7 Ways to Unschool Math Genius

 

Unschooling and math….one might think they blend as well as oil and water.

Honestly I know many families whom I suspect not only quit school because of math, but adopt an unschooling philosophy just so they can totally avoid this one particularly traumatic subject!

But there is of course no hard and fast definition of unschooling – it’s more a spectrum and on the far end of it is plenty of room for not only the basics, but indeed for accelerated math – whenever it is parents and children want to get around to it.

I’ve been working with math geniuses for the past 25 plus years going back to my high school days and over this time, as my knowledge of education has grown, I’ve formed some strong opinions on the most optimal ways to unlock mathematical genius.

As far as I’m concerned, and because they diverge from and contradict conventional approaches….dare I say they might qualify as constituting an unschooled approach?

1 – Emphasize Rapid Computation

When I first meet high school-aged math students I can assess their SAT math score quite well with one simple question: “What is 7 times 13?”

Apoplectic shock means they will score 600 at best.

More controlled emotions and “I need paper” means 650 at best.

“91” but done by carrying in one’s head has a chance at 700.

“91” but done by adding 70 + 21, in that order, means they can score north of 700.

I’ve never met a single highly adept mathlete who was not excellent at basic computation. In other words, the math genius who is terrific with concepts but sloppy adding, subtracting, multiplying, dividing, and factoring simply does not exist. Computational competence is a non-negotiable prerequisite for higher math, starting with pre-algebra. With this in mind, schools and parents ought to NEVER promote a C math student.

2 – Skip Word Problems

Nothing provokes more math-o-phobia than word problems! It’s a classic case of out-of-touch academic pinheads trying to impose their “theories” on the lumpen masses. And there’s no shortage of clueless math teachers online proclaiming that word problems are the MOST IMPORTANT part of mathematics.

Typically, math curricula and instructors teach a new concept and before the kids have even partially grasped it, they are embedding the concept in an indecipherable word problem.

What they don’t understand is that it’s simply too soon and what they are effectively doing is muddling math up with “reading comprehension”.

I’d always suspected there was something wrong with the insistence on injecting word problems but the taxi cab question is what convinced me once and for all. That’s the question that goes like this:

You have $12 in your pocket for a cab ride….the flat fare is $2.50 and you have to pay .30 for every one-fifth of a mile. You’d like to leave a $2 tip too. How many miles can you take the cab with your $12?

Now I can’t tell you how many A-math students in the New York City area I have seen struggle with this question. Yes, otherwise A-students. And it’s NYC too so there’s a very good chance they’ve actually ridden in a cab!

The reason they don’t grasp it is because THEY’VE NEVER ACTUALLY BEEN IN A CAB WITH A FINITE AMOUNT OF MONEY IN THEIR POCKET FROM WHICH THEY HAD TO PAY THE FARE THEMSELVES.

So if smart New Yorkers can’t do it…what chance do average suburban kids have seeing how they’ve probably never even been in a cab?

I don’t suggest totally skipping word problems. I just think they should lag learning the mechanics of computation. I used to have my 5th grade level students do 3rd grade word problems. And this was not as dramatic a lag as it may seem, perhaps only 5 months because of the speed with which we go through the concepts AND because the students could be as young as 5 or 6 years old instead of 10 or 11.

Word problems are one of the reasons that American math textbooks AVERAGE 800 pages in length. Meanwhile, international math books are just over 200 pages long. Note that they are generally much better than us at math!

3 – Verbalize

No matter what a child is working on in math (even up through calculus!), I’ve found that making them read and dictate aloud what they are doing at each step has a profoundly positive effect on their comprehension.

I have all my students read each and every question to me. Require this and you’ll be astounded at how hard it is for them to do accurately and in the proper rhythm; you’ll discover how many small but critical misunderstandings they hold; and of course you’ll have the opportunity to correct and explain things that would undoubtedly go overlooked for a very, very long time.

Verbalization works wonders at the early stages. A child learning multiplication facts who says all day long, “six times seven is forty-two” is going to own the facts faster than the child who simply sees 6×7 on a screen or worksheet and merely writes down “42”, silently.

I encourage and enforce “verbalization” in other things too like chess, musical instruments, etc. I’ve heard people say that it works wonders because it makes learning “multi-sensory”. Whatever. It just works.

Obviously this level of noise-making is neither encouraged nor practical in those antiquated group educational institutions (i.e. schools).

In addition to having your child verbalize….have them skip count, a lot.

4 – Generate Momentum

Apparently the average math student loses 2.4 months of math competence over the summer hiatus – you know, while the kids are back helping out on the family farms!

But I submit that 2.4 months is a an underestimation. BECAUSE a student could conceivably being doing math straight through those 2 months and GAIN 4.4 months or so of math over that time frame. And that would amount to essentially half an academic year of math!

By my calculation, if you take out the summer break, you can theoretically turn 12 years of math into…..only 6!

