Photos from our Math Party in December?

 I hope everyone has had a good holiday and that your new semester is well begun! Does anyone have photos from our class math party? I thought I had taken a bunch of— but apparently I didn’t! (I did take a lot of photos of our EDUC 450 class with the Wurzelschnecke, and I will post those on the 450 blog.) 

If you have some Math Party photos to share, please make a new post or two with them! I’d love to see them.

Happy New Year!

Sussn

An invitation to the upcoming Indigenous Math Education Symposium 2025 (online in May)

 Hi everyone. I just got the following notice from my colleague, Dr. Cynthia Nicol -- highly recommended if you can be there, virtually! Here's the link to the Indigenous Math Network too.

Cheers

Susan

***************

Dear Friends

 

 

SAVE THE DATE!

 

 

You are invited to the 2025 Indigenous Math K-12 Symposium – Virtual

 

To reach our urban and rural Indigenous Math Education network educators the Indigenous Math Education Symposium 2025 will be held virtually.

 

We invite you to 2 exciting virtual sessions:

 

Session 1: Tuesday May 13 3:30 – 5:00pm PT

Keynote address – in the process of confirming and it will be exciting!

 

Session 2: Tuesday May 20 3:30 – 5:00pm PT

Igniting the Sparkle Sharing Circle: Teaching mathematics with Indigenous perspectives and practices: What are we learning? Educators share their projects, questions, ideas, and learnings.

 

Registration will be available by April 7 2025 . Details to follow.

 

The 2025 Indigenous Math K-12 Symposium is an opportunity for teachers, administrators, Ministry representatives, community members, and academics to connect, explore, imagine and share new ideas, resources and research on Indigenous mathematics education from Kindergarten to Grade 12.

 

Purpose of the Symposium is to:

• share research and educational projects about improving Indigenous math education K-12
• develop community connections to facilitate and support improving Indigenous mathematics education

 

Visit the Indigenous Math Education Network: https://indigenous.mathnetwork.educ.ubc.ca/

 

Please direct questions about the symposium to: 
Cynthia Nicol cynthia.nicol@ubc.ca

 

Please share this email with your colleagues!

All the best to each of you for the holiday break

Cynthia

If you are interested in math, movement and dance...

 

Hi all! For those interested in the connections between math, movement and dance, you might be
interested in joining in on the monthly meetings of the DMAM group (Dance, Movement Arts and Math). This international group of teachers, researchers and dancers is an offshoot of Bridges Math and Art, and meets one Sunday morning per month online on Zoom. It's headed by Karl Schafer (of the math modern dance company, Dr. Schafer and Mr. Stern). Each session typically has one or two presentations and some lively discussion with really interesting people working with these ideas.

The next DMAM session is this Sunday, December 15 from 10:30 AM - 12:00 noon Vancouver time. (This one is a bit unusual -- they're usually from 10-11:30 AM). 

If you're interested in joining in, please let me know, and I can let Karl know to put you on the mailing list, and send you the Zoom link for Sunday! Hope to see some people there if you're interested!

Some math-y carols to sing

 Here are some silly and fun math-y songs. And surely you and your students could write some too?

https://docs.google.com/file/d/0B00n89L6TX5gWGJnaGJxSXFLS2M/edit?usp=docslist_api&filetype=msword&resourcekey=0-L7RHw26ZkRIAujSmX6jKkQ

This Wednesday Dec 11: Our end-of-term math party!

Hello everyone! Winter solstice and our holiday break from classes are coming up — and we have our
*MATH PARTY* this Wednesday Dec. 11! 

Please bring some snacks to share ('mathematical' snacks if possible!) and some math resources, games, movies and fun ideas -- we'll have time to share some of these as part of the festivities!

Looking forward to it, and I'm going to miss you all very much... it's been a wonderful semester with you, and I know you are all excellent, very thoughtful and resourceful new math teachers. You have a great community of colleagues from your classes here, and I hope these friendships will be nourishing to you throughout your careers.

As a final reflection on the course:

*** Please reread all your blog posts from the course, and write a post that reflects on your learning throughout the course, along with highlights and suggestions for the course in future years.

Playing with (binary and other) number bases through poetry, movement, sound and visual arts

 Here are some resources for designing highly interactive math lessons around binary numbers and other

number bases:

Mike Naylor's Hero Run poem (and several other very cool mathematically-structured poems!)

