Being a musician, I am always fascinated by the winding music boxes that play tunes and love to watch them work. Imagine my further fascination when I watched this week's Möbius Music Box video, and found two of my loves -- math and music -- combined into one! I'm intrigued by the inversion of the song. I wouldn't have predicted that the song would still sound...musical. I would have anticipated something that sounded incorrect to the ear, but instead this brought a sense of mystery; it drew me in further, which then resulted in further attention paid once the strip was back to its proper side. So cool!
For this week's activity I looked at Karl Kattchee's "Three Strange Dreams". It made me think of the the snowflakes that are made each year around Christmas time. From a young age, we teach kids to cut random shapes into folded up pieces of paper and unfold them to display snowflake decorations. I wonder, based on this week's activity, what it would be like to have students draw/represent various mathematical expressions and then cut out and unfold. Due to (what I believe is) long-COVID, I've been pretty absent at school, but once I'm back, I'm going to try this! Stay tuned for results!
Bridges: A World Community for Mathematical Art gives an overview of the progression that the Bridges Conferences have made over the years. The first conference had only sixty participants, while conferences now have 250-300 participants, with thousands of observers! Bridges has presented many opportunities and vehicles for merging mathematics and arts, two seemingly separate disciplines. Out of this movement have come the development of mathematical museums, research expeditions, and other events that lead society in exploring the possible connections between Math and the rest of life.
My wonderings:
- Working within the British Columbia curriculum, what could cross-curricular projects look like to encompass mathematics and humanities?
- For those who feel like they aren't "artistic or musical or creative", how can we walk with them in expanding their understanding of mathematics in this way?
I’m so sorry to hear that you are dealing with long-covid, I hope your symptoms improve quickly! It’s great to hear your thoughts this week.
ReplyDeleteAlthough I live in a home of musicians, I do not consider myself a musician. I took piano lessons for many years and did pass my grade 8 Royal Conservatory of Music piano exam, yet I still do not feel like a musician in any sense. It doesn’t come naturally to me. I have no ear for music. I was and still am always amazed that people can tell what notes are just from hearing them. On the opposite end of the spectrum from me is one of my boys who has perfect pitch. He can hear almost any sound and tell the corresponding note. This is truly amazing to me. I wonder if I understood the notes mathematically if this would help me to hear them differently, creating connections that my brain can understand. My guess is that it would help. I haven’t given up hope yet, of learning to play an instrument proficiently. Having short fingers hasn’t helped but my boys were actively involved in the Langley Ukulele Association and have travelled and performed in Canada and the US with this group (and my husband and I were lucky to be chaperones for many of the trips) so I’m thinking that the ukulele would be a good instrument for me to learn (maybe when this masters program is done!). Having said all of that, I was totally intrigued by the Vi Hart music videos and will be sharing them with others. It has given me a new perspective on understanding and ‘seeing’ music, which seems funny to say because we are so focused on sight already in our culture and would likely benefit from focusing on other senses as was considered in last week’s readings. It was thought provoking the different ways that music was represented in the Vi Hart videos.
I was thinking about the snowflakes, after watching the video that Zaman introduced last week, and I recalled when I taught Kindergarten and I had the students make snowflakes out of tortilla shells (with support!) and then we sprinkled them with butter and cinnamon and made delicious snowflakes! This doesn’t connect as much with this week’s ideas as a few weeks ago, but I think it is an example of your question about cross-curricular projects that encompass mathematics and humanities. For Kindergarten students, just making a snowflake is a feat. If I were to do this activity now, I would include mathematical concepts in the process of making the snowflakes. Even measuring the cinnamon and butter would add to the mathematics. I can see with high school students that an added challenge, like how can you make your snowflake with certain characteristics in a way that ensures you have the most tortilla in the snowflake to eat, could add the mathematical challenge to an embodied, multi-sensory learning opportunity.
I think when it comes to cross-curricular projects, we need to remember that not everything needs to be cross-curricular but when and if we are able, we can make the learning meaningful when we are able to connect across different subject areas.
For your second question, as someone who doesn’t feel artistic or musical, a way to walk with them in expanding their understanding of mathematics in this way, may be to not start with the fact that an activity is artistic. We often think of artistic in narrowly defined ways (drawing or playing music) and when we don’t fit in those ways we feel blocked. When I looked through the exhibits from the Bridges conventions, there were many types of ideas/projects where I felt, “Hey, I could do something like that!”. I choose to work with photography because I love to take photos… but as I worked with the piece from Bridges – the way I approached the photos and videos I took from a mathematical lens was completely different than how I would usually be thinking when taking photos. Which makes me think that another way of incorporating arts into a high school mathematics class could involve having students find and take photos of mathematical concepts.
How interesting, and what a great discussion, Fiona and Joy! (Zaman, we are missing your comments this week.)
ReplyDeleteFiona, first of all, best wishes for a quick and complete recovery! That must be awful... And then, thanks for the very interesting comments from a musician's point of view on the element of surprise and even suspense in Vi Hart's videos, especially the mobius strip music box. So fascinating to be able to experiment this way, in real time! Joy, if you did Grade 8 piano, I'd say you are not a musical novice by any means -- but it is interesting to think about how someone can be an accomplished music (or math) student, yet not feel intuitive or completely comfortable in inhabiting that world. What is that musical/ mathematical education if it leaves people knowing yet not feeling as if they know or belong in that world? Ukulele is wonderful, by the way, and well worth taking up!