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.