Mind Your Words

There are errors in teaching that easily go under the radar.  They cause a great confusion on part of the learners and yet the instructor hardly notices that it was he/she who has sent baffling directions.

A few times in the past, Robert was asked to find the value of a simple expression by substituting the variable (letter) by a number.

For instance: M+7 where M=4

3F where F= 5

and so on.

He did not have problems with those demands.  He learned quickly and sailed through those problems.

So I thought that I could move to the next step and with the help of the curriculum  Momentum Math grade 7, I asked Robert to write verbally presented expressions:

3 more than a number,

5 less than a number,

Add 8 and a number,

Subtract 10 from a number.

I did not analyze what such directions meant to Robert.

Thus when he hesitated after writing, “3+….” I did not understand his confusion.

Only when he later wrote “3+3” or “3+ 8” I understood the problems.

First, since I asked him to write a number, he responded with hesitation because I did not tell him what number exactly he should write.  But he also couldn’t ask, “What number?”,  He is not capable of using language this way yet.  So he tried to guess.  The first guess was the same number he already wrote, “3”.  The second guess was the number from another problem a little above this one, “8”.

I had to explain that the word “number” in this context, meant a letter.  Even more confusing. How can a number be a letter?  Such statement went against everything I was teaching him so far.

So I backed off and decided to first replace the word “number”  with a phrase “unknown number” and ask Robert to first replace such expression with a question mark and then with an empty square. I had to rewrite all the problems:

3 more than an unknown number.

Robert replaced it with: 3+ ?

I am still thinking about the next step to avoid confusion which I caused in the first place by not understanding what my words meant to Robert.

I wonder, how many times, while talking with Robert, I also gave him directions which did not make any sense as they went against everything he had learned before?

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