Wednesday, October 17, 2018

GAT Games

Wouldn't it be wonderful if you could turn your child into a genius by playing games and doing projects all day? Technically, you can, but none of us are willing to risk it except for home schoolers in Montana.

Here are some of our favorite games. On the way to 99% these games become very competitive high stakes cage matches. These games are fairly age independent and work through different levels of certain cognitive skills. All best practices from previous article apply here.

Find the dinosaur

When my child was between the ages of 2 and 5, we would play this game in lieu of getting to bed on time. Any dollar store or drug store has a pack of animals, dinosaurs, and fish. Get all of them.

Find a messy room. Uncleaned bedrooms are ideal. Ask your child to leave the room and close the door. Hide the animals in plane sight. Invite your child to come back into the room, sit down, and from their vantage point - without moving - identify each animal in their hiding place.

The rules vary at age 2. There's no way you can ask a 2 year old to sit in one place; instead she'll run around the room collecting animals.

GAT Extensions
  • As your child develops visual acuity, hide the animals more carefully so that only a small portion is visible.
  • Close your eyes, and ask your child to describe where and how the animal is hidden, including orientation. Vary the orientation.
  • Invite your child to take a turn hiding the animals for you. When the child is 2, he will hide the animals in the exact same places that you
  • did and jump up and down and dance next to each animal gesturing wildly and laughing while you pretend you don't see the turtle in the exact place you hid the turtle on your turn.
  • Don't forget to wiki each of the animals and use the proper name. Vocabulary is king in cognitive skills.

Over time, you should see the direct result of their growing skill set, e.g.in the nonverbal section of practice tests.

Find the word

Say a word backwards and ask your child what the word is. For example, is erutinruf is furniture.

One nice thing about this game is that it can be played anywhere, including the car. Another nice thing about this game is that it covers the gamut of cognitive skills from starter skills to very advanced IQ test taking skills. If your child has to sit for the WISC, this is your game. Finally, there are unlimited variants of this game, like anagrams and word scrambles.

If your child is learning phonics, stick with 3 letter words.

If your child is preparing for an IQ test, use a lot of simple 2 syllable words, like schoolbus or subway. There is an important reason for this approach. The path from an IQ of 100 to an IQ of 172 is algorithms, and IQ tests like words, so your child needs to become adept at word algorithms. In this case, the algorithm to solve subloohcs in 1/10th the time is to solve 'sub' and 'loohcs'.

In the absence of algorithms, your child will build working memory. This game is the working memory builder while your child struggles with sbuloohcs slowly and carefully with repeated do overs. It is both enjoyable and painful for me to watch a child plod along with the standard approach.

To make the game more fun, play the game in a public setting where there are posters and signs and billboards and choose a word that your child can find. Your child will be exercising a few important sub-skills while comparing each visible word to the backwards word. Repetition is an opportunity for your child to invent shortcuts.

The only way to get from linear thinking to algorithmic thinking is for you not to tell your child the rule that problem decomposition is 10 times as fast, but make them struggle the hard way (building working memory) until they figure it out for themselves. If your child is 10, and they don't show dramatic improvement in 4 weeks, explain the easier way.

I'm thinking of a color

The rules of this game are simple. You say, 'I'm thinking of something in this room and it's color is green'. Then your child looks around and guesses which green object you are thinking about.

How do you turn this game into a cognitive skills builder? The green object could be a the small plant in a painting on the wall, or the red object could be their lips. Not a bad start. Do these things as well. But no, this will not do.

'I'm thinking of an object that slightly smaller than the previous object but is used by the same profession'. You just nailed both figure matrices and word analogies. If your child has to sit for the COGAT and not the WISC 5, this is your game.

Conclusion

Games are a fun way to pass the time on the march to 99%, but you're not going to get there by playing the average version of games at the average level.

