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.

How I learned to teach

I started tutoring with no training or experience. I needed a job, they needed math tutors, I didn’t know there was anything more to it than helping with homework. I cringe at some of the things I did in my early years, but students gave me good reviews, and the director praised my habit of answering questions with questions.

I realized that most of math class was “monkey training” and I became determined to challenge students to a deeper understanding. I read books and articles about how we think and about unconventional methods of problem solving. I thought about my learning experiences over the years, and experimented while tutoring.

Then I started teaching at Chippewa Valley Technical College. Because of tutoring, I taught interactively. I wanted every class to be a conversation and an exploration. Unfortunately, my ingrained expectations of what schools and teachers should be interfered with developing my own style. I felt awkward being an authority figure over adults.

My first semester teaching, the older teachers said, “Trade students are stubborn. They won’t do anything unless they see how it will help them earn money.” They told me not to justify topics, but simply insist “It’s required for your program.”

By the end of the semester, I had decided trade students actually have trouble understanding if they can’t see how a topic relates to the real world. Then I went to a professional development seminar. And heard about contextual learning. And thought, “Egads, I was right! I’m not the first person to realize this!”

But even then, the only way I knew to be more contextual was to make up realistic word problems and use analogies to explain math rules. I wanted to help my students really understand math, but something wouldn’t click. I encouraged them to take risks, but other teachers and department policies made me hesitant to take risks myself.

At the end of my second semester, I had a week-long class on teaching methods. I dreaded the thought of sitting still for eight hours a day, four days in a row, cramming so much into my brain in a short time. I worried that I’d have to write a paper, and that the class would be graded.

To my great surprise, that class was exactly what I needed! The teacher, Deb Walsh, broke all the rules and told us it to do it too! She told us to form a partnership with students rather than pull rank. She told us to minimize lecture time and maximize opportunities for students to take responsibility for learning. She told us to quit blaming and punishing students for their natural reaction to the school environment. She told us to get students out of their seats, encourage community, and make our classes a positive, exciting experience. She proved that students would do more and better work, voluntarily, if we changed the whole system. She proved it by using us as a demonstration.

During the week, I was mentally overloaded and did less than half of the recommended reading. But Deb didn’t care, or maybe she couldn’t tell. I was so involved in processing these revolutionary ideas and thinking of ways to make the most of these new freedoms, I couldn’t take in any more.

The last day of class, Deb invited us to each write something on the whiteboard to sum up our experience that week. I wrote:

I have permission to be creative
and sing in class
and quit trying to act tough.
(I’m not very good at that.)

And I told her about a blog I had just discovered, and Standards-Based Grading.

I haven’t had the opportunity to teach in a classroom again (CVTC is as-needed), but I’ve been getting more unorthodox with every student I tutor. I’ve discovered more great teacher blogs, and I dream of starting a totally outside-the-box non-school where I would be more of a facilitator while students teach themselves.

But in the meantime, I have a lot to learn!

Play an addictive game to learn algebra!

DragonBox title

One of the best ways to learn something is by playing a game. Unfortunately, designing an effective learning game is a lot harder than it looks. So when I read a rave review for DragonBox, I was pretty excited.

DragonBox title page

I tried it out, and this is by far the most complete representation of algebra rules I’ve ever seen on a computer. It rivals the Algebra Models I wrote about before. It makes algebra so easy a five-year-old can learn it. And kids love the game — it’s more popular than Angry Birds on the AppStore.

There are a few relatively minor details I’d change, and I suggest you learn about the balance model of algebra along with playing DragonBox. But if you’ve had trouble with algebra, or if you’re a parent who wants your kids to avoid having trouble with algebra, DragonBox would really help.

Download it for Android, Ipad, Iphone, PC, or Mac. The 12+ version is only available for phones, but there’s a web version available until the game is ported to PC.

Order of operations is all out of order!

Math teachers frequently say that math, more than any other academic subject, is logically sequential. Each topic builds on the previous topics, chapter after chapter.

But that’s not always true. Some topics in math class seem to come out of nowhere, wedged in the middle of some apparently unrelated stuff. Teachers know it’s because they’re considered necessary preparation for future topics, or because they’re considered important even though they’re not directly related to the rest of the semester. Unfortunately, most students have given up asking why.

Possibly the best example of an awkwardly wedged-in topic is Order of Operations. Sure, we all have to agree on a standard set of rules for operator precedence. But there are good reasons for these rules; they’re not just convention.

Unfortunately, the rules look totally arbitrary, because of timing. We teach them as a prerequisite to algebra, so students have no basis for understanding them, so all we can do is fall back on convention. We claim that math is logical, but the way we teach isn’t very convincing!

I propose that we simply skip the section on order of ops. The first time students need to substitute numbers for letters, talk about terms. When you find the area of multiple rooms, first you need to find the area of each room, then you add the areas together. Terms are like rooms: 2x is a term, and -3y is a term, and before adding them together, we have to resolve them. The fact that x is closer to 2 than it is to anything else provides visual reinforcement. Division is usually written as a fraction, so if x is on top of 2, clearly that must be resolved before adding 4. This covers the MDAS of PEMDAS, and for now, I’d leave it at that.

When we get to distributive property, I talk about parentheses being like a picture within a picture, or a story within a story.* If you want to multiply the picture by 3, you have to include the whole picture. So you need to either resolve everything within parentheses before doing anything else with it, or you have to be sure to include everything. Of course, resolving should be preferred whenever possible. I also remind students that their calculator can’t see how long a fraction bar is, so sometimes they need parentheses on the calculator when they don’t on paper.

Finally, when we get to exponents, I explain repeatedly that x, x2, and x3 are like length, area, and volume. You can’t add 5 ft + 3 ft2; it doesn’t make sense. When you substitute numbers, you need to resolve the exponential terms down to just numbers, before you can combine them. Any operator only applies to what’s right beside it,** so 2x3 means 2 cubes or 2xxx, not (2x)(2x)(2x).

In my experience, most students see math as a labyrinth of inscrutable rules. No wonder they hate it! This way of presenting order of operations flows with the rest of algebra — students won’t even think about memorizing because it will just make sense.

This idea developed gradually when I taught a very basic algebra class. I refined my plan in response to two posts by Timon Piccini at Embrace the Drawing Board. Do you see any problems with this? How would you improve on it?

* I just thought of this analogy while writing, and I like it better than my previous explanation.
** Yes, this is also true of addition and subtraction. They only act on the result that’s right beside them, when it’s their turn to act.