During October 10 -17, 2017 a global phenomenon occurred. It was the world’s inaugural Global Math Week.
Over a million students and teachers from 168 different countries and territories experienced the uplifting joy of Exploding Dots. All was grassroots. All was volunteer. And all was propelled by a beautiful global community educators and math lovers simply wanting to share the joy and wonder of meaningful mathematics.
From our survey:
96.8% of teachers agreed or strongly agreed that Exploding Dots helped students see mathematics as more approachable, 96.6% as more enjoyable, 96.1% as making sense, and 93.1% as helping students be more confident in mathematics.
75.5% of teachers said that Exploding Dots changed their own perception of mathematics in some way with 97.7% agreeing or strongly agreeing that Exploding Dots made mathematics more enjoyable, 97.3% as more approachable, and 96.0% as more understandable.
You too can enjoy the wonders of Exploding Dots, here, in this course, or with the web app powered by Scolab.
Scroll down to see and access the Exploding Dots chapters. Play with them at your leisure. (Warning: When you start one, you won’t want to stop!
It all begins with a story that isn’t true:
When I was a young child I invented a machine (not true) that was nothing more than a series of boxes that could hold dots. And these dots would, upon certain actions, explode. And with this machine, in this non-true story, I realized I could explain true things! In one fell swoop I explained all the mathematics of arithmetic I learnt in grade school (true), all of the polynomial algebra I was to learn in high-school (true), elements of calculus and number theory I was to learn in university (true), and begin to explore unanswered research questions intriguing mathematicians to this day (also true)!
Let me share this story with you. See how simple and elegant ideas connect to elegant and profound ideas in mathematics as a whole. See how these ideas will COMPLETELY REVOLUTIONIZE your thinking of school arithmetic and algebra and beyond! This mathematical story will knock your socks off!
On a final note, here’s a fun wordless animation. It’s a teaser for the course. Can you figure out what is going on?
|1.0 EXPERIENCE ONE: The Machines|
|1.2 The \(1 \leftarrow 2\) Machine|
|1.3 Other Machines|
|1.4 The \(1 \leftarrow 10\) Machine|
|1.5 Wild Explorations|
|2.0 EXPERIENCE TWO: Insight|
|2.2 Explaining the \(1 \leftarrow 2\) Machine|
|2.3 Explaining More Machines|
|2.4 We Speak \(1 \leftarrow 10\) Machine|
|2.5 Wild Explorations|
|3.0 EXPERIENCE THREE: Addition and Multiplication|
|3.3 (Optional) The Traditional Algorithm|
|3.5 (Optional) Multiplication by 10|
|3.6 (Optional) Long Multiplication|
|3.7 Wild Explorations|
|4.0 EXPERIENCE FOUR: Subtraction|
|4.2 Piles and Holes; Dots and Antidots|
|4.4 (Optional) The Traditional Algorithm|
|4.5 Wild Explorations|
|5.0 EXPERIENCE FIVE: Division|
|5.3 (Optional) Division by 10|
|5.5 (Optional) Deep Explanation|
|5.6 (Optional) The Traditional Algorithm|
|5.7 Wild Explorations|
|6.0 EXPERIENCE SIX: All Bases, All at Once: Polynomials|
|6.2 Division in Any Base|
|6.3 A Problem!|
|6.5 (Optional) Remainders|
|6.6 (Optional) The Remainder Theorem|
|6.7 (Optional) Multiplying, Adding, and Subtracting Polynomials|
|6.8 Wild Explorations|
|7.0 EXPERIENCE SEVEN: Infinite Sums|
|7.2 Infinite Sums|
|7.3 (Optional) Should we believe infinite sums?|
|9.0 EXPERIENCE NINE: Weird and Wild Machines|
|9.2 Base One-and-a-half?|
|9.3 Does Order Matter?|
|9.4 Base Two? Base Three?|
|9.5 Going Really Wild|
|10.0 MAKE SPACE with EXPLODING DOTS|
|10.1 Invent. Create. Enjoy!|
|11.0 Kids Explain the Math to Kids|
|11.1 Kid Videos by Kids for Kids|
|100.0 Where did these ideas come from?|
|100.1 To answer …|
|Return to List of Courses|