The NCTM Standards, Common Core Curriculum and draft Catalyzing Change in High School Math

  

 

 The US-based National Council of Teachers of Mathematics (NCTM) has had an enormous effect on mathematics curricula worldwide -- including BC! Understanding the NCTM is essential for understanding our own curriculum.

Here is the link to the new NCTM Common Core executive summary, a link to the Common Core State Standards (something like our IRPs) with correlations to Canadian curricula, and a link to the executive summary of the NCTM Principles and Standards from 2000. We will look at this today to get a sense of one of the biggest influences on our curricular reforms and understand where it is coming from. We may also look at the new draft NCTM Catalyzing Change in High School Mathematics document.


Note that there are also standards for teachers, related to a neo-liberal climate of measurement, accountability and teacher testing in the US.

The general NCTM website is accessible at NCTM.org. It is well worth getting acquainted with the great lesson plans, puzzles, interactive activities and other resources included on this page too.

We will look at:

the 6 Standards,
the 5 Process Standards,
the 5 Content Standards,
the 8 Mathematics Teaching Practices recommended, and
the 16 Principles to Actions recommended for teachers (6), administrators (5) and policy-makers (5).

More info on your write-ups for your math art project

  Hi everyone! Looking forward very much to your math

art presentations in class this Wednesday and next Monday.

Here is what you will need to write up and post to your blog to document your project. Your collaborative account is due on your blogs on Tuesday September 22 (tomorrow) by 9 PM, and your individual reflection on the project is due by Sunday, October 4 at 9 pm:

(1) Your group should (collaboratively) write up an account of your exploration together of this math/art/ teaching project, including: 

• names of those in your group, the original artwork and artist(s)

• the ways you remade the original artwork piece, and any issues and insights that arose during this process 

• the ways you slightly altered the piece to make it your own, and what arose during this activity

• your interactive activity with our class around the project and any information on how you designed this.

Please illustrate this write-up with photos from your project!

Everyone in the group should post the same thing for this first part.

(2) Your own, individual response and reflection to the project and process: This will be different for each person in the group. Please post your own thoughts and reflections on what you learned and what you take away from doing this math/art project— mathematically, as a student, and as a teacher. What were the satisfactions, difficulties and insights for you personally? Where do you think this kind of work can take you as you begin to work with your own classes? What are the affordances and limitations?

Homework reading and blog response: Battleground Schools (for Wednesday Sept 23)

1. 

Here is a short piece I wrote for a book called Battleground Schools on conflicts within mathematics education in the US (and which affected Canada) in the past century. Please read this and blog about three 'stops' that you had when learning about the fraught history of mathematics education and curriculum in North America! 

Due on your blog for Wednesday Sept 23, 9 AM.

BC's 2019 "new curriculum" from the Ministry of Education

  

 Here is a link to the 'new' BC Curriculum, which was  fully implemented from K-12 in BC in 2019 https://curriculum.gov.bc.ca/ in all schools. This curriculum is based on competencies, described here.

We will start by looking at the new curriculum orientation guide and tools for educators that are used in the revisioned curriculum documents.

And of course, we will look at the structure, content and assessment guidelines of the BC Mathematics Curriculum.

In class today, we will look at the following particular questions, among others:

• How does the Math 8 curriculum connect with Math 7 as kids move from elementary to secondary school?

• Where does the math curriculum split into 'streams' -- and why?

• Where do particular mathematical ideas show up in the curriculum?

• What ideas or topics are not included explicitly in the curriculum?

• How do textbooks connect (or not) to curricular topics and concepts?

• What supports and flexibilities does the BC math curriculum offer us as teachers?

Finishing up our blog set-up: Here are the instructions on how to invite the rest of the class to be authors on your blog

Hi all! Some people have run into some snags in inviting others to be authors on their blogs, so I've written up the steps below that I hope will be helpful.

Please check your blog dashboard to see whether you have 30 fellow students plus Debby Knoke and me signed up as authors on your blog! If not, please follow the steps outlined below to invite everyone -- or if there are just a few people who haven't yet responded, please try deleting their original invitations and then re-inviting them. 

We're almost there!

Cheers

Susan

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

How to invite the rest of the class to be co-authors on your blog:


• Open your blog, and choose "design" from the menu on the upper right hand corner of the screen to get to your dashboard.

• Choose "Settings" from the menu on the left hand side of the dashboard.

• Scroll down in Settings to "Invite more authors"

• In a separate tab, open our class spreadsheet of emails and URLs.


