One 'stop' I had this week was to look into what Google Glass was. Check this out:
Watching the "Math Improv: Smarties" video made me think about an activity I did with my Foundations of Mathematics 11 class a few years ago. One unit in the course covers statistical analysis, and we did so using Smarties (the Canadian version). Each student received a box, we counted colours, sorted odd-shaped pieces, weighed boxes, and discussed mean, median, mode, range, scatter plots, histograms, and other ways that we could come and make conjectures and hypotheses about what to expect in a standard box of Smarties. My students were so much more engaged because this was "random knowledge" they would later be able to provide to friends as they were eating Smarties and it made their learning tangible.
Consider the snowflakes. It is commonly discussed that each snowflake is unique, which I think is why I was surprised to read that "snowflakes, when they first fall, and before they are entangled into larger clumps, always come down with six corners and with six radii" (Kepler, p. 33). I suppose I figured they would fall with a variety of numbered branches, finding patterns and symmetry in various shapes.
Kepler, in On the Six-pointed Snowflake: A New Year's Gift, marvels at the mathematics that is inherently found in nature. He discusses the fact that this mathematics is not learned nor planned by the creatures, simply instinctual in their nature and designed to exist. From beehives to pomegranates, apples to flowers, pattern and mathematical shapes, arrangements, and constructions present themselves. I found the following video that encompasses some of the mysteries:
These types of explorations are ones that I often share with my students. Looking at the wonders of the world and encouraging them to have curiosity and awe for nature is something I find extremely valuable. The question I constantly wrestle with is: how do we do this in a genuine way? And how do we connect the wonder and awe of mathematics with the scripted nature of the curriculum?
So fun to hear about how you use a box of smarties with high school students. It reminds me that although we teach different ages and complexity of curriculum, kids are kids and most kids love and engage with candy! In grade one, we would use a box of smarties to count, graph, add, subtract (eventually they need to eat the smarties). Food is a motivating object to learn about number sense – including how food grows, the patterns within, how the world of nature makes sense without human intervention (take the bee hive for instance). Students begin to make connections and see the interrelatedness of the world around them. This leads, I think, to a greater sense of responsibility to nurture and care for the world. This was not my experience as a student, or even when I began teaching, but I am excited about the possibilities of students today developing a great sense of how interconnected our world is and using mathematics to support that developing understanding.
ReplyDeleteI enjoyed watching the “Painted with numbers: Mathematical Patterns in Nature” video. It seems like no matter how often we consider nature mathematically, it is always amazing. Whether or not students can understand the mathematics, for instance in the Fibonacci sequence (quickly the numbers go beyond grade one students), creating awareness of the mathematics in nature, allows students to see nature in a different way. A flower is no longer something that is just beautiful, it is alive with wonders to be discovered and understood, filled with things to be learned. I love when students’ ability to look at the world around them broadens and deepens. Curiosity and awe are great ‘mathematical’ words.
A great question, “how do we connect the wonder and awe of mathematics with the scripted nature of the curriculum?”. I think we look for natural applications of the content of the curriculum as much as possible and we look for connections. We take the time to share the wonder of the mathematical nature of the world around us. As Prof. du Sautoy said in the video, we cannot create a symphony unless we first understand how notes work. But if we only teach students about notes, and never allow them to listen to a song… we (teachers) lose sight of why we are teaching and students never understand the purpose of what they are learning. Similar to the example of playing sports. If we only ever practice skills and never play a game, what is the point? Conversely, we need to practice the skills to successfully play the game. If we don’t understand numbers, the Fibonacci Sequence is mathematically meaningless. We need to find the balance between teaching the skills (and helping students see the value in learning the skills) and playing the game (allowing students to experience that because they have the skills, they can play the game).
Hi Fiona,
ReplyDeleteYour activity using boxes of smarties to teach about measures of central tendency and related topics in statistics is a great idea. You may recall that in EDCP 552 (Teaching Children Mathematics) each group had to select two problems from a set of problems. One of the problems our group selected was titled “How Many Towers”. The problem involved observing young children working with building blocks of only two different colors. First, they were asked to make two-block high towers. The question was how many different towers could they make? Then, they were to make three-blocks high, how many different towers? Next, four-blocks high … The children I was working with did well when using building blocks. I thought smarties would help them be more engaged. So, I gave the children smarties in two colors to do the same task. But they could not resist the temptation to eat the candies and were distracted. That left me with the question, when the use of such “manipulatives” is helpful for teaching a math concept, and at what point they have a distracting effect.
In connection with the beauty of snowflakes and ice crystals, we had cold weather in lower BC late last December. One morning I saw beautiful patterns of ice crystals covering the windows of my car. For me it was an amazing sight. I was wondering why in the past the glass would be covered with a sheet of ice, but this time there were beautiful patterns. I suppose it was not one factor, but the specific combination of the atmospheric conditions (temperature, humidity, pressure, etc.) which resulted in creating the patterns. Will further knowledge of math (geometry and pattern) and the sciences (physics and chemistry) help in understanding and appreciation of the beauty of nature?
Thanks Fiona. The Du Sautoy film is really nice, and a good one to show to classes! I'm not so sure that the Google Glass promotional film is really about multisensory mathematics though -- it seems to be about having a visual computer with you all the time, almost the negation of multisensory experiences.
ReplyDeleteI see lots of wonderings here, but not as nearly as much connection as I would like to see among the introduction, the activities, the viewing and the article of the week. I hope that, as you emerge from a period of illness and stress, you'll be able to bring together these aspects of our themes, which is what this course is all about.