Unleash the Mathematical Genius in You - Problem Solving Mastery
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The document outlines the importance of problem-solving mastery in mathematics, emphasizing critical thinking and systematic approaches to tackle mathematical challenges. It contrasts educational practices in Japan and South Africa, highlighting effective teaching strategies that promote engagement and reflection in problem-solving. The text also includes specific problem-solving steps and practical examples designed to enhance students' mathematical understanding and skills.
Unleash the Mathematical Genius in You - Problem Solving Mastery
- 1. 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: 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
- 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!
- 36. The End Contact us on: www.mathsgenius.co.za