Some key mathematics education journals & Bingjie Wang's MA thesis (2012)

In papers for this course, we will be working primarily with articles from three influential English-language journals and the proceedings of the International Group of PME. The aim is to help you get familiar with these important resources -- although there are many other significant journals in mathematics education as well!

Here are links to the sites for each of the three journals:

For the Learning of Mathematics (FLM)

Educational Studies in Mathematics (ESM) (and its wikipedia page)

Journal for Research in Mathematics Education (JRME)

Bingjie Wang's graduate thesis from 2012 involved textual analysis of these three journals:

Bingjie Wang's Masters thesis, pp. 52-64 only
Bingjie presents data here on three Western math education journals (FLM, ESM and JRME) as part of her textual analysis.]

The idea here is to "read" the whole issue as a text, rather than reading every article in depth.

That means, for example:
•reading the table of contents, and thinking about the titles and topics of articles.

What levels of schooling or age groups do they have as their theme (if any at all!)

What kinds of issues are addressed? How are these distinctive?

•looking at the articles themselves:

How long are the articles?

Are they usually illustrated (and if so, how?)

Are there a lot of references cited?

Are there subheadings on the articles? If so, are they the subheadings that you expect, or not?

What language is the article in?

•looking at the issue as a whole:

What is on the front and back cover, and why?

What did you learn from the author identifications?

What about the material on the inside of the front and back covers?

Is there any material between the articles? If so, what is it? What kind of tone might it set?

There's lots more you might look at too. The idea is to get a holistic sense of the journal as an entity, with a history, a community of writers and readers, etc. You might try looking up the name of the journal to see if there's anything interesting written about it elsewhere too.


Bingjie's full thesis is also available here, at Circle UBC.

Our readings for our Feb. 2 class on problem-solving, problem-posing and word problems

Here are our three readings for next week:

1) Alan Schoenfeld (1996, FLM). In Fostering Communities of Inquiry, Must It Matter That the Teacher Knows "The Answer"?

2) Stephen Brown & Marion Walter on problem posing

3) Susan Gerofsky (1996, FLM): A linguistic and narrative view of word problems

Our class discussion: Why -- and how-- did mathematics become disconnected from culture?

Quote from Musqueam weaver Debra Sparrow, from the cover of Hands of Our Ancestors:

"It is like somebody guides me
It's not me really
I feel that I'm only the hands
through which my ancestors work...
I feel that way, that I will be able to show people again
what we have and what we are."


In mathematics class, we just "do math" -- and then "do more math". Learners are seldom aware of even the mathematical topics they are learning about, never mind having a sense of being connected to powerful, ingenious, beautiful cultural knowledge and ways that connect them with their ancestors, with nature, with practical and beautiful arts.

How and why might this rupture have happened?

• The Industrial Revolution and the rise of public schools: this made by hand that took time to make were devalued.  Physical objects that showed mathematical relationships were devalued.

• Elitist education: upper classes would do a much higher level of math as a gatekeeper. Not everyone got access to the same math. This may still be the case in some places. (Streaming, AP and IB courses, underprivileged within public schools...)

• Introduction of Western education in colonized nations involved a lot of rote memorization, collided attitudes.
Weaving and other crafts involved in inner focus, concentration, expression of self and culture, and a depth of attention. There is a stillness and silence, and there may not be a lot of words accompanying -- not a very school-y thing!

• Did cultural connections get lost over time and translation across countries and cultures? For example, did Al Ktwarizmi's algebra lose its connections? But even Plato (500 BC) disconnected mathematics as an abstract thing from the world. Platonic and Cartesian thought valued abstraction over everything else.

• People think about mathematics in terms of culture-free, evaluative exercises -- including parents. Once established, the system can be very conservative. Kids ask 'why am I learning this?' -- is this only in math, because it is so disconnected from things.

Do we believe 'I shop, therefore I am'? We often justify learning things because it will make you money... Are there other values?

• Every culture has contributions to the creation of math. Colonizing cultures  dominate over other cultures -- and the abstraction of mathematics allows ideas to be 'extracted' from conquered cultures (and one's own culture)to be applied to many situations even in other contexts and cultures.

