Last month I learned about a terrific online random walk program to share with kids:
Here’s our project with that program:
Sharing a great random walk program with kids
Last week Dirk Brockmann shared a new program:
Today I showed the boys Brockmann’s original random walk program followed by the new “Anomalous Itinerary” program to see what the boys would think about them.
My older son played with the programs first. Here are his thoughts looking at the original program – he thought the this random walk would be a good description of a particle moving through air:
And here are his thoughts on the new program. One thing that I found really interesting is that he found it difficult to describe the difference between what he was seeing here vs the prior random walk program:
Next up was my younger son. Here are his thoughts on the original program – he thought this random walk would be a good description of how a chipmunk moves.
Here are his thoughts on the new program. He initially thought this was the same as the Gaussian random walk program, but was eventually able to describe the difference:
These programs are definitely fun to share with kids. The “Lévy Flight” paths are definitely not intuitive and very different from the Gaussian random walks. It is really interesting to hear kids trying to find the words to describe what they are seeing.
I saw a fun random walk program shared by Steven Strogatz yesterday:
Today I shared the program with the boys. It has 4 different types of random walks to explore. For each one I asked the boys what they thought would happen. At the end we looked at all 4 simultaneously.
Sorry that the starting videos are so blue – I didn’t notice that while we were filming (and didn’t do anything to fix it, so I don’t know why the last two vides are better . . . .)
Also, following publication, I learned the author of the program we were playing with:
Here’s the introduction and the first random walk – in the walk we study here, the steps are restricted to points on a triangular lattice:
In the next random walk, the steps were chosen from a 2d Gaussian distribution. It is interesting to hear what the boys thought would be different:
Now we studied a random walk where the steps all have the same length, but the direction of the steps was chosen at random:
The last one is a walk in which the steps are restricted to left/right/up/down. They think this walk will look very different than the prior ones:
Finally, we looked at the 4 walks on the screen at the same time. They were surprised at how similar they were to each other:
Definitely a fun project, and a really neat way for kids to explore some basic ideas (and surprises!) in random walks.
A week or so ago my older son did a short project on random walks out based on a page in Patters of the Universe:
Returning to Patterns of the Universe
By coincidence that week Kelsey Houston-Edwards’s new video was about random walks. So, we watched her video after that project:
Today my younger son is sick and wasn’t up to participating in a project. So, I thought it would be fun to revisit the random walk project and dive in a little deeper since my older son was a little more familiar with that topic.
I started by asking him what he remembered about random walks from the prior project and from the PBS Infinite Series video. One thing that he remembered is that 2d random walks do tend to return to where they started, but 3-d ones tend not to.
We started looking at specific random walks by studying a 1-dimensional random walk. We created a random walk by rolling dice and didn’t get quite what we were expecting, but that result led to a fun conversation:
In the last video we got more even numbers than we were expecting, so we decided to continue on to see if the walk would return to 0. Obviously we kept rolling even numbers . . . .
Next we moved on to studying a 3d random walk (and, of course, now rolled lots of odd numbers 🙂 )
We created the 3d random walk with snap cubes and it was pretty neat to see the shape that emerged from the dice rolls.
Despite the unexpected outcome with the even and odd rolls this was a fun project. I’d like to think a little more about how to make some random walk 3d prints. My guess is that those prints would be really fun to share with kids.
I got quite a surprise last night when I asked my younger son what he wanted to learn about in today’s math project. The answer – random walks.
Not quite the answer I was expecting (!) but it turns out that he’d learned about them in this book:
I really didn’t have any ideas at all about how to introduce random walks to kids, so we just starting by playing around with a simple 1-D example. It was fascinating to hear what they boys thought a random walk would look like. I’m not sure they even know the words or ideas that you would normally use to describe one.
Net we moved to Mathematica. I wrote a short program that kept track of left and right moves in a random walk. We looked at how far left and how far right you go (and also where you end up) after a certain number of steps. In this video we looked at 100 and 1000 step random walks.
The main focus (not counting a mysterious little glitch with Mathematica) was trying to get them to describe what they were seeing with the various numbers.
For the last part of the project we looked at a random walk with 10,000 steps. It was fun to hear the boys try to guess at what some of the max / min numbers would be. We’ll have to revisit the random walk idea a few more times to explore the ideas in a bit more depth. They boys were really interested to learn more after we finished up!