Balancing The Equation for ExcellenceOctober 15, 2010
Not too long ago I picked up a book by a certain Arvin Vohra called The Equation for Excellence: How to Make Your Child Excel at Math. I thought I probably wouldn’t like it. That word “make” in the subtitle made me bristle right away. Do we “make” children excel? Can we compel our students towards excellence?
Still, it’s important to read books that aren’t necessarily from your camp, so to speak. It was a quick read, and I’d like to review it thoroughly here.
This is in certain ways an interesting book, and I agree with much more of it than I expected to. I also find it a somewhat dangerous book, and I wouldn’t recommend it unless I knew it was going to a very careful and selective reader.
Fundamentally, Vohra’s perspective on math is fatally soulless. Studying math, to Vohra, is like training for the Olympics; you should do drills for one, two, or three (!) hours every day, including summers and vacations. But there’s no real reason to do it, except, arguably, to ace the SATs. He calls his method of constant drilling “the Asian system.” This is, in my experience, completely unrealistic, and wrongheaded.
However, there’s something to what he’s trying to accomplish. Having your facts memorized (and in a form where you own them) will help you deal with Vohra terms cognitive overload and distancing. If I ask you to measure the long diagonal of a unit hypercube, you’ll probably be stuck before you begin. Why? You don’t have all the facts at your disposal. But if you were familiar with what a hypercube is (a 4 dimensional cube), and could get a kind of picture of where the long diagonal was (i.e., you weren’t distanced from the problem by unfamiliarity), and you saw that you needed to use the 4 dimensional version of the Pythagorean Theorem, and you knew that unit means “length 1,” well then it’s a snap. We suffer cognitive overload when we aren’t familiar enough with the small stuff, and it gets in our way. Math builds on itself quickly, and yesterday’s great ideas are today’s obvious facts. Cognitive overload happens, and knowing your stuff can keep it at bay.
When you look a little more closely at what he’s suggesting, it doesn’t sound quite as bad. Is it just drilling, hour after hour? Maybe not. Consider this:
“I give a full explanation less than one percent of the time. The first time a student sees a specific problem type, I might tell him how to do it. For example, if a student has never multiplied fractions before, I may show him how (after making him struggle for a few minutes. Most students are actually able to figure out what to do on their own, though you will have to let them know when they get the answer right.)”
Lo and behold, he’s actually talking about student engagement, and the value in letting a student struggle it out on their own. You don’t just feed them the answers–they have to figure it out to own it.
Vohra is highly aware of certain elements of tutoring: incentives, for example.
Note that when a child says “I don’t know,” he is telling the truth. He probably does not know how to do the problem right away. It will probably take him several minutes to figure it out. Your job is to make sure that he has the incentive to figure out the problem on his own. As long as he has the incentive to put his full mental abilities to the task, he will be developing his ability and intelligence.
However, as the saying goes, a reputation takes a lifetime to build and a second to lose. Case in to even one “I don’t know,” and the child will know that he can extract help from you. He will then have the incentive to try to turn this into a regular pattern. Effort that could have been spent on developing the child’s mind is now wasted as he tries to get the answer another way.
For the purposes of incentivizing properly, Vohra recommends against calculators, computers, and monetary rewards for grades. I agree with him on all counts. I know that calculators are in a lot of classrooms today, but I’ve seen student after student ruined by them. There’s a way to use them properly, but virtually never are they used with the proper discretion, and you have students pulling them out to do single digit addition. We’d be better off without them, almost all of the time.
Vohra includes a passage toward the end of the book that demonstrates what he calls “the Micro-Challenge Method.” To me, it just looked like regular, good tutoring. Not amazing, but solid, tuned in, and aware of the ways a student will fake understanding in the hopes of bluffing onward without learning anything (very typical for high schoolers. Very untypical for elementary kids, incidentally, so one would presume they learn this skill in school).
I appreciate Vohra’s interest in challenging his students, and his observations about incentives are keen. But there is the total absence of poetry to contend with. Success seems to be measured only in top scores on the SATs and other standardized tests. Something’s very sad in this. We get a moment on the final page, though:
“When a weak math student undergoes intensive training to become an excellent math student, more changes than just his math ability. Often, the student realizes that many of the other limitations he once thought he had do not really exist.”
We get, finally, a point to the 1-3 hours of coercive training. Is there a reason to do math after all? Of course, this isn’t really anything special about math… you could replace “math student” with “long distance runner” and the gist would be the same. I would recommend to Vohra some mathematical poetry. Consider this quote by Ian Stewart:
“Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that — by some mysterious agency — capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.”
For this quote and many more like it, check out the wonderful blog Let’s Play Math. This post in particular is brimming over with mathematical inspiration.
If you’re a parent, you shouldn’t read Vohra. If you’re a teacher or tutor who is well grounded in their educational philosophy, there’s some good stuff in the book, but you have to know what to ignore.
Thus ends the review of the book. As for Vohra himself…
In prepping to write this article, I looked up Vohra’s website and checked for reviews, and there’s something disturbing about him. He has an incredibly professional website, but no reviews of his tutoring. Anywhere. None on yelp, none on google, none on his own site. His amazon reviews are all either 5 star or 1 star, with one of the 1 star reviewers claiming that he (Vohra) wrote most of the 5 star reviews. Another reviewer claims that Vohra has very little actual experience tutoring, but the link she provides has disappeared. He has a quote on his book from the President of the “American Alliance for Education” that says the book “promises to be the defining education work of the decade.” I googled “American Alliance for Education” and the president’s name. Nothing. Searching through the odd trail, smelling fraud, I start to feel like I was in some thriller. So I find myself trusting him less and less.
In any case, I’ve spent enough time with Vohra for a while. I came to math for the beauty, and it’s hard to spend too much time with anyone who doesn’t share that love.
UPDATE: Vohra commented below, and mentioned that he’s now on yelp, so my uneasiness about whether he’s currently tutoring or “legitimate” seems misplaced. He actually has eight glowing reviews on yelp.