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CONFIDENTIAL
28 May 2016
This document is solely for the use of MathsGenius Leadership Institute personnel and Advisory Board. No part of
it may be circulated, quoted, or reproduced for distribution without prior written approval from MathsGenius
Leadership Institute..
Mathematical Thinking for Problem Solving
Success in a Network Society
Gaussian Mind Trading and Projects
T/A MathsGenius Leadership Institute
Phone: +2778 585 8937
Title: Chief Genius
Website: www.mathsgenius.co.za
Email: info@mathsgenius.co.za
Presenter: Edzai Conilias Zvobwo
MathsGenius Leadership Institute
Twitter: @edzaizvobwo
MathsGenius Leadership Institute 2016 ©
Educational reform for the social media age
http://www.bizcommunity.com/Article/196/371/129436.html
Platform thinking is not a pipe dream; what SA can learn from Google
http://www.bizcommunity.com/Article/196/659/124914.html
Throwing laptops at schools won't solve the maths problem
http://www.bizcommunity.com/Article/196/659/124682.html
Google Helpouts shuts down: Are live video tutorials viable?
http://www.bizcommunity.com/Article/196/659/124518.html
Maths not SA's innovation holy grail
http://www.bizcommunity.com/Article/196/498/124206.html
Media articles by Edzai Zvobwo
MathsGenius Leadership Institute 2016©
Hi, My name is Homo Naledi
I am the coolest guy of my era.
I am a genius I discovered fire
Hi , my name is Edzai
I am the coolest guy of my era.
I am keeping the fire burning.
“We started from the bottom now we are here…” – Drake (Musician)
Evolution
MathsGenius Leadership Institute 2016©
Maslow’s hierarchy of needs
MathsGenius Leadership Institute 2016 ©
MathsGenius Leadership Institute 2016©
Industrial Age
MathsGenius Leadership Institute 2016 ©
Dude, Google is overworking us
I am jumping ship to Uber
Digital Age
MathsGenius Leadership Institute 2016 ©
World’s biggest brands 2015
• Platform thinking is the art of conceptualising
and implementing inclusive places (physical or
virtual) where different actors can interact,
communicate, co-create and share value.
• A successful platform is able to
1. Attract users
2. Facilitate the exchange of information
3. Foster co-creation of value
Andrea Cocchi
What is Platform Thinking?
MathsGenius Leadership Institute 2016©
• Value is created upstream
• Knowledge is acquired from
teacher
• Lessons are designed to
meet specifications
• Value is given by restricted
consumption
PIPES PLATFORMS
• Value is co-created on the
spot
• Learners are co-creators of
knowledge
• Products emerge through
interaction
• Value is appreciated by
interaction
Pipes vs Platforms
Benefits
MathsGenius Leadership Institute 2015 ©
• Interoperability
• Scalability
• Measurability
• Greater autonomy and innovation
• Confidence boosting
• Collaborative participation
The internet has revolutionised the way we interact
and has turned the world into one big virtual
village.
Possible Challenges
MathsGenius Leadership Institute 2016 ©
• Adoption by all stakeholders
• Establishing spectrum of control
• Curriculum responsive ICT systems
design
• Cyber Bullying
• Exposure to pornography
• Too many distractions
Enabling innovation culture
• “Teachers might consider a managed process of
idea generation that rewards risk taking and
effectively harvests entrepreneurial and
mathematical ideas.” (Accenture 2013)
• Today, there’s a glut of highly creative but
underserved learners. Let’s harness their idealistic
passion before they turn grey, using social networks
and data sharing to create an open, interactive,
dynamic model of mathematics education. (Ethan
Perlstein)
• It's always a tremendous opportunity for us to tap
into our learner’s passion, creativity and their own
interpretation of mathematics (Ben & Jerry's – Do
the Flavor a Favor competition)
What is mathematical thinking?
MathsGenius Leadership Institute 2015 ©
Are you an architect if you:
•Dig trenches
•Pour concrete
•Bricklaying
•Carpentry
•Do Plumbing
•Do electrical wiring
•Roofing
What is mathematical thinking?
