# Help Understanding Sheila Tobias Essay On Mathematics And Sex

**ACKNOWLEDGING MATH ANXIETY: **

**TECHNIQUES FOR TEACHERS, PARENTS, AND STUDENTS**

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**BY**

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**JODI ELIN EDELMUTH**

ABSTRACT OF THESIS

Submitted in Partial Fulfillment of the

Requirements for the Degree of

**Masters of Arts**

**Teaching**

** **

San Diego, California

**July, 2006**

**Table of Contents**

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__Page__

Chapter 1: **Introduction**................................................................................................................4

Background of Math Anxiety…………………………………………………………....4

Purpose of the Project……………………………………………………………….…...5

Significance of the Project……………………………………………………………….6

Areas of Investigation……………………………………………………………………7

Conclusion……………………………………………………………………………….7

Chapter 2: **Literature Review**.......................................................................................................8

** **Overview of Math Anxiety……………………………………………………………....8

Symptoms and Causes………………………………………………………...…9

Cognition………………………………………………………………..………11

Dropped Stitches…………………………………………………………..……11

Effects of Math Anxiety……………………………………………………...…12

Confidence and Motivation………………………………………………..........14

Math is Unavoidable……………………………………………………………15

Techniques for Teachers………………………………………………………………..15

Preventing versus Reducing Math Anxiety……………………………..………16

Keep It Positive…………………………………………………………………17

Classroom Environment/Teaching Style……………………………………….18

Take Away the Mystery………………………………………………….……..20

Avoid Surprises…………………………………………………………....……22

Try Something New…………………………………………………………….23

Conclusion………………………………………………………………………………25

Chapter 3: **Guidebooks**...............................................................................................................26

** **Guidebook 1: Tips for Parents………………………………………………………….27

Tip #1……………………………………………………………….…..………29

Tip #2…………………………………………………………………...………30

Tip #3……………………………………………………………………...……31

Tip #4……………………………………………………………………...……32

Bibliography……………………………………………………………..……..33

Guidebook 2: Tips for Students………………………………………………...………34

Tip #1…………………………………………………………………..…..…..36

Tip #2…………………………………………………………………..………37

Tip #3………………………………………………………………….....…….39

Tip #4………………………………………………………………..……..…..40

Bibliography……………………………………………………………..…….40

**References**………………………………………………………………………………...…..41

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**CHAPTER 1: INTRODUCTION**

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**Background of Math Anxiety**

Math anxiety, a “dread of mathematics that can interfere with manipulating numbers and solving mathematical problems in a variety of everyday life and academic situations”, is a relatively new concept (Furner & Duffy, 2002). It wasn’t until the 1970s that researchers began to investigate the concept that there were students capable of success in math whose block was mental and not related to intelligence. Sheila Tobias was a pioneer in the field of math anxiety who first set out to prove that it was anxiety, rather than a lack of ability, that was getting in the way. Before this investigation began, it was believed that those who were successful in mathematics were an elite group who were blessed with a ‘mathematical mind’ (Tobias, 1993, p.10). Mathematics achievement was not urged for every student, but only those who showed a good aptitude for it (Tobias, 1993, p. 11).

It was also believed that males would be the only students to excel at math and there was a pervasive myth of the ‘male math gene’ (Tobias, 1993, p. 10). Women who did make it to college were pushed out of higher education opportunities because they arrived with less math preparation than males. What was left were the ‘feminine’ fields of humanities, guidance and counseling, elementary education, foreign languages, and fine arts (Tobias, 1993, p. 21). By the late 1980s, researchers were declaring that “gender differences in mathematics performance are predominately due to the accumulated effect of sex-role stereotypes in family, school, and society” (Tobias, 1993, p. 72). Since then, women have gained a lot more equality due to the feminist movement that had been in action for decades: women were featured as scientists and mathematicians and the myth of the ‘male math gene’ began to fade away (Tobias, 1993, p. 10).

Even recently, there are still differences in the achievement and perception of females in math. Males still have greater confidence in mathematics, and females still underestimate their ability (Owens, 1993, p.27 - 28). In the mid 1990s, it was still recommended that “teachers, parents, and counselors…provide more encouragement for girls and other students who are less confident in their ability to learn mathematics” (Owens, 1993, p. 28). In 1995, research found that “although girls and boys believe society accepts multiple career options for women and men, their own career aspirations remain fairly sex-stereotyped” (Pettitt, 1995). Although female attitudes had improved, their lack of confidence and higher math anxiety, paired with less interest in math-related careers, suggested that important gender differences still existed (Thorndike-Christ, 1991). As of the early 1990s, women were entering professions such as medicine and engineering at increasing rates, and women seemed to no longer hide their interests or skills in the math field (Tobias, 1993, p. 12-13). Sheila Tobias stated that although it was the feminists that ‘sounded the alarm’ on math anxiety, recently both men and women are starting to reassess their math potential (Tobias, 1993, p. 23). It turns out that some men, too, have been denied the power that math and science provides.

In the last decade, the push has been to encourage society to acknowledge how pervasive and genuine math anxiety is. Research began to move to the field of neurology, specifically focused on cognition. Ashcraft and Kirk found in 2001 that “math anxiety disrupts the ongoing, task-relevant activities of working memory, slowing down performance and degrading its accuracy” (Ashcraft & Kirk, 2001). Now classrooms that used to focus on extended arithmetic and rote memorization are emphasizing problem-solving, mathematical creativity, and discussion of mathematical ideas (Tobias, 1993, p. 13). There has been a lot of progress since the emergence of research on math anxiety, but there is still a lot more progress that needs to be made.

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**Purpose of the Project**

This research project will prove the importance of acknowledging math anxiety and provide specific techniques that can help to both avoid and alleviate math anxiety. The issues addressed will be the acknowledgement and background of math anxiety, as well as resources, tips, and best practices for teachers, parents, and students. It is hoped that through this research, secondary school students, their parents, and their teachers will become more educated about math anxiety.

