I let that negativity roll off me like water off a duck’s back. If it’s not positive, I didn’t hear it. If you can overcome the negativity, everything becomes easier.
—George Foreman
The first step to success in math is a positive attitude. Yet that’s the last thing we can expect from many of our students. Many students, like their parents before them, come to our classrooms with valid feelings that make them unhappy doing math. A 2005 poll of 1,000 adults revealed that 37 percent recalled that they “hated” math in school. In the poll, more than twice as many people said they hated math as said they hated any other subject. One would think that once they were out of school, these folks would have found the real-world value of the math they disdained in school. In an evaluation of math literacy of a random sampling of adults 71 percent could not calculate miles per gallon on a trip, and 58 percent were unable to calculate a 10 percent tip for a lunch bill. Yet only 15 percent of those polled said they wished that they had learned more about or studied more math in school .
Myths and misconceptions about math abound, such as the following:
• You have to be very intelligent to be good at math.
• It is acceptable to be bad at math because most people are.
• Math isn’t really used much outside of special occupations.
In addition, many people have the attitude, “My parents said they were never good at math, so they don’t expect me to be any different.” Why is there so much negativity about math? Causes include low self-expectations as a result of past experiences with math, parental bias against math, inadequate skills to succeed at math learning, failure to engage math through learning strengths, and fear of making mistakes. As
teachers know all too well, math negativity has various consequences. These include stress, low motivation, decreased levels of participation, boredom, low tolerance for challenge, failure to keep pace with class lessons, behavior problems, and avoidance of the advanced math classes necessary for subsequent professional success.
Many parents of today’s students learned math by doing worksheets and drills, and they expect the same for their children. Parents who were successful in math through repeated memorization skills (rather than strong concept development) may resent alternative math instruction, such as inquiry and manipulatives, for their children. A possible result is that some parents may feel frustrated when they can’t help their children with the unfamiliar homework. However, it is likely that their children don’t share these parents’ verbal, linguistic, and auditory learning strengths. The top three intelligences found among students today are linguistic, visual-spatial, and tactile-kinesthetic. These are the same intelligences that characterized most learners 25 years ago, but the percentage of students in each category has changed. The proportion of linguistic (auditory) learners has dropped, and there is a greater preponderance of visual learners. Visual-spatial learners now account for more than 50 percent of students, 35 percent are tactile-kinesthetic, and only 15 percent are linguistic learners (Gardner, 2000).
In a study that looked at middle school students’ perceptions of academic engagement (Bishop & Pflaum, 2005), 5th and 6th graders were asked to draw their typical learning experiences and then draw learning experiences they liked. In the drawings of typical experiences, teachers and chalkboards were the focus, and the students usually did not include themselves in the picture. In the drawings of learning they liked, the students featured themselves prominently.
Th is finding is especially pertinent to math negativity. Consider the frustration that results when children learn math by memorizing facts and procedures instead of building on a firm understanding of concepts. Long division, for example, is an early math challenge, usually taught as a procedure to be memorized and incorporating subtraction, addition, and multiplication—often before these preliminary skills have been fully mastered. Therefore, children typically struggle to solve long-division problems with remainders (e.g., 67 ÷ 8 = 8 with a remainder of 3). Solving these problems is usually not very pleasant for students, but by the time they have completed enough drills and built the mathematical foundation necessary to succeed (usually around 5th or 6th grade), they are inexplicably asked to report quotients with decimals or fractions, not remainders. Textbooks and teachers alternately ask students to round the answer to the nearest tenth, round
to the nearest hundredth, express the answer in fraction form with mixed numbers, or express it in fraction form with improper fractions. Students are usually not told why they must make these changes. If they are given reasons, the reasons are often confusing or vague. I recall that the fi rst time I assigned textbook homework that asked for answers to be given in different formats, I did not have a clear rationale for my 5th grade students. No explanation is given for which representation of the answer is best, nor is one provided for when the diff erent variations should be reported; yet the demands to answer questions in these varying formats continually appears on homework and tests. In many schools, children don’t have the opportunity to participate in classroom discussions about the real-world implications—that can actually be significant—of remainders or decimals.
For example, when it comes to the rate of interest on large sums of money, the difference between 8.3 and 8.375 percent can matter to the borrower. Other times, decimal or remainder answers might be inconsequential, such as figuring how many eight-person tables are needed to seat 67 children at a pizza party. Whether the remainder is 3 or the decimal part of the quotient is .375 does not make any real difference because any remainder or decimal means that an entire additional table is needed. In this light, why wouldn’t students develop math negativity, frustration, and stress? Th ey are routinely asked to memorize procedures and are then told—without explanation or conceptual connections—that what was correct last year is no longer acceptable. Th e curriculum rarely primes their interest with opportunities to want to know how to represent remainders in diff erent forms. Without clearly evident personal value, the brain—operating
at the level of information intake and memory formation—doesn’t care.
Students truly “get” math when they see it applied in real-life ways they care about—in other words, when they see math as a tool they need and want. Th is motivation is not promoted in word problems about the number of books or the number of students in a classroom. However, when you give small groups of students 67 toothpicks and some index cards and then ask them to model the pizza party seating problem described earlier, they’ll build the experiential knowledge of a real-world situation where remainders are not helpful. When they consider dividing leftover pieces of pizza into parts, they will see that fractions or decimals are a valuable tool to make the pizza sharing process fair, whereas a “remainder” would imply that perfectly good pieces of pizza sit in the box because there is no way to divide them.
Most elementary arithmetic skills are “learned” by rote memorization and assessed on tests of memory recall. Children who do not excel at memorizing isolated facts are less successful, feel inadequate, and lose confidence in their ability to do math. Th e result is a cascade of increased math anxiety, lowered self-confidence, alienation, and failure. Th is is a pity because the ability to memorize basic arithmetic and multiplication tables does not determine who lives up to their math potential. With this goal in mind, the ability
to recognize patterns and construct mental concepts that use foundational math facts is far more valuable. Math that is “taught to the tests” has a negative eff ect even on the children who succeed with this approach. Th e problem is not that they won’t rise to standardized-test expectations; they will, but their achievement will stop there. If your math curriculum doesn’t include problems that students want to solve and discussions that connect those problems to what students need to learn, your intervention is critical to prevent increasing student ambivalence to and alienation from math.
When you help your students build a positive attitude toward math, they become engaged in the material and motivated to excel in mathematics because they value it. When you off er experiences and opportunities that inspire your students to measure, question, and analyze things around them, they will want to acquire the knowledge and mathematical tools necessary to achieve those goals. Once you reopen doors that were previously closed by negative feelings, math is revealed to students as an accessible, valuable tool to help them understand, describe, and have more control over the world in which they live.
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