Problem Solving Mastery using Mathematics is a presentation by Edzai Zvobwo revealing best ways of learning and teaching mathematics whilst keeping learners engaged.

1. 29 August 2015
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Problem Solving Mastery using
Mathematics
Gaussian Mind Trading and Projects
T/A MathsGenius Leadership Institute
Title: Chief Genius
Phone: +2711 073 1776
Email: info@mathsgenius.co.za
Website: www.mathsgenius.co.za
Presenter: Edzai Conilias
Zvobwo
MathsGenius Leadership Institute

2. MGLI Projects
MathsGenius Leadership Institute 2014 ©
MGLI Projects
Information
dissemination
Training Support
Spreading the word
that Everyone can
pursue STEM subjects
and careers
regardless of gender.
Promoting critical
thinking
Imparting skills on how
to succeed in STEM
and its application in
life
Enhancing learners
chances of success
through various
support mechanisms

3. Contents
 What is mathematics?
 Why do we study maths?
 What are your mathematical
experiences?
 What did geniuses have and do?
 What are the problem solving
frameworks?
 Practical Problem Solving

4. What is
mathematics?

8. Contents
 What is mathematics?
 Why do we study maths?
 What are your mathematical
experiences?
 What did geniuses have and do?
 What are the problem solving
frameworks?
 Practical Problem Solving

10. Contents
 What is mathematics?
 Why do we study maths?
 What are your mathematical
experiences?
 What did geniuses have and do?
 What are the problem solving
frameworks?
 Practical Problem Solving

16. Contents
 What is mathematics?
 Why do we study maths?
 What are your mathematical
experiences?
 What did geniuses have and do?
 What are the problem solving
frameworks?
 Practical Problem Solving

18. Open Minded
Focused
Systematic and structured approach to
problem solving
Die hard attitude/persistence
Creativity
Not polluting mind with garbage
Inquisitive like children
Passionate and driven
Pursuing truth
Art of visualisation
Confident
Selfless
Concentration

19. Contents
 What is mathematics?
 Why do we study maths?
 What are your mathematical
experiences?
 What did geniuses have and do?
 What are the problem solving
frameworks?
 Practical Problem Solving

20. Important mathematics
concepts and procedures can
best be taught through
problem solving, that is, tasks
or problems can and should
be posed that engage
students in thinking about and
developing the important
mathematics they need to
learn. Van de Walle (2001, p.40)

21. Japan vs. South Africa
Steps of a typical
Japanese eight-grade
mathematics lesson:
Teacher poses a complex
though-provoking problem.
Students struggle with the
problem
Various students present
ideas or solutions to the
class.
Class discusses the
various solution methods.
The teacher summarizes
the class’ conclusions.
Students practice similar
problems
Steps of typical South
African eight-grade
mathematics lesson:
Teacher instructs student
in a concept or skill
Teacher solves example
problems with class
Students practice on their
own while the teacher
assists individual students

22. Developing a Problem Solving
Lesson
Before
During
After
Getting Ready
Get students mentally ready to work on the task
Be sure all expectations for products are clear
Students Work
Let go Provide hints
Listen carefully Observe and
assess
Classroom Discourse
Accept student solutions with evaluation
Conduct discussions as student justify and
evaluate results and methods

23. Problem Solving Steps
 Understand the problem
 Devise a plan
 Carry out the plan
 Reflecting back on the process and
outcome

24. Understanding the Problem
 Can you state the problem in your
own words?
 What are you trying to find or do?
 What are the unknowns?
 What information can you obtain from
the problem?
 What information is not needed or is
missing?

25. Devising a Plan
 Look for a plan
 Look at a similar problem to determine if
the same strategies can be used.
 Make a table
 Make a diagram
 Use guess and check
 Work backward

26. Carrying out the Plan
 Implement the strategies selected when
devising a plan
 Check each step of your plan
 Write all necessary steps to your plan
(keeping records)

27. Reflecting (Looking back)
 Check the results in the original problem
 Look for another method for solving the
problem.
 Ask does your answer make sense, is it
reasonable?

28. Contents
 What is mathematics?
 Why do we study maths?
 What are your mathematical
experiences?
 What did geniuses have and do?
 What are the problem solving
frameworks?
 Practical Problem Solving

29. 29
Working on It – Carpet Problem
Hello Grade 4 students,
The carpet you have been asking for
arrives tonight. Please clear a space
in your room today that will fit this
new carpet. The perimeter of the
carpet is 12 m.
From your principal
1. What is the problem to solve?
2. Why is this problem a problem?
3. Show two different ways to
solve this carpet problem.
4. How do you know we have all
the possible solutions?
A Guide to Effective Instruction, Vol. 2 – Problem Solving, pp. 18–25

30. Are you a…….

31. Sam collects football cards.
How many more does he need to
Complete the set?
There are 10 to collect.
The cards cost £1 each.
On Friday Pat gave him 2 more.
On Monday he bought 5.

32. The answer is…
Well done!

33. In a tube of Smarties there are brown,
red, yellow and green sweets.
How many are brown?
There are 25 sweets in the tube.
There are twice as many red as green.
There are 2 less green than yellow.
There are 6 yellow Smarties.

34. The answer is…
Well done!

35. You are a
Maths
Detective!

36. The End
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