Saturday, October 13, 2018

Helping and Not Helping

Shortly, I'm publishing a 2 part how-to for parents who just found out about GAT.  It's not bad.  The bullet points from the first video would make up the table of contents if I ever write a book on how to cheat your way into a GAT program.  We have to reshoot the 2nd video because my 10 year old editor screwed up the audio. I'd help him fix it, but I don't know how to use Premier Pro.

The weird thing about cheating into a GAT program is that if you do it right, your child actually acquires GAT skills. The other way your child can acquire GAT skills is to put them in a GAT program.  In other words, GAT is a self fulfilling prophecy.  If you act like GAT, and walk like GAT, and talk like GAT, you'll end up GAT.    See Amy Cuddy on 'Fake it until you make it' for inspiration.

In my video, I cover coaching skills, including not helping.  This skill needs some elaboration.  For those of you who are thinking 'my child does their grade level or next year's math worksheet on their own with no problems', I'm talking about something insanely hard, age inappropriate, that requires concepts and skills that your child does not have.  Something they actually need help with.

But you're not going to help.

Easier said than done

From a very young age, my kids had daily math.  Someone once told me that Indian and Chinese schools are 2 years ahead in math, so their first math was a 2nd grade workbook in Kindergarten.  It seemed reasonable that if they took long enough on a single question, maybe 25 minutes, they would eventually get it on their own. 

When test prep season rolled around (in one case 2 months before we started doing math), we had to start all over again with figure analogies and classification.  Again, you spend enough time on a single problem, you'll eventually get it.

Why would you spend 25 minutes on a hard problem, when you could spend 25 minutes on 20 easier problems? Wouldn't your child learn 20 times as much doing 20 times the number of problems?    Good questions.  We're not trying to teach the child whatever the subject of the problem is, we're trying to teach them learning skills at the highest level.  Then 6 months later, they can teach themselves.  Or, in the case at hand, they can teach themselves how to do a problem they've never seen before in order to pass a GAT test and get into the desired program.  As I point out in the video, you won't be in the room to help.

What to do instead

So you're sitting there for 25 minutes not helping, your child is struggling (which is good), maybe crying (which is bad), what do you do to pass the time?  You the parent learn problem solving skills, and in the process, convey these to your child.

The first problem solving skill is to understand the question.  That seems obvious until you are faced with a question you don't understand, in which case most people give up and jump to the solving part.  Have the child explain it to you, one shape, one word at a time.

If your child is lacking some skill to put the pieces together - inching toward the solution step - then you need to backtrack on that step.  In math, this is double digit addition for the first time, which is actually multiple steps in one; maybe you need to work on adding numbers that are multiples of ten.  In figure classification, this is brainstorming the names of attributes and seeing which shape or picture has what attribute.  Sometimes it means cutting out shapes and comparing them, or drawing each shape and their 6 potential transforms, then coming back to the problem.

The child will have no idea what you are doing other than prolonging the question until the light bulb goes off.

Then the child gets the problem wrong and you don't care.  You carefully chose material beyond their abilities for this exercise.  Of course they got it wrong.  Start over.  There's no penalty.

What you accomplished

You child just mastered zero math.   They 'learned' nothing and if you show them the exact same problem tomorrow they'll be stuck again and get it wrong.

In fact, they just unlearned.  They unlearned that quantity is quality, that getting an incorrect answer is bad, that mommy loves you because you know something.  They unlearned going fast, memorizing, caring about the material.

Instead, the child just spent 25 minutes learning how to go slow, to look at details, to decompose a problem, to investigate a problem thoroughly, maybe taking a sidebar on sub-skills.  These are very advanced graduate level foundational problem solving skills.  In other words, we're teaching the child how to be gifted and talented.  The gift is going slow, and the talent is not giving up.

Are there shortcuts?

Suppose your child has to take a cognitive skills test in 2 weeks.  You've done nothing up to this point to prepare.  Will the approach above prepare your child for the GAT test, or do you want to teach them how to transform shapes and worry about learning after the test?

