Study of numbers and their operations.
Skill with mathematics is as important as literacy for daily living. Mathematics are used daily—to keep score in sports, to calculate the amount of change due when making a purchase, to measure a room for wallpapering, etc. While most parents find it enjoyable to read with their young children, few would describe sharing math experiences in the same positive terms. Social scientists report that Americans are the only citizens of developed nations that describe themselves as "not good at math," and point to supporting evidence from standardized tests administered worldwide—U.S. students rank below those of many other nations in math proficiency.
In 1989, the National Council of Teachers of Mathematics (NCTM, founded in 1920) issued "Curriculum and Evaluation Standards for School Mathematics" establishing a plan for mathematics education reform in the
|8th graders||4th graders|
|Indicates countries that do not adhere to international standards (students tested may be over the age, for example)|
|1. Singapore||1. Singapore|
|2. Korea||2. Korea|
|3. Japan||3. Japan|
|4. Hong Kong||4. Hong Kong|
|5. Belgium||5. Netherlands*|
|6. Czech Republic||6. Czech Republic|
|7. Slovak Republic||7. Austria|
Note: Average scores for test-takers from Slovenia (8) to Israel (14) are not significantly different.
|9. Netherlands*||9. Ireland|
|10. Slovenia*||10. Hungary*|
|28. United States||11. Australia*|
|12. United States|
elementary grades. "Professional Standards for Teaching Mathematics" followed in 1991, offering ways mathematics teachers can create an effective learning environment and establishing standards for evaluation. In 1995, "Assessment Standards for School Mathematics" was published to provide criteria for judging the quality of mathematics assessment.
These three documents propose a mathematics curriculum with the following features:
- More extensive study of mathematical ideas and concepts and their uses in today's world;
- Learning that shifts toward more active student involvement with mathematics, including mathematical problems that relate to their world, and the use of a variety of mathematical tools for solving those problems;
- Creating classrooms that are stimulating learning environments in which all students have the opportunity to reach their full mathematical potential;
- Assessment practices that shift toward student evaluations that are continuous and based on many sources.
The standards proposed by the NCTM state that children will:
- Be engaged in discovering mathematics, not just doing problems in a book;
- Have the opportunity to explore, investigate, estimate, question, predict, and test their ideas about math;
- Explore and develop understanding for math concepts using materials they can touch and feel, either natural or manufactured;
- Be guided by the teacher in learning (i.e., the teacher will not dictate how mathematics problems must be solved);
- Have many opportunities to look at math in terms of daily life and to see the connections among math topics such as between geometry and numbers.
In June 1997, President Bill Clinton held a Rose Garden ceremony at the White House to recognize the improvement in U.S. fourth-graders' ranking among their peers around the world in math and science, based on results from the Third International Mathematics and Science Study (TIMSS). U.S. fourth graders averaged 63% correct answers to the items on the test, compared to 59% average correct for the students from all 26 countries who took the test. Results from the eighth-grade TIMSS were released in November 1996: U.S. eighth graders averaged 80% correct answers, compared to 83% for eight graders from 41 countries who took the test. The ranking of U.S. fourth graders was 11th out of 26, and U.S. eighth graders ranked 28th out of 41. The accompanying table lists the rankings for TIMSS. In 1998-99, further results from TIMSS are scheduled to be released, including information on teaching techniques, use of calculators for math computation, and other educational practices worldwide. By examining the teaching strategies used in those countries where students outperform U.S. students in math, educators and curriculum development specialists may be able to address areas of weakness in American classrooms.
President Bill Clinton's education agenda presented during his 1997 "State of the Union" address called for all students to master challenging mathematics, including the foundations of algebra and geometry, by the end of eighth grade.
GENDER DIFFERENCES IN MATH
In the late 1970s, political scientists Sheila Tobias and others called attention to the trend for girls to avoid and feel anxiety about math, a fact she attributed to social conditioning. Girls historically were discouraged from pursuing mathematics by teachers, peers, and parents.
In the early 1990s, two studies suggested that there might be differences in how boys and girls approach mathematics problems. One study, conducted by researchers at Johns Hopkins University, examined differences in mathematical reasoning using the School and College Ability Test (SCAT). The SCAT includes 50 pairs of quantities to compare, and the test-takers must decide whether one is larger than the other or whether the two are equal, or whether there is not enough information. Groups of students in second through sixth grade who had been identified as "high ability" (97th percentile or above on either the verbal or quantitative sections of the California Achievement Test) participated in the study. The boys scored higher than the girls overall, and the average difference between male and female scores was the same for all grade levels included in the study. Another study by Australian researchers at the University of New South Wales and La Trobe University gave 10th-graders 36 algebraic word problems and asked them to group the problems according to the following criteria: whether there was sufficient information to solve the problem; insufficient information; or irrelevant information along with sufficient information. (There were 12 problems in each category.) Students were grouped into ability groups according to prior test scores. Boys and girls performed equally well in identifying problems containing sufficient information, but boys were more able than girls to detect problems that had irrelevant information, or those that had missing information. Next, the researchers asked the students to solve the problems. Girls performed as well as boys in solving problems that had sufficient information, but no irrelevant information. On the problems that contained irrelevant information, girls did not perform as well as boys. The researchers offered tentative conclusions that perhaps girls are less able to differentiate between relevant and irrelevant information, and thus allow irrelevant information to confuse their problem-solving process. The researchers hypothesized that this tendency to consider all information relevant may reflect girls' assumption that test designers would not give facts that were unnecessary to reaching a solution.
