Presentation Sildes: coding in classrooms

Hi everyone,
I have booked the presentation "coding in classrooms" in Burnaby Elian Center. I received some inspiring feedback from the audience earlier in Richmond. Please take a look of the link and I am looking forward to your comments.
Ting

https://docs.google.com/presentation/d/1eZJoewpUo6FxLEojo7U9lE9mKOn6z_c0T2-K1Fiv8dg/edit?usp=sharing

Mathematics Education and Cultural Connections Presentation

https://drive.google.com/file/d/0B-VgrdpDAFIjNXRJRUZHYkV6R2M/view?usp=sharing

malihe

https://docs.google.com/presentation/d/1AuGFqilq28KqD-f8CtwjcB0fxvc0Pxs-2Lrgigb5eVs/edit?usp=sharing Malihe

Problem Posing Presentation

Problem Posing Presentation by Sharon Nijjar

Details about your 20-minute presentation this Thursday April 13

Hi everyone. It's our last class for this course, and we will run it as an in-class conference, with each student presenting their long paper and an interactive activity in 20 minutes.

Some requirements:

• Base your presentation on your long paper
• Please include 10-12 slides (which might contain text -- at least 18- 20 point font--and/or pictures, videos, etc. Please post your slides on your blog by Thursday.
• Include a 5-10 minute brief interactive activity for the rest of the class to try, to help everyone understand your topic and research.
• Don't read your slides or text-- but talk to the group directly!

Looking forward to a very interesting session.

We will also need to have some snack (who's bringing food this week, or will it be a potluck?)

It's also important that everyone fill in your course evaluations on line. These provide valuable feedback for me to help me improve the course from year to year. If you can, please fill out the course evaluation before class...or we can leave time to do them at the end of class.

Looking forward to seeing you and having a great culminating class for our course this Thursday!

Some interesting visual & historical approaches to algebraic problem solving

From Sawyers' Vision in Elementary Mathematics (on even and odd numbers and visual algebra)

From Joseph's Crest of the Peacock (on Ancient Egyptian fractions)

From Olivastro's Ancient Puzzles (on Ancient Egyptian division of loaves of bread)

Readings for our Thursday April 6 class on early algebra

Hi everyone! I hope you've enjoyed Spring Break and that you are continuing to contribute to our virtual class (which will be open until next Thursday's face-to-face class).

As usual, we have three readings for next Thursday. Here they are -- and see you soon!

1) Carraher, Martinez & Schliemann (2008): Early algebra and mathematical generalization







2) Moss & Beatty (2010): Knowledge building and mathematics

3) Kieran (2004): Algebraic thinking in the early grades

Detailed information for researching and writing your long paper

Hello everyone! I hope you are enjoying our Spring Break week from class (taking the place of the February Reading Week.  I have been following the comments added to the article on math education and technology for our virtual class, and I'm happy to see that things are off to a good start. Please do remember to participate in our virtual class  between now and our next face-to-face class on April 6, and check the instructions on the blog posting about how you are expected to participate.

Several people have asked for more information about the long paper for class. Here are some further details -- and don't hesitate to contact me if you need information on anything I may have omitted!

From our course outline: 
Long paper (to be submitted as an email attachment by 9AM on the day of Class 13. Peer review by classmate one week before.) Approximately 4,000 words.

Following up on your short paper, choose a research theme in mathematics education (preferably the same one used in your first paper, but could be different with instructor’s permission). Write a critical review of research in this area, considering work from the 1980s or earlier up to the present. Your review should review approximately eight key works, which should come from a variety of authors, major journals and conference proceedings. Your paper should consider work on this topic in chronological context and in light of the authors’ own positioning. (50%)

Additional information: Your long paper for this course is intended to be a first go at the literature review for your thesis, graduating paper or dissertation, taking into consideration the breadth of major work in mathematics education relating to your area of interest and topic. So it should show a consideration of the history of research in this area (as this is a course in Foundations of Mathematics Education) as well as more contemporary work related to your interests. You should also include articles from the four major sources used in your short paper (PME proceedings, FLM, ESM and JRME), but you can also include articles from other journals, books and conference proceedings.