These tests are not designed to measure how much your child knows.  They are designed to measure how they go about learning and problem solving.  These tests are really well designed to meet this objective.  On the hardest questions, the ones that lift the score above the cutoff, prior knowledge and practice is not going to help.  The only thing that will help your child is the learning skills. 

Saturday, September 22, 2018

Test Prep Season Has Begun!

Registration in Chicago will open next month for their gifted and talented programs which have the code name 'options programs'.  About this time, many parents find out about the gifted and talented programs in their school districts.  Some will not find out until right before the registration deadline in December.

This year, I'm thinking of reserving a room in the library at the end of my block and presenting a free seminar.  Unfortunately, I don't think I have any readers in my neighborhood and I don't have time to advertise.  Also, 'free' makes many parents uncomfortable, including my free consulting, like the work I'm doing with a couple of kids in the 3-4 ranges on my block.

My 10 year old has agreed to film me and he has Adobe Pro, so I think we'll do videos instead.

My target is going to be K-1st grade for a couple of reasons.  First, there is plenty of material on the market for this age group and none of it is mine so I don't have to sell my books, as awesome as they are.  Secondly, this is the most competitive of all age groups and there's nothing more enjoyable than a daunting competitive challenge.

Chicago has reorganized their GAT programs recently so most of the slots are for Kindergarten.  Personally, I think 2nd grade is a better grade for waking up early to catch a 7 am bus, but a program is a program.

I need a catchy title for my series, like '100% Guaranteed Pass Rate For Less Than $100 of Books Except You May Not Get Your Act Together On The First Try Or Your Child May Have A Bad Day', only shorter.

Sunday, September 9, 2018

Tiny Clients

A few years ago, babies began moving into our neighborhood. They brought their parents. Occasionally, maybe at a block party, I'll run into one of their parents and ask how things are going?

'How are things going?', I'll ask.

Things are fine, the parent replies.

'What is your plan for your child's academic future?', I'll ask next.

Who are you?, the parent asks.

Test prep season is now beginning and these babies are in the 3 to 4 year old range. Between now and February, kids in Chicago are preparing for a GAT test, and I know the secret - so do you if you've read any of this website. My track record is 100%. I just got all of my books back last month, and now they are going out the door again.

The pitch

Chicago has some of the top elementary schools in the country. Kids need to pass a test to get in, and by 'pass' I mean score somewhere in the 99% range on a test that evaluates cognitive skills. These skills are great predictors of academic success. If you take your child's academic future seriously, at some point you'll want to cultivate this skill set. If you are overly concerned about elementary school, you'll want to do this as soon as possible, ideally before kindergarten.

Our GAT program is at a school that has some slots available in what they call 'the neighborhood program'. Personally, I'm impressed with the neighborhood program. The little sister of my child's classmates is going to the neighborhood program. I'm on the case. There's no reason why any child can't get into the gifted program.

What's happening in New York?

Schools Chancellor Richard Carranza recently lamented the fact that certain ethnic groups that represent 70% of the city only represent 10% percent of the seats at the best programs in New York. We have the same problem in Chicago. This is a big problem in a democracy where people vote. Why would 70% of the voters be interested in spending money on 1 or 2% that already seem to have a lot going for them?* It's a problem that needs to be fixed.

Carranza is taking some steps that Chicago did, like a proposal to set aside 20% of the seats for underrepresented minorities. He's also increasing test coverage.

I'm still waiting for both Chicago and New York to ask a more obvious question. Why are the underrepresented groups not taking education as seriously as the parents of kids in GAT programs, and what can we do about it? The leaders in Chicago have a view that things are unfair. Those in GAT programs tend to have money, and those who are left out tend to have a lot less of it. That must be the problem.