A film from this class a few years ago: 

New math teachers riff on Kandinsky in Binary

...which refers to Marc and Marion Chamberland's 2016 artwork, Kandinsky in Binary -- a beautiful and unique way of representing numbers in different bases with concentric circles.

And a more recent film from Malmö University in Sweden, The Binary Balcony!

Playing with the Etch-A-Sketch to experiment with linear functions, circles and sinusoidal functions

 The Etch-A-Sketch toy has been around since the 1960's, at a time when lots of people were first getting TVs. The TVs of that era had horizontal and vertical hold knobs to stabilize the picture -- so the Etch-A-Sketch has knobs that control the horizontal and vertical movements of an internal mechanical cursor. No electricity required, and the image is erased by shaking the screen (something like sand inside erases the image.) Some people have figured out how to do amazing drawings with this simple drawing tool! We will aim to use it to understand some aspects of algebraic geometry in a more visceral way, with a fun retro toy.

You can access a virtual Etch-A-Sketch here, by the way!

Here are some experiential ways to play with an introduction to linear functions (and then circles and sinusoidal functions) with students working in groups of 3 with an Etch-A-Sketch!

Instructions:

1. Form a group of 3: one person operating the horizontal (H) knob, one the vertical (V) knob, and one person as timekeeper.
   
   
2. Start by playing a bit with drawing on the Etch-A-Sketch. Most people try to draw a house with a slanting roof. Notice how you have to use both the H and V knobs together to get a diagonal line (or anything that's not strictly horizontal or vertical!)
   
   
3. Use a permanent marker to mark a dash as the home position for the H and V knobs, so that you'll be able to tell when you've done a full turn, a half turn, etc.
   
   
4. Now have just one person operate the H knob, and a different person the V knob, and cover the screen with a piece of paper so that you can't see what you are drawing till it is done. You'll need the help of the time keeper to keep a steady beat by clapping or counting or otherwise directing the actions of the H and V people. Try the following:

• (a) Turn the H and V knobs the same distance, in the same direction, at the same rate. What have you drawn? (Take a photo of it, and of each successive drawing).
• (b) Turn the H and V knobs the same distance, in the opposite direction, at the same rate. What have you drawn, and why?
• (c) Turn the V knob two turns for every one turn of the H knob, in the same direction (and then in the opposite direction). What do you predict will be the result, and why? Did the result match your prediction?
• (d) Turn the H knob two turns for every one turn of the V knob, in the same direction (and then in the opposite direction). What do you predict will be the result, and why? Did the result match your prediction?

    5. Let's do some translation from "turn the knob" instructions to linear equations:

• (a) V is the same as H -->
  V = H --->
  ??
• (b) V is equivalent but opposite to H -->  ??
• (c) V is equivalent but twice as much as H --> ??
• (d) H is equivalent but twice as much as V --> ??
  
  Any surprises or revelations? How was it to do this with the screen covered with a piece of paper (as opposed to what it would be like looking at the screen while you draw)? What difference did it make to your mathematical noticing or awareness to have two people separately operate the H and V knobs, rather than doing it all yourself?

And now: CIRCLES!

1. Again with one person on the H and one on the V knobs, the timekeeper coordinating, and a piece of paper covering the screen, think about how you could draw a circle -- and then try doing it several ways! Keep a record of your results with photos, and caption them if you can with the strategy you tried.
   
   What strategies worked best for drawing circles? Was it easy or hard -- and why?
   What does this tell you about what a circle is? Does it shift your sense of the definition of a circle in any way? 
   
   
2. As an interesting extension: Now try drawing a sine (sinusoidal) curve, also with one person per knob, the screen covered with a piece of paper, the timekeeper keeping everyone on track.
   
   What did you notice about what the person on the H knob and V knobs did differently?
   What does this tell you about what a sinusoidal curve is?
   Did it connect with the way you drew a circle in any way?
   Did this experience connect at all with ideas from differential geometry?
   
   Once everyone has tried this, we will share and discuss what we noticed and discovered about these shapes using this fun toy!
   
   
   

Circle geometry, proofs and dynamic geometry explorations with Desmos/ Geogebra

 Here are resources for four guided lessons using free, dynamic geometry software online -- either Desmos or Geogebra. These circle geometry theorems are currently included in the BC Geometry 12 curriculum, though they were in the Math 11 precalculus curriculum for many years. (If your school is not offering Geometry 12, these are some very interesting geometric ideas that could be introduced as an enrichment topic in the senior year classes!)