Your topic can be more focused than in your first paper, but should relate fairly closely to the first paper. If you would like to change to an entirely different topic for some reason, please email me to give a rationale for the change and get approval for the new topic.

You may use any or all of the four articles from the short paper if that is helpful, or you could go with eight entirely new articles if you choose to. You can refer to things you wrote in the short paper and even quote yourself (briefly), but the long paper should not include the entire short paper. It must be a new piece of writing that integrates all eight articles in a literature review.

 You may want to refer to the outline of a typical thesis or dissertation Review of Literature as outlined on our EDCP webpages. Here is a version of that outline relevant to this paper:

• Briefly outline the major headings and issues that you will be addressing in the paper. Discuss the context of the research problem you will be considering and why it matters to you.

• Make sure that this is a critical review where you comment on the strengths and weaknesses of the articles or books. 

• As in the short paper, give a brief summary of the main points of each article, your 'stops' in it that are relevant to your research question, and how this article relates to other articles you are reviewing in light of your research interests. In other words, have a written conversation with each of these articles and among these articles, and use this conversation to clarify where you stand on the issues in relation to what has been done before.

• Use this review to make an argument for why you are doing your study. Possible arguments might be: a) there is a lack of literature in the area; b) there are conflicting reports in the literature and clarification is required; your work is an extension of existing studies in terms of scope and context.

• Be sure to include the literature regarding any theoretical perspectives you are using in your
study.  Make a connection between these perspectives and your own study.

Hope this is helpful -- please let me know!

Our wonderful guest speaker for our April 6 class: Visiting professor Luneta from University of Johannesburg

I am very pleased that we will be having a guest speaker for our April 6 class on "Early algebra
learning: Generalization and abstraction." Dr. Luneta is a professor of mathematics education at the University of Johannesburg in the Republic of South Africa. He is visiting our department for the next few months, and is a specialist in early mathematics learning.

He is also involved with teaching and learning gardens and mathematics and art (so you can imagine we have lots to talk about!)

Have a great Spring Break, and looking forward to seeing everybody back on April 6.

Embodied, multisensory math prompts for our class discussion

[Free Event] WALL EXCHANGE with Cédric Villani: The Hidden Beauty of Mathematics

Please allow me to share the fascinating event with you here!

If you are interested in the interface between math and art, I recommend that you check the below link.

Title: The Hidden Beauty of Mathematics
Presenter: Cédric Villani
Date & Time: 2017/05/02  7pm 
Venune: Vogue Theatre
Ticket: Free

http://voguetheatre.com/events/wall-exchange-with-cedric-villani-the-hidden-beauty-of-mathematics/

Upcoming weeks: Our virtual class on technology and math education!

For the next three Thursdays (March 16, 23 & 30), we will not be meeting in person (sob!)

March 16 counts as our Reading Break week, and March 23 as our virtual class.

On March 30, I will be away at a conference in Berlin, so we will be adding an extra class at the end of our course (on April 13) to make up for missing this class. Your long papers and presentations will be due on the April 13 class -- more on the details in another blog post!

MORE ON THE VIRTUAL CLASS:

Here is a link to the article we will all read for our virtual class:

Oi-Lam Ng & Nathalie Sinclair on "Young children reasoning about symmetry in a dynamic

geometry environment"

Here's what to do to participate:

• First, read the article in depth by March 23 at the latest, and make your own notes on it.

• Then go to the "comments" section of this blog post, and join the discussion. Read what others have posted, and then add a comment with your thoughts, ideas, quotes, stops, arguments, agreements, speculations, alternate versions, questions, etc. around the article and the ongoing discussion of it.

• Dates: The discussion of the article can, in practice, stretch from tomorrow (March 10) to our next face-to-face class (April 6). I expect most of the discussion to take place between March 16 and 30.

• How much is enough? I will be monitoring the discussion throughout the period from March 10 - April 6. I expect that each person in the class will post at least 4 substantive postings, spread out over at least 7 days.

• A substantive posting should not be super-long (keep your postings to a maximum of two paragraphs each). However, it should be responsive to the article (and should refer back to the article frequently), and it should be responsive to the ongoing class discussion. It is not enough to say, "Great!", or "Yes, I agree". (You can certainly add those kinds of comments, but they will not count as substantive postings.) A substantive posting should be an interesting, engaging, in-depth comment, like the best of your regular blog posts.

