Building math confidence for a high-tech world.

Abstract

This article makes the argument for the importance of having confidence with mathematics in order to compete globally in a high-tech world which relies very heavily on mathematics, science, and technology. This article is geared toward educators in hopes that they can ultimately excite young people about mathematics, encourage students to be confident in their ability to solve problems, understand mathematical concepts, and see math as a human endeavor. The authors believe that as students feel less anxious about, and more confident in their abilities to do math their performance will improve. As math test scores are often a concern for principals, teachers, and society at large. Math anxiety has become a growing concern in the United States, as well as in many other countries around the globe. A young person's ability and confidence to do mathematics is critical for their future success and decisions they will make in our current high-tech globally competitive world.

Introduction

Often students who are anxious, bored, fearful, or who simply believe that math is unimportant, are likely to avoid the study of mathematics. The shortage of workers in many technical fields, especially in the area of mathematics, is a matter of national concern (Dawson, Interact n.d.). Much has been written about the decline of mathematics scores on the Third International Mathematics and Science Study (TIMSS), Scholastic Aptitude Test (SAT), American College Test (ACT), and a general weakness in mathematics performance overall (Hiebert et al, 2003; TIMSS Video Mathematics Research Group, 2003; Young, 2002; Stigler, Gonzales, Kawanaka, Knoll, and Serrano, 1999; Schmidt, 1998). The practice of setting higher standards, as well as other reform measures, has not had an appreciable effect (McNair, 2000; Battista, 1999; Stigler and Hiebert, 1999). It may be beneficial for PreK-16 teachers to develop a better understanding of current issues related to assessment and intervention strategies in order to promote better attitudes toward mathematics among students at all ages and grade levels (Ross, 1996).

In today's high-tech world, it is important that our young people grow to become confident in their ability to do mathematics in an ever-increasingly high-tech globally competitive society. This article shares with the reader, from an educator's perspective, approaches that could be used to ultimately excite students about mathematics, encourage students to become more confident in their ability to solve problems, understand mathematical concepts, and see math as a human endeavor. The authors believe that as students feel less anxious about and more confident in their abilities to do math, their performance on standardized tests will improve, which is often a concern for principals, teachers, parents, and society at large. The instruction of mathematics seems to play a critical role in shaping one's attitudes toward math (Jackson & Leffingwell, 1999). NCTM (1995a and 1989) recognizes math anxiety as a problem and has specifically included the detection of this phenomenon in its assessment practices, since a teacher's job is to assess his/her students' mathematical dispositions. Burns (1998) contends that two thirds of American adults loathe and fear mathematics. Dawson (Internet n.d.) has found that Americans often times are not qualified for many high-tech jobs, and that companies seek employees outside the U.S. requiring special H1-B Visas. Dawson (Internet n.d.) also contends that our K-12 educational system is not preparing students for future studies in math and science. Lane (1999) contends that we must support high quality mathematics and science education in every way we can so that we are ensured an adequate talent pool for our country. Mathematics anxiety in students has become a concern for our society, and should be addressed in teacher education programs, along with falling performance in the area of Mathematics.

Steen (1999) points out that national and international studies have shown that most U.S. students leave high school with far below even minimum expectations for mathematical and quantitative literacy. Neunzert (2000) feels that mathematics is critical for people living in the 21st Century in order for them to be successful. Yet, Gallup (1983) found that the American public rated math first in importance when compared with the other academic fields. NCTM (2000) recently published a revised version of standards for teaching mathematics, as a response to strong public interest in the area of math. NCTM (2000) recommends the following 10 standards for grades Pre-Kindergarten through 12. Content Standards: Numbers and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability. Process Standards (all of which highlight ways of acquiring content knowledge): Problem Solving, Reasoning and Proof, Communications, Connections, Representations. Building on Marzano's (1992) concept that students must have good attitudes and perceptions toward learning, students must have good attitudes about learning math before they both truly understand and develop confidence in their ability to do math. Now, with the advent of computer technology, the need for the understanding of mathematics is critical. McLeod (1991) claims that affective factors such as teacher sensitivity, patience, and providing a caring environment play a central role in mathematics learning and instruction.

