I have been following along with Annie Perkins' twitter #MathArtChallenge. She has been posting a starting point each day and whenever I have had time I've joined in.
Here is the initial prompt for the similar triangles activity:
I had a moment and some coloured paper so I joined in. My explorations can be seen in this twitter thread.
I wanted to take a moment to reflect on the process I went through while working on this project.
I started out with Annie's examples in my mind. I liked the spiral she had created and I wanted to examine it closely. Why does it spiral? Which sides match? How quickly does it shrink and so on.
Once I had the pieces in my hands however I realised there was so many possibilities to explore. I did explore a whole load of spirals but I also explored other series of similar shapes, zigzags, and also some effects of layering which I hadn't even considered when I started. I have the pieces on my dining table and have kept on rearranging them every time I pass. My very own Maths Play Table.
I documented each pattern I made, even ones I wasn't that fond of. The process reminded me a bit of creating my art sketchbook at A-Level, Lots of play, exploration, some research and plenty of inspiration from other people. And every now and then some time for reflection and a bit of commentary. My mind was not on a final piece but on the process and the journey.
As teachers we often show students a straight forward solution, polished over years of experience but many mathematical experiences do not consist of a single route. I have been inspired by David Butler's #trymathslive where he shares his entire problem solving process on the public platform of twitter. I sometimes need reminding that I don't need to hide all the mistakes and dead ends.
While exploring this task I found that I had many aha moments and so I labelled it a many-ended task. I think I might revisit this idea and flesh it out a bit but initially I think it might be a way of introducing students to more open questions with some constraints so that they can be frequently and repeatedly successful.
I am sure that this task will stay with me for some time and I will reflect on it some more but in the mean time here are some of my favourite patterns.
Here is the initial prompt for the similar triangles activity:
The #mathartchallenge today is from @shskaercher: similar right triangle patterns.— Annie Perkins (@anniek_p) April 19, 2020
See below for a link to a fabulous video he made explaining. pic.twitter.com/RP1HV4tJJa
I had a moment and some coloured paper so I joined in. My explorations can be seen in this twitter thread.
I wanted to take a moment to reflect on the process I went through while working on this project.
I started out with Annie's examples in my mind. I liked the spiral she had created and I wanted to examine it closely. Why does it spiral? Which sides match? How quickly does it shrink and so on.
Once I had the pieces in my hands however I realised there was so many possibilities to explore. I did explore a whole load of spirals but I also explored other series of similar shapes, zigzags, and also some effects of layering which I hadn't even considered when I started. I have the pieces on my dining table and have kept on rearranging them every time I pass. My very own Maths Play Table.
I documented each pattern I made, even ones I wasn't that fond of. The process reminded me a bit of creating my art sketchbook at A-Level, Lots of play, exploration, some research and plenty of inspiration from other people. And every now and then some time for reflection and a bit of commentary. My mind was not on a final piece but on the process and the journey.
As teachers we often show students a straight forward solution, polished over years of experience but many mathematical experiences do not consist of a single route. I have been inspired by David Butler's #trymathslive where he shares his entire problem solving process on the public platform of twitter. I sometimes need reminding that I don't need to hide all the mistakes and dead ends.
While exploring this task I found that I had many aha moments and so I labelled it a many-ended task. I think I might revisit this idea and flesh it out a bit but initially I think it might be a way of introducing students to more open questions with some constraints so that they can be frequently and repeatedly successful.
I am sure that this task will stay with me for some time and I will reflect on it some more but in the mean time here are some of my favourite patterns.
Finally I would like to thank the people on twitter who inspired me in this project and my thinking.
So thank you to Annie Perkins, and Mark Kaercher for the problem, Christopher Danielson for probing some of my thinking and David Butler for inspiring me to be more free in sharing my processes publicly.
Oh my gosh the spikes at the end!
ReplyDeleteI love this. And I love it’s reminder to keep on keeping on at something even after you’ve hit an undesirable result. One downside to (my end of) the math art challenge is that I don’t feel I’ve had much time to play and linger on the challenges that really speak to me, but I look forward to doing so in the future. It has been absolutely worth it, however, to be able to see the joy and beauty others have created.
Yes! You have set yourself a huge task of getting out a MathArtChallenge every day! I often feel when I'm directing learning or a student project there is always too much for me to do and so I don't get totally into the experience. Following your lead has given me space to explore and I have taken a few days to explore just one task. I have really appreciated being on this end!!
DeleteSara Van Der Werf's article had a big impact on me and how I designed my classroom. The Play With Math table is a popular space for me and for my students.
ReplyDeleteI'll also put in a plug for Sunil Singh's "Math Recess" book, which talks about the need for math play by students of all ages.
Thanks again Becky for playing along!
I agree, a perfect place to share with students a wider view of mathematics!
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