Money is not the problem. Money is highly correlated with education, and educated parents are highly correlated with educated children. A child can get into a GAT program with a spend of less than $100, but with a time spend of about 10 to 15 hours per week per child, mainly reading to the child or yelling at the child because they just missed a problem for the 5th time and is now laying under the table crying. There are large under-represented groups who either don't have 10 to 15 hours a week, don't think it's important, don't know about it, or can't do it without some help. I help parents with less than 1 hour per month, but these tend to be highly educated parents. When I help the parents in underprivileged groups, it takes more like 5 to 10 hours a week. I volunteer to help any underprivileged minority family with whatever it takes.

I'm simply waiting for a leader in Chicago or New York to ask 'what can we do to step up?'. This is a different question than 'what is unfair about the system?' or 'how can we provide a top notch education to a child who isn't ready for it?'. Increasing GAT screening coverage and setting aside seats are two great ideas, but the problem is not going to be solved until we ask how we can pass on our education values and know how to the parents who are not at the table.

*To answer my question above - why spend money on the best and the brightest? The answer is that the best and the brightest are going to lead this country in the next generation and we need to get them ready. Cutting their funding is not going to solve our problems. I'm counting on this group to solve our problems.

Saturday, August 25, 2018

The Cognitively Charged Classical Education

In this article, I'm going to explain how I supercharged the classical method by interjecting cognitive skills training. In short, I introduced a few new stages, created a new R, and changed the approach to the other R's.

The timing and approach varies for each child. There are only so many parents per child in each family, it takes parents a while to get up to speed, and most of us didn't start early enough. None of this matters. The child will catch up.

A short summary of the classical education

Stage 1 Pack as much information as you can into your child's brain. Doing this will of course expand the brain as fast as you pack it in, so it's a losing battle. This is usually ages 4 to 9.

Stage 2 Teach your child how to think so that they can disagree and dispute everything during dinner conversation. This stage takes up the rest of grade school.

Stage 3 The child becomes a teenager and formulates their own opinions. But you would never know this unless you stay up late because they do not talk before 10 p.m. This age is when real writing begins.

The classical education traditionally includes subjects like Grammar, Logic, and Rhetoric.

The Cognitively Charged Classical Education

To start, we can throw out logic and grammar as subjects because these concepts will permeate all instruction. Similarly, test prep is logic overkill. The CCCE subjects are now Reading & Vocabulary, Math & COGAT Test Prep, and Everything Else like Science and Video Game History. Music and craft projects are ancillary activities that your child does to get out of doing math or COGAT test prep.

Stage 0 Starting Early

My neighbor just returned a stack of books I let him borrow so he could put is 2nd child into our GAT program. At the top of the stack was Pre-K Phonics and Conceptual Vocabulary. What a great book. It's patterned after the early phonics courses from the 1970's. But it contains 400% of the phonics and 10 times the vocabulary. I noticed that one of the Amazon reviewers hated the book. Maybe they didn't read the introduction. We started this book on the 4th birthday (turned out to be a less than fun birthday activity - this is a no-nonsense book and you have to provide your own fun) and 6 months later my child was plowing through books and asking questions like 'what does disconcerting mean?'

Starting at age 3, you get a stack of books and read nonstop. By the end of age 4, there's still a stack of books but you do less and less of the reading.

During reading you don't have to worry about challenging your child to think. I'm not recommending that you crush the wonder out of books by explaining everything; maybe you ask a few questions and count to 20 before crushing the wonder out of books by explaining everything. But you use lots of vocabulary; talk like an adult. You've never met a sentence that couldn't be improved by the addition of a few subjective clauses. Pack the brain.

Get a vocabulary workbook. Post words on the word board. And when you see a word on the word board, add 10 more that are related. (Think like an GAT test analogy question.)

I remember my child staring at the word board when there were 100 words on it. He might get one or two each day, but 5 more would go up. One day it was empty. Two and 1/2 years later words never went up there because they were memorized on sight. The word board discussion and the discussion during reading is more than enough grammar.

Stage 1 COGAT Test Prep & Math

This stage ideally begins at age 5, and begins with a math book your child won't see for 2 more years in school.

