How important is it that a child can explain their math steps in words?

[kalanamak]

Kiddo is fairly intuitive with math. We are working on SM 5A. Sometimes he gets stuck on all the steps of long division with larger numbers, or with adding mixed fractions where the common denominator is not a snap to guess. I try to walk him through the steps, and once he "gets it" he rushed on and doesn't want to hear the rest of the steps. I sympathize. I was the same way about math.

 

So, I tried to get him to tell me the steps he has taken to see where he is stuck. He HATES this. It seems an important step to my grown up mind to be able to say something like: first we find the common denominator, then we ....

 

Is this too much for a 10 year old? Should I stop trying to get him to tell me why he has done what he has done, or is my hunch correct?

 

Thanks for your opinions.

[Trillian]

For DS, when he is consistently having trouble with a type of problem and then gets it, I make him write down the steps. He hates it, but I've noticed it does cement it in his mind. If I don't, he seems to forget how to do the problem with next day. I don't know how universal that is.

[Crimson Wife]

This is a big fight I'm having with my DD right now. She is resisting writing down the step-by-step-by-step series of equations in a way that someone else can follow. At this stage (pre-algebra/early algebra 1) it's necessary for her to do this. She can do it if I scribe for her, but I can't always be sitting there with her.

[redsquirrel]

I think 10 is just the right time to start to develop the skill. It is coming up more and more now in pre-algebra. DS is taking AoPS and it is important enough that every week he has a problem that he has to solve while explaining (in writing) each step. It has been a great challenge for him. For the past three weeks he got full points for those questions and he was so happy and proud I thought he was going to float.

 

So, consider yourself at the beginning of mastering this skill. At that age, I would ask and sometimes force the point if need be. But I also did a lot of 'I told you so' when we had difficulty because he would not do it.

 

I also think it can be helpful to teach by example. If he doesn't see you do it on a regular basis then he might not know where to begin. I also think scribing at 10 or 11 is a totally valid way to start. Or, you can have your child start and then you scribe when he becomes frustrated. It is a long process.

[Dana]

I make my son do the explanations.

He also gets to hear regularly how my students at the cc make similar errors and how much I take off for those errors :) I think that gives him some motivation!

 

I've also pulled out algebra texts and shown him why finding a common denominator by adding missing factors is essential for working with rational expressions. So he sees where this technique will recur.

[Bang!Zoom!]

When we were living without a printer this year, everything was done longhand and she also worked on "translating" if you will (verbally) problems. It is almost like a entirely different skill. I was quite amazed about it in fact.

 

Try sitting across the table, the math problem facing you and ask him to write it out.

 

I saw all sorts of things..whether to lay it out horizontally, vertically, unknown words, not connecting the concept with symbols. It was really interesting. It led to a lot of great discussions. Although aggravating at times, I think it's worth messing around with.

[letsplaymath]

It might help to recognize that you and he have different priorities regarding the math lesson. His goal is to get it done with as little effort as possible -- and if he's always been intuitive in math, he may have come to think that it really shouldn't require effort at all. Your goal is that he understand it deeply so that he can build on that understanding in the future.

 

One way that I have tried to reconcile these goals in my lessons is to go by the clock rather than by the exercise or page count. We work X minutes (for my daughter in 8th grade, X=45), and then we stop. No matter whether we finished 30 problems or only 3. Therefore, taking time for extra explanations doesn't increase the level of work -- in one point of view, the more we explain, the less work (fewer problems) we do.

 

Another thing I find helpful is to model the level of explanation I want, by doing the lesson buddy-style. And because we work on a whiteboard, I'm not requiring a lot of formalism in the writing of solutions. My daughter's work is not neatly presented like a finished essay, but more like a first draft work in progress -- and I'm okay with that, as long as I'm convinced she understands what is going on.

[mommymilkies]

My 12 yo has this problem. She is a VSL and an excellent reader. She's very good at math, but can't explain her "how" to save her life. In fact, were about to dump AoPS for good because its just too hard for her to mix the verbal explanations she needs to give with what she knows.

[Penguin]

The Practical Arithmetics series has sections called "Problems without Numbers." I am having DS work through these sections orally, and I think that this exercise is doing wonders for his ability to verbalize how to do a math problem. I had to back up quite a bit to problems that he knows how to do very easily, but I have quickly seen progress in his ability to explain.