Causes of Math Anxiety

Kutner (1992) asserted that teachers and parents who were afraid of math could pass on math anxiety to the next generation, not genetically, but by modeling behaviors of their own discomfort with the subject. Brush (1981) contended that the development of math anxiety carried some symptoms that included the following: (a) mathematics became difficult during early years of school, (b) students spent excessive amounts of time relearning what they had been previously taught, and (c) students were not exposed to the everyday applications of the material covered. Crawford (1980) found that many people often blamed their failures on their lack of a mathematical mind, the notion that men were better than women at math, or that they had poor memories or learning disabilities rather than any of the other aforementioned obstacles. Tobias (1987) suggested the importance of diffusing two myths: 1) that higher level math is too difficult for otherwise intelligent students to master, and 2) that without mathematics you can live a productive intellectual and professional life. Fear of mathematics may reflect on students' career choices in the future if they do not challenge themselves to take higher-level math courses. Hendel and Davis (1978) suggest that current conceptions of test anxiety may be useful in clarifying the nature of math anxiety. Sarason (1987) contends that math anxiety, like test anxiety, may be composed of two major components: cognitive concerns about performance (worry) and emotionality (autonomic reactions that are evoked by stress).

It appears that there has been a great deal of research related to gender issues and mathematics. Bernstein (1992) found that at age 12, males felt slightly more math anxiety than females; however, by the age of 14, females were more anxious about math than males. Saxe (1991) and Scribner (1984) support the idea that an individual's mathematics ability is significantly influenced by his or her participation in everyday applications such as: Going shopping in a supermarket; Selling lemonade in the street; Packing crates in a dairy; Completing worksheets in class; Sequencing pages when creating a webpage or Powerpoint presentation. Making connections between math inside and outside the classroom may help students realize that math is not something from which they can escape, but a tool they need to learn how to use. Davis and Hersch, (1990) take an incisive look at how math is applied in the real world today, particularly the influence of computers on mathematics, science, and society. They contend that math is everywhere--in business, in warfare, and in social sciences as a propaganda tool. It is estimated that by 2008, the top three areas of employment growth will be in technology fields: computer engineering 108%, computer support specialist 102%, and systems analysts by 94% (Bureau of Labor Statistics, 2000). The U.S. has led the world in the Information Age; however, it is questionable as to whether or not this success can continue if we are unable to solve some of the technology labor shortages and if we do not start better preparing our children for the digital world (Dawson, Internet n.d; National Commission on Mathematics and Science Teaching for the 21st Century, 2000; Lane, 1999).

Preventing Math Anxiety

Research by Tobias (1993), has found that the NCTM Standards: (a) present mathematics as a thinking and decision making tool; (b) direct teachers to teach with concrete materials (c) allow students to see that math makes sense in their everyday experiences; and (d) convey that math is first and foremost a language used to organize and communicate valuable information. The way to prevent math anxiety is by instilling confidence through the implementation of the NCTM Standards. Math anxiety really is a complicated matter and may involve what happens to kids inside and outside of the classroom. NCTM (1995a, & 1989) has made the following suggestions for preventing math anxiety: Accommodate for different learning styles; Create a variety of testing environments; Design positive experiences in math classes; Refrain from tying self-esteem to success with math; Emphasize that everyone makes mistakes in mathematics; Make math relevant; Let students have some input into their own evaluations; Allow for different social approaches to learning mathematics; Emphasize the importance of original, quality thinking rather than rote manipulation of formulas; and Characterize math as a human endeavor. Zemelman, Daniels, and Hyde (1998), based on a culmination of research, have put together a list of what are considered to be the "best practices" for teaching math, which are: (a) the use of manipulatives (make learning math concrete); (b) the use of cooperative group work; (c) the use of discussion when teaching math; (d) the use of questioning and making conjectures as a part of math; (e) the use of justification of thinking; (f) the use of writing in math for: thinking, feelings, and problem solving; (g) the use of the problem-solving approach to instruction, making content integration a part of instruction; (h) the use of calculators, computers, and all technology;, (i) the role of the teacher as being a facilitator of learning and (j) the assessment of learning as a part of instruction.

Reducing Math Anxiety

Teachers almost need to take on the role of a counselor to help lower or overcome such anxiety toward mathematics, using a gradual success or systematic desensitization approach (Hembree, 1990). Davidson and Levitov (1999) advocate the use of relaxation in conjunction with repeated positive messages and visualizations. Teachers must help students understand how their math anxiety was created. Tobias (1987) suggests that one way for students to reduce math anxiety is to recognize when panic starts, to identify the inactiveness in their analytic and retrieval systems, and to clear up the static without ceasing to work on the problem.

