on the other hand describes math anxiety as an inability for intelligent people to cope with mathematics. Yet this “math anxiety is an extremely common phenomenon among high school, college and university students today” (Perry, 2004 p. 106) Math anxiety is an emotional unpleasant feeling inside a person that will hinder the learning process. Everyone has a certain amount of anxiety but it is different in the way it is managed individually (Eehai, 2007). Causes and Effects of Math Anxiety Terror, frustration, despair, anxiety and anguish, these are words of panic and they are rarely used by any competent adult in ordinary life. However, when people are asked 15
to describe the feelings that are brought on by mathematics, this is what you get (Steen, 1999). It is actually common for mathematics to carry this intense emotional baggage. For most adolescents and adults, the emotional baggage of mathematics is an overwhelming burden with no redeeming value, only mind-numbing thoughts of boredom and embarrassing frustration remarked Steen. The essence of the study done by Steen (1999) is that emotion blocks the faculty of reason to prevent otherwise capable students from coping with mathematics. Math anxiety is caused by repeated negative experiences related to mathematics. It is an effect of a conditioned mathematical fear that develops into a belief of an inability to perform mathematical problems. Physiological symptoms of math anxiety are nausea; sweaty palms difficulty breathing, tightness in the throat and chest, headaches, heart palpitating, restless behavior, and forgetfulness as found in the research of (Jackson and Leffingwell, 1999) Kunzig (1999) suggest that students’ efficacy related beliefs influence their performance and academic choices in mathematics. Students’ performance very strongly predicts their grades, but not their intentions for course enrollment. Students’ ratings of the importance of math, however, predict their course enrollment but not their grade. Kunzig (1999) agrees with treatment programs for math anxious students to help the students manage their emotional stress, but the research exposed by Kunzig on math avoidance was to face up to the cost of math avoidance and emotional stress and start the process of healing. Eehai (2007) also reported that mathematics anxiety causes a person to dislike math, because the guilt of failing to solve a math question causes one to lose self-esteem 16