During reading time, I was not reluctant to share any thoughts, ideas, topics, and information that came to mind. I explained everything. When we got to Math and COGAT, I explained zero. Zero. Cognitive skills are not about what your child knows, but what they can figure out on their own ('their' is the grammatically accepted way of representing 'his' or 'her'). If it takes them a week to figure out the 1st problem on page 1, then that's where they are. Their learning process will accelerate, but only if it's 'their' learning process. There are plenty of ways to help the learning process which I explain the the Test Prep Math series, but none of these ways involve you telling your child something, like how to do addition.

Some days (I call these bad days) I had to jump in their and share the work, or even do the whole workbook page just to stop the tears. But most days, I just asked questions and helped him backtrack. If there was a 5 step problem with 20 mini-sub-steps, and he only got 1/3 of one of the mini-steps, that was what he got. We would plod on another day.

I also lump music into this bucket. I'm a fan of 'here's an instrument and some books, teach yourself.' I should write more about 'teach yourself' because we're a bit over the top there as well. It's amazing what a child can accomplish on their own if a parent is patient enough to let them.

Until the end of 1st grade, we would alternate cognitive skills training (4 or 5 months) with math.

By the end of this stage, you're out of the explaining and teaching business in all subjects until you teach trig in 4th grade.

Stage 2 Science, History, and Everything Else

Between 2nd and 4th grade, we have a mini-stage while topics drop off. By 2nd grade, reading and vocab are already overcharaged. Math goes on autopilot until the end of 4th or 5th grade when we get serious again. There's no reason why your child has to know how to do long division with decimal fractions at this age - or ever - because it's boring and a useless skill. Stage 2 is what we do waiting for Stage 3.

Science has always been present in reading and projects. Science is wonderful at age 6 and 7 because it's all baking soda, wiki, and molecular white boarding. Magic School Bus is great. Looking up the earth's core to prove your textbook wrong is fun. Taking a few minutes to find out the who and when for each science topic is fun, at least for me, and if it's fun for me, we keep doing it. Try to teach your child molecular biology in one sitting, then do some historical research to determine that this 30 minute topic which is incomprehensible took many brilliant minds 3,500 years to figure out. This is true of algebra and calculus.

History is also great at this age. Thanks to Star Wars and Disney, movies are no longer plot and characters, they are part of an historical stream of directors, writers, cannon, and a 9 part series. Take advantage of it. This is true of video games as well which have been building off each other since Pong. I like to see 2 hours of research, discussion, arguing and more wiki'ing about screen topics for every hour of screen time.

If you are all 'telling' during reading, and no telling at all with math, Science and History and Art are somewhere in the middle. You can have fun delving in, exploring, doing your own thing, but - and this is a really important but - DO NOT ENCOURAGE your child in any way. As soon as you try to 'help' by signing your child up for a science camp or getting a stack of books or having your child talk to the neighbor who does physics at Fermilab, you will permanently destroy your child's interest in that subject.

For this reason, I leave At Home formal writing and science for 8th grade. I'll have to explain this in my other blog. For now, I'll just end with a Stage 4 story. That also leaves Stage 3 out of this article. The Cognitive Skills addition to the classical education ended around 3rd grade which is why I only cover stages 0 through 2 above.

Epilogue

My 6 year old showed a strong understanding of how advertising manipulates people. I publicly declared him the writing guy and told him to admit defeat in math and science. It turns out that he's really good in math. Who knew? But advertising is exciting and he can be very successful making people buy things that they don't need.

Last night at dinner the 13 year old version of himself announced this about his intended profession. 'I still say that I'm interested in advertising, because it's goes over well in conversation, but what I plan to do is to study astrophysics so I can write a computer program to find the galaxy that looks like Yoda.' Yes, there is a galaxy that looks like Yoda. He saw it on a trip to the Planetarium.