MathsGenius Leadership Institute 2016©
“Mathematical thinking is the equivalent of
architecting. You need all of those individual
house-building skills to build a house. But
putting those skills together and making use
of them requires a higher-order form of
thinking. You need someone who can design
the building and oversee its construction.” –
Keith Devlin
What is mathematical thinking?
MathsGenius Leadership Institute 2015 ©
Mathematical thinking is a whole way of
looking at things, of stripping them down to
their numerical, structural, or logical
essentials, and of analysing the underlying
patterns. Moreover, it involves adopting the
identity of a mathematical thinker.
How does a mathematician think?
Why mathematical thinking?
MathsGenius Leadership Institute 2014 ©
1.Prepares you for optimal complex problem
solving and decision making (e.g. knowledge
of key ratios and other magic numbers)
2.Builds resilience and confidence.
3.Promotes resourcefulness(effectual
thinking vs. causal thinking)
4.Helps you become more creative and
critical.
MathsGenius Leadership Institute 2016 ©
Thinking like a mathematician - Steps
1.Identify the correct problem to solve.
2.Understand the problem.
3.Devise a plan.
4.Carry out the plan.
5.Evaluate.
In 1994, Saunders Mac Lane, offered intuition, trial, error, speculation,
conjecture, proof as the sequence in which we come to understand and
develop mathematics.
Why school maths sucked
MathsGenius Leadership Institute 2015 ©
• A series of rigid rules and methods.
• No meaning in everyday life
• Timed exams
• No room for risk-taking and faith.
• Failure/wrong answer frowned upon
• Too much emphasis on neatness.
• Too abstract.
• Many teachers don’t appreciate the
subject
What can be improved?
MathsGenius Leadership Institute 2015 ©
• Emphasis on brain platform development.
• Mathematical modelling and application.
• Room for creativity, open-mindedness and
versatility.
• Design and art thinking + faith
• Embracing of failure as critical to learning
• Efficiency in problem solving
• Frameworks for achieving first principles
• Appreciation of maths as a language
What can be improved?
MathsGenius Leadership Institute 2015 ©
• Role playing e.g. Hackathon
• Root-cause analysis (Appreciation of
cause and effect)
• Presentation of problem solving as a
continuous process
• Framework driven success.
• Redefinition of genius
• Change in mathematical blueprint
Effectual thinking is a heuristic way of
reasoning that requires imagination and
risk-taking. And it this heuristic attribute
of the entrepreneurial reasoning that
makes mathematical training
advantageous to any aspiring
entrepreneur.
MathsGenius Leadership Institute 2016©
www.mathsgenius.co.za
MathsGenius Leadership Institute 2016©
“Maths is to the mind, what love is to
the heart” – Edzai Conilias Zvobwo
Bibliography
“Accenture Management Consulting (2013) “Corporate Innovation Is Within Reach: Nurturing and
Enabling an Entrepreneurial Culture”, downloadable from Accenture website
Andrea Cocchi (2012) “Platform Thinking - How to foster cooperative innovation and creativity”, New
York, USA
Bianchi M. (ed (2007) “Evolution of Consumption: Theories and Practices”, Bingley, U.K. : Emerald
Bianchi M. (ed.) (1998) “The Active Consumer Novelty and Surprise in Consumer Choice”, London:
Routledge
Choudary (2013) “Why Business Models Fail: Pipes vs. Platforms” Wired
http://www.wired.com/insights/2013/10/why-business-models-fail-pipes-vs-platforms/
Bonchek and Choudary (2013) “Three elements of a Successful Platform Strategy”, HBR blog
(blogs.hbr.org/2013/01/three-elements-of-a-successful-platform/‎CachedShare)
Evans, Hagiu, Schmalensee (2006) “Invisible Engines How Software Platforms Drive Innovation and
Transform Industries” The MIT Press Cambridge, Massachusetts, London, England
Dayport, Sviokla (1995) “Exploiting the Virtual Value Chain” Harvard Business Review 1995 (november-
december), pp. 75-85
Shapiro and Varian (1999) “The Standard War”, California Manegement Review , Vol. 41. No 2
Edzai Zvobwo (2010), The Mathematical Genius in You, Pretoria, South Africa
Edzai Zvobwo (2014), Spreading Mathematical Happiness, Johannesburg, South Africa
Keith Devlin (2011), Mathematical Thinking, USA

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Parent and Child Maths MasterClass: Part 1 - Johannesburg (Mathematical Thinking for Problem Solving Success in a Network Society)

