What’s a parent to do after a child finishes Singapore Math 6B? After even the Challenging Word Problems 6 supplement? I’ve googled that question, asked other homeschooling moms on forums, and pondered it with friends each time a child neared that mathematical cliff. There is, of course, no perfect answer. If your child is mathematically talented and young, delaying the algebra, geometry, algebra II, precalculus, calculus chain should at least be explored. (The Art of Problem Solving folks explain why rather well.) My older decided to start that chain immediately just before turning ten (albeit taking it at a slower pace), and he’s been largely happy with that choice. My younger son, ten, more recently began life after Singapore 6B, so his path is still in its evolution.
So here are some possibilities. I’ve divided them up depending on whether we’ve made use of them at the pre-algebra/algebra level or not. Some are linked to my reviews while others remain on my ever-growing list of curriculum to review here. Hopefully, the lists will provide some options for the child that gets to that point several years before his or her teens as well as for kids who reach it later. If you have more ideas, add them (with any links) to the comments section.
What We’ve Done
- Jacobs’ Elementary Algebra: When my older son was done with Singapore 6B at nine years old, he wanted to go right into algebra. Honestly, I didn’t know of any other path to offer, although his insistence was strong enough that I’d likely not have swayed him. Harold Jacob writes with humor, which appealed to my older son. Jacob quickly moves through the pre-algebra basics not covered in the Singapore series (negative numbers, exponents, absolute value, order of operations, and various mathematical properties) and onto a sound algebra program. (Review here.)
- Keys to Algebra: My younger used the first of these ten books while working on Singapore 5. The series is a consumable set of low-cost workbooks designed for a student to use alone. They are fairly dry but provide plenty of practice and start with pre-algebra concepts. I’ve known of families who have used these before a deeper study of algebra or along with the last books of Singapore.
- Algebra Survival Guide: This book breaks algebra down into bite-sized components, starting with a fair amount of pre-algebra (properties, exponents, negative numbers, radicals, etc.) Each page presents one concept, and many concepts are briefly proven along the way. For practice, there’s a consumable workbook with answers. While not a full algebra course in my opinion, it certainly does a fine job introducing many concepts that could make a more challenging algebra class more manageable. My younger is enjoying this book now.
- Penrose the Mathematical Cat: Theoni Pappas has a number of books for children and adults that introduce a variety of mathematical ideas that sit well beyond the traditional curriculum. My younger son and I started reading these together during the Singapore books and enjoyed discussions about fractals, mobius strips, infinity and more. These are definitely our antidote to math anxiety and traditional math blues.
- Life of Fred Prealgebra: Life of Fred has a growing body of followers. We’re not part of them. We tried the first book (reviewed here) and found it rather dull and lacking much math. If you’re looking for a light diversion for a few months, this may work for you. It didn’t hold interest here.
- Challenge Math: Edward Zaccaro presents an array of largely pre-algebra topics that are generally accessible before the end of Singapore 6B but could also be enjoyed after completion as a way of strengthening problem solving skills. His 19 chapters explore some pre-algebra basics (fractions, percents, volume, for example), trigonometry, algebra, and even a bit of calculus. With three levels of problems at the end of each chapter, there’s plenty to play with here. He has an algebra-specific title, Real Life Algebra, that sits on my Amazon wish list.
- The Number Devil: Fiction meets math in this playful trip through math topics that won’t be found in most math books. The author plays with combinatorics, fractals, Fibonacci numbers, roots and exponents, and more. A few folks on the web have created study guides and lesson plans for this book, which go a long way to flesh out this rather content-heavy book. Again, it could be appreciated before finishing Singapore 6B.
- Calculus By and For Young People: Here’s another book that takes meaty, real mathematical concepts and presents them in accessible ways for kids. While the author cites that kids as young as 7 could use it, it’s likely to be best appreciated with kids with a good understanding of fractions and decimals. It contains plenty of hands-on work with excellent explanations.
- Descartes Cove: Distributed by Johns Hopkins Center for Talented Youth, these six CDs make a quest out of math problems. The math is quite obvious and the pace is slow — it’s not a high-speed video game sort of experience. It’s aimed for middle schoolers and covers some algebra, geometry, measurement, probability, and more. The math demands higher-order thinking skills, putting it in a different league than the fast-twitch math fact games designed for the younger set. My older enjoyed this when he reached the last levels of Singapore.
What We’ve Not Done — Yet
- More Singapore Math: Two options exist for families that want to carry the Singapore experience through Algebra II. Both mix geometry, algebra, and other topics throughout four levels covering four years of math. I’ve held back, not wanting to commit to a program that makes moving to another more traditional program more logistically challenging. Both programs are said to be quite challenging. It’s still on the list of possible next steps.
- Art of Problem Solving: This publisher is known for rigor and deep thinking and is aimed at those that not only excel at mathematics (mine do) but really love it (mine don’t). Their pre-algebra book would be a fine place to start the series, which largely covers ground that Singapore 6 does not. Online classes (for a fee) and online problems (for free) could complement the text, although these books stand alone quite well. It’s still on my short list as well. My older tried the online Introduction to Probability and Counting course and was overwhelmed and discouraged. Like I said, it’s best for those students who love math, have ability, and really want to work hard.
- Thinkwell: This company offers a host of math courses from middle school to college. Instruction is via video, and problems can be done and graded online. Dr. Burger is an engaging instructor who adds enough humor to make the lecture interesting. My older son used Thinkwell for College Algebra (before they offered Algebra II) and found it appealing. However, for the child who needs a live human for instruction (and my older son does), this may not be the best choice.
- ALEKS: ALEKS is another online learning system. Unlike Thinkwell, it contains no lectures. Like Thinkwell, it generates and grades problems. My older son used this for some of precalculus, but it has courses at the pre-algebra and beginning algebra level. Here’s my full review, but in summary, I recommend ALEKS as a supplement rather than a full curriculum.
- Khan Academy: This amazing free educational resource is a repository of chalkboard-style videos about math, science, economics, history, and more that’s growing by month. For many of the K-12 levels of math, practice problems follow lessons. We’ve used this for some cosmology, history, math, and chemistry over the years, largely as a supplement to other curriculum. He may not appeal to kids who need pizzaz to pay attention, but his methodical, clear presentation makes for fine watching for more patient viewers. Tracking a student’s watching and practicing progress is available. My younger son has watched largely non-math topics, while my older son has worked through much of the precalculus lectures. Like ALEKS and Thinkwell, we’ve not used this for the pre-algebra or algebra level.
I’m sure I’ve left many post-Singapore 6B avenues left unexplored. If you have paths you’ve taken and would be willing to share, please add them to the comment section. Links to the sources are appreciated. It seems my next step is to review the resources we’ve used. That’s a bit larger job than I imagined when I set to making this list, which grew far longer than I imagined. I best get started.