My unschooled or “anti-school” approach to math would be a 365 day regimen – even if only 15 or 20 minutes of computation on those quieter days. On a cellular level, the child who just memorized that 6+7 is 13 on Friday….will have forgotten it and have to re-learn it on Monday. But if there was weekend reinforcement, he’d be on to 8+9 and additional facts come Monday.

Sound farfetched or too “tigermom-ish” to do math on weekends and in the summer? I’ll address it again in the conclusion.

[youtube http://www.youtube.com/watch?v=XwinA3M1xyk&w=560&h=315]

5 – Mental Math

Sure your child can multiply 23×78 on paper….but what about in his or her head?

Forget that, can they even multiply 7×13 mentally? Most people actually can’t. And those that can, are, again, overall quite competent at math.

Too many smart people CAN multiply 7×13 in their head but instead use scrap paper (or a calculator) as a crutch – with the consequence that each and every time they waste a chance to get better at math.

While it may seem like it’s more work and slower….it’s easier to do these questions in your head than on paper, it’s usually faster, AND mental math is actually more accurate because its practice makes you better at catching your own mistakes.

Not convinced and wondering how?

Then read Arthur Benjamin’s terrific book – Secrets of Mental Math or watch him on YouTube.

I was blown away by his book and got to work right away. (That is indeed my son, age 7 at the time, in the video above.)

6 – Competition Math Curriculum

School math curricula mostly stinks. The really good stuff can all be found “outside the system” in MathCounts, AMC math, AoPS, USAMTS, ARML, etc. all of which have far more elegant content.

Elegant? That means that the problems are created and posed in a manner that generally allows more than one possible way to solve them…..er…..sort of like problems in the real world!

There is simply no reason why a homeschooled child has to use ANY inferior school, and school-ish textbooks. I even think there’s plenty of value in just using math SAT study materials as a spine for some students. Just don’t wait until they are 16 to start prepping for the exam!

7 – Individualize Instruction

Of course all education should be individualized – it almost goes without saying in an article like this BUT….

All too often I see homeschooling parents signing their kids up for a math class so that they can “check a box”. One unschooling parent who has a huge following online recently admitted that she drives her kids a full hour (each way) to go to a math class. What a waste of time!

Math is not a social endeavor. It’s learned by sitting down, alone, for hours at a time and wrestling with the material until lightbulbs flip on. Even with access to the best math teacher on Earth, your child should be spending multiples of that amount of time on their own, solving problems if they are to get really good at math. Help on any question or difficulty imaginable is just a Google or email away.

Ideally your future math genius should be working at the very frontier of his or her learning curve, that’s on material that is not too easy and not too hard – though the latter is far more desirable. Thankfully we have Khan Academy today and it’s 100% free!

It will pull your child right up to material that’s just out of their reach. Khan liberally permits jumping around from sub-topic to sub-topic and clear across grade levels. It features graphical interactivity that just isn’t possible in a book. And it scientifically spirals back through old material. For us parents, Khan logs TIME – the most important variable for success in any endeavor and sends weekly reports. I recommend seven hours a week!

Sure, it has some flaws like many verbose, contrived word problems, a little bit of political correctness/propaganda, and “Common Core” adherence (which should be dismissed). Sal Khan is certainly in love with the sound of his own voice and “lecturing” old school style. I simply tell my students to skip ALL the videos and just use the hints and worked examples.

But the MAJOR benefit of online math is “instantaneous negative feedback” – meaning, when a student inputs a wrong answer they are informed IMMEDIATELY. In the old days a child might do a whole worksheet incorrectly…have to wait for someone to correct it…and only then discover that they did the entire thing wrong!

Conclusion

Now, as a math aficionado I’m admittedly biased, but I think that skipping math is an overreaction to the horrible way we were “taught” math in schools.

I think if you can sculpt the ideal math curriculum – one emphasizing rapid computation, that incorporates verbal and mental components, uses better subject matter and implement it more efficiently and less stressfully (no “gotcha” quizzes and tests!) – then maybe, just maybe your kids will find math appealing, even though you didn’t.

A couple of final notes…

I say if your child is going to do math at some point, then just get it over with. Start early, go hard (365 days a year), and then you can stop completely. This describes the path of my son. He had finished 6th grade at 5, and started calculus at 7. Shortly thereafter, age 8, we basically stopped doing math for good.

Yes it was hard work getting him to that point, with occasional 3-hour math sessions punctuated by tears here and there. But better to, like I said, get this over with then drag out the crying through the high school years and into college!

Read my previous column – Early, Organic SAT Prep for Homeschoolers to see how John did on his math SAT at age 11, after 3 years of doing ZERO math.

While my approach might seem draconian, anti-unschool, and difficult to relate to…consider the case of Erik Demaine.

Erik was unschooled by his single father, an itinerant glass-blowing artist who I believe never went to college. Somehow, with that pedigree Erik became a math genius and the youngest professor ever at MIT.

I hope my 7 Ways to Unschool Math Genius gave you a couple new ideas, a little inspiration, and most of all a confident understanding that there are some highly effective and unconventional ways to accelerate math in your homeschool. If you ever need any help in the department, please don’t hesitate to contact me through my website.

~Dan