The need for research in the management of math anxiety is crucial because it can change both a student’s confidence and success in mathematics. By joining forces, a student can be brought closer to their full potential. This education is needed to alleviate the state of attitudes toward math in the United States today. Research has shown that only about “7% of Americans have had positive experiences with math from kindergarten through college” and that about “two thirds of adults fear and loathe math” (Furner & Duffy, 2002).

**Significance of the Project**

Even during the early years of math anxiety research, it was learned that the effects of math anxiety were felt more among students with inadequate high school math backgrounds and that math anxiety was related to low math achievement test scores and high levels of test anxiety (Betz, 1977). Today, with the continuance of high-stakes standardized achievement tests, there is even more pressure on students to test well. Unfortunately, that is not always synonymous with a true understanding of the material. This has led to more research regarding the alleviation of math anxiety in the hopes that less math anxiety will therefore increase test scores for schools.

In California, there is also a push to have all U.S. students taking Algebra in the eighth grade by 2014, rather than the ninth grade (Saavedra, 2005). As recently as 2003, Algebra in the eighth grade was considered ‘accelerated’ (Ma, 2003). The fact is that students are dealing with more and more pressure, and support for math anxiety is not keeping up. Math students of all ages deserve the acknowledgement of their anxiety, although many professionals don’t believe it exists and that it is one more excuse for a lack of success in class.If society is educated about math anxiety, it could have positive effects on not only students, their parents, and teachers, but also adults who still ‘fear and loathe’ math.

**Areas of Investigation**

The first area to be investigated will be an in-depth synthesis on math anxiety. Definitions, symptoms, and causes will be discussed, as well as progress that research has made in recent years on the topic. Its byproducts and dangers will be covered. Secondly, specific techniques and reminders of best practice will be provided for teachers. Lastly, techniques will be offered for students and parents to work toward positive thinking and confidence in math class.

**Conclusion**

** **In mathematics, those who fall behind because of math anxiety or any other factor could experience “extreme difficulty in trying to catch up to their expected level of performance” (Clawson, 1991, p. 2). Middle school and early high school students are extremely vulnerable to math anxiety: “although some students develop a dislike for math in elementary school, students most commonly have negative experiences with math between the seventh and tenth grades” (Clawson, 1991, p. 2). If students of this age can be made more aware of math anxiety and how to work with it, they might be able to bypass those negative experiences. “The facts are these: millions of adults are blocked from professional and personal opportunities because they fear or perform poorly in mathematics. Most of these adults are capable of learning more mathematics. Theirs…is not a failure of intellect, but a failure of nerve” (Tobias, 1993, p. 9). The fear that many teachers and researchers address is that these students with math anxiety are likely to become the adults that ‘fear and loathe’ math if there is no intervention.

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**CHAPTER 2: LITERATURE REVIEW**

This research project will investigate whether math anxiety can be improved due to the education of all involved parties. The literature review and guidebooks will cover a history and overview of math anxiety as well as resources, tips, and best practices for teachers, parents, and students. This relates to the purpose of the research project which will support teachers, parents, and students by increasing their acknowledgement of math anxiety and learning specific techniques that can both avoid and alleviate it.

**OVERVIEW OF MATH ANXIETY**

** **To begin to understand and acknowledge math anxiety, one must first understand how it is defined. Math anxiety has most often been explained according to the inability to perform math calculations, such as “an inability by an otherwise intelligent person to cope with quantification, and more generally, mathematics” and “feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (Godbey, 1997; Perry, 2004). Math anxiety has also been explained according to some of the feelings and sources of those feelings that sufferers describe, such as “a state of discomfort that occurs in response to situations involving mathematical tasks that are threatening to self-esteem” and “the panic, helplessness, paralysis, and mental disorganization arising among some people when they are required to solve a mathematical problem” (Bursal & Paznokas, 2006). There are also varying degrees of math anxiety, from the more severe symptoms of panic to the more “moderate and intermittent variety found in a student who has mixed feelings toward the subject” or who has found that over time they feel frustrated and have a great dislike for the subject of math (Perry, 2004).

Acknowledging the varying degrees of anxiety, it is important to understand how common math anxiety truly is. Perhaps the commonality explains the lack of acknowledgement for so many years. By the time that students take introductory math courses in college, up to 85% feel at least mild math anxiety (Perry, 2004). The widespread phenomenon of math anxiety brings with it many myths. Sheila Tobias, a pioneer in the field of math anxiety who has been abreast of new discoveries and insights, describes the harmful and misunderstood state. “Hundreds of studies confirmed my hypothesis that perceived incompetence is often the result of common myths about mathematics: Myth 1, that mathematics ability is inherent; Myth 2, that mathematical insight comes instantly if it comes at all; Myth 3, that only the very few can do mathematics: and Myth 4, that mathematics is a male domain” (Tobias, 1993, p.12).

**Symptoms and Causes**

Math anxiety is quite varied, in both its symptoms and some of its hypothesized causes. Often the symptoms when encountering math are physiological, such as sweaty palms, nausea, heart palpitations, a hot tingling feeling, stomach aches or stomach cramps, and/or tightening muscles (Clawson, 1991, p.2; Godbey, 1997; Perry, 2004). Sometimes the symptoms are more psychological, such as paralysis of thought, extreme nervousness, an inability to hear the teacher, a tendency to become upset by noises, an inability to concentrate or loss of concentration, attention to or even preoccupation with intrusive thoughts and worry, negative self-talk, and/or a general sense of uneasiness (Ashcraft & Kirk, 2001; Clawson, 1991, p.2; Godbey, 1997; Perry, 2004). Often, both physiological and psychological symptoms are exhibited. A variation on math anxiety can be that of test anxiety, defined as “an otherwise confident student’s state of panic during a test where self-doubt leads to a failure to realize potential in a testing environment” (Perry, 2004). This is not as much related to the subject of math as it is to a testing environment, although they are often present together.