Best Practice: Practical Ideas for Teachers

A practical idea for teachers and students is for teachers to assess their students attitudes toward math at the beginning of a school year by having them complete the following mathitude survey. Mathitude: (1) When I hear the word math I.... (2) My favorite thing in math is.... (3) My least favorite thing in math is.... (4) My favorite teacher for math is.... Math anxious students at all levels should use journals to express their understanding of mathematical concepts. Students are rarely asked how they feel about learning different concepts and branches of mathematics; they may benefit from being asked how they feel about learning mathematics. The following sample list of journal/discussion questions may be used for students to write about alone or to discuss and share with each other as a class. Examples of Journal/Discussion Questions

1. Pretend that you have to describe mathematics to someone. List all the words or phrases you can think of that you could use.

2. Imagine doing or using math either in or out of school. What does doing or using math feel like? Describe.

3. If math were a color, an animal, a piece of music, or type of food what would it be?

4. Describe how you feel in a math class.

Scieszka & Smith (1995), in their hook entitled Math Curse, created a character by the name of Mrs. Fibonacci, an elementary school teacher, who tells her class that they can think of almost everything as a math problem; as a result, one student becomes overwhelmed by the scope of math. However, the student eventually realizes that math is everywhere and there is no way of escaping it in daily life; therefore, the math anxious youngster recognizes math as a means of making one's life easier. Teachers may want to use Math Curse to conduct a bibliotherapy session with students so that they can relate to the character. Another practical idea for teachers is to actually teach test taking and study skills, using the following tips. Test-Taking/Study Skills: Teach note-taking skills; Teach test-taking skills; Teach relaxation techniques; Teach the importance of homework/studying; Teach how to read and use the textbook; Teach positive "I" messages; Teach visualization of success in math; Encourage peer or tutor practice/study.

Kathy Acker (Internet n.d.) developed the Math Anxiety Code of Responsibilities, these responsibilities while geared toward adults or college students may be adapted for any grade level Pre K-16, they are as follows:

1. I have the responsibility to attend all classes and do all homework as assigned;

2. I have the responsibility to recognize the rights of others to learn at their own pace;

3. I have the responsibility to seek extra help when necessary;

4. I have the responsibility to see the teacher during office hours or to schedule an appointment for assistance;

5. I have the responsibility to come to class prepared, with my homework finished and/or questions to ask;

6. I have the responsibility to speak when I don't understand;

7. I have the responsibility to give math at least the same effort I give to other subjects;

8. I have the responsibility to begin my math study at my current skill level;

9. I have the responsibility for my attitudes about my abilities; and

10. I have the responsibility for learning and practicing relaxation skills.

Math Testing Anxiety

Much research shows that often a large part of math anxiety is due to test anxiety (Anton and Klisch, 1995; Alexander and Martray, 1989; Alexander and Cobb, 1984). Students seem to show understanding of the math concepts when they have little to lose, but when grades or time limits are placed on such practices; students tend to become nervous, as demonstrated by sweaty palms (Furner, 1996; Tobias, 1978). Ruedy and Nirenberg (1990, p. 61), recount the poem by the Chinese sage, Chuang Tzu, from thousands of years ago: which may serve as a means to instill confidence in students: The Need to Win

   When an archer is shooting for nothing, he has all his skill.
   If he shoots for a brass buckle, he is already nervous.
   If he shoots for a prize of gold, he goes blind
   Or sees two targets--
   He goes out of his mind!
   His skill has not changed. But the prize divides him.
   He cares.
   He thinks more of winning than of shooting--
   And the need to win
   Drains him of power.

Often, superintendents place pressure on principals, who then may place pressure on teachers to have their students perform well on standardized tests in mathematics. Day in and day out teachers send messages to students stressing the importance of the class as a whole doing well on the test. Often the purpose or focus of why this test is important is lost or never understood by students. Reys (2004) and NCTM (2000, 1995b, & 1989) feel that assessment should allow for multiple sources of information with tasks that show different kinds of math thinking as well as present the same math concept or procedure in different contexts, formats, and problem situations. Teachers need to employ alternative forms of assessment in math classes, as suggested by Reys (2004), such as: observations, questioning, interviews, performance tasks, self-assessments of students, work samples, portfolios, writing samples, paper and pencil tests, and standardized tests. Teachers need to emphasize more communication in the classroom through discussion, problem solving, discourse, and writing.