• Highlight and then copy the whole column of our emails


• Go back to your blog Settings --> Invite more authors and paste the column of emails there. Check to make sure you are not inviting yourself! You can delete just your own email from the list.


• Press "send", and you should have invited the whole class to be authors on your blog.


Once everyone has finished these steps, and we have everyone accepting one another's invitations, we will take the next step to set the privacy setting to Reader Access --> Private to authors. (But please don't do this till we get everyone signed on!)

Thinking Mathematically, Second Edition

     

Here is a link to the PDF of Thinking Mathematically -- a classic and wonderful book in mathematics education, with many very interesting problems (and while extensions are provided, solutions arent!) 

I suggest that you also get yourself a hard copy of this book as one of the starting volumes for your classroom library.

Our first class math puzzle: The locker problem (for Wednesday September 16)

 

A school has 1,000 students and 1,000 lockers. On the first day of school, all the lockers are open. 

Student #1 closes each locker.
Student #2 opens each second locker.
Student #3 changes the state of each third locker (i.e. opens them if they are closed, or closes them if they are open)
...and so on, until all 1,000 students have had their turn.After all 1,000 lockers are done, which lockers are open? Which are closed? Why?

Think about how you approach and work on this problem. What mathematical thinking and mathematical problem solving strategies do you do?

Save your notes, drawings, diagrams, right and wrong turns, conjectures, changes of approach and other notes to post on your blog by Tuesday Sept 15 in the evening and discuss with classmates on Wednesday Sept 16. 

Introspective writing: Favourite and least favourite math teachers (for Wed Sept 16)

 As part of revisiting our own histories as math learners to inform our futures as math teachers: 

Write in class about your favourite and least favourite math teachers -- and why. These could be people who formally taught you mathematics in K-12 or university classes... and/or those who taught you ways of thinking mathematically in less formal settings (parents, siblings, grandparents, or other relatives and friends; tutors; classmates; people at work, and others).

(Please don't include identifying information, like people's actual names or the names of schools... you can use pseudonyms.)

Think about why they were great or not-so-great math teachers, and what you can learn as a new teacher by contemplating your experiences with them. Please include important details that might influence you as you take up the 'mantel of the teacher'!

Please post to your blog by 9 am on Wednesday Sept. 16.  

What is meant by 'curriculum'? (Homework reading and blog response for Mon Sept 21)

What is your first thought about what is meant by the term 'curriculum'? We will start to work on this as a prelude to our consideration of the BC Math Curriculum.

Here is a very influential article by US art educator Elliot Eisner, Three curricula all schools teach
(from his book, The Educational Imagination).

Please read this and comment on:

• Two or three 'stops' you have in this article

• Ways that this might expand our ideas about what is meant by 'curriculum'. How does the mandated BC Provincial Curriculum connect with Eisner's ideas?

Your post is due on Monday Sept 21 at 9 AM.  Hope you enjoy this important reading!

Getting organized for your Math/Art assignment (first major assignment for the course)

 Looking forward to your work with this exciting initial project! 

We will self-organize into groups of three (with one group of four, since there are 31 students in our class).

Each group should go to the Bridges Math and Art 2026 math art gallery online (follow the link to this

site). There are many math/art works on this webpage (over 150!), and some others that you could also consider from the Bridges 2026 math fashion show and mathematical short film fest.

Each group should choose one of these works of mathematical art that particularly appeals to you (because you like the way it looks and you are interested in the mathematical topic). It is important that each group chooses a different work of mathematical art from this page. Please self-organize by signing up with the names of the people in your group and the name of the art work your group has chosen in the comments to this post. If another group has already chosen a work, choose a different one -- there are many to choose from!
I will post the list on our class blog.

Your tasks with this work of mathematical art:
(1) Reverse-engineer it so that you reproduce your own version of the work of art in order to understand the mathematics and art content more deeply.
(2) Extend the mathematical and artistic ideas to take the idea of this art work to a new level, mathematically and artistically.
(3) Design a way that you could use the big ideas from this work of mathematical art to teach in your own classroom.
(4) Design a brief interactive activity to engage your classmates in trying out and understanding this work of math/art when you present it in class.

**EDIT: Here's some additional information, responding to questions from the class:

1) You are to submit TWO pieces of artwork: (a) your own reproduction of the original work, and (b) your extended version, where you have changed some parameter(s) in terms of the math and the art and seen how that plays out in a new piece. You should ALSO submit any materials related to your interactive activity for the class!