Overview and lesson one (retyped)
Lesson 1 again (scanned version)
Lesson 2 (scanned)
Lesson 3 (scanned)
Lesson 4 (scanned)
Older textbook deductive proofs (scanned, somewhat blurry)

In the olden days, students used to doing geometry with pencil, compass, straightedge and paper, but from the 1990s on,  many online dynamic (as opposed to static) geometry tools became available. Geometer's Sketchpad, Cabri, Cinderella and many more are listed on a Wikipedia page here.

By far the most popular of these is now Geogebra, as it is free, open-source, and contains many lesson ideas developed by and for teachers. Take some time to look at Geogebra and experiment a bit with it.

Desmos is also taking on many similar functions to Geogebra, and is also free and available to students and teachers. You will likely use Desmos and/or Geogebra with your classes


What are your thoughts on these guided geometry experiences? How do you feel they relate to more formal deductive proofs? Do you feel that these 'prove' the theorems?

In thinking this through, please refer to John Mason's three levels of proofs --
1) Prove it to yourself,
2) Prove it to a friend or ally,
3) Prove it to a sceptic.

Here is an excellent short article by John Mason on this topic, for your reference!

For Taha and Jacob's curricular microteaching Mon Dec 2

Hi all! Here are the criteria for your peer/ self evaluations for Jacob and Taha's curricular microteaching lesson for tomorrow. (Thanks for offering clear and constructive comments as well about what worked and what might be improved -- and thanks to Mark for writing these so beautifully on the whiteboard!)

 

On 'popsicle stick bombs', longsword dancing, and (stellated) polygons!

 Here is a link to slides on this fascinating topic that we'll explore today!

And here are the two short films we saw on the geometry of longsword locks:

Steel Phoenix 

George Hart's Simons Foundation film

And here are a few photos of our class making coffee stir stick longsword locks. (If you have stills or video of us doing the longsword dance, please do post them on the class blog too!)

Planning our upcoming EDCP 342 classes to the end of term

 

On Monday Nov 25, after Jacob and Taha's curricular microteaching, we will work with popsicle stick and longsword polyhedra!

On Monday Dec. 2, we'll explore classical labyrinths and their connections with magic squares

On Monday Dec. 9, we'll engage with a math drama.

Looking forward to our workshops, guest speaker and math party in the coming weeks!

Homework reading on textbooks and how they position their readers: please post blog response

   

 

Here is an interesting critical-thinking take on the ways that math textbooks may 'speak to' their 
readers (assuming that people actually do read and listen to math textbooks...)


Wagner & Herbel-Eisenmann on math textbooks and the ways they may position their readers

Please read this thought-provoking article and blog on:

•How you respond to the examples given here -- as a teacher and as a former student
•What are your thoughts about the reasons for using/ not using textbooks, and the changing role of math textbooks in schools?

Textbooks, their history and their future

 Today we'll look at a number of textbooks, new and old, and assess them in the terms listed below. 

As you begin working as a member of a math department at a secondary school, you will be called upon to help assess textbooks that the department and school is considering purchasing. You will also be asked to make professional judgements on various alternatives to textbooks. How might you assess textbooks and their alternatives? That is what we will address in class today.

Some things to start noticing in terms of textual analysis of math textbooks, old and new. (Each observation should be considered in terms of its potential effect on mathematics teaching and learning, and on the ways students might begin to think about mathematics.) Notice:

• The qualities of the physical object. Is it heavy or light, durable or fragile? How does the paper feel and the ink smell? Does it come with a teacher guide? student workbook? CD (seems a bit old fashioned now)? web links? Will it fit in a student's backpack?

• How much does it cost? What would the investment be for a school to take on a new math textbook?

• What is the writing like? Who does it address, and what does that tell you about its view of society and mathematics learning? Does it include definitions, explanations, examples, counterexamples, word problems, instructions, stories, extensions?

• Who are the authors? What is their expertise? Who put the project together, and why? Try reading the introductory material (which hardly anyone ever reads...)

• Is it easy to navigate? Table of contents, index, glossary, answer key, appendices, diagrams, tables, different kinds of pages colour coded, ...?

• What are the graphics like? Photos, diagrams, graphs, boxed information, use of colour or not,...

• How is it designed? Use of white space, sidebars, font size and style, page layout,...

• Any examples of alternatives to paper textbooks, from publishers, or teachers, or organizations, or ...