• You cannot do all your postings in a clump.  This is meant to be a class discussion or conversation on-line -- so you can't do four postings in a row, or do them all on the first or the last day. You should plan to space your postings over the course of a week or more, and take time to read and consider what others have written before posting.

In my experience, our virtual class is often one of the best discussions of the course! With this great group, I have no doubt that this tradition can be continued...

Enjoy!

Bobby McFerrin teaches the audience to sing

Here is a link to that interesting video we saw in class tonight -- where, very much like Dave Hewitt teaching algebra and integers by tapping the board with a ruler!

Sociomathematical norms

T: This is a combination of traditional method and inquiry base method.

M: I think this is not traditional way, I do not know the name of methods, and it is new to me.

We thought the traditional way might be different among countries, but when we discuss we realize that these are similar: Teachers explain the contents of textbook while students just take notes and answer to the questions that teachers asked.

Teacher use the traditional method to control the student and class when he continues to knock the board until the students get the same ideas of the lesson.

Sociamathematical Norms

Objectives:
Introduction of algebraic equations
number line
large numbers
negative numbers
order of operation (+)


Students:
we don't know the question at the beginning
we need to focus otherwise we loss the track of the questions.

Teachers:
Teacher doesn't command the class
The teacher will never explicitly give the answer
The teacher will repeat question and demonstration for better understanding
Discussion is not encouraged during the demonstration stage

Sociomathematical Norms

Dave Hewitt

-sometimes calling out, sometimes students raised hands (did teacher give a signal?)
-when it was a more difficult question, students would put their hands up
-math as performative; teacher would engage everyone to talk
-safe for students because teacher started easy
-sometimes introduced something matter of factly (didn't explain it)
-used things "x" in context
-oral and verbal; auditory processing by students
-sound
-giving students the chalk (power symbol)
-abstract (not contextual in terms of objects)
-solicited answers and for students to correct him (the teacher)
-students in table groups
-working together
-the students were only singled out when they wanted to be
-the teacher went clockwise (like a number line)
-teacher wasn't always at the front of the room
-when students were at front, teacher was not
-inquiry
-constructivist; building knowledge; students contributed in building the knowledge
-participatory
-incremental
-teacher eventually prompted students to use "x"
- ... , integers, place value, beginning of algebra
-paused a lot
-sometimes takes things into a new thing an old thing
-blended
-imagining, picturing something

Our readings for our March 9 class on Visualization and Embodiment in math education

1) Norma Presmeg on prototypes, metaphor, metonymy and visualization in high school math

2) Francesca Ferrara on imagination, multimodality and embodiment in young children learning graphing










3) Martha Alibali and Mitch Nathan on gesture and embodiment in mathematics learning

Some short films for discussion of sociomathematical norms in classrooms

1) Annie Fetter, NCTM Ignite talks for mathematics teachers on Hidden Decision-Making in the Math Classroom and an alternative to SWBAT.

2) Teacher Lynn Simpson on student participation strategies and reasoning about division.

3) Lessonsketch.org -- a project of Pat Herbst and colleagues from the University of Michigan. Create a log-in and explore two of the films.


Please watch these films with a critical eye to the sociomathematical norms (endorsed, intended, perceived) that are apparent here. Remember that there is no one 'right' way to establish or enact particular norms in a classroom -- but there are intended and unintended effects on learning, on relationships, on student beliefs and understandings, and of power structures in schooling that play out according to these norms.

Sociomathematical norms, curriculum & some parallel ideas from linguistic pragmatics

In our readings for this week's class on sociomathematical norms, researchers talk about several ways to think about these norms:

• endorsed norms (the norms that teachers talk about as positive, or that are part of the official curriculum)

• enacted norms (how norms are played out by teachers and learners in the everyday life of the classroom, as observed by researchers or other outside observers)

• perceived norms (students' uptake or understanding of classroom norms as they experience and interpret them)

Those who are familiar with ways of thinking about aspects of The Educational Imagination) have thought about related ideas like "the mandated curriculum", "the intended curriculum", "the enacted curriculum", as well as "the hidden curriculum" (hidden from teachers, many times!) and "the null curriculum" (the many human knowledges that are omitted from the curriculum).
curriculum influenced by Elliot Eisner's work (especially in his book,

There is a similar way of thinking that comes from an area of linguistics called 'pragmatics' -- the study of language in use and in context.