The causes of math anxiety are varied. “Anxious students might have difficulty learning in the first place, difficulty using or transferring knowledge they do have, and difficulty demonstrating their knowledge on tests” (Slavin, 2003, p. 346). Some causes “include underpreparedness, school absences, parents perpetuating the myth that math ability is hereditary, and negative past experiences with teachers” (Godbey, 1997). Math anxiety has been related to personality type, a negative attitude toward mathematics, mathematics avoidance, mathematics background, instructor behaviors, level of mathematics achievement, lack of confidence, and negative school experiences (Bursal & Paznokas, 2006). What is perhaps most unfortunate about the initial cause(s) of math anxiety is that it often compounds; anxiety can lead to less understanding and confidence with math, which leads to more anxiety, and so on. “An extremely common occurrence is the following: a student has a superficial understanding of mathematics limited to computational skills, with little conceptual understanding and hence no mental framework within which to organize his/her knowledge. As a result, this type of student forgets what he or she learns very quickly, and experiences chronic frustration” (Perry, 2004). It is recommended that when a student of any age exhibits symptoms of math anxiety, steps are taken to keep the cycle from continuing.

Math anxiety stems from a fear of failure or a feeling of inadequacy, which can be related to elements of a student’s life outside of the classroom (Perry, 2004). Especially with younger students, such as those in middle school, students feel an extreme fear of looking silly or being embarrassed in front of their peers, which can lead to feeling overly self-conscious (Perry, 2004; Slavin, 2003, p. 346). Psychologists state that “the main source of anxiety in school is the fear of failure and, with it, loss of self-esteem” (Slavin, 2003, p. 346). Sometimes the cause of initial math anxiety can be identified, especially with the aid of counseling, to find a specific traumatizing event or experience. For example, a single insensitive math teacher can create a recurring sense of anxiety (Perry, 2004). Avoidance can also explain a student’s continued sense of math anxiety. “[B]ecause of their long-term avoidance of math, and their lesser mastery of the math that couldn’t be avoided, high-math-anxiety individuals are simply less competent at doing math” (Ashcraft & Kirk, 2001).

**Cognition **

Even after researchers began to acknowledge that math anxiety really did exist in physical form, it was still considered to be largely psychological. Over time, researchers began to experiment with the neurological considerations of math anxiety. It was decided that there could be neurological mechanisms underlying math anxiety that deserved more attention, especially in the area of working memory capacity and functioning (Ashcraft & Kirk, 2001).

Before 2001, it had not been considered that an on-line effect, described as “an effect on underlying cognitive processes as the individual performs a math task”, could affect an individual’s math performance (Ashcraft & Kirk, 2001). Mark Ashcraft and Elizabeth Kirk (2001) found that working memory capacity was negatively associated with math anxiety. That is, as math anxiety increases, memory capacity decreases, and vice versa. This was somewhat groundbreaking and they stated that “[g]iven the importance of working memory functioning to a variety of cognitive and intellectual tasks, it becomes genuinely important to explore the relationship between working memory and math anxiety more fully” (Ashcraft & Kirk, 2001). This research evidenced that “math anxiety is related to the actual doing of math, to the mental processes involved in working with numbers”, rather than solely psychological issues (Ashcraft & Kirk, 2001).

**Dropped Stitches**

A very specific cause of math anxiety is called the dropped stitch. This is defined as “a gap in a student’s prior math education that holds him or her back from learning more complicated concepts” (Farrell, 2006). Since it is rare for even the most mathematically inclined students to master every mathematical lesson they learn in school, dropped stitches are very common. What complicates the situation further is that “[s]tudents are often afraid to ask questions about concepts they feel they should know already, which creates a snowball effect. The student falls behind, and his or her confusion grows with each new mathematical concept. Catching up can seem like an insurmountable task” (Farrell, 2006).

Most math teachers will agree that dropped stitches are a fact of learning math, whether they are due to absences, a lack of time on a particular subject, or a variety of other reasons. However, dropped stitches are not reason to surrender. Quite the contrary, identification of a dropped stitch (whether it is by the student, teacher, parent, math specialist, or tutor) should be reason to go back and repair it. “True, math is especially cumulative. A missing link can damage understanding much as a dropped stitch ruins a knitted sleeve. But being sick or in transit or just too far behind to learn the next new idea is not reason enough for doing poorly at math forever after” (Tobias, 1993, p. 60).

The bright side of the identification of dropped stitches, even at a much later time, is that older students can catch up quite quickly. “As we grow older, our facility with language improves; we have many more mathematical concepts in our minds, developed from everyday living; we can ask more and better questions” (Tobias, 1993, p.60). Although a student might need help with their identification, dropped stitches can be repaired, confidence in further math situations can improve as problems begin to make more sense, and anxiety can slowly be alleviated.

**Effects of Math Anxiety**

Math Anxiety is often compounded over time and can affect students of math in a variety of ways. Math anxiety can begin at any age of schooling, even as young as elementary school, but most students most commonly have negative experiences between seventh and tenth grades (Clawson, 1991, p.2). Unless addressed directly, this anxiety often continues or even worsens through high school, college, and into adulthood.

This anxiety is not only difficult for the student to deal with, but it compounds into a lack of understanding of major concepts. This can close doors for students who not only may have otherwise chosen careers that would deal with math directly, but indirectly also. The lack of understanding of basic mathematical principles can result in an inability to solve chemistry, engineering, and other scientific problems (Bursal & Paznokas, 2006). It also prevents students from acquiring logic and reasoning skills that can be used in a variety of areas, even outside the realm of mathematics.

Mathematics anxiety in high school is directly related to choices made in college. In a research study of middle and high school students, “[r]esults showed that attitudes toward mathematics were predictive of final mathematics course grades and the intention to continue to participate in mathematics courses once enrollment becomes optional” (Thorndike-Christ, 1991). The number of math courses a student takes in high school and college will affect their career choices and future salary. Starting salaries are estimated to go up an average of $2,000 per year for every math course taken after the ninth grade (Tobias, 1993, p. 34).

Math anxiety can come full circle to affect even the youngest of students, if their teachers are the ones battling their anxiety. In the last three years, there have been studies that show alarming rates of math anxiety in pre-service elementary school teachers. It has been found that those pre-service teachers with higher levels of math anxiety have less confidence to teach math and science to their own students (Bursal & Paznokas, 2006). “Nearly half of the preservice teachers having higher math anxieties than their colleagues believe that they will not be able to teach mathematics effectively” (Bursal & Paznokas, 2006).