  • 1. www.the1873network.org CONFIDENTIAL 28 May 2016 This document is solely for the use of MathsGenius Leadership Institute personnel and Advisory Board. No part of it may be circulated, quoted, or reproduced for distribution without prior written approval from MathsGenius Leadership Institute.. Mathematical Thinking for Problem Solving Success in a Network Society Gaussian Mind Trading and Projects T/A MathsGenius Leadership Institute Phone: +2778 585 8937 Title: Chief Genius Website: www.mathsgenius.co.za Email: info@mathsgenius.co.za Presenter: Edzai Conilias Zvobwo MathsGenius Leadership Institute Twitter: @edzaizvobwo
  • 2. MathsGenius Leadership Institute 2016 © Educational reform for the social media age http://www.bizcommunity.com/Article/196/371/129436.html Platform thinking is not a pipe dream; what SA can learn from Google http://www.bizcommunity.com/Article/196/659/124914.html Throwing laptops at schools won't solve the maths problem http://www.bizcommunity.com/Article/196/659/124682.html Google Helpouts shuts down: Are live video tutorials viable? http://www.bizcommunity.com/Article/196/659/124518.html Maths not SA's innovation holy grail http://www.bizcommunity.com/Article/196/498/124206.html Media articles by Edzai Zvobwo
  • 3. MathsGenius Leadership Institute 2016© Hi, My name is Homo Naledi I am the coolest guy of my era. I am a genius I discovered fire Hi , my name is Edzai I am the coolest guy of my era. I am keeping the fire burning. “We started from the bottom now we are here…” – Drake (Musician) Evolution
  • 4. MathsGenius Leadership Institute 2016© Maslow’s hierarchy of needs
  • 6. MathsGenius Leadership Institute 2016© Industrial Age
  • 7. MathsGenius Leadership Institute 2016 © Dude, Google is overworking us I am jumping ship to Uber Digital Age
  • 8. MathsGenius Leadership Institute 2016 © World’s biggest brands 2015
  • 9. • Platform thinking is the art of conceptualising and implementing inclusive places (physical or virtual) where different actors can interact, communicate, co-create and share value. • A successful platform is able to 1. Attract users 2. Facilitate the exchange of information 3. Foster co-creation of value Andrea Cocchi What is Platform Thinking?
  • 11. • Value is created upstream • Knowledge is acquired from teacher • Lessons are designed to meet specifications • Value is given by restricted consumption PIPES PLATFORMS • Value is co-created on the spot • Learners are co-creators of knowledge • Products emerge through interaction • Value is appreciated by interaction Pipes vs Platforms
  • 12.
  • 13. Benefits MathsGenius Leadership Institute 2015 © • Interoperability • Scalability • Measurability • Greater autonomy and innovation • Confidence boosting • Collaborative participation The internet has revolutionised the way we interact and has turned the world into one big virtual village.
  • 14. Possible Challenges MathsGenius Leadership Institute 2016 © • Adoption by all stakeholders • Establishing spectrum of control • Curriculum responsive ICT systems design • Cyber Bullying • Exposure to pornography • Too many distractions
  • 15. Enabling innovation culture • “Teachers might consider a managed process of idea generation that rewards risk taking and effectively harvests entrepreneurial and mathematical ideas.” (Accenture 2013) • Today, there’s a glut of highly creative but underserved learners. Let’s harness their idealistic passion before they turn grey, using social networks and data sharing to create an open, interactive, dynamic model of mathematics education. (Ethan Perlstein) • It's always a tremendous opportunity for us to tap into our learner’s passion, creativity and their own interpretation of mathematics (Ben & Jerry's – Do the Flavor a Favor competition)
  • 16. What is mathematical thinking? MathsGenius Leadership Institute 2015 © Are you an architect if you: •Dig trenches •Pour concrete •Bricklaying •Carpentry •Do Plumbing •Do electrical wiring •Roofing
  • 17. What is mathematical thinking? MathsGenius Leadership Institute 2016© “Mathematical thinking is the equivalent of architecting. You need all of those individual house-building skills to build a house. But putting those skills together and making use of them requires a higher-order form of thinking. You need someone who can design the building and oversee its construction.” – Keith Devlin
  • 18. What is mathematical thinking? MathsGenius Leadership Institute 2015 © Mathematical thinking is a whole way of looking at things, of stripping them down to their numerical, structural, or logical essentials, and of analysing the underlying patterns. Moreover, it involves adopting the identity of a mathematical thinker. How does a mathematician think?
