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Problem Solving as a way of Teaching

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Problem Solving as a way of Teaching Presented by CW MiNZC MiNZC page 11 Put simply! Problem solving in mathematics is about the application of mathematical knowledge. – PowerPoint PPT presentation

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Title: Problem Solving as a way of Teaching


1
Problem Solving as a way of Teaching
  • Presented by
  • CW

2
What do you mean by problem solving?
3
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.
4
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.
5
Put simply!
  • Problem solving in mathematics is about the
    application of mathematical knowledge.

6
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

7
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.

8
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..?

9
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.

10
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)
11
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?

12
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)

13
Exclusive to Maths?
  • English Critical thinking
  • Science Investigation
  • Social Studies Inquiry
  • Problem Solving is the Process of Mathematics

14
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.

15
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.
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