This cycle of anxiety needs to be acknowledged so that teacher credentialing programs can address and work with their students, who will in effect be the first to formally introduce the youngest of students to math. “Some of the blame for the generally poor instruction in elementary schools must ultimately like with teachers who aren’t sufficiently capable, and who often have too little interest in or appreciation of mathematics. In turn, some of the blame for that lies…with schools of education in colleges and universities which place little or no emphasis on mathematics in their teacher training courses” (Paulos, 1988). Murat Bursal and Lynda Paznokas (2006) provide a specific recommendation to schools that take the responsibility for training teachers. “[A]s teacher educators, our task should be designing the methods courses in a way that all teacher candidates, especially those who are severely anxious about mathematics, will have chances to reduce their anxieties and develop positive attitudes toward mathematics and mathematics teaching”.

**Confidence and Motivation**

Perhaps the most obvious factor with math anxiety is a lack of confidence, which often leads to decreased motivation. Those students with math anxiety will often perceive their math skills as less than those in other subjects, and will not enjoy math or have the desire to teach it (Wright & Miller, 1981). “Confidence is one of the most important affective factors studied by mathematics education researchers. It plays a role in students’ mathematics achievement and ability to solve nonroutine problems. There is also evidence of theoretical or empirical connections between confidence in learning mathematics and students’ achievement motivation, intrinsic motivation, self-concept, and self-esteem” (Owens, 1993, p. 25-26). Success is directly related to confidence level by students in a subject such as mathematics, as proven over and over again by researchers. “Confidence in learning mathematics shows one of the strongest positive relationships with mathematics achievement of any affective variable” (Owens, 1993, p. 26). This carries over to pursuing math and science careers. “The self-confidence in one’s ability to learn, or math self-efficacy, was the strongest predictor of persistence in science and engineering careers” (Khourney-Bowers, 2005).

There was, until recently, a long-lived myth of the ‘mathematical mind’ in education. Sheila Tobias (1993, p. 52) spoke of the incorrect assumption that some people have inborn math intelligence and others do not have ‘the gene’ for it. When interviewing math students, teachers, and parents from Taiwan, Japan, and the United States, it was shown just how damaging this myth can be. “When asked to explain why some children do better in math than others, Asian children, their teachers, and their parents point to *hard work*, their American counterparts to *ability*” (Tobias, 1993, p. 52). When it comes to math and science achievement, “Asian-American students score higher than any other students in the world” (Bracey, 1998). A great deal of research has been completed regarding the success of many Asian students in math and science, compared to that of Americans. Asians tend to complete more courses in math and science and during high school and tend to learn more (Hoffer, Rasinski & Moore, 1995). Perhaps the motivation for working hard to achieve success, rather than the belief that math ability is inherent and out of the realm of control of a student, can partially explain the higher test scores.

**Math is Unavoidable**

Math anxiety is common, but math is an unavoidable fact of life. Those who suffer from math anxiety and make no progress toward its improvement, not only suffer academically, but in many facets of their life. “Basic mathematical calculations are the oil that keeps the machinery of society running smoothly. If you can’t quickly and confidently carry out basic calculations, you are always at the mercy of others. Math is relevant to almost all your daily activities: working, earning money, buying groceries, driving a car, making home repairs, educating children” (Tobias, 1993, p. 5). It is human nature to avoid things that are unpleasant. “People who don’t like math don’t like to talk about math. Part of their avoidance mechanism is to pretend it does not exist. But math does not go away” (Tobias, 1993, p. 240). Hopefully, though, the anxiety related to math can.

**TECHNIQUES FOR TEACHERS**

Most teachers are hard-working, dedicated professionals that are often underpaid and underappreciated. However, there is always room for improvement for even the hardest working teacher. This section is meant to make math teachers more aware of some best practices that will help students who suffer from math anxiety.

Many of these best practices are extremely logical and well-known. However, it can be refreshing to read a reminder of those that help to put students at ease. Some suggestions even come from students themselves, such as the importance of inquiry-based classrooms with a reduction in structured time, an increase in time and openness to student questions, and more relevance to students’ lives. In general, students want to feel safe to take risks in the classroom, to learn from their mistakes without embarrassment, to be encouraged to question ideas, and to view problems from multiple perspectives (Khourney-Bowers, 2005). “Instructors can improve students’ confidence and performance by being mindful of their students’ feelings, introducing humor into the classroom setting, sustaining enthusiasm for the subject matter, and motivating students to change pessimistic learning styles to optimistic ones” (Godbey, 1997).

Most math teachers aim to maximize what their students take away from class, even if the math classes that teachers took as students weren’t the ideal models. “We basically teach the way we were taught, and the system essentially replicates itself” (Farrell, 2006). It is a teacher’s responsibility to try new ideas in their teaching and step outside their own comfort zone from time to time. There has been a large push to move toward more student-centered classrooms, but Claudia Khourney-Bowers (2005) found that “many classrooms [still] rely on traditional approaches such as presenting vast bodies of factual information and neglecting to make connections between important concepts and the interests and experiences of students.” While it is understandable to settle into what is comfortable for the teacher, those methods may not always be the best practice of what is comfortable for the students. “It is the obligation of teachers to see that their students value and feel confident in their math abilities, because ultimately, decisions and career choices may be determined based on a student’s disposition toward mathematics” (Furner & Duffy, 2002).

**Preventing Versus Reducing Math Anxiety**

There are two different approaches that teachers must acknowledge when they work against math anxiety. Working to keep children from developing math anxiety can require a different set of tools than working to ease the math anxiety that a child arrives with. “Reducing math anxiety is much different from preventing math anxiety” (Furner & Duffy, 2002). Even the National Council of Teachers of Mathematics (NCTM), the same group that pioneered standards for the math classroom, acknowledges the difference. They recommend that teachers work to reduce math anxiety with methods such as desensitization, counseling, and discussions on the topic, while they recommend methods such as the use of manipulatives, cooperative groups, technology, and discussion of feelings about math to prevent math anxiety from manifesting in the first place (Furner & Duffy, 2002). Many of these methods involve teacher training and some should even be left to specialists. For some broad goals, it is recommended that teachers change student attitudes about math “by using effective instructional techniques, focusing on what students can do, encouraging multiple outcomes, and being sensitive to past histories of frustration and failure” (Furner & Duffy, 2002).