• Every culture views math from different angles -- for example, Ancient Greek mathematicians focused on geometric shapes, but contemporary Asian mathematicians focus on numerical relations. By abstracting math away from contexts, these different foci can be brought together.

An additional resource for Culturally Responsive Mathematics: Nicol, Archibald & Baker UBC Report

This is a longer and very interesting 2010 report on culturally responsive mathematics in the British Columbia context, written by our UBC colleagues Cynthia Nicol, Jo-ann Archibald and Jeff Baker.

Here also is a link to the Alaska Standards for Culturally Responsive Schools.

Our readings for our Jan. 26 class on Culturally Responsive Mathematics

It was hard to choose readings this week, as there are so many important questions about this topic, in Canadian and other contexts! I made the decision to go with one article from a Maori cultural context in New Zealand, and two from Canadian Indigenous contexts. For those who are interested, though, there are perspectives from many other cultural perspectives, and there is much work needed in this area too.

1) Averill et al (from NZ): Culturally Responsive Teaching of Mathematics: Three Models from Linked Studies (2009)

2) Lunney Borden (Canada): Learning mathematics through birch bark biting: Affirming indigenous identity (in Proceedings of Mathematics, Education and Society Conference 2015 -- starts on p. 756)

3) Two short, related readings -- note that you must read both!

a) Doolittle (Canada): Mathematics as Medicine (in Proceedings of the Canadian Mathematics Education Study Group (CMESG) 2006, pp. 17-25).

and:
b) Doolittle & Glanfield (2007): Balancing Equations and Culture: Indigenous Educators Reflect on Mathematics Education. FLM, pp. 27-30.

Proposed field trip this evening to MOA for Debra Sparrow's talk on Coast Salish Weavings (and our mathematical take on this!)

This evening from 7 - 8 PM at the Museum of Anthropology on UBC Campus, there is an interesting talk scheduled: Musqueam weaver and artist Debra Sparrow will be talking on Coast Salish Weavings. The talk is free with entry to MOA, and MOA entry is always free to UBC students, staff and faculty with your UBC card.

I propose that we walk over at about 6:40 and take part in this talk and tour as part of our exploration of ethnomathematics (our topic for next Thursday's class). We can listen to the talk and ask questions from a mathematics education point of view.

I know that not everyone will be able to stay past 7:30, and we can let the speaker know that. For those who are able to, it would be great to stay till 8:00 -- but if you can't, that should be OK too!

Paulus Gerdes' books at Lulu.com --many available as free pdf downloads!

Very sad to say, Paulus Gerdes passed away two years ago at a relatively young age, and the world has lost a great ethnomathematician.

Gerdes' books are all available at this Lulu.com site, many of them as inexpensive or free pdf downloads. Here is an example of one of them:

Explorations in ethnomathematics and ethnoscience in Mozambique



One of the ways to work against neocolonialism and ethnocentrism is to work reflexively -- that is, to view one's own culture as the subject of anthropological or other study, inspired by a sense of the importance of all cultures.

Reading chapters 1, 2, 3 or 5 from this book by Gerdes with your group, can you think of things (or activities) in your own cultural world (and/or that of your students) that might lend themselves to mathematical study, exploration or exemplification? Would you consider using these in your teaching? Why or why not? How, when, with what focus?

Readings for our January 19 class: Ethnomathematics

Hi all! Here are our readings on ethnomathematics:



1) Paulus Gerdes on "frozen mathematics" and geometry

2) Carraher, Carraher & Schliemann on street mathematics and school mathematics

3) Marcia Ascher on Marshall Island wave maps as an example of ethnomathematics

Snack rota -- for our "mostly healthy" snacks!

1. Jan. 5: Susan
2. Jan. 12: Ting and Sharon
3. Jan. 19: Malihe and Amanda
4. Jan. 26: Nancy and Tsubasa
5. Feb. 2: James and Susan
6. Feb. 9:
7. Feb. 16:
8. Feb. 23: Meeting off campus during Reading Week
9. Mar. 2:
10. Mar. 9:
11. Mar. 16 & 23: Virtual class during Spring Break
12. Mar. 30:
13. Apr. 6: 

Remember to include lots of fruits and veggies, perhaps some protein like cheese, humus, nuts, etc., some bread or crackers, and perhaps a little something sweet...

