Getting Ready for (Gasp!) Algebra & Beyond
By Bill Pride
Printed in Practical Homeschooling #65, 2005.
"I'm scared to death of teaching high-school math." "I just don't feel ready to teach algebra." "I wasn't any good at math in school myself, so how can I teach it to my kids?"
In this article and those that will follow, I hope to ease your anxiety and increase your confidence. Like thousands of math-phobic homeschool moms and dads before you, you will be able to do a much better job than you think.
What Makes You Think Math Teachers Know Anything You Don't Know?
If you knew the pitiful qualifications of many high-school math teachers, you'd be less intimidated. Depending on where you live, between 10 and 80 percent of these folks can't even pass the equivalent of an eighth-grade-level math test. For example, in 2004 two-thirds of Philadelphia middle-school teachers failed a math content test, according to a September 17 article in the Philadelphia Inquirer.
School teachers get lots of courses in how to teach math in college, but not necessarily much in the way of actual math courses. There's a big difference between studying theories of how kids learn math and actually knowing algebra, geometry, trig, and calculus. As Richard Ingersoll pointed out in his ground-breaking 1998 article, "The Problem of Out-of-Field Teaching,"
Almost one-third of all high school math teachers have neither a major nor a minor in math or in related disciplines such as physics, engineering, or math education. Similarly, the same proportion of math teachers do not have a teaching certificate or license in math.
Since then the problem has worsened. In January 2003, the Committee for Economic Development reported the alarming fact that 93 percent of science students and 70 percent of math students were taught by "out of field" teachers (who neither majored or minored in the subject they teach, and may not even possess a teaching credential for that subject). In California, for example, "950 middle school teachers, or about 40 percent of the workforce assigned to teach Algebra I in middle school, do not have a subject matter credential in mathematics and may lack the background and preparation necessary to effectively teach the subject," according to an April, 2005, Center View article. And even qualified teachers have their efforts diluted when they have to handle 15-30 bored, restless kids, some of whom may be on drugs or in gangs.
So if you're expecting Euclid or Albert Einstein to be holding court in your local high school math classroom, think again. High-school math at home can be as successful as you want it to be; who you get to teach your kids math at school is a crapshoot.
One other thought: Being good at math in an American public school doesn't exactly make you popular. Scrawny kids who are good at math are at extreme risk of getting bullied, either physically or verbally. This problem you won't have at home.
Get Your Student Ready For High-School Math
OK. Time to dig in. You're willing to believe there's a chance you can do this.
Here's how to start.
First, make sure your student knows all his arithmetic facts cold. Learning high school math is no joke and while you are trying to learn how to solve equations, you can't be struggling with arithmetic. On standardized tests and college exams, you have to be able to do the arithmetic part of problems quickly and without hesitation.
Homeschool students sometimes don't get the practice they need in doing math under a deadline and as a result their math fluency could be improved.
As our fluency expert Michael Maloney pointed out in PHS #59, "Children who are fluent at using arithmetic operations can add, subtract, multiply, or divide simple math facts at 60-80 facts per minute with no more than two errors." If your child falls short of these goals, fill in the gaps with Barnum Software's Quarter Mile Math, Providence Project's Calculadder, or another drill product of your choice.
If your kids need help with arithmetic "how tos" and not just with speed, consider the Bonnie Terry Reference Pack, Math Essentials, or Developmental Math. All three are handy for quickly plugging in any math "holes."
Math facts are not the only area you need to check. If you discover your children are weak in the areas of fractions and decimals, don't move on to algebra until this problem is fixed. If you're looking for help, the "Key to" series from Key Curriculum Press is an outstanding worksheet approach, and the Math-U-See manipulatives-based program is great for hands-on learners.
Note: While being able to answer questions verbally is great, for arithmetic fluency in real-world environments, your children need to be able to legibly write that many answers in that time. If they can't do that, it is time for some handwriting practice, as Michael points out in his article in this issue.
Learning the Lingo
One thing that makes a big difference when making the transition from arithmetic to algebra is learning and becoming comfortable with the terminology and conventions of algebra.
By "terminology" I refer to the names for things. For example, algebraic operators are +, -, x (sometimes written as *) and ÷. A "convention" is the usual way something is written out. For example, in algebra, variables (unknown quantities) are usually labeled with letters near the end of the alphabet, such as x, y, and (when graphing in three dimensions) z, while constants (unchanging quantities)are commonly named with letters near the beginning of the alphabet - a, b, c, and so on.
It might be a good idea to go through the book's glossary before starting, to see how many words your student can actually define. Another option is to use a review tool, such as the QuickStudy Guide for the course you plan to teach. Each QuickStudy subject guide covers all the typical terminology, facts, and conventions your student needs to know for that course. Reading through the material ahead of time will make it seem familiar when your student covers it later on.
Your Many Curriculum Options
As is usual for every homeschooling subject these days there is no lack of materials or methods for teaching mathematics. You can:
- Buy a textbook or workbook curriculum and use the answer key and/or solutions manual. With this method, you or one of your older children grades the problems, and the solutions manual helps your student figure out where he or she went wrong if a mistake was made. With this option, it's important that the person correcting the work be able to recognize equivalents answers - answers that are algebraically the same, but written differently. For example, 1/4 is the same as 2/8 or .25 or .250, and x2-x is the same as x(x-1).
- Sign your student up for an online course. The online tutor and/or interactive software grades the work.
- Use interactive educational software courses. Again, the program grades the exercises and provides some level of feedback, ranging from whether the answer was right or wrong to detailed solutions.
- Use a video/DVD course, such as Math-U-See, Videotext, Chalk Dust, or D.I.V.E. Into Math. The advantage is that your student receives high-quality lectures - probably better than if he or she was sitting in an actual classroom. These courses all have accompanying workbooks or worksheets (D.I.V.E. uses Saxon math books), and some offer free online tutor-on-call or tutoring options.
- Don't forget math contests! Though not instructional in themselves, math contests can be highly motivating for kids who otherwise would waste their competitive impulses on video games.
With all these resources at your disposal, how can you fail? You're ready to take on the first challenge - teaching algebra - and we'll tell you how next issue.
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