**Keep It Positive**

In speaking with students with math anxiety, researchers have learned that there are many common traits that teachers exhibit which need to be avoided to prevent math anxiety. In 1999, Jackson and Leffingwell listed some “covert (veiled or implied) and overt (apparent and definite) behaviors exhibited by math instructors that cause math anxiety in students, including being hostile, exhibiting gender bias, having an uncaring attitude, expressing anger, having unrealistic expectations, and embarrassing students in front of peers” (Furner & Duffy, 2002). In 1982, Oberlin found that several common teaching techniques can lead to math anxiety, including but not limited to assigning the same work to everyone and insisting on only one correct way to complete a problem (Furner & Duffy, 2002). Many caring and sensitive teachers employ these two techniques, and sometimes they are the best course of action, but perhaps teachers can reevaluate if they are always necessary.

Whether a teacher aims to prevent or reduce math anxiety, the avoidance of negative teacher traits is only a start. “Perhaps the most important counter-anxiety technique is simply to keep a positive attitude” (Perry, 2004). Positive attitudes from role models such as teachers, parents, and successful peers can put math anxious students at ease. Even early in the research of math anxiety, it was found that students who perceived their parents and teachers to have positive attitudes toward math tended to have lower levels of math anxiety (Betz, 1977).

Even with students who do not have a positive attitude or liking for the subject of math can focus on some positive experience they have had. “Nearly every student has had some positive experience with mathematics. Thinking about this happy experience, and especially writing about it, reminds an individual that he or she has the potential to be successful in mathematics, and serves as an inspiration. It is imperative that a student be reminded…of his or her continuing accomplishments in mathematics, as a source of inspiration. If necessary, the student can remind him or herself, but ideally, external validation should be provided as well” (Perry, 2004). It could be helpful to start out the semester or school year reflecting on a positive experience, or perhaps at a stressful time such as before a big test. Positive thinking is helpful throughout the school year, whether in the form of verbal encouragement, positive comments or stickers on papers well done (yes, even secondary school students enjoy them), supportive posters on the walls, or encouraging students to literally pat themselves on the back from time to time.

**Classroom Environment / Teaching Style**

From the first day of the school year, students get a feel for the general environment of their classes. Wheelock (1988) contended that “students must be provided with a classroom climate that is rich in intellectual stimulation, meaningful relationships, and support structures if they are to be expected to reach standards of excellence” (Irvin, 2005). Creating a classroom climate that is comfortable, noncompetitive, and accepting helps to reduce and prevent anxiety (Slavin, 2003, p. 346).

Math is a uniquely intimidating subject in which students are taught theorems, rules, and formulas discovered by very intelligent people, which are so undisputed they are taken as fact in the math world. Defeated students often stop questioning math, which also breaks down the communication between teacher and student. A particularly successful professor boasts of her personal connection with students. She encourages her students to interrupt her with questions at any time (which might not be conducive to classrooms of younger students), and even has signals for those who are too shy to communicate their confusion. “I tell students that if they are afraid to ask questions then to just pull on their earlobe so I know they aren’t understanding it” (Farrell, 2006). Students of math who truly understand the mindset acknowledge that it borders on philosophy, in that it should be questioned regularly. “While authentic pedagogy is built around the teaching of important concepts or standards, it also implies that learners question and challenge the content to better understand and remember it” (Khourney-Bowers, 2005).

Both students and teachers should be asking questions in every math class. Most pre-service teachers are taught about wait time as a means to allow students to fully think through a concept before responding, but even experienced teachers can struggle with this concept due to the increasing number of time constraints in the classroom. “When expected to think deeply about a question, students need time to do it. A teacher who consistently gives insufficient time to students to think is teaching only superficially, at the lowest cognitive level, and is destined to have problems in student motivation and classroom control” (Callahan, Clark & Kellough, 2002, p. 194). Students who need more processing time can have the satisfaction of truly understanding material on their own taken away from them without sufficient wait time. “Since it is always easier for the teacher, the tutor, or the text to provide one image for the learner to apply than to wait for the learner to develop her own, some people never even find out that they can invent images for themselves” (Tobias, 1993, p. 143).

Time constraints can be stressful for insecure students, both with lack of wait time and in testing situations. Test anxiety, a facet of the larger problem for many who battle with math anxiety, can be reduced by closely linking tests to course content, announcing tests in plenty of time for students to study and get their questions answered, and by giving plenty of time on tests (Slavin, 2003, p. 472). Without the pressure of time, students can adequately skip problems, analyze problems in multiple ways, and check their work. “Tests that begin with easy problems and only gradually introduce more difficult ones are better for anxious students, and tests with standard, simple answer formats help such students” (Slavin, 2003, p. 346). There are ways to write tests only slightly differently to achieve better results, without necessarily making the problems any easier.

One very humbling way of easing math anxiety for an insecure student could be for a teacher to willingly show their own imperfections. This could help to erase the myth of a ‘mathematical mind’, which some people are born with and others can never achieve. “Sometimes the math teacher contributes to this myth. If the teacher claims to have had an entirely happy history of learning mathematics, she may contribute to the idea that some people…are gifted in mathematics, and others…are not. A good teacher, to allay this myth, brings in the scratch paper he used in working out the problem, to share with the class the many false starts he had to make before solving it” (Tobias, 1993, p. 53). This can humanize math as a process. Every teacher makes mistakes in front of the class, so talking openly about that reality can certainly alleviate the pressure of perfection for anxious students, especially those who pride themselves on their intelligence. “Anxiety is a constant companion of education. Low achievers are particularly likely to feel anxious in school, but they are by no means the only ones. [V]ery able, high-achieving students who are also very anxious may even be terrified to be less than perfect at any school task” (Slavin, 2003, p. 346).

