Problem Solving as a way of Teaching Presented by CW

What do you mean by problem solving?

Mathematics needs to be taught and learned within the context of problems which are meaningful to the students and which lead to an understanding of the way mathematics is applied in the world beyond school. MiNZC

The solutions to problems worth solving seldom involve only one item of mathematical understanding or only one skill. Rather than remembering the single correct method, problem solving requires students to search the information for clues and to make connections to the various pieces of mathematics and other knowledge and skills they have learned. Open ended problems encourage thinking rather than mere recall. Closed problems develop only a limited range of skills. They encourage memorisation of routine methods. While fluency with basic techniques is important, such routines only become useful tools when students can apply them to realistic problems. MiNZC page 11

Put simply!  Problem solving in mathematics is about the application of mathematical knowledge.

What knowledge is in the tool box? Look back at the framework. For each stage:  Identify the knowledge that should already be in the children’s tool box.  Identify the knowledge that should be being added to the children’s tool box

There is too much reading! Literacy in Numeracy  Do you read mathematical problems as part of your reading programme?  Problem solving requires the application of literacy skills.

What is a meaningful context?  Not necessarily a real life situation – but recognise one when it arises – it may be incidental.  Selected by the teacher – Figure it Out, Mini Project, NZ Maths, other  Selected by the pupil – often arises as the result of solving a problem selected by the teacher, what if……..?

“Is it an add Miss?”  Often referred to as word problems.  These types of problems require the solver to choose what mathematical operation to apply.  To do this, the solver needs to understand what the question is asking and then select an appropriate operation.

Word Problems  Result unknown problems.  Change unknown problems.  Start unknown problems.  Mixed operation problems. The problem to solve is which operation do you need to use? Can you solve the problem in more than one way? (remember addition is the opposite of subtraction and multiplication is the opposite of division)

Number Problems  Often referred to as Investigations  How many different answers can you get from…….?  How many different strategies could you use to solve…….  Can you find a pattern?

Extended Mathematical “project”  Figure it Out Theme Books  Pearson Primary Maths Mini Projects  NZ Maths website (  NZAMT Maths Week (10 th – 16 th August)

Exclusive to Maths?  English: Critical thinking  Science: Investigation  Social Studies: Inquiry  Problem Solving is the Process of Mathematics

Curriculum Integration  Learning to transfer the process skills from one area of the curriculum to another.  Life is not organised into curriculum areas.  Knowledge may “belong” to a curriculum area but learning to use the knowledge does not occur in isolation.  Learning the processes does not occur in one lesson, one week etc, It occurs over time.

Assessing the Processes  What are you assessing?  A specific problem solving skill (e.g draw a table)  Getting the answer right. (if there is a answer)  The ability to solve problems – attitude, skills, knowledge and strategies.