29 August 2015 This document is owned by MathsGenius Leadership Institute. No part of it may be circulated, quoted, or reproduced for distribution without prior written approval from MathsGenius Leadership Institute.. Problem Solving Mastery using Mathematics Gaussian Mind Trading and Projects T/A MathsGenius Leadership Institute Title: Chief Genius Phone: +2711 073 1776 Email: [email protected]Website: www.mathsgenius.co.za Presenter: Edzai Conilias Zvobwo MathsGenius Leadership Institute
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Unleash the Mathematical Genius in You - Problem Solving Mastery
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29 August 2015This document is owned by MathsGenius Leadership Institute. No part of it may be circulated, quoted, or reproduced for distribution without prior written approval from MathsGenius Leadership Institute..
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.