Homeschooling High School Math

photo by ddluong via flickr
photo by ddluong via flickr

Feature photo (above) by Sphinx The Geek via flickr.

Most homeschoolers feel at least a small tinge of panic as their students approach high school. “What have we gotten ourselves into?” we wonder. “Can we really do this?” Here are a few tips to make the transition easier.

Before you move forward, it may help to take a look back. How has homeschooling worked for you and your children so far?

If your students hate math, they probably never got a good taste of the “Aha!” factor, that Eureka! thrill of solving a challenging puzzle. The early teen years may be your last chance to convince them that math can be fun, so consider putting aside your textbooks for a few months to:

On the other hand, if you have delayed formal arithmetic, using your children’s elementary years to explore a wide variety of mathematical adventures, now is a good time to take stock of what these experiences have taught your students.

  • How much of what society considers “the basics” have your children picked up along the way?
  • Are there any gaps in their understanding of arithmetic, any concepts you want to add to their mental tool box?

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How Can I Teach Math If I Don’t Understand It?

Our childhood struggles with schoolwork gave most of us a warped view of mathematics. We learned to manipulate numbers and symbols according to what seemed like arbitrary rules. We may have understood a bit here and a bit there, but we never saw how the framework fit together. We stumbled from one class to the next, packing more and more information into our strained memory, until the whole structure threatened to collapse. Finally we crashed in a blaze of confusion, some of us in high school algebra, others in college calculus.

Continue reading How Can I Teach Math If I Don’t Understand It?

How to Understand Fraction Division

photo by Scott Robinson via flickr

A comment on my post Fraction Division — A Poem deserves a longer answer than I was able to type in the comment reply box. Whitecorp wrote:

Incidentally, this reminds me of a scene from a Japanese anime, where a young girl gets her elder sister to explain why 1/2 divided by 1/4 equals 2. The elder girl replies without skipping a heartbeat: you simply invert the 1/4 to become 4/1 and hence 1/2 times 4 equals 2.

The young one isn’t convinced, and asks how on earth it is possible to divide something by a quarter — she reasons you can cut a pie into 4 pieces, but how do you cut a pie into one quarter pieces? The elder one was at a loss, and simply told her to “accept it” and move on.

How would you explain the above in a manner which makes sense?

Continue reading How to Understand Fraction Division

How to Conquer the Times Table, Part 2

Photo of Eeva times 6, by Eric Horst, via flickr.

The question is common on parenting forums:

My daughter is in 4th grade. She has been studying multiplication in school for nearly a year, but she still stumbles over the facts and counts on her fingers. How can I help her?

Many people resort to flashcards and worksheets in such situations, and computer games that flash the math facts are quite popular with parents. I recommend a different approach: Challenge your student to a joint experiment in mental math. Over the next two months, without flashcards or memory drill, how many math facts can the two of you learn together?

We will use the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.

Continue reading How to Conquer the Times Table, Part 2

How to Conquer the Times Table, Part 1

Photo of Evil Erin times 5 (and dog times 2), via flickr.

Perhaps the biggest challenge for any middle-elementary math student is to master the multiplication facts. It can seem like an unending task to memorize so many facts and be able to pull them out of mental storage in any order on demand. Too often, the rote aspect of such memory work overwhelms students, eclipsing their view of the principles behind the math. Yet rote memory is not enough: A student may be able to recite the times tables perfectly and still be reduced to counting on fingers in the middle of a long division problem.

We will use the world’s oldest interactive game — conversation — to learn the multiplication facts one bite at a time. But first, let’s take some time to think about what multiplication really means.

Continue reading How to Conquer the Times Table, Part 1

The Cookie Factory Guide to Long Division

[Photo by scubadive67.]

Help! My son was doing fine in math until he started long division, but now he’s completely lost! I always got confused with all those steps myself. How can I explain it to him?

Long division. It’s one of the scariest of the Math Monsters, those tough topics of upper-elementary and middle school mathematics. Of all the topics that come up on homeschool math forums, perhaps only one (“How can I get my child to learn the math facts?”) causes parents more anxiety.

Most of the “helpful advice” I’ve seen focuses on mnemonics (“Dad/Mother/Sister/Brother” to remember the steps: Divide, Multiply, Subtract, Bring down) or drafting (turn your notebook paper sideways and use the lines to keep your columns straight). I worry that parents are too focused on their child mastering the algorithm, learning to follow the procedure, rather than on truly understanding what is happening in long division.

An algorithm is simply a step-by-step recipe for doing a mathematical calculation. But WHY does the algorithm work? If our students could understand the reason for the steps, they wouldn’t have to work so hard on memory tricks.

Continue reading The Cookie Factory Guide to Long Division