Thursday, April 23, 2015

Lack of Motivation 3 - Hard Problems

If you are taking advantage of my recommendations for either math or test prep, you and you child will encounter a really hard problem that you don't know what to do with.  Your child may sit there and become frustrated.

When your child is in school, he may become frustrated with material that is new and hard, and he may be stuck.

This is a huge demotivater, and top 2 on the list of things that demotivate children.   The other 1 is the opposite - the material is really easy.  I'll come back to the easy material later.

The thing I like the most about test prep is that it teaches skills to tackle hard problems.  This is what makes gifted kids gifted, provided that they have an interest in academic work and a home life that puts academic work 1st as the number one value.  What I'm worried about is that I'm recommending super hard material - at least one year advanced, and readers and their children will run into a brick wall trying to do it.  Therefore, this article provides the ladder to get over the brick wall.

First of all, as a parent, the child has to do all of the work.  (Look at my prior article about public speaking.)  Your job is to hand the work to the child.  If the child says that the work is hard, and you do any of it, any at all, then you have failed the child.  The learning process is taking hard material and figuring it out.  The main failing of our school system and parents is that we teach this material to the children.  They know it, but they don't know how to learn because we do that work for them.  (The school system will be covered in a future article).

So what do you do?  Here's what I do.

#1  Read the Question
I ask the child to read the question to me and explain it to me.  I am looking for them to acknowledge parts of the question that they did not see before.   The question may include a diagram.  They have to read, describe, explain every part of the diagram to me.   Kids tend to not think this is part of the question, but it is the main part of the question.

#2  What Do You Recognize
What parts of the question do you recognize?   What words or definitions do you know.  Have you ever seen any problems that are similar to parts of this problem?

#3  What Do You Not Recognize
Kids tend to skip right over words, phrases, or syntax that they are not familiar with.  Saturday, my son saw 10√2.  He had no idea what 10√2 was and worked on the problem for 5 minutes before I asked this question and he point it out.

When asking these 3 questions, you are giving the child the first few tools to do something with the problem other than just sit there and give up.  Think about this approach.  You aren't really helping by teaching the child the material.  Don't ever explain the material.   What you are doing is teaching the child how to learn for themselves, which should be the goal of every parent and teacher.

In school, especially in math, the kids are supposed to know everything and be able to do it quickly.  Think of times tables.   The children develop this expectation that academic work is about knowing things.  This expectation puts them at a distinct disadvantage, because academic work is about learning things and figuring things out.  When they get challenging material, they think they should know it - and they don't, or else why would I be giving it to them - and then they come to the conclusion that they are big dummies. 

You as the parent have to undo this bad habit, first with yourselves as academic coaches, and secondly within your children as learners and figure-outers.  There are other questions I ask after questions involving the problem, but the 3 questions above are the most important for Step One because they get the parent out of the explaining business and make the child think for himself.

When I encounter a child who is a genius at math tables for arithmetic, I assign a book of word problems or brain teasers.  I have got crying and frustration from the kids for this assignment, but down the road the parents are very appreciative.

Spending a lot of time reading the question is a good first step.  What you have to do next varies a bit with whether you are doing math or whether you are doing test prep with a set of answer choices.  

Here's an example that my 10 year old and I worked on.  In the diagram below, side a and side b are both 10√2, and the line running through the middle of the triangle is parallel to the bottom of the triangle.   (The actual question was convoluted and I'm not going to type it here because it's hard to present in HTML.)  What is the area of the rectangle made up of the 2 squares?

After struggling with this problem to the point of tears, my son asked for help.   I had no clue what the answer was or how to solve it.   We started with him reading the problem to me for about 5 minutes until I was sure he knew what all the pieces were.   The we discussed what square roots are and why the square root of 2 is just left there as notation and not a number.  That took 10 more minutes.

I asked him to tell me what he knew about area, and he knew the formula for the area of a triangle, which was good.  He also told me the area of the rectangle was half of the area of the triangle which was pretty astute.   (Apparently I taught him something.  We didn't prove it formally, but good enough.)  Then we had to figure out the area of any of the triangles.  It took about 45 minutes, and in the process, we learned a lot of math.   We learned not to give up.   It was not easy for me either.

I am not sure I could figure out this problem on my own without the problem solving steps we went through.  I know for certain that without these problem solving steps, I wouldn't be able to help my son with math.

This question came out of the SAT practice test book we are going through.  It's getting harder.  We're down to about 1 to 3 questions per session.  A lot more learning takes place with one question than a whole workbook of easy calculation questions.  Like public speaking, the parent or academic coach just has to go really slowly and wait a lot.  Sometimes, like in the case of this problem, the kid can get through one or 2 important steps in problem solving, but needs help with the other 9.  That's OK.  He can learn some by doing and some by watching, and eventually, maybe in a classroom setting, he'll be able to put all of the pieces together himself on something easier.

