The question arises for the modern Mathematics teacher: “Do Maths students need to be problem solvers or simply be able to recognise a context and remember the process/algorithm to get an answer?”
Why has this question even arisen?
In the late 1980s in Australia, a large international company was looking to employ university graduates with problem solving skills. Of course, their first port of call was maths graduates. After all, don’t maths students solve problems? The answer to that question that the international company found was “no”! They simply recognised the context of the “problem” and applied an algorithm. What the company did find was that Arts graduates were indeed better problem solvers than maths students. They could think “outside the box” more effectively than the Maths graduates.
Around this time syllabus writers in our education system were looking at the Mathematics curriculum. With advent of computers and scientific calculators, much of what was taught in school maths was redundant. The world of maths had expanded dramatically, particularly in statistics and probability, areas that were part and parcel of the modern world. Students were staying at high school longer and many could not see the relevance of Mathematics to their life. Many students were not maths-logic thinkers but learnt in different ways to traditionally “good” maths student.
Bearing all these issues in mind, syllabus writers began the task of modernising the Mathematics syllabuses. This involved a number of steps. They included:
• Removing items from the syllabus that were no longer relevant e.g. using logarithms for calculation
• Introducing new teaching pedagogues
• Introducing the use of technology
• Introducing the idea that problem solving should look at using Mathematics in unfamiliar contexts
• Introducing new content areas e.g. earth geometry and expanding areas such as statistics and probability
• And, finally, introducing the concept of alternate assessment techniques.
For most teachers of Mathematics, these syllabus changes created a need for professional development not only with new content material but with the new pedagogue; the use of technology and the new approaches to the assessment of Mathematics. Chalk and talk lesson, maths-logic thinking, lots of practice exercises and formal examinations were no longer to be the only framework of Mathematics teaching.
But, at this point, let me return to the question raised in paragraph one above.
Do Maths students need to be problem solvers or simply be able to recognise a context and remember the process/algorithm to get an answer?
In the preceding paragraphs, I have detailed why this question has arisen. It is my contention that many Maths students can be educated to do both.
Before a student can be a problem solver of real life problems in unfamiliar contexts, he or she must know and be able to use effectively all the skills they learn from their teachers. You can’t solve problems without the knowledge of the skills required to solve them. This should always be the starting point for the teaching of problem solving.
What students and perhaps some inexperienced teachers don’t realise is that the solution of an exercise based on a new topic is in itself solving a problem in an unfamiliar context. So the student has begun their problem solving career without really knowing it.
Many students think Maths is hard. It is important that teachers instil the idea that every exercise must be treated as “simple” initially. That way, students will at least make a start on solving the question.
Once teachers have students understanding that idea, they can teach students a variety of approaches on how to solve problems.
The final point that needs to be made is that problem solving exercises in unfamiliar contexts must be a regular part of most lessons, even if it is only a five minute exercise. It must not be a process saved to be done prior to an examination. That way, the teacher lessens the fear that these exercises bring to the student.in an examination situation
Once teachers adopt these sorts of approaches, the answer to the question raised at the beginning of this article is “NO”!