One day, he'll be studying math in college and find out that there is a Yoda in advertising as well, and it will take a math program to find it. I'm not going to say this but it will happen.

Saturday, August 11, 2018

The Appeal

I've spent all week pondering a question for a Power Mom who just entered the GAT Hall of Fame. I've gotten the same question at least 20 times in the last five years.

What do you do when your child is a few points shy of the cutoff and your school district has an appeal process?

Let's spend a little bit of time - like most of it- studying the question before answering it.

The appeal process will consist of you convincing the teacher and possibly a gifted administrator that your child belongs in that gifted class despite the deficient scores.  You are either a) a laid back parent or b) a pushy high stress competitive parent or c) somewhere in between.

Meanwhile, the teacher has had 100 of these meetings with a variety of parents across the spectrum.  Most of the kids, 95 to be exact, are not in the top 5%.  The average parent has no idea what a gifted kid looks like, no metric or way to compare, is totally enamored with his perfect son, and demands a seat in the gifted program because he is a lawyer. 

Then you walk in and the teacher is already in a bad mode.  If you watch America's Got Talent, or even better, the music themed precursors where Simon Cowell was a cynical jerk with little patience for untalented contestants, you know the mood of the teacher.

I've seen 6 year olds explain advanced physics or talk with a high school vocabulary.  Let's hope one of these kids wasn't in the room for the last appeal.

Step 1: Prepare

Across all subjects, what makes your child top 5%?  Prepare concrete examples of maturity, interest, effort, going deeper, exploring, asking questions, teaching herself things across school subjects, art and projects.

Reading and vocabulary are essential.  However, if your child reads 6 hours a day, only admit 3 hours a day, and make the last hour something with talking, drawing or acting.  GAT teachers hate kids who read 6 hours a day, because it disrupts class participation and group activities when a child is willing to sit silently because she's smarter than everyone else by about 5 years. Most GAT kids are gregarious, making the reader look less intelligent, when in fact a strong reader should probably just skip grade school.

Does your child show an interest in science or history?  If not, make it happen ASAP and then write it down.  In other words, cover your bases.  Get 20 Magic School Bus books, make your child read them all in 1 day, and then say 'She read 20 Magic School Bus books in one day!'

Step 2: Be Nice

You are walking into the presence of an expert.  He may be short and green and have big ears and a funny way of talking, but he's 926 years old and can lift space ships using the force.  Plus he's in a bad mood and is skeptical that this parent will be different.

Step 3:  Don't Give Up

Some of you are far too nice about the whole thing, which is good, but niceness should never cross the line to 'OK, I guess my kid doesn't belong in this program' if in fact your kid spends 2 or more hours a day working on academically related topics and is only a few points shy of the cutoff.

The Hall of Fame

The family I mentioned earlier put 3 kids in a GAT program in one year.  I got an email about the youngest who missed the cutoff by a hair.  You should be giving me advice.

I'm also inducting another family who put twins into a GAT program.  It was a reasonable academic effort, but the kids were already over the top smart when I met them.  The mom went through the most frustrating complicated bureaucracy imaginable, and no analogy will suffice to demonstrate how bad it was.  But she didn't give up, appeal after appeal.

Congratulations inductees.May your children grow up to fix our world.

Sunday, July 29, 2018

Goal Effort Outcome

When I set out to be a better parent edjumacation-wize, I chose 3 goals:

  1. My children would get 98.6 or higher on the COGAT
  2. So they could succeed at the really hard program they qualified for with that score even if we cheated to get in 
  3. They would learn how to teach themselves math and thus do well in all subjects and life because I'll be darned if I'm going to teach them math.

The 3 goals are the exact same thing; not close, not related, but identical. 

Unfortunately, teaching your child how to learn is counter-intuitive and very frustrating.  89% of parents will not let their child learn how to learn enough for the child to get into the 90's on the COGAT.  94% of parents don't go far enough so that their child gets to 95.  You get the picture.

