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Problem Solving as a way of Teaching

- Presented by
- CW

What do you mean by problem solving?

MiNZC

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 page 11

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.

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 childrens tool box. - Identify the knowledge that should be being added

to the childrens 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 (www.nzmaths.co.nz)
- NZAMT Maths Week (10th 16th 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.