Gifted Issues Discussion homepage Forums General Discussion Downside to over- verbalizing math?

This is probably the only forum where I can ask this question and not come off appearing a little nuts. Is there a downside to over-verbalizing math?

DS10 is taking an onine algebra course through his school district and also has a live teacher (also provided by district) checking his progress one day a week. Perhaps I am rather old-fashioned but I feel more comfortable with step-by-step math equations as a method of showing your work. For DS, he is able to answer the mutliple-choice questions mentally so almost never writes anything down unless he is required to for an "essay" question. There are many essay questions, including "show your work" type questions and "explain" type questions as well as projects. I check his progress online every so often and what I have noticed is that he tends to verbalize most of his essays, sometimes even the "show your work" questions. When I questioned DS, he responds that "essays" imply words so he feels that he must use a lot of words rather than just write equations step-by-step. I am a bit skeptical of his approach even though his essay answers tend to be well-written and fairly succinct and get 100%.

The bottom line is that I feel he is not getting enough practice writing his work step-by-step and it might become an issue later. However, it appears that neither his online instructor nor his once-a-week teacher is concerned. Maybe I am nuts. With my older DS in Algebra, I was once accused of expecting him to learn how to built a car from the grounds up rather than just learning how to drive the damn car. Math is its own language and the fact that he can look at a math problem and verbalize the solutions so easily may be a good thing. I am comforted when I think of it kind of as being bilingual, where your brain naturally thinks in both languages without translation. However, I am concerned that it may result in DS having trouble consistently writing step-by-step solutions down the line. I also find the language of mathematics beautiful by itself without the clutter of words, no matter how accurate and necessary for purposes such as teaching.

I think the challenge exists in the converse. I think if you cannaccurately verbalize, then you can pare it down to the equations. But I know for many mathy people the converse is very challenging. DS7 is a very verbose math kid, and it strikes me as very useful as he decided a year ago that he plans to be a math professor when he grows up.

Real mathematicians write sentences (albeit with lots of symbols in them) not lists of equations. Provided that he's making rigorous arguments that he completely understands and that other mathematicians accept, I'd say it's fine - I'd expect him to be able to adapt to a required format as and when required, if it's straight in his head.

DD is like this, as well.

She's not a calculator by nature-- but a mathy kid nonetheless. She's a concepts girl.

I can only tell my own experience. At a younger age, I had trouble showing my work, I could look at a problem (word problem or otherwise) and know the answer but it took me a while for showing my work to click, but then I became very good at equations. Then, while in grad school working on an Engineering PhD, I had to take a course from the Math department where we had to write proofs. I was horrible. It was a shock to my system because the proofs were not equations and algorithms. They were sentence explanations. I barely got through it with a lot of help from a friend and I frankly still get headaches thinking about it. However, I am now trying to figure out the best way to train my DDs for that type of thinking because I do see the value in it.

My personal soapbox answer is leading them to improve their metacognitive skills. Understanding what you are thinking and the nature of how the mind puts thoughts together enables the articulation. One way to start is through modelling, i.e. making a point of procedurally speaking out loud what you are thinking as you make decisions, calculate something, plan a meal, etc.

What a great idea. I'm going to try this.

My DS10s teacher wants them show their work. You can do it anyway you want as long as the answer is right. If you don't show your work and get the wrong answer it is wrong. If you showed your work you might get a bonus if you are anywhere in the ball park. If you show your work in the way the teacher has explained it you might get a bonus+1.

They are working on problems lately that make you work backwards. I believe your son might have an edge with his verbalized solutions.

I have no idea if you should be worried or not. I do know the kids love to work on there verbal explanations with each other.

There are people who don't do this naturally? Maybe this is why my DS is bright :-)

This would seem to go against the other way to solve problems, which involves throwing everything into the hopper and let your subconscious deal with it.

This is how I solve a number of legal problems at work (and general questions about reality, normally of an esoteric nature, sometimes years after I first asked the question.)

And normally I get a good solution by the time I need it.

Half the time, I couldn't begin to tell you *how* i got the solution. And, I generally don't *care* how I got it as long as it works.