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!