In linguistic pragmatics, linguists may analyze a speaker's intentions in making an utterance and the utterance as a 'speech act'

in a number of interesting ways (from philosophers of language John Austin and John Searle):

• the locutionary force of the utterance -- the literal meanings of the words
• its illocutionary force -- what the speaker intends to say that goes beyond the literal meanings of the words
• its perlocutionary force -- what the speaker's utterance does in the world, or what it makes the listener do
• the listener's uptake -- how the listener perceives and interprets the utterance

This terminology may be helpful in thinking out how the intentions of teachers, learners and others are played out in classroom situations -- and how they relate to classroom sociomathematical norms!

Judith Butler video: Gender as performance

Here is the link to this short video!

!

Our off-campus class

Thanks for posting this great photo, Sharon! I'll add a few more too. - Susan

Gender and other categories: The 'No True Scotsman' logical fallacy

The 'No True Scotsman' logical fallacy is one that shows up quite often in discussions/ arguments about gender, ethnicity, religion, culture and many other discussions that involve categorizations of people or things. 

Here is an explanation of this logical fallacy from <http://www.logicalfallacies.info/presumption/no-true-scotsman/>:

‘No True Scotsman’ Fallacy

The no true scotsman fallacy is a way of reinterpreting evidence in order to prevent the refutation of one’s position. Proposed counter-examples to a theory are dismissed as irrelevant solely because they are counter-examples, but purportedly because they are not what the theory is about.
Example

The No True Scotsman fallacy involves discounting evidence that would refute a proposition, concluding that it hasn’t been falsified when in fact it has.

If Angus, a Glaswegian, who puts sugar on his porridge, is proposed as a counter-example to the claim “No Scotsman puts sugar on his porridge”, the ‘No true Scotsman’ fallacy would run as follows:

(1) Angus puts sugar on his porridge.
(2) No (true) Scotsman puts sugar on his porridge.
Therefore:
(3) Angus is not a (true) Scotsman.
Therefore:
(4) Angus is not a counter-example to the claim that no Scotsman puts sugar on his porridge.

This fallacy is a form of circular argument, with an existing belief being assumed to be true in order to dismiss any apparent counter-examples to it. The existing belief thus becomes unfalsifiable.
Real-World Examples

An argument similar to this is often arises when people attempt to define religious groups. In some Christian groups, for example, there is an idea that faith is permanent, that once one becomes a Christian one cannot fall away. Apparent counter-examples to this idea, people who appear to have faith but subsequently lose it, are written off using the ‘No True Scotsman’ fallacy: they didn’t really have faith, they weren’t true Christians. The claim that faith cannot be lost is thus preserved from refutation. Given such an approach, this claim is unfalsifiable, there is no possible refutation of it.

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

Another example, this one about things:

One could make a statement like, 'All teacups can hold hot tea' -- and that is generally so, as holding hot tea is generally the function of a teacup.

However, there are counterexamples, like Oppenheim's fur teacup, or a broken teacup.









The 'No True Scotsman' fallacy would claim that such counterexamples were not true teacups. An alternative approach would be to open up the question, asking what these and other counterexamples offer us as new spaces for thinking about what a 'teacup' might be.

These questions also lead to ideas from Eleanor Rosch's Category Theory (1978), where some things or qualities seem very central to a particular human-made category, and others lead to questions of whether our definitions work at all.

Readings for our March 2 class: Sociomathematical classroom norms

Here are our three readings for next week's class!

1) Yackel & Cobb's foundational article from 1996 (note that Tsubasa should pick a different reading as this was part of his paper!)

2) Yackel & Rasmussen: Beliefs and norms in an undergraduate mathematics class 2002

3) Levenson, Tirosh & Tsamir: Students' perceived mathematical norms 2009

Video interview with Rico Gutstein

Here is a link to a filmed interview with Rico Gutstein on math education and social justice!

Photos and whiteboards from our classes to date!