Thursday, April 30, 2015

Scaffolding Hard Problems

In recent articles, I've been pointing out that parents and teachers - but especially parents - undermine the learning process by telling the child how to do things and what the answer is.   This results in a child who knows a lot of stuff but can't think and will have a hard time on a GAT process.

When the parent breaks this habit, the long hard process of learning how to think begins for the child.

If you are in the middle of test prep, or if your older child has to get through a math homework assignment, you'll have to accommodate this process with "Scaffolding" so that you don't waste the entire half an hour having your child sit there dumbfounded.

The goal of Scaffolding is to let the child think through things - to a point - and jump in with lots of questions and guidance.   If your child needs 12 skills to get though the work, but only has the first 3 (these 3 are reading the questions skills which I already outlined and I hope you already taught them), their current work will be painful process without more help.

What I like to do with the homework process is ask the child to look for things - anticipating the next few steps - and satisfied that the child started exercising skills 4 and 5, and maybe 6, I'll just guide them through the rest of the assignment and hopefully they'll pick up more skills the next time.  For example, the child is never going to derive the Pythagorean theorem on his own no matter how gifted he is, or even know it exists, so just tell it to him and let him apply it.  My 10 year old is not going to get through some of the questions in the SAT book unless I jump in there and help out, and some of these questions, frankly, I don't remember how to do.  As we do these super hard problems together, he is picking up bits and pieces of problem solving techniques.  I've noticed in subsequent sessions, on some problem types, he now just jumps in there and solves the whole thing whereas before, he couldn't get past the question.

With test prep, on the other hand, I usually don't guide the child in the same way.  First of all, it's easy material (aka squares and circles) but tricky, and if you guide the child over the trick you ruined the lesson.   In this case, I keep an easier workbook handy (eg Building Thinking Skills, whatever page they can actually do) and see how far the child can get in the harder work book (eg a COGAT test prep book) before we just stop and switch back to the easier work book.  

Sometimes with test prep, I keep some paper, scissors and crayons handy.  If we get stuck on a question like the folding questions, we'll either do a lesson on multiplication with blocks, or pick up a hole puncher and start punching holes.  I'll ask a lot of questions and they'll do the work.  Something easy.  Then they can take another shot at the harder material.  In the past, I've given hard material to a child that took 4 to 6 months before they could actually do it.  Oops!  My bad.   As the World's Most Awesome Academic Coach, I know that I can just wait and try again.  As a first time parent, I did not know this and I spent many frustrating hours trying to teach this material to my child.

To illustrate this, I'm going to give an example from my recent research with a 3rd grader doing a simple division math worksheet.   He's a bright little kid with a bright future, but he stinks at problem solving.   You'll see why.

After a few minutes of doing his work quietly, he came in to the room where I was talking to his mom about my research and asked "What's 121 divided by 11?"  By this point, his mom knew not to say anything, but I asked her anyway what she would normally do.   What would you as a parent do?  So here's how the conversation went.

Kid:  "What is 121 divided by 11?"

Me:  "You tell me."

Kid:  "I don't know.  That's why I'm asking."

Me:  "It's your homework.  You tell me."

Kid: "If I knew the answer, I wouldn't ask you."

Me:  "Go back to your desk, take a blank piece of paper, and write down the multiplication table for 11, starting with 11 x 1 and ending with 11 x 12"

Kid  (Comes back in 5 minutes):  "Is the answer 11?"

Me:  "You tell me."

Kid:  "I don't know."

Me:  "Look at your multiplication table.  What is 11 x 11?"

Kid:  "It's 121".

Me:  "OK, what is 121 divided by 11."

Kid:  "Is it 11?"

Me:  "You tell me."

I've had this same discussion with both of my sons at various points and with other kids I've coached.   They won't give up asking until they are 110% certain that no help will be forthcoming from the adult.   I would only do 2 things with my kids.  The first thing is that I'll gladly point out their errors as many times as they would like.

The second thing is that I will gladly point out the parts of their assignment which they didn't know were there.  In this case, we looked at the multiplication table of 11 for a pattern and found one.   Then we googled patterns for multiplication and found out that all numbers have them.  I asked him to write the multiplication tables for 3 and 9 and tell me the pattern.  It was hard to do so I helped.  Then we discussed how he could use these patterns to determine if he got an answer wrong, but this wouldn't help him know for sure that he got it wrong.

Finally, I told him that every single arithmetic problem he encounters requires cheating, and if he cheats good enough, he can do them all in his brain without having to memorizing anything.  For example, 6 x7 is hard, but 5 x 7 + 7 is easy.   9 x7 is hard, but 10 x 7 - 7 is easy.  And so on.

When your 3rd grade child asks you what 121 divided by 11 is, you now have 2 options.  You can say "11", and the child can finish their homework.  Or you can give them full responsibility for their work and dig deep into all of the things they are not learning, and you can unleash the Gifted and Talentedness of your child.

If you are currently doing test prep for some test, you are probably also doing some academic work, even with 4 year olds, who are learning to read and do simple counting and arithmetic.   I generally did about 60% academic work and 40% or less test prep.  Then I realized that the skills that the test wanted were the exact same skills used by top students in academic work.  From that point on, everything is test prep, even division.


  1. Any advice on how to teach multiplication and division? I have a 5 1/2 year old who likes math but we're struggling with this part.

    1. It went a lot like reading, which started with the "a" sound and took six months to get to cat. Don't go fast. Do doubles with your hands, then do triples with your hands. Like a beginning reader, we spent a lot of time multiplying 2 before moving to 3 and 4. Don't provide any shortcuts, mnemonics of any kind in math. Le the kid figure out his or her own.