2) There are two written parts, both to be submitted via your blogs:

(a) As a group, please write up a concise, clear account of what you did as a group for the project. It should include a description and photos of your remake of the original artwork, your extended artwork, your interactive activity for the class and possibly some process pictures showing how you did it (and any snags and observations that might be interesting to anyone trying to do what you did.

This post can be collectively written by your group, and the SAME post should be posted in each of your individual blogs.

(b) After you have presented, each person in the group should write an individual short (1-2 paragraph) reflection in what you personally take away from the project. Did it go as expected or differently? What did you learn from it? Would you try something related to this with your own classes or not, and why? Any new realizations about math, art, learning, teaching, etc.?

The due dates for this project are Sept. 23 & 28.
Groups will book a time during these classes to do a 15 minute presentation showing (a) the mathematical artwork that you reproduced, with an explanation of the mathematical ideas ; (b) the extensions to the mathematical art that you have produced, with an explanation of how you extended it mathematically/ artistically; (c) a brief (5-7 minute) interactive demonstration for your classmates to show how you might use this mathematical art to teach math in your own classroom.

Hope you enjoy getting started with this project! If you have questions, please feel free to ask me.

 

Presentation schedule, Scarfe Room 1211 (tentative schedule )
**EDIT: Note times -- swaps still available!

Wednesday Sept. 23

1:00 - 1:15: Keith, Tara, Emily K., Alina: Regina Bittencourt, On-by-one

1:15 - 1:30: Mehda, Josh, Helen: Gauthier Cerf, Fibonacci art

1:30 - 1:45: Tiffany, Sarah, Kia: Dru Horne & Shannon McKillip, Sudoko without Numbers

1:45 - 2:00: Eleiah, Emily S., Adam: Lisa Marks & Owen Rohm, Cable Knit Truchet Tiles

2:00 - 2:15: Joe, Kieran, Nick: Hiu Fung Tai - Trio of Shapes


Monday Sept. 28
1:00 - 1:15: Hendo, Jackie, Brandon: Georgina Ryan, binary tree

1:15 - 1:30: David, Eric, Henry: Caroline Bowen

1:30 - 1:45: Jasmeet, Parminder, Francisco: Josep Rey Nadal - Desconstrucció d'un dodecàedre (Deconstruction of a dodecahedron)

1:45 - 2:00: Malik, Izhar, Mahnaz: Tom Verhoeff

2:00 - 2:15: Pla, Leo, Jarrad - Amanda Taylor Lipnicki - Little Wire Quadrics

Revisiting our histories, thinking forward to our future careers in math education

 

  All of us have histories as students of mathematics, with teachers that will serve as role models for us
in our own teaching. How can we become more aware of the influence of our past teachers in our own teaching work, so that we can choose what we want to take (and leave behind) from our own past experiences?

In setting out on a new career and life as a teacher, we also have our own hopes, dreams and worries about how things will be. How can we bring our own thoughts to mind to help us be aware of the teachers we want to be?

We will do some writing in the next few classes (and possibly for homework) to start to think about these processes that come up throughout our teaching careers.

Google sheet with blog URLS and emails

  Hi everyone. Here is a link to a Google sheet where we can add our blog urls and emails (gmail, if you have it).

We will all be inviting everyone in the class to be co-authors on our blogs, and then setting the privacy to 'blog authors only', so that our blogs are private within our class group.  

UBC Orchard Garden information

Hello! Here's some information on the Orchard Garden, where we'll be holding our classes for the next

weeks till Thanksgiving. 

As mentioned in class and on our tentative course outlines, we are planning to hold our classes in the UBC Orchard Garden outdoor classroom from now till Thanksgiving (Oct. 12), weather permitting. For next week, the long range weather forecast looks beautiful for Monday at least, so we will plan to be in the garden then -- we'll see how Wednesday and Thursday look closer to the dates.

How to get to the UBC Orchard Garden:

Address: Totem Field Studios, 2613 West Mall (1 block south of Thunderbird)

Go through the wooden gate between the buildings at Totem Field (the pedestrian gate on the left side is always open -- just push!) Turn right and walk about 100 steps through the 'Xmas tree farm'/ conifer research project, and you will be at the Orchard Garden.

Walking: It's about a 10-15 minute walk south and slightly west of Scarfe.