Some researchers have argued that offering all-girl math classes is an effective way to improve girls' achievement by allowing them to develop their problem-solving skills in an environment that fosters concentration. Others feel this deprives girls of the opportunity to learn from and compete with boys, who are often among the strongest math students.
To succeed in higher level mathematics, and even to solve complex problems encountered in daily life, students must acquire the skills necessary to use mathematics with ease. Students must master procedures (addition and division, for example), but they must also understand the problem-solving strategies that apply to mathematical procedures and concepts. Effective school curricula are designed to build student's critical, creative, and logical problem-solving abilities. The National Commission on Teaching and America's Future made this strong statement in its report, What Matters Most, "Today's society
Parents can support the development of math skills by making math a family activity, much the same as reading. Opportunities for math practice include adding prices while shopping, calculating the amount of discount of sale items, calculating the price per ounce of grocery items, and practicing estimating the temperature in Celsius when hearing the weather report. While traveling, devise "mental math" games that the family can play together. Use the clock to give practice in addition and working with fractions.
When parents express positive attitudes toward math—and avoid making negative observations about the subject—they are helping their children to keep an open willingness to succeed in math. Even when a parent feels unable to help with math homework, he or she should avoid expressions of failure or inability. By helping the child construct strategies for getting help—using the school's tutoring center or asking the teacher for extra help—the parent is showing the child that math is a subject that can be tackled, and that there are pathways to success.
PERIODICALS FOR STUDENTS
Dynamath, published by Scholastic Press School Division.
For children in grade 5 (appropriate for grades 4-6)
Cames Junior (ages 7 and above) magazine, P.O. Box 10147, Des Moines, IA 50347.
Older children may enjoy Games magazine, available from the same address.
Math Power, published by Scholastic Press School Division.
For children in grade 3 and above.
Puzzlemania, published by Highlights, P.O. Box 18201, Columbus, OH 43218-0101. Includes spatial reasoning, logical thinking, and word puzzles.
Zillions, published by Consumer Reports, P.O. Box 44861, Boulder, CO 80322.
Children's version of Consumer Reports, focusing on products of interest to young people. Illustrates data gathering and analysis.
Kanter, Patsy F. Helping Your Child Learn Math. Washington, DC: U.S. Department of Education, Office of Educational Research and Improvement, 1992.
Martinez, Joseph G. Math Without Fear: A Guide for Preventing Math Anxiety in Children. Boston: Allyn and Bacon, 1996.
Measuring What Counts: A Conceptual Guide for Mathematics Assessment. Washington, DC: National Academy Press, 1993.
Sternberg, Robert J., and Talia Ben-Zeev. (eds.) The Nature of Mathematical Thinking. Mahwah, NJ: L. Erlbaum Associates, 1996.
Tobias, Sheila. Math Anxiety. New York: W.W. Norton, 1995. Vinton, Layne T. Math Assessment: Grades 5-6. Huntington Beach, CA: Teacher Created Materials, 1994.
. Math Assessment: Grades 1-2. Huntington Beach, CA: Teacher Created Materials, 1994.
. Math Assessment: Grades 3-4. Huntington Beach, CA: Teacher Created Materials, 1994.
Kloosterman, Peter, et al. "Students' Beliefs about Mathematics: A Three-Year Study." Elementary School Journal 97, September 1996, pp. 39-56.
"The Learning Lag: You Can't Blame TV. (Third International Mathematics and Science Study Finds That American Students are Far below Japanese.)" U.S. News and World Report 121, December 2, 1996, p. 16.
"The Quest for Qualified Teachers." U.S. News and World Report 121, September 23, 1996, p. 19.
Get Ready to Read. Get Ready for Math. Racine, WI: Golden Book Video, 1989.
(One 54-minute videocassette.)
National Council of Teachers of Mathematics (NCTM)
Address: 1906 Association Drive
Reston, VA 22091-1593
Telephone: toll-free (800) 235-7566; (703) 620-9840
FAX-on-demand line: toll-free 24-hours a day (800) 220-
8483 (order information to be sent by fax)