**Take Away the Mystery**

Mistakes are a fact of life in every math class and learning from those mistakes can be priceless. There are very few math problems that can’t be given a second try once the student knows they got an incorrect answer. This can be especially helpful when attempting word problems, often an enemy of the anxious math student. What must be remembered is that “when people come up with the wrong answers to word problems, they may have the right answer to another question. Therefore, a key to treating fear of word problems is to discover the question the student was answering by analyzing the error he made” (Tobias, 1993, p. 135). While incorrect answers are not the desired end product, they can be invaluable in teaching, perhaps showing a student that they are not the only ones to make the same mistake and sometimes showing a teacher where their students are going astray. Inviting students to share their answers with the class (perhaps during a warm-up or with a class set of whiteboards during a review session), right or wrong, might “relieve some of the panic that comes when students fail to get the answer the teacher wants” (Tobias, 1993, p. 67). Giving students a chance (and the time) to correct errors before they turn in their work can also alleviate anxiety (Slavin, 2003, p. 346).

Many students mistakenly assume that math is a very rigid subject, comprised only of right or wrong answers, with no flexibility. But the truth is that “math is quite capable of dealing both with qualitative data and with uncertainty” (Tobias, 1993, p. 48). Students can also mistakenly assume flexibility where it shouldn’t be, especially if they misinterpret the language, vocabulary, or directions. For students that already feel insecure about math, “linguistic confusion increases their sense of being out of control” (Tobias, 1993, p. 59). Once math and its language are properly explained, so is its flexibility.

Proper study skills and test taking methods are aspects of a math class which few students receive adequate exposure. Some even battle with both test anxiety and a lack of these skills. While some methods are discovered on a trial and error basis, teachers rarely spell out effective study skills (Taylor & Wood, 2005). Because a specific method may be more effective for certain students, a teacher should teach a variety of skills (Taylor & Wood, 2005). These methods should be modeled for students until they are confident using them on their own. Researchers “encourage teachers to model these strategies for students and to bring them to students’ attention before tests and other assignments for which students need to study” (Taylor & Wood, 2005). Without study skills, students are often overwhelmed with the material and lack focus. Teaching study skills should begin by middle school, as high school teachers often assume students have already been exposed to them. Studies now suggest that “many students leave secondary schools lacking potentially useful study skills that are necessary for success at the university level” and that “there is a need to introduce such strategies earlier in the American educational system” (Taylor & Wood, 2005).

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**Avoid Surprises**

Most would agree that one of the biggest fears in this world is fear of the unknown. For a student that is prone to anxiety, not knowing what could come next could be very worrisome. Although it sounds illogical, increasing the difficulty level of basic math problems beyond simple acquisition can help with math anxiety. “[S]tudents should be encouraged to develop an ability to respond not only accurately, but also quickly. When students progress beyond the initial acquisition stages and over learn material to the extent of being fluent or automatic, these students may be less likely to exhibit higher mathematics anxiety levels for basic skills” (Cates & Rhymer, 2003).

Having high expectations for students can convey a faith in their abilities. “[T]he expectation of individual intellectual growth and capacity” is referred to as academic press (Irvin, 2005). The presence of academic press in a classroom has been shown to enhance motivation and foster positive self-images (Khourney-Bowers, 2005). “Students who perceive academic press are more likely to ask the teacher or their peers for help, are more open to constructive criticism, and feel more engaged in the classroom” (Khourney-Bowers, 2005). This confidence, especially when shown to students regardless of prior success, can help students who were previously too self-conscious to ask for help. Perception of press “was associated with lower reported avoidance of help-seeking behaviors, especially for girls” (Khourey-Bowers, 2005).

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**Try Something New**

The above suggestions are best practices that many teachers have heard before. Below are a few more suggestions that are a little more unique and require a teacher to step slightly further outside their comfort zone.

Many students who suffer from math anxiety feel most anxious when solving word problems (Slavin, 2003, p. 346). Even though there is usually one method that is most effective and time-efficient, most word problems have varied logic and strategies that could be used. Teachers struggle to show students how to solve word problems, and most settle to have their students practice, practice, practice, acknowledging that not every strategy can be covered. Some educators are developing units to teach problem solving strategies while others are creating new elective classes. “Some educators are beginning to teach problem solving (heuristics) independent of any particular field or discipline” (Tobias, 1993, p. 163). This type of class might work best as an elective in high school and has many possibilities. A teacher could involve game strategy and logic that is not necessarily mathematical in nature.

Variety might just be something that anxious math students need. The same routine every day can stifle their creative process, which helps them to solve problems correctly in the end. Test anxiety is the byproduct of a generation of students who deal with high-stakes testing on a regular basis, whether it be chapter tests or state mandated standardized tests. “With the emphasis on paper-and-pencil and standardized testing, a great deal of pressure is placed on our students. Teachers need to consider alternate forms of assessment that can help students gain confidence. Journal writing, self-reflections, portfolios, and interviews/observations are just a few alternatives that can take the pressure off the student to always perform well on a right or wrong paper-and-pencil test” (Furner & Duffy, 2002).

A counseling approach can also be very helpful for students who suffer from math or test anxiety. However, many teachers feel they don’t have time for these techniques in their classroom, nor do they feel they have the expertise to administer them. These might be best suited for a counseling environment or a math support class where there is more time to work on study skills, attitude, and positive thinking.

There are many broad techniques that would help students, including asking students to “discuss/write about their math feelings, evaluate their own learning, use gradual, repeated success to build math confidence, and develop calming/positive ways to deal with fear of math, including visualization, positive messages, relaxation techniques, and frustration breaks” (Furner & Duffy, 2002). Especially if a psychologist or therapist is working with a student, it is helpful to have “learners…first recognize when the panic starts…Then, to be able to cope, they must use techniques such as controlling their breathing , visualizing success, using positive ‘I’ messages, and so on” (Furner & Duffy, 2002).

Many of the above-mentioned techniques are just not realistic in some classrooms. “Although probably effective, both desensitization and vicarious learning techniques require resources, trained facilitators, and lengths of time that may simply not be feasible for widespread replication” (Shobe, Brewin & Carmack, 2005). However, below is a very simple visualization technique can be quickly and easily used in a classroom by any teacher. “A highly feasible and sustainable visualization exercise is one that is easily administered within a few minutes without prior training sessions, and done in the test setting on the day of the test, immediately prior to the test” (Shobe, Brewin & Carmack, 2005). In Elizabeth Shobe’s (2005) visualization research, the following instructions were read to students.

