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Rethinking Midschool/High School Math
From the Older Kids column, by Cafi Cohen, originally published in the January-February 1997 issue of Home Education Magazine.

M-A-T-H. What thoughts come to mind with the word MATH? One of the three R's. A government school "required subject," according to many state statutes and some local regulations. An essential topic in any homeschool.
Past that point, what official guidance are you given for teaching math? Often, none. What you cover and how you cover it is up to you. In the absence of specific directions, many homeschooling families pursue what I call School Math. School Math is how most parents studied math when they attended school; and it is how most schools still teach math.

School Math involves textbooks, workbooks, and exams. Older kids pursuing School Math study the subject sequentially -- in other words, arithmetic, followed by algebra, then geometry, second year algebra, trigonometry, and so on. Those using a School Math program must always "show all the steps" and reason exactly like the author of the text reasons. Alternate approaches to problem solving are unacceptable. Getting the right answer is emphasized, often to the exclusion of understanding the process.

School Math texts often include unrealistic problems. Typical is the following. A 20-ft. telephone pole falls across a street and the two ends extend one foot and three feet either side of the street. How wide is the street?
That's it. A real problem from a real math text. It makes me wonder. When would a person ever measure a street this way? And why? Ambiguous situations are a second deficiency illustrated here. How do we know the telephone pole is perpendicular to the street? Obviously, the "correct" answer would vary with the angle between the pole and the street.

A steady diet of School Math also often means that math applications (using math in real life situations) are accorded supplementary status. Kids whose math experience is dependent on texts do real life math seldom - if and only if they complete an exhausting set of math text problems.

Given all this, we homeschooling parents have to ask ourselves, is school math the right way to inculcate mathematical skills and processes? Let's look at the evidence. With respect to formal math instruction, 80+% of high school graduates in the United States get no further than consumer math, general math, and introductory algebra (this ignores the 30% of students nationwide who don't graduate at all).

Of those students who do graduate, a majority need cash register picture keys to add up purchases and make change. Sometimes, even the best math students, those who take the advanced math courses, forget how to accomplish basic tasks like calculating a percentage or cutting a recipe in half. Scores on the math portion of the Scholastic Aptitude Test (a college entrance exam) continue to decline.
When I speak to groups of adults, I sometimes ask how many fear or dislike math and how many consider themselves math-phobic or math illiterate. Consistently 1/3-1/2 of any adult audience identifies themselves as having a strained relationship the topic.

So, given all this - the relatively low level of formal math course completion, the lack of math application skills, poor standardized test performance, and pervasive math anxiety in the general population - we home educators have to ask ourselves: do we want to copy a method that yields these results? Do we gain anything by patterning our homeschooling after the programs of the educational establishment?
I don't think so. Emulating a failing system is not the way to go. Fortunately, as homeschooling families, we have the latitude to try something else.

We homeschooled two kids from grades six and seven through grade twelve and eventually enjoyed success with the math "program" we developed. We began as many of you probably did: with textbooks and workbooks and tests and grades; with lessons and problems every day; with pencils and papers and rulers and protractors; and almost always, with serious, sometimes grim looks on our faces.

As we progressed through early middle school math (prealgebra and then algebra), we spent less time with the texts and more time on topics most schools consider supplementary. These included:
* Consumer math and everyday accounting
* Math applications (also called "hands-on" or real life math)
* Mental math
* Recreational math (math games)
* Probability and statistics
* Calculator math
* Math history

And, as I observed my kids' reactions to these topics, we changed our emphasis, and My Ideal Math Program evolved. My Ideal Math Program consists of equal proportions of textbook math and alternative math activities (those "supplementary" topics listed above). Our kids spent approximately half their time with instructional math program materials with which we are all so familiar (we used Saxon Math, but any program which your teenager thinks is straightforward and clear is acceptable). And fully half of our kids' math time was devoted to the other topics listed above.

We found that alternating the emphasis weekly - one week program math, one week alternative math - worked out well for us. You may find that daily or monthly or even randomly timed alterations fit your situation better.
An example of this approach for a seventh grader follows. On week one, the kid completes one lesson daily of Saxon Math 76. On week two, she works on a 4-H Project which incorporates consumer and hands-on math. On week three, she returns to Saxon Math. On week four, she works with mom on mental math techniques. On week 5, it's back to Saxon. On week 6, we play math games each day.

How will your kid complete his program text if he's only doing it half the time? A good question. What we found was that our kids did not need to do every problem in the text. Because of time spent with alternative materials, our kids grasped and mastered text concepts and operations more readily. With a program like Saxon, I would recommend that kids try reading all the lessons, but only doing every other problem set.

What about a tenth grader using Key Curriculum Press materials as the formal math program? On week one, he works 30-45 minutes daily on Key To Geometry. Week two, he plays games taken from the book Family Math each day. Week three, he is once again working on the Key To - book. Week four, he works on the accounting for his lawn-mowing business and plays with the techniques in a calculator math book. And so on.

I am recommending an approach that integrates textbook math with topics like hands-on math and recreational math and puts them on an equal footing. Some regard this as radical thinking. Why should you consider it? Here are five reasons.

First, an integrated approach increases the likelihood your kid will cover math topics in which your program may be weak. No one text is perfect; no program complete, regardless of the advertising. Your program may do a superb job explaining concepts but lack good drill material. Or it may be drill-heavy and come up short in problem solving or hands-on activities. As an example of a deficiency of some higher level math programs, your Algebra II or Trigonometry text may omit statistics and probability.

Point two. Alternative math materials and activities help students relate math to The Real World and acquire skills they will use throughout their lives. Kids learn to estimate gallons of paint needed for a room by running through the calculations and then trying them out (in this case, painting the room). They master budgeting and balancing checkbooks by helping you juggle (or even taking responsibility for) the family finances. They will never forget how to obtain price per unit after they have stood in a store aisle with a calculator and crunched the numbers several times.

Third, alternative activities and materials encourage a problem- solving, can-do attitude. That is, after all, the goal of all the school math programs: teaching kids to solve real world problems. Unfortunately, many school programs have gotten lost in their own didacticism. We don't have to.
Fourth, an integrated approach may be the best way to reach the math phobic teenager and the kinesthetic (hands-on) learner. The alternative materials may be the only things that gets through to the math-phobic kid. And the kinesthetic learner will probably understand his text material only after he has had the chance to "play" with hands-on math materials.

Finally, incorporating hands-on and real life and recreational math materials in your program can help you and your student feel more relaxed about math. Math games are fun. Homeschooling catalogs carry many recreational math games, but often you need not look any further than your hall closet. Monopoly, for example, provides excellent practice and review of the four basic arithmetic operations, lots of mental math, as well as fractions, decimals, and percents. Frequent Monopoly players retain "easy" math skills. They do not forget how to calculate 10% mentally just because they happen to be studying geometry this year.
1997 Cafi Cohen

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