Recommended resources (not just for homeschooling)

resources.jpgWhen I visited Homestars in October, I shared a lot of information and it may have been overwhelming. As a reminder, here are the resources I had on display that day:

Alpha-Phonics, or How to Tutor, is essentially a book of word lists organized by phonetic pattern. The only difference is that Alpha-Phonics has large print intended for a child to read, and How to Tutor has additional sections on math and handwriting. I don’t recommend what he says about math and handwriting, but the advantage of using How to Tutor is that it’s easy to find used, and it causes you to use the methods I recommend instead of just having the child read from the book. With spelling practice, the game I’m working on, and UpWords (below) a beginning reader never needs to actually read the word lists. The best place to find this is on Bookfinder.

UpWords is similar to Scrabble, but instead of just building onto existing words, you can change them. MAT becomes MAP becomes MOP becomes FLOP becomes DROP and so on. This is a wonderful way for children to practice seeing the patterns in words, and much more fun than reading from a list. The best place to find this game is at thrift stores. If you’d rather not wait, it’s available at Wal-Mart/Kmart/Shopko/etc.

The ABCs and All Their Tricks is an encyclopedia of spelling patterns, based on analysis of over 17,000 common words. This isn’t necessary to teach reading, but it’s great for anybody who wants more detail. It’s more detailed than any phonics book I’ve seen. If I had had this book when I was ten, I might have made it to the national spelling bee. Which isn’t an important accomplishment in the whole scheme of things, but I would have been gratified. The best place to find this is on Bookfinder.

Cuisenaire Rods are a way for children to figure out how math works and understand more deeply than they would with traditional methods. Even when a child is playing with these, they’re learning math without knowing it. Rods are so versatile that I once taught binary to a fourth-grader, without even intending to! I can order these at wholesale prices, cheaper than you can buy them anywhere else.

Algebra models do for algebra what Cuisenaire Rods do for basic math. I can also order these at wholesale prices.

Fraction circles are a great way to represent fractions. You can visually demonstrate finding a common denominator, and why it’s necessary. I can order these at wholesale prices.

Geoboards are a hands-on way to learn two-dimensional geometry, allowing experimentation and correction without having to redraw. I can order square grid, isometric, and circular geoboards at wholesale prices.

Zome is a wonderful building system that can be a toy, or a tool for research scientists. People use it to teach geometry, chemistry, art, algebra, probability, physics, and intangible skills like critical thinking and collaboration. The best place to buy this used is probably eBay, but compare the prices there with new prices, because sometimes they’re close. If your budget is tight, you can start building with pipe cleaners and stir sticks.

Koosh balls or puffer balls help with concentration and lateral thinking, even for people who don’t have ADD. I’ve been amazed by how many people who don’t think they need it, think better with a toy in their hands. These are rarely available in stores, but I can order them.

Weapons of Mass Instruction is an expose of the traditional education system, written by a former teacher who had worked in a great variety of schools. After he had been named Teacher of the Year, he eventually quit in disgust, feeling he had wasted his time by trying to work within the system. He makes a compelling case for throwing out the script and encouraging students to learn freely. Even people who already encourage independent learning will be challenged by this book. The best place to find this is on Bookfinder.

The best innovation since the Cartesian coordinate system

I wrote previously about the analogy of an algebra equation being like a pan balance, and recommended a website to use for practicing the concept. But there’s no practical way to do this with three-dimensional objects, because the weight of x would have to change for each equation.

However, there is a way to learn algebra with physical objects — you just have to remember the basic rules without any help from gravity. It’s still much easier than the letters and numbers that have plagued generations of teenagers.

Okay, so what is this system? A set of algebra manipulatives includes little squares to represent ones, two different sizes of narrow rectangles to represent x and y, and larger pieces to represent x2, y2, and xy. The most common way of representing negatives is that the back sides of the pieces are a different color.

What’s so great about them? First, you can use them to solve algebra equations. Rather than a bunch of numbers and letters on paper, you have objects to rearrange. 3x + 6 becomes 3 x pieces and 6 one pieces. These help a student learn algebra just as counters help a first-grader learn addition, because they can do concrete actions to each side of an equation, and see what 3x + 6 = 5x – 4 actually looks like.

Second, and even more exciting to me, is that these manipulatives provide a visual representation of multiplying and factoring polynomials. Rather than trying to remember all the apparently arbitrary rules, a student can see that x times 3 forms a 3x rectangle. The trial-and-error of factoring becomes a simpler matter of rearranging the pieces to make a rectangle, adding pairs of opposites as needed.

It’s algebra without anxiety! Using manipulatives makes the mechanics less error-prone, and reinforces the logical concepts automatically. Over time, students gradually transition to doing algebra exclusively on paper, when they’re ready. These simple plastic pieces are a visual aid as innovative as the Cartesian coordinate system, and I wish more teachers would use them in the classroom.

Now, where can you get some? The best designs are three dimensional: Lab Gear and Algeblocks. Unfortunately both are pricey, and the 3D Lab Gear parts are unavailable as far as I know. The set I use for tutoring is called Algebra Models and is comparatively inexpensive. I recommend the “Cooperative Group Set” for one student — the individual set doesn’t have enough pieces for most algebra problems, unless you use a book designed for the manipulatives. It would be nice to have the “Small Group Set” for even more pieces.

Another option, which may not be much of a cost savings over the Algebra Models, is to cut the pieces out of cardstock. There is also a virtual representation of the manipulatives, but that format is far from ideal.

In the future, I’ll write in more detail about how to use these. Which topic in algebra would you most like me to explain?