If you have any foods you don't eat or a restricted diet, for whatever reason, please let others in the class know so that they can bring foods you like and can have!

Jan. 5 class readings for next class: Is mathematics education a 'field'?

1) Higginson: On the foundations of math education


2) Wheeler, Nesher, Bell, Gattegno: Research program for math education (1)


3) Kilpatrick: Reasonable ineffectiveness of research in math education

Writing responses to articles -- talking back to text

As you read academic books and articles, view videos, films and works of art, hear lectures, etc., it is helpful to engage with these 'texts' in a real or imagined conversation. Thinking and engaging critically doesn't necessarily mean being negative about what you're reading! It just means that you
ask questions, connect your reading to your own knowledge and experiences, think about what is not included or what could have been as well as what is included in the piece, etc.

Some good starting prompts for engaging in a critical dialogue with a text:

• I was surprised by...
• I was excited to read that ....
• I was annoyed to read ...
• I wholeheartedly agreed/ disagreed with the author on this point.... because....
• I wondered why ...
• I would illustrate this piece as follows ... (with a story, a diagram, a drawing, a comic strip, a graph, etc.)
• I could predict .... but not ... in this piece
• If I could talk to the author, I would ask them...
• This relates to my own life/ knowledge/ experiences in this way...
• Something that was not included in this piece was ...
• This piece reminded me of (something else I've seen/ heard/ experienced), in this way...
• If you extended this idea to the limit, it would result in ...
• This fits into the author's other work in this way...
• I see the following influences in this piece: ...
• The author interprets .... in the same (or a very different) way than I would: ...

"The Stop": Giving attention to things that stop you in your tracks as you read

David Appelbaum, The Stop (1995)


A "stop" is something that stops you (in your reading, in your observations, in your teaching/ learning). The metaphor is suddenly coming across a big rock in your path that stops you from smooth and continuous (and unconscious) walking. It must be attended to. It is a moment that allows for an opening to new paths, new ideas, new approaches if you are able to give it the attention it demands.

A stop in your reading might be something you didn't expect -- something confusing, or difficult, or exceptionally beautiful, or something you strongly agree or disagree with, or an unknown word or phrase. A stop touches you deeply in some way (by irritating, or moving, or perplexing you, for example).

The stops allow for a change of heart, a change of mind, a political and/or intellectual engagement, a reconsideration of strategy, or even a reconsideration of world view.

From Lynn Fels, "Coming into presence: The unfolding of a moment" (Journal of Educational

Controversy):



"A stop is a calling to attention; a coming to the crossroads, in which a choice of action or direction must be taken, oft-times blindly, as experienced by Appelbaum’s (1995) blind man as he tap-taps the obstacles he encounters with his white cane—there are as yet unknown consequences of the subsequent action or decision as yet to be taken and embodied.


Between closing and beginning lives a gap, a caesura, a discontinuity.

The betweenness is a hinge that belongs to neither one nor the other.
It is neither poised nor unpoised, yet moves both ways . . .
It is the stop. (Applebaum, 1995, pp. 15-16)

A stop is a moment that tugs on our sleeve, a moment that arrests our habits of engagement, a moment within which horizons shift, and we experience our situation anew. A stop occurs when we come to see or experience things, events, or relationships from a different perspective or understanding; a stop is a moment that calls us to mindful awareness of Arendt’s appeal for renewal through action in the gap between past and future.

How we choose to respond and how that choice of action or non-action impacts on our lives and on the lives of those around us speaks to the risk, the opportunity, to the possibility of action. As media philosophers Taylor and Saarinen (1994) remind us, in spaces as familiar as the London tube, or as unmapped as cyberspace, we must “mind the gap” (p. 5). Applebaum’s moments of stop are moments that call our attention to the gap; moments that interrupt, that provoke new questioning, that evoke response, reflection, and hopefully, lead to meaningful and moral action."

Welcome to our class blog! Draft course outline here too...

Hello, and welcome to our EDCP 550 class blog! This is an online space where we can share ideas, links to readings, discussions, and links to our own personal blogs for the class.

Here is a link to the first draft of our course outline (and any revised course outlines will be posted here too). Here is the second draft of our course outline, taking into account the topics that received the most votes in our first class poll.

It's going to be a great class! Looking forward to working together to explore origins and issues in math education.