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Problem Solving Mastery using Mathematics

Gaussian Mind Trading and Projects

T/A MathsGenius Leadership Institute

Title: Chief GeniusPhone: +2711 073 1776Email: info@mathsgenius.co.zaWebsite: www.mathsgenius.co.za

Presenter: Edzai Conilias Zvobwo

MathsGenius Leadership Institute

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

ContentsWhat 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

What is mathematics?

ContentsWhat 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

ContentsWhat 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

ContentsWhat 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

Open Minded Focused

Systematic and structured approach to problem solving

Die hard attitude/persistenceCreativity

Not polluting mind with garbageInquisitive like childrenPassionate and driven

Pursuing truthArt of visualisation

ConfidentSelfless

Concentration

ContentsWhat 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

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)

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 classStudents practice on their own while the teacher assists individual students

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

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

outcome

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?

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

Carrying out the Plan Implement the strategies selected

when devising a planCheck each step of your planWrite all necessary steps to your

plan (keeping records)

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?

ContentsWhat 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

Working on It – Carpet ProblemHello 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

Are you a…….

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.

The answer is…

Well done!

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.

The answer is…

Well done!

You are a Maths

Detective!

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