  • 19. Why mathematical thinking? MathsGenius Leadership Institute 2014 © 1.Prepares you for optimal complex problem solving and decision making (e.g. knowledge of key ratios and other magic numbers) 2.Builds resilience and confidence. 3.Promotes resourcefulness(effectual thinking vs. causal thinking) 4.Helps you become more creative and critical.
  • 20. MathsGenius Leadership Institute 2016 © Thinking like a mathematician - Steps 1.Identify the correct problem to solve. 2.Understand the problem. 3.Devise a plan. 4.Carry out the plan. 5.Evaluate. In 1994, Saunders Mac Lane, offered intuition, trial, error, speculation, conjecture, proof as the sequence in which we come to understand and develop mathematics.
  • 21. Why school maths sucked MathsGenius Leadership Institute 2015 © • A series of rigid rules and methods. • No meaning in everyday life • Timed exams • No room for risk-taking and faith. • Failure/wrong answer frowned upon • Too much emphasis on neatness. • Too abstract. • Many teachers don’t appreciate the subject
  • 22. What can be improved? MathsGenius Leadership Institute 2015 © • Emphasis on brain platform development. • Mathematical modelling and application. • Room for creativity, open-mindedness and versatility. • Design and art thinking + faith • Embracing of failure as critical to learning • Efficiency in problem solving • Frameworks for achieving first principles • Appreciation of maths as a language
  • 23. What can be improved? MathsGenius Leadership Institute 2015 © • Role playing e.g. Hackathon • Root-cause analysis (Appreciation of cause and effect) • Presentation of problem solving as a continuous process • Framework driven success. • Redefinition of genius • Change in mathematical blueprint
  • 24. Effectual thinking is a heuristic way of reasoning that requires imagination and risk-taking. And it this heuristic attribute of the entrepreneurial reasoning that makes mathematical training advantageous to any aspiring entrepreneur. MathsGenius Leadership Institute 2016©
  • 25. www.mathsgenius.co.za MathsGenius Leadership Institute 2016© “Maths is to the mind, what love is to the heart” – Edzai Conilias Zvobwo
  • 26. Bibliography “Accenture Management Consulting (2013) “Corporate Innovation Is Within Reach: Nurturing and Enabling an Entrepreneurial Culture”, downloadable from Accenture website Andrea Cocchi (2012) “Platform Thinking - How to foster cooperative innovation and creativity”, New York, USA Bianchi M. (ed (2007) “Evolution of Consumption: Theories and Practices”, Bingley, U.K. : Emerald Bianchi M. (ed.) (1998) “The Active Consumer Novelty and Surprise in Consumer Choice”, London: Routledge Choudary (2013) “Why Business Models Fail: Pipes vs. Platforms” Wired http://www.wired.com/insights/2013/10/why-business-models-fail-pipes-vs-platforms/ Bonchek and Choudary (2013) “Three elements of a Successful Platform Strategy”, HBR blog (blogs.hbr.org/2013/01/three-elements-of-a-successful-platform/‎CachedShare) Evans, Hagiu, Schmalensee (2006) “Invisible Engines How Software Platforms Drive Innovation and Transform Industries” The MIT Press Cambridge, Massachusetts, London, England Dayport, Sviokla (1995) “Exploiting the Virtual Value Chain” Harvard Business Review 1995 (november- december), pp. 75-85 Shapiro and Varian (1999) “The Standard War”, California Manegement Review , Vol. 41. No 2 Edzai Zvobwo (2010), The Mathematical Genius in You, Pretoria, South Africa Edzai Zvobwo (2014), Spreading Mathematical Happiness, Johannesburg, South Africa Keith Devlin (2011), Mathematical Thinking, USA