Most parents are happy when their child does slightly challenging material like math facts or fractions, practices until mastery, followed by a baby step in complexity and practices a lot until ready for the next baby step.  I get really frustrated when working with these kids.  I ask them to show me how they did the problem, and they provide polished mechanical algorithms that were invented by an adult.  Some kids understand these mechanics, some kids don't care.

When children invent their own mechanical algorithms, their innovations have breathtaking complexity and apply widely to a variety of fields.  It takes very little brain power to learn an algorithm.  It takes a lot of brain power and a long time to invent one.  Each time the child invests an algorithm, their brain increases by 15% in size. 

The worst part of letting your child learn to learn is that it doesn't appear that anything is happening.  Most of the time, it looks like they are just getting dumber.  It's horrible.  It's very hard for a parent not to yell at their child while they are learning to learn.  With the math fact step-by-step approach mentioned above, it looks like the child is getting brighter because their brain is filling with the mastery of learned math concepts.  At least they have a high ITBS score to show for it.

Yesterday, a Power Mom complained about question 15 in Test Prep Math Level 2. The author and Test Prep Kid spent three days on the question and have yet to reach an agreement.  I consider it one of those questions where learning to learn takes place.

In response, I got on Skype with the kid to discuss 3 x 31.  It took us an hour.  She's barely mastered single digit addition.

I would love to get one of these kids an mom or dad in a video to show you how this works, but it would be embarrassing for all involved.  Therefore, I'll offer a rough transcript.  I'm going to demonstrate the crutches I use to distract me from yelling at my own kids.  There are 3 categories of crutches:

  • I stay focused on learning.  Learning is a priceless skill.  Multiplying 3 x 31 is a useless skill.  If knowing 3 x 31 was important, I would just tell them it's 93.  While they struggle to make sense of what 31 is, I can see learning.  
  • I can see what is happening as we go through the process, and I have already seen the result in 1 or 2 years with kids who do this.  The pay off is huge.
  • I've replaced scaffolding with advanced problem solving techniques.  The kids never adopt these until high school.  Until then, the parent has to suggest them.  On the bright side, it gives me an alternative to frustration and yelling.  That's why I'm so chipper when I coach.

I want to start with an easier problem and then we'll work our way up from there.  Here's how it went:

First, we started with 1 x 30, 2 x 30 , 3 x 30.  This didn't go well.

Next we went to this list.

  • 2 x 3 = ?, 2 x 30 = ?
  • 3 x 3 = ?, 3 x 30 = ?
  • 3 x 4 = ?, 3 x 40 = ?
  • 3 x 5 = ?, 3 x 50 = ?

I was pleased to find that every time I asked 3 x 4 = ? the child had to think for about a minute to answer the question.  I asked 8 times.  I got 8 blank looks.   A child who does not learn their math facts is slowly building number sense.  Eventually, probably in 3rd grade, she'll know that 3 x 4 = 12, but she will really know it intuitively, and this will pay off during pre-algebra.

We were so close to taking the leap to 3 x 31 or 3 x 35, but we ran out of time.  With my kids, we repeated this exercise once a week for 3 weeks, and then 82 x 5 was totally doable.  116 x 56 in school a few years later required no mental effort or parental involvement.

What's really cool is when a child sees 48 x 4 and their eyes get wide, and they totally understand it.  I don't exactly know what they are thinking, but they can tear apart more complicated arithmetic problems with whatever they discovered, except when they get 4 x 4 = 18, which they get a lot, because I won't let them memorize math facts.

Could you as a parent sit with your child for 60 minutes working through problems in the vicinity of 3 x 31?  What happens when the child can't remember what 3 x 4 is even though you've asked the same question 8 times?  Of course you can't, no sane parent can.

We did just that, week after week, year after year.  We're still doing it.  I'm in charge of finding unsuitable problems that take at least 25 minutes of struggling each, and each child is in charge of doing something at school that may involve math but I've never seen it.