Mathematics: A Teaching Problem

 

 

“If you have taught

And there is no learning,”

Said a tutor many years ago,

“Then you have not taught.”

 

I struggled with this

For it did not make sense

And in my view way back then

This tutor had to be dense.

 

It was one of my early courses

At Erdiston Teachers’ College

And as far as I was concerned,

This was utter garbage.

 

He was blaming the teacher

For a pupil not learning:

For him, it was a teacher problem:

Transmitting not receiving.

 

I was young and cocky then

And I would have none of this

For, regarding my teaching prowess,

There was a lengthy list.

 

I was not only a natural

But I was endowed with passion,

Add to that a love for children

With subsequent flair and fashion.

 

I’d had a fair bit of success too

With pupils passing exams,

So, this tutor’s nonsensical ideology

I was forced to body-slam.

 

He was a mathematics tutor

And his grading was very tough,

After a few assignments results

You knew it was going to be rough.

 

For that mathematics course

I averaged just C+

And I must truthfully confess

At times I felt almost crushed.

 

He assured me years later

That I was a very good student

And he took some of the responsibility

For my subsequent achievement.

 

“If you have taught

And there is no learning,”

This tutor had stated,

“Then you have not taught.”

 

Back then he was my teacher

And the reason I was distraught,

My not learning was a teacher problem,

Yes!  It was his fault!

 

C+ was his mental set!

It was not really mine,

He was clearly annoyed with himself

Over a fixation back in time.

 

I have come a mighty long way

Since those early days

 And slowly but surely

I have mended my ways.

 

Much experience has been gained

From the exposure I have had

And the truth be told,

The good has eclipsed the bad.

 

I am retired now,

It is almost twelve years

And I am proving more and more

My greatest fear.

 

That that tutor was right

I now have no doubts,

One by one, the arguments I held

I have thrown them all out.

 

It’s a teaching problem

That retards pupil-learning

And this is particularly evident

In basic problem solving.

 

“Expose the pupils

To many and varied problems

And by the time of the examination

They will be able to solve them.”

 

Sounds good, Yes?

But so very wrong

Yet many teachers’ hold on this

Remains very strong.

 

“Practise, practise, practise!”

That’s the way some others go

But this too is just as wrong

As one practises what one knows.

 

Often the foundation is shaky

Or there may be none at all

And so, the scaffolding put in place

Must eventually fall.

 

The syllabus reigns supreme

At the expense of pupil learning

And it is often covered down

With little understanding.

 

“Telling” the pupil is optimum

Like the baking of a cake,

"This is what you do next,

Hurry up! It's getting very late!"

 

Most pupils are asking HOW?

Very few are asking WHY?

And with concept building non-existent,

There is little to apply.

 

Three basic levels to doing Math:

Skill, comprehension, application,

Problem solving rides on all of these

And is based on investigation.

 

Concept building is critical

And must never be treated lightly,

It must be informed by models

Either concrete or pictorially.

 

Much of math is outside

And of an informal nature,

Bench-ridden within the classroom

Is like old-age stricture.

 

 

From the intuitive to the concrete,

From the concrete to the semi-concrete,

From the semi-concrete to the abstract,

Not one we should delete.

 

Then the application should follow

With the communication right behind

And if the student can reflect all this,

How to learn is right on time.

 

The best learner is a teacher

That communicates what he learns

And with the passion that he derives,

For more learning he will yearn.

 

Learning is not the target

But how to learn is, instead,

And when the pupil hits the bullseye

We can say he is well-read.

 

Learning-strategies will develop

Problem solving will be a breeze,

And with less teacher-dependency

Pupils will learn with ease.

 

Learning is the ‘fish’ one catches,

How to learn is the “how to fish”,

The former is not sustainable,

The latter is the desired wish.

 

Do not ignore a pupil’s ‘why’

With a “This is the way to do it”,

Instead, encourage intelligent questioning

To make him better equipped.

 

Teacher, take responsibility

For the learning of every pupil,

Treat each one as your own offspring

And do not suffer in silence.

 

Encourage pupils to share

Ideas and methodologies,

Utilize their composite brain power

To come up with strategies.

 

 

Assign yourself a mentor

Or, maybe one or two or three,

And with the input from them all

The better you should see.

 

Mathematics is a teaching problem

And one the teacher must solve,

The student’s learning is the variable

That each teacher must resolve.

 

Stewart Russell © April 4, 2023