Driving Creativity Through Mathematics

These videos introduce the philosophy of the course
To benefit from this course, participate-be active; answer questions; think.
Stories illustrate the power of understanding deeply and of making and learning from mistakes.

This section of the course uses puzzles to introduce strategies of thinking and creating ideas.
By the end of this part of the course, students will know that the way to finding creative solutions to difficult challenges is to use your mind in effective ways.
Each of the 5 Elements of Effective Thinking are described and their use is illustrated through the puzzles.

Numbers let us understand the world with more nuance and precision
Even the most basic aspects of numbers, like how to write them, are great examples of human creativity and clarity of thought
Simple counting leads to insights, such as the fact that every person is unique
Estimation is a habit that can open doors of insight and nuance
The Pigeonhole Principle allows us to deduce insights about the world that are unexpected, such as the fact that there must be two people on Earth who have exactly the same numbers of hairs on their bodies
The Fibonacci numbers come from looking at nature and abstracting a pattern
Exploring number patterns illustrates a creative strategy for exploring and creating ideas
Seeing how to develop the incredibility important idea of numbers shows you how you can create and explore ideas on your own.

The mathematical concept of infinity is a wonderful example of taking a basic idea like counting and extending and abstracting it to imagine creative new concepts that are fascinating
The core method is to look at the familiar idea of everyday counting and finding the essence of that process
We see that the idea of one-to-one correspondence is at the heart of counting
When we explore the consequences of applying the simple idea of one-to-one correspondence to infinite collections, whole new worlds open up
Thought experiments lead the way
Struggle is part of learning. Struggling with ideas is part of the way to make them meaningful and permanent.
One of the greatest strategies for creativity is to make mistakes and learn from them. Mistakes are great guides to insight and creativity.
Old ideas are perhaps the best source of creative new ideas. Think about how to modify the familiar to create the new.
Following the consequences of ideas leads from new idea to new idea.
If you can see how to tame infinity, your possibilities are limitless.

Creating a concept through analogy
The mantra for the creation of the fourth dimension is 'retreat'
For any question about the fourth dimension, don't work on it-retreat to the analogous question about lower dimensions and then teach yourself how to extend the idea
View the familiar in unfamiliar ways
Getting accustomed to slices
Playing with consequences of the fourth dimension
Flatland-looking at the unfamiliar, but simpler, 2-dimensional world
A 4D cube-creating it by analogy
Unfolding the boundary of a 4D cube
The fourth dimension is a great example of how to create and explore ideas.

Course Curriculum