Academic journal article
By Gervasoni, Ann
Australian Primary Mathematics Classroom , Vol. 5, No. 4
Numeracy is tied to human intentions. It is about effectively using mathematical insights, understandings and skills to solve the problems we face during the activities of the day. Problem solving is therefore inextricably linked to numeracy.
For a number of years in Australia, problem solving has been emphasised as an important aspect of mathematics education. It is argued that a problem solving approach makes mathematical learning more meaningful and relevant for students and promotes thinking, flexibility and creativity. A problem solving approach can therefore be viewed as an important way of enhancing students' numeracy development. However, some students are horrified when the words 'problem solving' are uttered in the classroom. Consider this scenario recently described by a colleague:
This term we have been focusing on the problem solving process. My P/1 children have participated in many input sessions where I have provided them with many strategies to solve problems e.g. draw pictures, write a number sentence, make a model, use a calculator, look for a pattern, work it out mentally. We have also worked in groups and individually to solve problems using all these strategies. My dilemma is that I have a student who has a fear of failure and starts to cry as soon as the words 'problem solving' are mentioned. She is a perfectionist and enjoys the comfort of structure, otherwise she feels threatened and withdraws from the grade. She becomes so overwhelmed and distressed that not even my assistance is any reassurance for her. She is a fairly bright student who is usually independent and able to cope with most of the classroom activities.
Questions to consider
What is your response to this dilemma?
What dilemmas have you faced when using a problem solving approach with your students?
What alternative course of action did you consider as a response to this dilemma?
Was the dilemma resolved?
Although most students thrive on problem solving, no doubt each of us recalls instances when students have reacted in a similar way to the student described above. It is alarming to discover that at age seven, a child can be so frightened of problem solving. Situations like this call on us to reflect on why we use a problem solving approach and whether such an approach does indeed enhance mathematical learning and numeracy development.
I believe that there is a great deal of value in using a problem solving approach to enhance numeracy development. However, for some students, problem solving involves a very different type of mathematical activity to that which they have experienced in the past. Often, mathematics tasks in classrooms consist of closed questions, which do not require complex thinking to solve, or any justification of the solution. Such questions often follow careful demonstrations and explanations by the teacher, are routine in nature and deal with aspects of mathematics pre-determined by the teacher. Hence, when students are faced with real problems, they feel quite lost. Such students need support to develop their understanding of mathematical activity.
The value of problem solving
Problem solving activities, involving problems that have no immediately obvious solution, can quite significantly change the nature and power of the mathematical thinking in which children engage at school. This, I believe, is the greatest value of problem solving.
Questions to consider
What do you believe is the greatest value of using a problem solving approach?
How does problem solving enhance mathematical thinking and numeracy development?
Presented below are six reasons to support my belief that mathematical problem solving enhances mathematical thinking and numeracy development.
1. Problem solving resembles the work of mathematicians
Problem solving in mathematics classrooms is closely aligned to the work of mathematicians. …