Untense those muscles. Breathe deeply and exhale slowly 3 or 4 times. Let your body relax, put your arms to your sides, close your eyes, and let your mind go blank. Now, sitting comfortably, and breathing deeply, close your eyes. Think of a safe place for you – beach, mountains, golf course – wherever you feel relaxed. Continue breathing and paint a picture in your mind of this safe place. Feel a cool breeze against your skin, the sun’s warmth, the sound of birds. You are the artist here; create an environment that is calming for you. Feel the quiet.

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Her research used visualization for both easy and difficult tests. The above “visualization exercise may significantly reduce test anxiety for difficult and easy tests, but this translates to an improvement in performance for difficult math tests only” (Shobe, Brewin & Carmack, 2005).

**CONCLUSION**

The fact is that the myths, the intimidation surrounding math, the misunderstandings, and many people’s missed opportunities have affected a large percentage of the population in this country (Tobias, 1993, p. 22). If the public is not educated on this subject, the future looks even grimmer. “As long as parents, teachers, athletes, and entertainers publicly indulge in fear or indifference to mathematics, and as long as people who succeed at mathematics claim an innate superiority over people who don’t, the myths surrounding mathematics and the math anxiety that is the consequence of these myths will probably not go away” (Tobias, 1993, p. 14).

As a team, teachers, parents, and students can have an effect on the all too prevalent situation. “Parents, educators, and society as a whole must work toward making a difference in students’ attitudes toward math” (Furner & Duffy, 2002). It is important to be educated about math anxiety and how pervasive it has been to multiple generations of students. Most importantly remember that math anxiety is most often a lack of confidence, not of ability, and that it can be overcome using the right techniques.

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**CHAPTER 3: GUIDEBOOKS**

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Math anxiety can be crippling for students who are quite capable of success in the subject but are held back by their own fears and anxieties. This can be frustrating for both parents and students, and even once the anxiety is identified it can be challenging to improve the situation. Many students struggle with math anxiety and could use some simple tips and techniques to work toward overcoming their fears. Others simply need to be aware that math anxiety exists and can emerge at any time. The public needs to become educated on the subject to understand how prevalent the situation really is.

Once math anxiety is understood and acknowledged, both parents and students need to know what to do next. The following guidebooks are research-based, but meant to be comprehended by students (middle school and older) and parents who want to work toward change and understanding.

The guidebooks are not comprehensive by any means, but a good starting place toward understanding the situation and what can be done about it. Test anxiety, which is often a partner with math anxiety, is spoken of briefly. If that is the area where students struggle the most, especially if that anxiety is present while learning other subjects, one might want to do further research specifically on test anxiety.

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**References**

Ashcraft, M.H. & Kirk, E.P. (2001). The Relationships Among Working Memory, Math

Anxiety, and Performance. *Journal of Experimental Psychology*, 130, 224-237.

Betz, N.E. (1977). Math Anxiety: What is it? *Research Report.*

Bobango, J. & Milgram, J. (1993). Establishing Family Math. *Middle School Journal*, 24,

44-47.

Bracey, G.W. (1998). Test Scores of Nations and States. *Phi Delta Kappan*, 80, 247-248.

Bursal, M. & Paznokas, L. (2006). Mathematics Anxiety and Preservice Elementary

Teachers’ Confidence to Teach Mathematics and Science. *School Science and *

*Mathematics*, 106, 173-180.

Callahan, J.F., Clark, L.H. & Kellough, R.D. (2002). *Teaching in the Middle and*

*Secondary Schools*. London: Merrill Prentice Hall.

Cates, G.L. & Rhymer, K.N. (2003). Examining the Relationship Between Mathematics

Anxiety and Mathematics Performance: An Instructional Hierarchy Perspective.

*Journal of Behavioral Education*, 12, 23-34.

Clawson, C. (1991). *Conquering Math Phobia*. New York: Wiley.

Farrell, E. F. (2006). Taking Anxiety Out of the Equation. *Chronicle of Higher*

*Education*, 52.

Fay, J. & Funk, D. (1995). * Teaching with Love and Logic: Taking Control of the*

* Classroom*. Golden, Colorado: Love and Logic Press.

Furner, J.M. & Duffy, M.L. (2002). Equity for All Studenets in the New Millennium:

Disabling Math Anxiety. *Intervention in School and Clinic*, 38, 67-74.

Godbey, C. (1997). Mathematics Anxiety and the Underprepared Student. *Classroom*

* Teacher Guide.*

Hoffer, T.B., Rasinski, K. A. & Moore, W. (1995). *Social Background Differences in*

*High School Mathematics and Science Coursetaking and Achievement*. National

Opinion Research Center. Chicago: National Center for Education Statistics.

Khourey-Bowers, C. (2005).Cultivating Positive Attitudes and Higher Achievement in

Middle Level Mathematics and Science. *Middle School Journal*, 36, 50-56.

Ma, X. (2003). Effects of Early Acceleration of Students in Mathematics on Attitudes

Toward Mathematics and Mathematics Anxiety. *Teachers College Record*, 105,

438-464.

Owens, D.T. (1993). *Research Ideas for the Classroom: Middle Grades Mathematics*.

New York: National Council of Teachers of Mathematics.

Paulos, J.A. (1988). * Innumeracy*. New York: Hill and Wang.

Perry, A.B. (2004). Decreasing Math Anxiety in College Students. *College Student *

*Journal*, 38, 321-325.

Pettitt, L. (1995). Middle School Students’ Perceptions of Math and Science Abilities and Related

Careers. * Research Report*, 21 pages.

Rathvon, N. (1996). *The Unmotivated Child*. New York: Simon & Schuster.

Saavedra, S. (2005). *County language, math scores gain*. Retrieved July 23, 2006 from

http://www.signonsandiego.com/news/education/20050816-9999-1m16scores.html.