Interestingly, even a math textbook is very much a reflection of the time, place and society it comes from! No matter that the mathematical content is slow to change -- the social and educational contexts (and printing technologies) change much quicker.
Are there any classes in high schools that don't use textbooks?

Could you imagine teaching a math class without textbooks? What is the future of the lucrative business of textbook publishing? Do you think we will soon be creating teacher-written, collaborative shared materials online that will replace current (retro) textbooks -- or not??

Here is a blog from a workshop on textbooks at CMESG (the Canadian Math Education Study Group). It has fascinating links to many of the earliest math textbooks in English (from the 16th and 17th centuries) and other varied textbooks. We will use several of these today: 

1. Sample pages from Robert Recorde's The Grounde of Artes (1632), one of the first mathematics 'textbooks' in English..and Robert Recorde, The Whetstone of Witte (full text)
   
   
2. Social Arithmetic selections part 1 (US, 1926)
Social Arithmetic selections part 2 (US, 1926)


3. Modern Algebra and Trigonometry part 2 (Dolciani et al, US,1963)
   
   
4.  Mathematics: A Human Endeavor (Harold R. Jacobs, US, 1970) part 1 and Part 2
   
   
5.   Mathquest 8 (Addison-Wesley publishers, Canada, 1988)
   
   
6.  Precalculus 11 (McGraw Hill Ryerson publishers, Canada, 2011)
   
   
7.  Math that matters (Stocker, 2006, Toronto)
   
   
8. Khan Academy Math as textbook?
   
   
9.  Excerpts from Stewart's Calculus

Blog reflection on flow in the secondary math class for Monday Nov 18, 9 AM

 

Hi all! As a follow-up to our exploration of 'flow' , please write a short blog post reflecting on the film we saw in class on Monday: Mihalyi Czikszentmihalyi's TED talk on 'flow' and happiness.

In your post, please reflect on what you take away from this talk and the idea of 'flow':

Have you experienced a state of flow through certain experiences? What prompts it? Is it sometimes connected with mathematical experiences?

Is it possible to achieve a state of flow in secondary math classes? Can we, as teachers, help create the conditions for a flow state for our students as they learn math? If so, how -- and if not, why not?

Looking forward to reading your blog posts, and to following up with more on flow states and ideas about The Thinking Classroom!

Czikszentmihalyi & 'flow', Liljedahl and 'flow' in the Thinking Classroom

 

 Mihalyi Csikszentmihalyi, the late Hungarian-American psychologist, has studied a state he calls 'flow', where people are completely engaged and delighted in a process of problem-solving, and our normal sense of time is suspended. Here is a link to his TED talk on this topic from 2004.  

Professor Peter Liljedahl from SFU Math Education has taken up the idea of 'flow' in both a descriptive and prescriptive way for our math classrooms. Here are his slides shared from his session at the Northwest Math Teachers' Conference in 2015. Peter's books on Building Thinking Classrooms in Mathematics K-12 have resonated strongly with math teachers in Canada and internationally. Here's a link to his website on Thinking Classrooms, an interesting
short article on Edutopia about Thinking Classrooms

How can we, as teachers, promote "flow" and happiness in our mathematics classes? What kind of activities might help students feel immersed and excited in problem-solving and other mathematical undertakings?

FREE Virtual Math Ed Pro-D Event - Nov. 15-17 (open to everyone, and especially needed if you missed the October 24/25 pro D!)

  From Erica Huang's 442 blog:

Here is a free, virtual Math Ed Pro-D event that may be of interest: 2024 Make Math Moments Virtual Summit. There are some high-profile math educators presenting at the event, such as Jo Boaler (Mathematical Mindset), Peter Liljedahl (Building Thinking Classroom), and Ben Orlin (Math with Bad Drawings), just to name a few.

Make Math Moments is a popular math education podcast host by two Ontario math educators, Jon Orr and Kyle Pearce. Check out their work if you enjoy podcasts!

Homework reading and response: Arbitrary and necessary

  

For homework, please read this classic and very influential piece by UK mathematics educator Dave Hewitt. Think about what he means by 'arbitrary' and 'necessary', and then please write a blog reflection about how this might affect the way you plan your lessons and units as a math teacher! Blog posts are due Wednesday Nov. 6 at 9AM.

