While mastering math facts is an important aspect of the elementary curriculum, at the high school level such mastery takes on almost desperate significance. As wildly improbable as this may seem, without a calculator many high school students cannot add or subtract negative numbers. They cannot multiply or divide a number greater than 5. They cannot add or subtract a fraction if their lives depend upon it. These are such basic math skills that one must wonder how such a student made it to 9th grade? They are normal, everyday students, with ipods and iphones and Playstations at home. How on earth can they learn enough math to pass Algebra or Geometry? Well, they can, if they are given the right tutoring.
For the last several years, I have had the job of giving students like these basic math tutoring in order to catch them up with their more math-literate peers. I have learned a few things. At the teenage level, “math games” are a hard sell. Those colorful cartoon characters on popular children’s software are just not going to hold the attention of a 15-year-old. But there are some things that do work. If you are trying to help your own teenage son or daughter learn these skills, perhaps these tips will help:
1. One-on-one drills with a competent, patient, and encouraging tutor is an essential part of remedial math instruction.
Why one-on-one? Because a student who has progressed to high school without knowing basic math facts has clearly managed to slip through the cracks of large classes and is an expert at pretense. The trend for the last decade in math instruction has been to teach it with a “spiraling” curriculum. In other words, math has not been taught at the lower levels for mastery, but rather for exposure – the theory being that if a student did not master multiplication or fractions in fourth grade, perhaps he will in fifth grade when he sees multiplication again for a few weeks… or in sixth grade… Unfortunately, sometimes the student does not get it until and unless a professional tutor addresses the math skill directly with the student. There are no pretenses when a student sits next to me with a small whiteboard and we speak the language of math back and forth until the student gives a visible sigh and smile, and suddenly, that student “gets it” and proves it by completing more examples of increasingly more-difficult equations.
2. Repetition is everything.
Let’s take an example: adding and subtracting negative numbers. This skill is confusing to students because they have been taught to memorize phrases like, “when you want to subtract a negative number, you add it.” This phrase just doesn’t connect with anything in the student’s experience. It seems counter-intuitive. Instead of teaching students rules like this, we should be showing students example after example of subtracting negative numbers using a number line and manipulatives that are color-coded for “positive” or “negative” values. For students to break away from a calculator with a “change sign” button, they need to experience an intuitive grasp of number values. Repetition is the best method for providing such an intuitive grasp to students.
2. Multiplication tables are a root of mathematics.
They are first taught in third grade. By fifth grade, they are supposed to be memorized and readily available in a student’s recall. Yet many, many students progress into high school without knowing these elementary facts. There are tricks: when multiplying by 2s, just double a number; when multiplying by 4s, double the number you got by multiplying by 2s; multiply any number by an even number and you MUST end up with an even number; multiples of 5s end in 5 or 0; two-digit multiples of 9 add up to 9 (thus, 3 times 9 equals 27; 2 plus 7 equals 9). There is no substitute for practice when it comes to multiplication. A first step is to discover where a student is weak in the multiplication tables, and focus on those areas for drilling practice.
3. Math baggage
As a tutor, you have to remember that different students have different math backgrounds, and you have to overcome the failures and emotional baggage of the past before you can build on the successes of the future. A consistent, calm, and encouraging demeanor is essential to building trust with such a student. Students who struggle with basic math in high school have already built up a lot of angst, and tutors MUST keep a calm and encouraging demeanor when students stumble… they will not make progress if frustration is vocalized, because the emotional weight of past failures will flood a student’s brain until it is struck dumb. Successes can be paraded with smiles, laughs, triumphant “yes!”es, and hugs; but failures should only be met with calm encouragement. An effective professional math tutor is worth the money.
If you are a parent, you may already realize that YOU have been the cause of some of the emotional baggage that I am talking about. For a parent, the difficulty of tutoring teenagers in math is infinitely more difficult, and the pitfalls are very real. It is certainly possible for a parent to tutor his or her teenager in basic math, but it may be much more difficult for a parent to maintain a calm demeanor in the face of a teenager’s inability to solve problems.
Basic math skills are actually very rewarding to teach; in my experience, students will grasp them quickly if they are taught one-on-one, away from the distractions of peers or classrooms. You will never forget the grateful looks of students who finally complete math problems correctly and with confidence.