This issue is one that has been coming up lots on message boards, blogs and within the discussion community at the SelfDesign program we’re part of. What do we do with young children who have quickly and efficiently mastered the primary mathematics curriculum? The obvious answer is to move ahead into the secondary mathematics curriculum. But it’s not quite that simple, for two main reasons.
First, the presentation of the material, when intended for a teen audience, often becomes dry and dense all of a sudden. Our beloved Singapore Math curriculum is a case in point. Look at the difference in presentation between the end of Primary and the beginning of the Secondary NMC books:
Goodbye friendly cartoon kids. Goodbye white space. Goodbye clever self-checking ‘secret code’ exercises. From a book which covers two problems in a two-page spread, we move to a book with over 70 short problems on a single page. My unschooled 8- to 10-year-old kids, who think of math as a nifty brain game occasionally aided by some fun pencil-and-paper exercises, have not been ready to make the transition illustrated above. It just looked too nasty and grown up, even though they were ready for the mathematics.
The other major issue is that the vast majority of homeschool curriculum choices out there are US-based, and follow the standard US practice of discarding almost all the interesting mathematical threads for two years in order to delve deeply into one particular thread, that of algebra. Variety and the discovery of inter-relationships between different areas of mathematics has always been what has kept math interesting to my kids. To set aside probability, number theory, geometry, statistics, series, patterns, algorithmic logic, topology and all that in order to focus exclusively on algebra seems such a misguided approach, particularly for fairly young children for whom math has typically been interest-led, capricious and playful.
I wish I could say that we’d found the solution. We have found a few non-solutions, and maybe a mix of partial solutions. First, the things that didn’t work:
- Singapore’s secondary programs. Though Erin did eventually get through Book 1 and part of 2, these were too dry and killed her interest in math for about four years.
- Teaching Textbooks was mathematically shallow and too slow-paced. The computer-based presentation was fairly friendly, but my computer-loving kids preferred their math not to be dressed up as computer entertainment (just like they prefer to just eat their broccoli, rather than having it sneaked into something else) and opted to use just the textbook. We all detested the algebra-only mono-diet as well as the excessive repetition and review.
- Life of Fred was a refreshing change. The humour and quirky narrative approach grabbed Noah’s attention for a while. But again it was that algebra-only mono-diet that tired him out. And after a while the narrative thread began to feel like broccoli being disguised as something else.
What I’ve decided so far for certain is that for young pre-teens a straight algebra course is not the best way to go. That pretty much eliminates most US-based math curricula. And that’s not a bad thing, though it makes for pretty slim pickings. In terms of English-language offerings it leaves Canadian school curricula, the Singaporean selections, and a few eclectic American offerings. (There may be some British or Australian or New Zealand stuff out there, but I haven’t stumbled upon anything yet that has been readily available or impressive enough to warrant ordering sight-unseen from overseas.)
Eclectic is really where we’re at right now. Over the past year and a bit, as Sophie closed in on the end of the Singapore Primary Math sequence, we’ve done a lot of eclectic grazing. I wish we’d done more, and I intend to keep grazing with her for a while. By the time I take Fiona through this transition maybe I’ll have it down!
Here’s what we have used, or have on hand, or are planning to use for our eclectic grazing.
- Calculus by and for Young People. Sophie delved into this at age 8 and it was great fun.
- Theoni Pappas’ children’s books. Delightful exploration of mathematical topics through stories, explanations and demonstrations.
- Hands-On Equations by Henry Borenson. Wish I’d had this for the older kids. Fiona is loving it.
- Alge-Tiles manipulatives and resource binder. Great fun for factoring quadratics and exploring negative unknowns and integers.
- The Man Who Counted by Malba Tahan. A story about a fictional mathematician full of brain-teasers woven into the story.
- The Number Devil by Hans Enzensberger. A very fun fictional story which romps through some of the basic concepts of number theory in creative ways.
- Art of Problem Solving introductory books. These are US-based but unique in that various topics like number theory, probability, geometry and algebra can be taught in parallel. I can’t see us working systematically through the whole shebang, but we’ll likely keep at least two or three of these around as resources. We just received our first AoPS book in the mail today and we’ll see how it pans out as time goes on.
- MathPower textbooks. Overall these are the best systematic texts I’ve seen for my kids, and I found them right under our nose at the local public school. They’re Canadian and cover a variety of topics at each level, but are friendlier and more varied that their Singaporean counterparts. They’re visually busy though, with some classroom-oriented garbage (“discuss with a classmate and formulate a hypothesis, then present it to your class…”) but they feel less intimidating than the book above. And mathematically robust? To a degree. They are conceptual and expect a fair bit from students, especially in the sidebar challenge projects and exercises.