Archive for the Research and Projects Category

The making of Pixar in a Box

Posted in Research and Projects with tags , , , , , on September 25, 2015 by Brit Cruise


In early 2014 Tony DeRose (Senior Scientist and Lead of the Research Group at Pixar Animation Studios ) and Elyse Klaidman (Director of Pixar University and Archives) approached Khan Academy with an idea. They wanted to answer a question everyone asks in school at some point: “Why do I need to learn this?” Previously, Tony had given talks which try and engage children in mathematics by demonstrating how math lives at the intersection of design and technology at Pixar. It was clear that you could motivate kids to learn math and science by showing them how concepts they encounter in school are used at Pixar to make movie magic… Continue reading

Markov Chains: The link between Plato, Bernoulli, Markov & Claude Shannon

Posted in Research and Projects, Video / Theatre with tags , , , , , , , , on June 27, 2013 by Brit Cruise

Why did Bernoulli mention Plato’s Theory of Forms in Ars Conjectandi? What does this have to do with free will?

This video is a broad introduction to the Weak Law of Large Numbers, the Central Limit Theorem and how it all led to Markov Chains…

Next, play around with this interactive, graphical Markov simulator!

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3 decades later, Claude Shannon famously applied this idea to generate “english looking” messages in his Mathematical Theory of Communication:

Conditional Probability (Bayes Theorem) Visualized

Posted in Research and Projects, Video / Theatre with tags , , , on January 24, 2013 by Brit Cruise

It’s powerful to understand how conditional probability can be visualized using decision trees. I wanted to create an alternative to most explanations which often start with many abstractions. I was drawn to the idea of looking at the back pages of a choose-your-own-adventure book, and deciding how you could have arrived there. Here I present a visual method using a story involving coins… allowing you to decide how to formalize. Once we grow tired of growing trees, we may ask the key questions: how can we speed up this process?:

This is followed by a game I designed (built by Peter Collingridge) which introduces how branches can be weighted instead of counted.

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Thanks to Kalid Azad for reviewing this lesson.

Information Theory, a practical approach

Posted in Research and Projects, Video / Theatre with tags , , , , , on January 15, 2013 by Brit Cruise

In order to understand the subtle conceptual shifts leading to the insights behind Information Theory, I felt a historical foundation was needed. First I decided to present the viewer with a practical problem which future mathematical concepts will be applied to. Ideally this will allow the viewer to independently develop key intuitions, and most importantly, begin asking the right kind of questions:

I noticed the viewer ideas for how to compress information (reduce plucks) fell into two general camps. The first are ways of using differentials in time to reduce the number of plucks. The second are ways of making different kind of plucks to increase the expressive capability of a single pluck. Also, hiding in the background is the problem of what to do about character spaces. Next I thought it would be beneficial to pause and follow a historical narrative (case study) exploring this problem. My goal here is two congratulate the viewer for independently realizing a previously ‘revolutionary’ idea, and at the same time, reinforcing some conceptual mechanics we will need later. It was also important to connect this video to previous lessons on the origins of our alphabet (a key technology in our story), providing a bridge from proto-aphabets we previously explored….

This is followed by a simulation which nails down the point that each state is really a decision path

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Observational Science – Teaching without words

Posted in Research and Projects with tags , , , , , on November 8, 2012 by Brit Cruise

Lately I have been thinking about ways of blending various aspects of history into math/science lessons on Khan Academy. The traditional model of: lesson, experiment, lesson, experiment makes sense – though it’s important to do the experiment part in a natural way. All experiments begin with observations in the real world. So, I’m going to make a series of short silent videos which reenact observations made by our ancestors and first inventions/technologies which result.

Later on, lessons using modern technology can reference these videos (Karl mentioned we could call them Building Blocks) as experimental foundations everyone can understand. In this case I begin with a simple video of someone finding rocks in a river with seemingly magical properties. Then these properties are harnessed to create new things. This will lead us into electromagnetism, and more modern inventions such as the telegraph. Check out the progress here

Magic in the classroom: teaching our ancestors

Posted in Research and Projects with tags , , , , on July 18, 2012 by Brit Cruise

When I have an idea for how to teach something I always ask myself if it’s the best way to teach a distant, yet equally intelligent, ancestor…

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Khan Academy Labs: Exploratory Exercises

Posted in Research and Projects with tags , , on March 30, 2012 by Brit Cruise

One of the most exciting aspects of joining the Khan Academy team, was the potential to explore new ways of integrating video and software. Continue reading