Knows answers but not how to write problems

Frequent topic of discussion is whether getting the “right answer” off the top of your head is enough and why you have to write all this stuff down if you know it anyway. Talk to people who are battling in high school and college levels — yes you DO have to write it down; just seeing in your head reaches a limit and if you haven’t built up systematic skills it is very difficult to go back and get them later.

I also put “right answer” in quotation marks because I find more and more that students are answering the wrong question — for example the question is to write an algebraic equation and solve it, and the student “sees’ the number by estimate-and-check. Well, recognizing the correct number is a good thing, but the goal was to write and solve an equation so you have the skill for the harder questions that you can’t guess — this student fails algebra because he isn’t doing algebra; and he is very angry about it because he is convinced he knows, but he doesn;t even know enough to recognize that he has missed the whole topic .

Yes, keep working on it. I find that I have to break down the problem-writing process in tiny tiny pieces and then put them together slowly:
How many apples does John have? OK, write a 2.
How many apples does Mary have? OK, write a 3.
What are you doing with the apples? OK, write a plus — where do you put the plus?
Now, what sign do you put after your problem?
And what does it come out to? OK, write a 5
Yes, this is slow. Usually the kid catches on to the system fairly soon, and yes, it speeds up.

This is very, very common in gifted childen, who often have the ability to instantly and intutively know the answer without being able to articulate why or break it down into logical steps. An added issue may be physical difficulties with handwriting. As Victoria points out, however, doing it in your head can only get you so far. In first grade he probably can do what he needs to do without writing it down. By fourth grade, it will be infinitely more difficult. Having gone through this experience with my own gifted children, I can sympathize. What worked for us as far as the cognitive aspect of the problem was me asking lots of questions designed to help my children “see” the logical steps involved in obtaining an answer. Be warned, your child may think this is tedious and ridiculous, because he likely labors under the assumption that things that are obvious to him are obvious to everyone. Keep it up though and eventually he will see what you mean. If handwriting and keeping numbers lined up on the page is a problem, try big box graph paper.

I totally agree with the responders. Early math skills are as conceptual as later math skills. Verbally going over the problem and writing responsively to the problem demands is an absolutely crucial math idea that must be developed early. It would be easy to jump ahead because he got the right answer but it wouldn’t serve him well in the long run. Be persistent. Perhaps you could develop forms that would reduce the writing aspect but he’s got to see what’s “turning the learning” as I like to say.

Doug McFarland

what about using manipulatives as an intermediate step between numbers and writing? Would he create problems (ie write them down) for someone else to do? What about rebus stories?