September thinking together: What is math?

Posted on: September 19th, 2017 by jnovakowski No Comments

This year I am going to share a monthly focus as a way for educators in our district (and beyond, of course!) to think together, collaborate and share ideas around K-12 mathematics education. On the list are number sense, estimation, reasoning, spatial awareness…it is a list in progress so suggestions are welcome.

My intentions are to begin each month with a blog post highlighting the focus area in our BC mathematics curriculum and connecting it to the broader field of mathematics education. I plan to share links to websites and resources, share books that I have found helpful and provide examples of mathematical tasks from Richmond classrooms. During each month, I will also tweet out related links, ideas, blog posts and photographs from classrooms.

For September, I thought we’d start with What is math?

I am fortunate to have opportunities to sit around tables with educators from many contexts – elementary, secondary, post-secondary as well as working with parents and students. What I have found over many years of having the conversation around What is math? is that there is much diversity in definitions and responses. Some views are quite narrow and focus on number, computation and operations while other views are much broader in topic but also in what it means to be a mathematician.

Mathematicians such as Fields medallists Maryam Mirzakhani and Cédric Villani have said that mathematics is a creative, collaborative endeavour. Other mathematicians emphasize that mathematics is more about justification and proof than getting the “right answer”. One thing that pretty consistently comes up from those who engage in mathematics is that it takes time – sometimes a problem or proof takes days, weeks, years.

How do these ideas about mathematics resonate with you? with your mathematical story?

As a classroom teacher and when working with pre-service teachers at UBC, I began the year with an individual brainstorm or web around “What is math?” – and these responses were added to a collective chart or web. For the pre-service teachers I worked with, I also asked them to tell my a little a bit about their background and experience with mathematics. These short narratives and webs usually gave me quite a bit of insight and where we needed to begin as a class.

What assumptions, conceptions and understandings about mathematics do students carry with them into our classroom communities? What feelings and beliefs do they hold?

This week a grades 2 and 3 class visited The Studio at Grauer and we began by talking about what is math? I then invited them to explore the materials, images and books in the studio space and to investigate something that piqued their interest.

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As we gathered back together, the students added to our original list. Interestingly, there additions were much more focused on mathematical experiences, different from naming mathematical content.

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What do our classroom environments say about what mathematics is? Do the images, books and materials we offer inspire our students and nurture connections? Do all students see openings to engage in mathematics? 

 

Ideas to nudge students’ thinking about what mathematics is:

What is math?

Create a class chart or math graffiti wall that can be added to as the school year progresses. Students can add images, diagrams, words, phrases, etc. Students can also use materials to create representations of what math is. The following is “math sun” created by a kindergarten student at Grauer last year – when I asked her what made it a math sun, her reply was that it was “full of math”.

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Where do we see math? What math lives here?

Encourage students to think about math beyond the classroom and school. Where do they experience and see math outdoors? in the community? at home? Create an area in the classroom to add photographs and materials found in the local environment that might inspire mathematical thinking and connections.

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A grade 4&5 class I worked with in The Studio at Grauer shared some of the math they experienced over the summer and then the grade 2&3 class added to their list this week:

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Many elementary classrooms have “wonder windows” to encourage students to observe and wonder the local environment. This year, we have added a math window to The Studio.

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I facilitated a K-7 place-based mathematics project at Byng a few years ago and one of the tasks classes engaged in was math walks around the school and in the community. Sometimes a specific focus was selected such as What shapes can we see? but we mostly looked for math to world connections. One class created a photo book while others created math problem posters (sharing problems the students posed inspired by their photographs) or concept panels.

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For the last three summers I have participated in a Twitter challenge with mathy types from around the world. Each week a math concept is posted and the challenge it to take photographs of the world around us that connect to that concept. Concepts such as estimation, tessellation and scale were explored this year. You can find this year’s posts on Twitter by searching #mathphoto17 – and here is a photo book I created of my photos and tweets from this year’s challenge:

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I will be launching a district-based K-12 math photo challenge on Twitter soon – hashtag #mathphoto38 (the 38 for school district 38) with plans to document and share the photos over the school year. We will begin with photos that respond to the question: What is math?

Make mathematics visible in your classroom and school

I also try and make different ideas about what math is visible to students, to parents and to colleagues. The following panel was created with images of the representations created by Kindergarten students as they responded to the question, What is math?

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A middle school teacher created an interactive bulletin board based on the instructional routine Which One Doesn’t Belong? to engage the whole school population in mathematical reasoning and communication – important mathematical work and this idea builds mathematical community in a school.

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source: Twitter

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source: Twitter

And for high schools – I think this is inspiring and helps to expand students’ notions of what math is. High school math teacher, Sara VanDerWerf, from Minnesota, has created a play table space in her classroom to engage students in thinking and playing with mathematics in different ways. She shares photos on twitter HERE and shared a blog post about play tables in high school classrooms HERE. Is there a secondary math classroom in Richmond that would like to set up a play table? I’d be happy to help.

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Think about how mathematics is experienced across cultures, across the world and across time.

Mathematics is a human construct and is often narrowly define through a Western or European lens. There is much evidence that mathematics as it is typically defined, existed in Asia long before it was “discovered” by Europeans.  There is a long history of cultural practices across cultures from all over the world that we would now label as mathematics. Alan Bishop has done considerable research in this area and describes six mathematical practices or activities that exist in all known cultures – counting, locating, measuring, designing, playing and explaining. I have found students find it interesting to learn about different number systems or how measurement is often contextual to a culture and environment. Some examples of these cultural practices are included in the elaborations for the learning standards in our BC math curriculum.

Seeing and experiencing mathematics as a creative endeavour

For the past three years, Dr. Jo Boaler and her “youcubians” have launched a week of inspirational math to begin the school year. There are a variety of videos and open mathematical tasks available for grade bands from K-12. The focus is developing a mathematic mindset  with messages such as: we can all learn math and we learn from mistakes. Resources can be found HERE.

There are many videos available that show mathematics as creative and inspiring but a particularly interesting youtube channel is created by self-defined mathemusician Vi Hart, daughter of acclaimed mathematical sculptor George Hart. I think her videos are particularly great for students in grades 5-12. Her channel is HERE.

There are lots of ways to nurture the creative thinking core competency (BC curriculum) while engaged in mathematics.

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The three facets of the competency are: novelty and value, generating ideas and developing ideas. I see these facets enacted when children engage in number talks and consider different strategies for solving mental math questions, when children engage in a rich open task or problem or when they apply mathematics to create or design something.

 What is math?

How will you investigate this idea yourself and how will you investigate and extend your students’ thinking about this over this school year?

~Janice

 

References

A Mathematician’s Lament by Paul Lockhart (with new books Measurement and Arithmetic)

Mathematician Keith Devlin’s blog: Devlin’s Angle

Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms by Tracy Zager

The Crest of the Peacock: Non-European Roots of Mathematics by George Gheverghese Joseph

Bishop’s six universal cultural activities

Mathematical Mindsets by Jo Boaler

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