Teachers' Own Anxiety

Teachers' own math anxiety can interfere with and often create math anxiety for their students. It is important that all teachers are consistent in terms of having a knowledge base for teaching mathematics. Taking refresher courses/workshops on new research-based best practices for teaching mathematics is critical in a world where technology is quickly changing what and how math is taught. Teachers can often damage their students' own dispositions toward and confidence in their ability to excel at math, even though this is not these educators' intention.

Family Math

Parents need to take a proactive role in the education of their children. Family Math Nights (Stenmark, Thompson, Cossey, & Hill, 1986) are becoming a popular means of bringing families to school so a family can do math together. Parents can learn about the new math standards, math manipulatives, problem solving, and active approaches to learning math. Parent involvement in schools has drastically improved student success. Stenmark, Thompson, Cossey, & Hill (1986) have made suggestions for parents who want to help their children with doing math at home. Schools and teachers may want to provide the following list as tips for parents in helping their children with mathematics at home:

1. Let your children know that you believe they can succeed at math.

2. Be ready to talk to your children about math and to listen to what they are saying or feeling.

3. Be more concerned with the process of doing math rather than getting the correct answer.

4. Try not to tell your children how to solve problems; it may be best to ask questions and guide them to the process.

5. Practice estimation with children whenever possible (i.e. in a store or on a trip)

6. Provide a special place for study, allowing for the child's learning style to be used.

7. Encourage group study.

8. Expect that homework will be done.

9. Don't expect that all homework will be easy; don't rush your child.

10. Seek out positive ways to support your child's teacher and school.

Teachers may want to share this information with parents. It is important that parents work closely with their children's teachers by asking their child's math teacher for a schedule of math topics to be taught. Parents also need to encourage their child to concentrate positively, especially if their child is insecure about his or her math abilities.

The Internet

The website "Professor Freedman Math Help" provides support for students, teachers, and parents one can access the Math Teacher's Ten Commandments, the Math Anxiety Self-Test, Ten Ways to Reduce Anxiety, Students' Math Bill of Rights, Study Skills Tips, Math Anxiety Code of Responsibilities, and many other links for math help. The Internet is an invaluable instrument for the teaching and learning of mathematics in this day and age, the possibilities with Internet Field Trips is endless in the area of mathematics (Furner, Doan-Holbein, & Scullion-Jackson, 2000).

Improving Student Learning

Although many factors inside and outside of school influence students' level of achievement, the quality of classroom teaching is a key to improving students' learning (National Commission on Mathematics ad Science Teaching for the 21st Century, 2000). The similarity in successful ways that mathematics is taught through working on mathematics problems (TIMSS Video Mathematics Research Group, 2003; Schmidt, 1998) probably can be explained by a convergence of global institutional trends (LeTendre et al, 2001). As Furner (1996) has pointed out, making the relationship between mathematics and life is a way to reduce math anxiety. Many mathematics educators advocate the use of real-life contexts in mathematics classrooms (Lesh and Lamon, 1992). Although the U.S. does not have a large-scale mechanism for sustained teacher learning (Stigler and Hibert, 1997), there is a growing sense that long-term, continuing teacher learning is a key to improving practice (Darling-Hammond and Sykes, 1999). With improved mathematics instruction for students and decreased levels of math anxiety, students will be better prepared, in terms of their math confidence and abilities, to experience success in a technological and mathematical world.

Summary

A U.S. national curriculum may be something for educators to ponder as we look to the future where our kids will be competing with students from around the globe for high-tech jobs. Our students' careers, and ultimately most of their decisions in life, could rest upon how we decide to teach mathematics. If schools do more in terms of addressing student dispositions toward math, educators may see a correlation with student achievement in mathematics. In overcoming a major obstacle to the improvement of student mathematics performance, that of math anxiety, schools may want to begin considering how they can first begin to prevent and reduce this phenomenon and address poor dispositions toward mathematics. Students who feel more confident in their ability to do math will do well in all the decisions they make and especially help them function and compete in our ever-advancing high-tech world.

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Joseph M. Furner, Florida Atlantic University

Barbara T. Berman, Contra Costa County Office of Education, CA

Furner , Ph.D., is an Associate Professor of Mathematics Education. Berman , Ph.D., is the Manager of Instructional Services