Dave Hewitt 2020 video for the Assoc of Teachers of Mathematics (UK) on awareness and fractions (13:31)

Dave Hewitt 2022 video on Grid Algebra (8:00)

The Giant Soup Can of Hornby Island: A puzzle due on your blog Wednesday Nov 13 by 9 AM

 

  

A geometric puzzle with real-life connections:

On Hornby Island, BC, local artists were commissioned to paint the volunteer fire department's water tanks in a dozen different locations around the island. Artist Pix Sutherland noticed that this tank was in exactly the same proportions as a Campbell's soup can and painted this (controversial) tribute to Andy Warhol's famous 1960s soup can pop art paintings.

Lots of math problems could come out of this story. Here's one: given the size of the actual Campbell's Soup can (of normal size) and the height of the bike in the photo, what are the dimensions of the volunteer fire department's water tank? What is its volume? Does it hold enough water to put out an average house fire?

Your task: work on this puzzle yourself, and let your 'teacher bird' and 'student bird' notice how you approach it, where you can use reasoning and where you need to research, where you get stuck and un-stuck.  

Then work on either: (a) extending this puzzle, or (b) coming up with your own puzzle for secondary math students based on a real-life observation you have made (and include a photo or graphic to support it).

Your unit planning assignment!

   

 

A unit of work in secondary school mathematics (on a linear timetable) generally lasts 4 to 5 weeks, and includes about 10 to 12 lessons. In most courses, there are 9 or 10 units of work per year -- approximately one per month, speaking linearly. Your unit planning assignment should get you started planning for one of the units of work that you will actually be teaching for your long practicum!

Note that each of your sponsoring teachers will have slightly different requirements for unit planning, and for your practicum, you will need to work with those individual requirements.

For this course, I am most interested in seeing your background thinking and planning for designing the unit. I want to see that you can:

•answer the question "why are we learning this?";
•make connections for yourself and your students with the history, social/environmental/Indigenous connections, artistic connections, fascination and beauty of this topic;
•think deeply about the pedagogy of this topic and the possibilities for teaching it;
•work out formal and informal ways of assessing students' progress in learning this topic;
•design a large or small student mathematics project that will be part of the unit.

You will also need to think out the sequencing of your 10-12 lessons and outline this in a chart.

In planning a complete unit for your practicum, you will need to write a lesson plan for each of the lessons. But for our class purposes, I am only asking you for three lesson plans. However, these should be for especially inspiring, creative and actively engaging lessons that do not follow the traditional pattern of lecture/exercises/homework. (I expect that some but not all of your lessons in the unit will follow that traditional pattern -- but I would like to see your plans for ones that do not!)

Please download the template linked here to write up your unit plan, and stick closely to the suggested word counts for each section. You will see that you are asked to produce short paragraphs for each section, but I will expect them to be well-researched and well thought out.

Your first draft of your unit plan is due on your blog on  Nov. 27 at 9 AM. Then we will go through a process of peer editing and revision, with the revised version due for marking on Dec. 11 at 9 PM. 

Please talk with your SA about a unit you will actually be teaching in your long practicum — then post the grade, course and unit topic in the comments here by this Wednesday November 13!

Hope you enjoy the process, and then the teaching!

What are your plans for the province wide Pro-D day Oct 25?

 

Friday October 25 is an exciting day: the annual BC Province-wide Professional Development day for teachers across the province! This is an important chance for us all to meet, share new ideas and skills, and improve teaching across BC. It's something teachers have fought for through our union (the BCTF), and we need to use it well every year.

***There are all kinds of conferences and professional development activities happening on Friday, and you are expected to attend one of them, let me know on your blog which one you will be attending, and to report back and reflect on your experiences on your blog afterwards! Your reflective blog post should include a brief summary of the session(s) you participated in, and your thoughts on what you learned, what you liked best, what surprised you, and what you would like to follow up on.

Many of us will be at the BCAMT/ Northwest math education conference at Whistler, but there are other events available too:

• The BCTF website has links to all the provincial PSA (Provincial Specialist Association) conferences 

• The UBC Teacher Education Office (TEO) has links to both PSA and other UBC and museum-based pro D events on Friday

• For those with literary interests, the Vancouver Writers' Festival at Granville Island always coordinates with the Province-wide Pro D day so that teachers can attend

You may find other museums, etc. that have special Pro D activities for teachers this Friday.

Whatever you decide to attend, you should be attending and fully engaging with the opportunities to learn from fellow educators, network with other new and experienced teachers, and gather resources and ideas for your own teaching and learning.

Have a wonderful Pro-D!