Presentation on platform thinking in maths education to South African maths teachers at the 2015 AMESA conference held on the 1st of July 2015 at the University of Limpopo.

1. CONFIDENTIAL
This document is solely for the use of MathsGenius Leadership Institute personnel and Advisory Board. No part of
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Leadership Institute..
Platform Thinking is not a pipe dream: What South
Africa can learn from Google
Gaussian Mind Trading and Projects
T/A MathsGenius Leadership Institute
Phone: +2778 585 8937
Title: Chief Genius
Website: www.mathsgenius.co.za
Email: edzai@mathsgenius.co.za
Presenter: Edzai Conilias Zvobwo
MathsGenius Leadership Institute
Twitter: @edzaizvobwo
AMESA CONGRESS – LIMPOPO - 01 July 2015

2. What is mathematical thinking?
MathsGenius Leadership Institute 2015 ©
Are you an architect if you just:
Dig trenches?
Pour concrete?
Bricklaying?

3. What is mathematical thinking?
MathsGenius Leadership Institute 2015 ©
“Mathematical thinking is the equivalence of
architecture. You need all of the 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

4. What is mathematical thinking?
MathsGenius Leadership Institute 2015 ©
From a Reductionist perspective:
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.

5. 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.

6. MathsGenius Leadership Institute 2015 ©
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.

7. Why school maths sucks
MathsGenius Leadership Institute 2015 ©
• A series of rigid rules and methods.
• No meaning in everyday life for learners
• 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 fully

8. What can be improved?
MathsGenius Leadership Institute 2015 ©
• Emphasis on 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

9. What is Platform Thinking?
• Platform thinking is the art of conceptualising
and implementing inclusive places (physical or
virtual) where different actors can interact,
communicate, co-create and share …
• A successful platform is able to
1. Attract users
2. Facilitate the exchange of information
3. Foster co-creation of value
Andrea Cocchi

10. Popular Platforms

11. • Value is created upstream
• Knowledge is acquired from
teacher
• Lessons are designed to
meet specifications
• Value is given by restricted
consumption
Pipes and Platforms
PIPES PLATFORMS
• Value is co-created on the
spot
• Learners are co-creators of
knowledge
• Products emerge through
interaction
• Value is appreciated by
interaction

12. Enabling innovation culture
• “Companies (teachers) might consider a managed
process of idea generation that rewards risk taking and
effectively harvests entrepreneurial (mathematical)
ideas.” (Accenture 2013)
• Today, there’s a glut of highly trained (creative) but
underemployed scientists (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) basic life
sciences research. (Ethan Perlstein)
• It's always a tremendous opportunity for us to tap into our
fan's (learner’s) passion, creativity and their own
interpretation of "Peace, Love and Ice Cream.”
(mathematics) (Ben & Jerry's – Do the Flavor a Favor
competition)

13. What can be improved?
MathsGenius Leadership Institute 2015 ©
• Role playing e.g. Hackathon
• Root-cause analysis (Appreciation of
cause and effect)
• Use of Blended learning
• Presentation of problem solving as a
continuous process
• Framework driven success.
• Redefinition of genius
• Change in mathematical blueprint

14. MATHSGENIUS QUESTION &
ANSWER PORTAL
www.mathsgenius.co.za
MathsGenius Leadership Institute 2015 ©

15. “Maths is to the mind, what love is to
the heart” – Edzai Conilias Zvobwo
MathsGenius Leadership Institute 2015 ©

16. 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