We should be teaching mathematical thinking

July 4, 2009 at 11:50 am 1 comment

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The use of IT in the math classroom raises implications for pedagogy in the math classroom.

This brief discusses the purpose of math education and tests the arguments for thinking more in terms of teaching creative math thinking skills instead of the current practice of teaching a series of mostly algorithmic skills. In particular the brief argues for a new form of assessment reflecting students attempts at math thinking as opposed to an ability to demonstrate facility with applying algorithms.

The brief concludes that such changes could mean more students feel success in math, grow to enjoy their math and attain more useful math skills — math thinking skills.


WHAT’S the point of teaching and learning math?

For some time now, I have increasingly felt that a major issue in math education is that math teachers — plus those that create and administer the structures within which math teachers work — are not clear in giving good reasons to students about why it is so essential to study mathematics, exactly what is it we are all trying to achieve.

Current course structures, strict curriculum, standards, the emphasis on testing… all do not help teachers to reflect on or explain the purpose of what they do. Probably a majority of students, but certainly significant numbers, remain confused&hellp; and uninspired.

Part of the problem arises from the fact that just about all involved — except the students and the parents — are at least reasonably good at math, they get it, they enjoy it, they value it for its own sake, they see its value in the wider world. Few will have experienced the debilitating confusion, demoralization, despair that is the lot of substantial numbers of their students.

They see math education as turning out kids like themselves, mathematicians or one sort or another. This is fine when they encounter kids who get it, enjoy it, value it, etc.

This approach is compounded by political forces, which can include some mathematicians and their associations such as the NCTM, which view math education as little more than a utilitarian function at the service of corporate America.

For this latter group in particular, the maximum of math teaching is the delivery of a numerate workforce. And, it should be acknowledged, that is an aim of math teaching.


There are swathes of young people, children, who do not get it, do not enjoy it and do not see any value in their math education. Yet many of these young people may, indeed, have math thinking abilities. They will certainly need math thinking skills, math understanding, in the fast-changing world in which they will live.

Crudely put, these children are not always well served by mathematician math teachers. Or, are not well served by mathematician math teachers who do not reflect wider on issues of pedagogy or wider (social, political and philosophical) concerns about education in its widest sense.

One dire result is that math education in the public schools is often confined and restricted to training children to be numerate, with little more.

The emphasis on standards, state testing and curricula driven by textbook adoptions, militate against wider reflection. Math teachers simply have too much on their plates to reflect… or they do reflect, and then knuckle down.

Students themselves give the clue to solving the dilemma when they ask — and they always do — “when am I going to use this in real life?”

The frank answer is most are not going to use much of it at all, and certainly not the math that gets tested in multiple-choice computerized testing. One realistic answer to the question is that math education is attempting to teach abstract thinking skills, or problem-solving skills.

But that doesn’t go far enough. It’s not just about what and why students are learning&heliip; but also how they are learning. Indeed, the how can really be the embodiment of the what and the why.

Focussing on how children learn math may be the answer to the student-question. If the experience in the classroom is totally focussed on math thinking — with the student feeling in meaningful control of the progress, mentored Vygotsky-style within the zone of proximal development by adult guidance and peer collaboration — then the teaching pedagogy itself may give real meaning, be itself the explanation of what math education is all about.

And if the assessment supports this approach, helps guide it forward, focussing on helping the student to find their own thinking skills — rather than seeking to reward or punish — the student will not so much be learning math thinking skills but experiencing using math thinking skills.

The how becomes the what and the why.


The how does not include didactics, the pressure of tests and quizzes, points, grades.

The how does include peer collaboration, teacher as mentor, student control… and time for the child to play, think and work out their own solutions.

That can be done without technology. But there is no doubt that technology can really aid the approach, providing the classroom atmosphere and activities allow the child to get lost in their thought, explorations and discussions. Indeed, the creative use of technology almost demands a new approach to pedagogy in the math classroom.

It also demands a new approach to assessment…. still working on this!


Entry filed under: Technology in the classroom, Thoughts from the classroom, What's on the PiFactory blog....

Avis foregoes the restroom and expresses some geometry Relax… and watch the kids shoot some squid or crash a car

1 Comment Add your own

  • 1. thu thuat  |  July 4, 2009 at 3:00 pm

    Very impressive and worth reading.


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