Friday, January 12, 2018

The Language of Math

There is a strong and important connection between math and language.

Think about a child learning language before the age of 2.  You point to a blue ball and say 'blue'.  The child sees round, blue, rubbery, your finger, you making some weird noise, you're looking at him or the ball or both, and you're probably smiling.   What is blue?  Then you point to a blue wall and say 'blue' and the kid is more confused than ever. 

In order to figure out blue, ball, yellow, green, box, toy, your child has a lot of confusion to sort through, is going to make 5,462,298 mistakes, and you're going to be smiling the whole time, and on top of that the child is going to have to identify patterns, sort through permutations and eliminate candidates until he comes down to blue is an attribute of color.   The child may not see round or plastic or squishy yet, maybe he can sense it, but when there is a word tossed out there for 'round', his ability to think logically will be substantially improved.

By 1915 or 1911, I'm still debating, cognitive psychologists determined that the process of reading uses 100% of all cognitive skills.  100%.  This will never happen again.

If you want to know why I'm so over the top obsessed with reading and vocabulary during age 4, so much so that I created Pre-K Phonics Conceptual Vocabulary and Thinking to jam as much 2nd grade material into the brain of a child who can't pronounce C-A-T, you now know why.

Don't Lose The Magic
Learning to talk and learning to read, not to mention learning to walk, are much harder by a factor of a gazillion than anything a child will learn thereafter, including Pre-Algebra.   But somewhere after learning to read, maybe around addition, the parent loses the Magic Learning Environment that allowed your child to overcome insurmountable learning objectives.  You used to sit there smiling dumbly mistake after mistake totally happy every time your child rose an inch off the ground and then fell.  Now you're yelling at your child for forgetting what 8 + 4 is or struggling with x-1.  At least I am.  We ALREADY discussed the exponent graph 3 times.  Would you just pay attention once?

The magic was that you were willing to try to teach your child what words mean, despite not having the slightest clue how this works, through mistakes and trying over and over and over again, usually smiling the whole time, and learning just exploded.

This is the first connection between language and math and it's pretty lame compared to what follows.

Reconnect the Two Dots
If math uses a certain sub set of cognitive skills, but learning to read (definitely) or learning word definitions (probably) used 100% of cognitive skills, wouldn't it be great if you could bring the missing cognitive skills back to the math learning process?

I think this is theoretically possible and in practice I just ask them to explain verbally to me how to what the question is asking, what do they know, is there anything they have learned before that can help, can you articulate your solution strategy?  I also throw in anything I can think of related to a problem, like 'Polyhedron' or some other word to get that verbal section of the brain working.

But mostly I like to talk through problems and concepts.

Recently, we came across this question:  What is 42% of 66?  This is an advanced post TPM problem.  I got it off a high school Algebra I final that has 190 questions and would be very hard for high school   We're doing about 5 problems per session and learning a lot.  This is an opportunity for a long discussion involving fractions, decimals, and %, as well as problem decomposition and lining up multiple steps, followed by cheating with algebra.  In other words, in addition to math, it's going to be about 25 minutes of talking.

Here's some fun verbal math discussions for a younger age.  In these cases, I did very little talking and just left key questions out there for 3 or 4 weeks while the math sank in.  Then we discussed, and I asked why? or prove it to me.

  • The definition of 'square root' is this.  2 is the 'square root' of 4 because 2 x 2 = 4.  What is the square root of 9?  Does 10 have a square root?  (Not yet, but it will later).
  • What is the square root of negative one?  It's call 'i'.  What is i * i?  Why is this important (because the Fundamental Theorem of Algebra does not hold true without i in case you're wondering).  What is the square root of - 4?  
  • What is 2 - 5?  I love this discussion.  It goes like this: "Three".  If 2 - 5 is 3, what is 5 - 2 and why are they both 3?  This can't be right.  If you have 2 and you give away 5, what do you have left?  "You can't do it".  Oh yes you can my friend, yes you can.  
If I can't find something to discuss in math work, I'll start looking for more math.  y = mx  + b and f(x) = mx + b are great topics for discussion and not writing.   That's why we end up covering advanced math at a young age, simply to have something to talk about.  How's this going?  About as well as learning how to talk in the first place.

Is Any of This Going To Help?
I'm not 100% sure yet, but it might help with math learning.  It's definitely helping with writing.  Trying to compose an explanation for a complicated mathy topic just learned is really hard.  It is a foundation leadership skill.  It's similar to a reading comp skill, but only vaguely.  It's easier than any classroom speaking task.  I'm certainly not going to end up with a wall flower, what with me demanding a thorough explanation to a complicated explanation.

Product Recommendation
I highly recommend IQ Twist or IQ Puzzler Pro.  We've had these sitting around for the last few years and my kid and his class are now obsessed with them.   His 4th grade teacher is buying them for the classroom.

It wasn't until I solved a problem myself that required turning and flipping multiple shapes when I realized that it's NNAT and somewhat COGAT training.  We started talking through the solution to one tough problem and how one shape could only go in one certain place before I realized that this is all logic, visualization and math.  If you run out and buy these for a 1st grader like I did, feel free to reach out for help because it took me a few years to figure out how to use these with a younger child.


  1. I've been following your blog for 3-4 years now and your suggested curriculum and your test prep books (both of them) religiously. You've been always so responsive and helpful via email as well. I'm happy to report that my second grader got 99% on both NNAT and COGAT. I know what it means in my local district but I'm very hopeful that we will make it (we will know the final results in the spring). Thank you so much for sharing your incredible knowledge and resources here. I don't know what I would have done or where we would be if I didn't find your blog by accident.

    1. Sounds like you're off to a good start. In the next few years, I'm going to be skipping around on topics, as usual, but one of the things I want to put together is a gifted reading program for grades 2-6, which no one seems to have, and answer this question: How to get a 1400 on the SAT by 7th grade.

    2. Totally love this!! Can’t wait!

  2. Do you know about WISC test? Is it a test also that can be prepped? This is the only test that our district accepts for GT. Where should I start?

    1. As a matter of fact, this has come up recently. Google this: "wisc" (without the quotes, the key is "site:") and you'll see what I have to say. Look in the comments on some of these. Control F for 'wisc'.

  3. My 2nd and 3rd graders are struggling with writing and spelling. What would be a good approach for sentence structure, grammar and spelling. They’re both advanced readers and in the top reading group in class but writing is the problem.

    1. Sorry for the late reply. Writing, spelling and grammar come with writing practice. Grammar also benefits from lively adult level conversation. I’m going to assume that English is the language spoken in the house. My wife’s father taught high school English his whole life and I think she read everything ever written in the 18th and 19th century 7 times. Our approach is to ignore bad writing and grammar and spelling because it tends to show up somewhere around 5th or 6th grade on its own. In fact, it wasn’t until 6th grade that I bothered to sit down and spend hours refactoring sentences and working on how to properly formulate, reformulate, reformulate, reformulate and reformulate again a sentence. But you didn’t want to hear this. Instead, what I also did in order to spur createive conversation was to post something on the word board (science, math, vocab, social studies) and make my child explain it to me and answer 20 questions. Very good speaking practice as a preface to writing. We also read Shel Silverstien over and over and over again. For 3 months instead of weekend math, I had weekend writing. I would give them 1 min to come up with a topic before choosing my own and then asked for 5 sentences, 2 paragraphs, 3 paragraphs. It was silly and fun and their work stunk in 2nd and 3rd grade. Strong readers are late on everything, but when they get there (it won’t be until 6th grade), their work is stunning. That’s all I know.