Cycling or scootering: Faster -- about 5 minutes from Scarfe

Bus: There is one of the smaller community buses (#68) from the UBC Bus Loop that I have seen has a drop-off point right outside Totem Field. However, it is scheduled only every 20 minutes on school days (for example, at 12:20, 12:40, 1:00,...) Google maps say to get off after 5 stops at eastbound Thunderbird @ Eagles Drive, but it's still a 450m (4.5 block) walk from there (I've done that...) I'm not quite sure how to access that bus stop right in front of Totem Field, but maybe you can figure it out and share this?

Car: There's no street parking on West Mall and they do ticket. You are probably ok parking inside the Totem Field gates -- or at the UBC Botanical Gardens lot across Marine Drive? (I don't have a car).

What to bring/ wear:

• A sun/ rain hat -- very important!
• A water bottle -- remember to hydrate frequently
• Any medication, epipen, etc. that you need. (Please let me know about any relevant allergies or medical conditions for safety precautions)
• Appropriate layers of clothes for the changing weather
• Appropriate close-toed shoes or boots for walking on uneven or muddy ground
• Light jacket or windbreaker
• Sunscreen and lip balm with sunscreen (I've had sunburned lips, and it's not fun!)
• Laptop, tablet and/or phone for accessing the internet and writing
• Notebook and pen may be helpful as well
• Snacks

Looking forward to seeing you at the Orchard Garden for our classes in September and early October!


Cheers

Susan

An early-bird notification about the BCAMT Fall Conference in Vancouver (Gladstone Secondary)

Every year, there is a province-wide Professional Development (Pro-D) day for all teachers in BC. Each Provincial Specialist Association (PSA) has the possibility of offering a conference for teachers to share ideas, approaches, questions and resources with colleagues. You are expected to develop your professional skills by attending one of these amazing conferences (or a parallel event offered by a museum or other organization on that day).

Most people in our class will likely choose the BCAMT Fall Conference. You can get a discount student early-bird registration rate up till September 30. I'd advise you to register soon so that you don't miss the discount! Here's the link: https://bcamt.ca/fall2026/

Registration: https://bcamt.ca/fall2026/index.php/home/registration/

Introduction to the BC Association of Math Teachers (BCAMT) email discussion group

 I will ask everyone in our class to sign up for the BCAMT listserv, as part of our class. Please do give it a try at least until January -- or if you like it, you may want to stay on and participate throughout your teaching career!

Here is a link to information about the BCAMT listserv/ email discussion group. Note that you should be able to join the listserv for free -- though you might want to join the BCAMT at the reduced student rate for the upcoming October 23 conference, etc. We used to be able to join the email discussion group directly, but I may need to send a list of our class emails to the BCAMT exec to make this happen these days...

Please post a confirmation on the comments to this post to let me know you were able to sign up for this email discussion group.

Hope you enjoy the conversations with fellow math teachers!

 

Skemp on two approaches to teaching and learning mathematics

 

Here is our first article, an old but influential one:

Richard Skemp on instrumental and relational ways of understanding mathematics

Please read this article and write a response on your blog by 9 AM Monday September 14.

Your response should be brief (1-2 paragraphs), but full of interesting ideas. You should NOT summarize the article in this response, but you should talk about:

• Three things that made you "stop" as you read this piece, and why
• Where you stand on the issue Skemp raises, and why

Welcome to EDCP 342, and your career in secondary math teaching!

Hello everybody! Welcome to our class together on Curriculum and Pedagogy in Secondary Math. Here is

a link to our tentative course outline (which may be revised as needed over the semester).

Looking forward very much to working together and exploring the teaching and learning of mathematics in BC secondary schools! Wishing you good learning and a great year!

Note that:  blog posts will be assigned a mark from zero to 3 each week:  3: extraordinarily thoughtful & insightful  2: very good, showing understanding, engagement and thought  1: adequate, showing that the reading has been completed although the response is not strong.  0: assignment is not complete/ reading has not been completed.  Most of your blog posts will get a mark of 2, and if you have all 2's, you will receive full marks for your blog! A mark of 3 is just to let you know that you did an exceptionally impressive piece of writing and thinking from our points of view, and a 3 counts as full marks as well.

If you receive a 0, 1 or 1.5, you will need to write or revise that blog post before the next marking date (in about a month) or by the end of the course. The comments you receive should let you know what needs to be added or revised. Please don't delete the original post, but add an **EDIT to let us know what you have added that is new! Most of your smaller blog posts and responses will be assigned from September to early November -- after that, you can concentrate more fully on your culminating assignments.