Wild About Math!

Review: Numbers Juggling - Times Without the Tables

Brian Foley runs a web-site, Math Mojo and a blog, The Math Mojo Chronicles. The web-site aims to make, in Brian’s words, “Math meaningful.” While I enjoy the site, I struggled to explain what Math Mojo was about until I found this description in the What is Math Mojo page:

Math Mojo is a way of looking at math that fosters a sense for numbers. The more new ways you learn and practice, the more of a feel you will get for manipulating and understanding how numbers work. They will become less of a mystery, and you will feel better about your ability to do math. These methods are based on several different speed-math techniques. They all work at least as well as the methods that you were taught in school. In fact, schools that teach these methods do much better than the national average.

Once I read that description it clicked for me why I like the site so much; Brian and I share the same idea that, to do arithmetic well, you need to have a relationship with numbers. I have always enjoyed writing about mental Math tricks because the more tricks you learn and practice the deeper your appreciation of and your relationship with numbers becomes. Once you have that relationship, you won’t find arithmetic to be a chore. And, once you enjoy arithmetic, and see patterns in it, then you will have the itch to enjoy all of mathematics more. So, I find arithmetic to be the foundation of all things mathematical and I find arithmetic to be very simple and very very deep at the same time.

I was curious about one of the booklets that Brian sells at Math Mojo, Numbers Juggling - Times Without the Tables. From time to time I get questions about ways of effectively teaching the multiplication tables. Since I’m not an educator, I have to defer to the experience of those who have experience teaching these things, and in this booklet I find some real gems.

Before I dive into my review I need to disclose that I received a review copy of the booklet, which sells for $9.95 as an electronic download. As always, there were no conditions placed on my review. I will always give my impressions, positive and negative, on any product I choose to review. I will never review a product I don’t believe in, for pay or otherwise.

The “Numbers Juggling” booklet impressed me. I’ve been around the block; I know lots of mental Math tricks as readers of this blog can attest to, and I learned some new things. But, first, some basic data. The booklet is short, 32 pages, and that includes a preface, introduction, glossary, and an about page. And, the booklet comes with a series of seven followup lessons that come via email. I can already hear you asking, “Why would I pay nearly $10 for a booklet and some emails?” This is my biggest criticism of the booklet, not the cost, but the fact that the booklet and emails weren’t marketed as a “learn the times table” course because the material reads like a course and marketing it as a booklet does the valuable content a great disservice.

Here’s my take on the cost vs. length question: If the booklet gets your child past a major struggle then the $10 is insignificant. If the booklet doesn’t meet your expectations then return it and Brian will return your $10.

Onto the content. There are three parts (lessons) to the booklet and Brian suggests you not do more than one part per day, even though you can certainly read the entire booklet very quickly. Part I teaches multiplying by 0 through 4, and using commutativity. The concepts are basic but no multiplication table is used and Brian covers some sticking points that learners run into. Part II covers multiplication by 5 and 10. Again, nothing earth shattering - yet. Once a student understands the trick to multiplying by 5, which I’m sure many of you can guess, you can multiply huge numbers by 5 very quickly. To a student who has never seen this trick this will be an exciting experience which will spark his interest in learning more about arithmetic.

Part III of the booklet teaches a very clever technique, which I’ve seen hinted at in the Vedic Math community but haven’t learned until now, for multiplying together two single-digit numbers where each digit is greater than 5. So, with this approach it becomes easy - once one learns the trick and practices it a little - to do these multiplications: 6×8, 7×9, 8×8, 9×9, and so on. And, there’s still no times table to memorize. These “big digit” multiplications are sticking points for lots of learners and, if they’re not good at memorizing, can be frustrating.

So, in a short number of pages, in three parts, the booklet has shown how to multiply by 0 through 4 (Part I), how to multiply by 5 or 10 (Part II), and how to multiply by 6 through 9, especially when both digits are in that range (Part III).

The followup lessons provide some material that’s even better than what’s in the booklet. There are seven of them and here is what they cover:

1. Why the method for multiplying numbers from 6 to 9 works

2. How to multiply numbers from 6 to 9 on your fingers ! (It’s super easy!)

3. Why the method of multiplying numbers from 6 to 9 on your fingers works

4. How to multiply numbers from 11 to 15 on your fingers ! (It’s even easier than 6 - 9!)

5. Why the method of multiplying numbers from 11 to 15 on your fingers works

6. The mathematics of all the methods - in algebraic form (For all teachers and smart parents. By the way, the algebra is not hard, and you don’t even really have to know “algebra” to understand it. Even if you know algebra, I promise you will gain some insights from it.)

7. Next steps

The techniques in the followup lessons are innovative. Quite a bit of this material is new to me which means you’re not likely to find much of this information on the web for free since I surf the web A LOT for this kind of material and haven’t found much of it. The followup emails deepen one’s understanding of multiplication, they’re enjoyable, and they’re very well explained.

So, as you can guess, I give the booklet and emails a thumbs-up! Is there anything I didn’t like about “Numbers Juggling?” Yes. I believe that different people learn in different ways. For kids who are highly kinesthetic or intrapersonal, I recommend that they first try Mark Wahl’s “Math for Humans” which I reviewed a while back. Wahl uses Howard Gardner’s multiple intelligences to design approaches to teaching Math, including the basic Math facts. While “Numbers Juggling” does incorporate the kinesthetic into its techniques with finger multiplication, Brian’s approach will work best for kids who learn by pattern matching and use of simple logic. I learn well that way and I believe that many others do as well. For kids who are deathly afraid of numbers to the point that they wouldn’t even engage in seeing patterns in numbers, a gentler approach might be Wahl’s. If your child loves to paint, and tell stories, and skip, and jump, there are ways to teach material through those sensory paths.

Having said all I have about Wahl’s approach, Brian’s approach is efficient. It may be the case that your child has not learned the multiplication facts because he or she hasn’t learned an approach that’s easy and accessible. In this case, Brian’s booklet and followup notes will work well. Plus, your child, once he or she has learned Brian’s tricks, may really enjoy teaching them to friends. I find that teaching others is the best way to learn things myself. The possibility of having something really fun to teach others, in itself, is worth the $10 many times over.

A final note: You can get a flavor for Brian’s approach to teaching multiplication here and here.

If you enjoyed this post, make sure you subscribe to my RSS feed!