Test Prep
Test prep has a lot of the same elements but I usually go about it differently because the problems are much different.  The goal of a cognitive abilities test is to present the child with a completely unfamiliar problem with it's own set of brand new rules and let the child figure these out.   The goal of the parent is to teach the child these skills so that they do better in school and in life and on the SAT test prep math book they'll get later.

Here is a sample problem.  The directions state that there is a relationship between the squares in the top row.  Which shape would you pick for the blank box so that the same relationship holds true for the bottom row?

This one is pretty confusing, and would be preceded by some examples where the shape at top shrinks or grows along one or more dimensions, or turns or flips.  The test intentionally sets the kid up for failure on this question.   I don't think I got it the first time I saw it.  I would have failed a 1st grade cognitive abilities test.

The first step in the test prep process is to understand what it means that there is a relationship between the two top shapes.  We spent 3 months on that.  What are all of the things that a square can do?  Draw them. Cut out a square or find one in the toy box, and have your son demonstrate the basic operations, especially rotate and flip. What does the square look like when it is turning or flipping? Ideally, you would work with other shapes and a list of math vocabulary before attacking a question like this.

The children must look carefully and patiently at this question for a long time and start thinking about all of the things that may happen.  Children who do well will linger on the question.  Children who will bomb the test completely will look at the problem, immediately realize that they don't know the answer, and guess or move on without trying.   Or they may ask the parent for help, the parent will explain the problem, and no learning will take place.

When really great teachers present problems in class at this level of challenge, they'll just change the subject and move on without telling the kid whether or not they got it right.  They'll move on to working with things that can happen to shapes, and how each shape looks when it grows, rotates, widens, gets shorter, etc.  (They of course don't do with COGAT questions but academic material.) At some point, either the lightbulb goes off for the child or they can come back to a problem like this and succeed where once they failed.

This problem could be out there unsolved for months.   When we did test prep (aka Cognitive Skills building), I would skip lots of material or leave it ungraded and we would eventually come back to it.

The child learns by learning.   If a parent explains this problem to the child, learning has failed.  Also, test prep books are expensive and don't have a lot of problems in them, so don't waste even a single problem.  If your child is stuck or doesn't know the answer, save it for later.  If they say "I can't do this", say "You can't do this yet."

Parents often wonder why their child does so well on standardized tests but not cognitive abilities tests.  In Chicago, kids can take the Classical test to get into an Academic Center, or a cognitive skills test to get into a Regional Gifted Center.   The Classical test is a standardized test (eg what kids are learning in school) and the Academic center is an accelerated program.  The gifted test is a cognitive abilities test and the gifted programs are accelerated, but the kids are expected to learn the material even though they spend most of their time on projects and field trips.

Back to the question.  Why the disparity in scores?  In short, the parent can teach the child academic material without teaching them how to think.  It works for a while, and then by middle school the kid is failing.

I say don't teach your child anything.   When they get stuck on hard material, do something else for a while.   Let them make up their own test questions (we did this and it was fun) and see if they can make a test question with only one correct answer.  Make up your own test question and let the child find the mistakes, like a question that has multiple answers or a question that doesn't have any answers.  We did a lot of this.   I noticed that much more learning was taking place when the test prep book wasn't open.

I better summarize because this article is so long.  Here are the rules for a parent:
#1.  Don't tell your children anything.  Let them learn it on their own.  Be prepared to wait a long time for them at first until they pick up these skills.
#2.  If you have to explain something, don't.  You can ask lots of questions, and don't forget the questions I presented in the math section. Make these questions opened ended, not prompts for the answer you want.   Ask them over and over again until your child gives up expecting any useful help from you and starts doing the thinking on his own.
#3.  Be prepared to spend an hour on a single question or save if for another time.
#4.  Fill in the gaps with do-it-yourself projects that make it more fun.
#5.  Have an easy workbook standing by as a crutch so that regardless of your child's skill level, they can do something productive and not wallow in their frustration for ever.  As they grow, they can handle longer periods of frustration, or better yet, learn the skills to overcome the brick wall.

This list is a lot better than the advice you'd find in a parent magazine (e.g., get a good night's sleep before the test).  I have a much more detailed list of problem solving steps to review later .   This is just the part of the list to break the parent of the bad habit of undermining learning. 


  1. I am assuming when you said you didn't know how to solve the triangle problem, you were joking. Just in case you weren't, the problem is a test to see if one knows the Pythagorean Theorem and how to apply it. If you know the theorem, the problem takes 10 seconds and can be done in your head.

    I remember back when I was on math team, our instructor gave us a problem like this, and used it as a starting off point for a group activity in deriving the Pythagorean Theorem for ourselves. Granted, that was in 8th Grade, but I do remember it being a fantastic activity that really increased my understanding of triangles.

    And if I remember the SAT correctly, back then, 100% of the problems that had a picture of a triangle on it was about the Pythagorean Theorem. It should definitely be test prep material.

  2. Sorry about this comment, I see you came to the same conclusion I did 2 posts later. That's what I get for reading chronologically. I need to stop commenting until I catch up to real time.