Shobe, E., Brewin, A., Carmack, S. (2005). A Simple Visualization Exercise for

Reducing Test Anxiety and Improving Performance on Difficult Math Tests.

*Journal of Worry and Affective Experience*, 1, 34-52.

Slavin, R. E. (2003). * Educational Psychology*. Boston: Allyn and Bacon.

Taylor, B.D. & Wood, K.D. (2005). Activating Study Skills in the Middle School

Classroom. * Middle School Journal*, 36, p. 51-55.

Thorndike-Christ, T. (1991). Attitudes toward Mathematics: Relationships to

Mathematics Achievement, Gender, Mathematics Course-taking Plans, and

Career Interests. *Research Report.*

Tobias, S. (1993). *Overcoming Math Anxiety*. New York: Norton.

Wright, D.E. & Miller, L.D. (1981). Math Anxiety: A Research Report. *Research Report.*

### Bibliography of resources for math

**Purplemath**lessons, practical tips, examples, and common mistakes in Algebra.

**Khan Academy** www.khanacademy.org/

A library of over 3000 videos covering everything from arithmetic to physics, finance, and history and hundreds of skills to practice

**Math self testing**

ThatQuiz Andrew Lyczak

**Professor Freedman's Math Help**provides information about basic math and algebra, specifically addressing the needs of the community college adult learner

**A+ Math**tests math in a fun fashion, including flashcards, the game room, homework helper, and worksheets.

Open Directory Project: **Science and Math directory**

**Print Resources:**

American Preparatory Institute. **Math Skills by Objectives. **New York: Cambridge Book Company, 1985.*Math Skills by Objectives* is a series of three workbooks with accompanying answer booklets and a test booklet. The workbooks provide explanations and drills in a number of math skills. *Book One* explains whole numbers, fractions, decimals and percents. *Book Two* explains graphs and tables, consumer math skills, measurement, and basic geometry. *Book Three* reviews basic arithmetic, geometry, algebra, and test-taking skills. These books would be a good choice for anyone who thinks they need to brush up specific math skills.

Ashley, Ruth.** Background Math for a Computer World.** New York: John Wiley & Sons, 1980.*Background Math for a Computer World* introduces those with a limited background to the math needed to work in the machine language of computer programming. The book introduces the binary number system, computer logic, and linear equations.

Chernow, Fred B. **Business Mathematics Simplified and Self-Taught**. New York: Arco Publishing, Inc., 1984.*Business Mathematics Simplified and Self-Taught* provides detailed explanations of a number of basic arithmetic functions, such as rounding off, dividing by 10, 100, 1000, etc., before discussing fractions, decimals, percentages, interest and other business math applications.

Deese, James, and Ellin K. Deese. **How to Study .** New York: McGraw-Hill Book Company, 1969.*How to Study* is an introduction to study skills for on-campus students. The book covers time management, reading, and essay writing. It also provides tips for studying foreign languages, math and science.

Goldish, Dorothy M.** Basic Mathematics for Beginning Chemistry. **New York: Macmillan Publishing Co., Inc., 1983.*Basic Mathematics for Beginning Chemistry* is intended to refresh students' mathematical memory for university chemistry. The book introduces mathematical concepts, illustrated with examples, and provides exercises and answer keys.

Hackworth, Robert D., and Joseph W. Howland.** Programmed Arithmetic**. Clearwater, Florida: H & H Publishing Company, Inc., 1983.*Programmed Arithmetic* teaches arithmetic. Each idea is explained then followed with examples and exercises. There are tests for each chapter with answers at the back of the book. Students who have never mastered multiplying and dividing fractions, or do not understand the meaning of ten to the seventh power, will find this book helpful. The book's table of contents is thorough enough to locate the most relevant topics.

Hartkopf, Roy. **Math Without Tears.** Boston: G.K. Hall & Co., 1985.*Math Without Tears* will expand students' knowledge of mathematical languages and show the relationships between them (e.g., the relationship of trigonometry to calculus). The book explores and refutes the common idea that mathematics yields one correct answer. The author shows that, depending upon the mathematical system one uses, one plus one could equal two, three, or more.

Parson, Ted.** Demystifying Math.** Victoria, B.C.: University of Victoria, 1985.*Demystifying Math* is a workbook to refresh math skills. The book begins with arithmetic and proceeds to algebra, sets and Cartesian products, graphs of linear equations and inequalities, systems of linear equations, exponents, and quadratic equations. There are exercises and self-tests throughout. Students who find these words familiar but cannot remember what they mean may find this book useful.

Selby, Peter H. **Quick Algebra Review. **New York: John Wiley & Sons, Inc., 1983.*Quick Algebra Review* is intended as a refresher for those who studied algebra in high school. There are brief explanations, examples, and many exercises with answer keys. The table of contents and index will help readers identify specific topics for review.

Thompson, J. E. **Trigonometry for the Practical Worker.** New York: Van Nostrand Reinhold Company Inc., 1982.*Trigonometry for the Practical Worker* contains just about everything students would want to know about plane trigonometry from the basic ideas to their application to measurement. The book has exercises with answer keys to help students test and deepen their understanding.

Tobias, Sheila. **Overcoming Math Anxiety**. Boston: Houghton Mifflin Company, 1980.*Overcoming Math Anxiety* examines the cause of the difficulty, paying special attention to the biases that make women feel incapable of learning and using math. The author explores the problems in words and illustrates the ideas with examples and drawings. The book also has explanations and exercises to help readers overcome common mathematical stumbling blocks

###### Curricular guides and resources:

#### Using feedback in the classroom | Teaching critical thinking | Bloom's taxonomy |

Teaching with questioning | Preparing guided notes |

A curricular idea! | Curricular resources and guides |

Learning Exercises & Games | Exploring learning styles |

Constructing true/false tests | Constructing multiple choice tests |

Constructing essay exams | Cross language resources including digital translators |

Online Learning/eLearning books and resources for teachers

Print resources reprinted with permission from**Selected Study Skills Books in the AU Library**

http://www.athabascau.ca/html/services/advise/ssbib.htm#sec6

An Annotated Bibliography by Arlene Young Tutor, Athabasca University

(January 5, 1999)

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