Supporting Secondary Mathematics Teachers’ Purposeful and Powerful Discourse

Michelle Cirillo, Beth Herbel-Eisenmann, & Mike Steele MDISC, PIs

Thank you• RAs: Kate Johnson, Jen Nimtz, Sam Otten,

Shannon Sweeny, Alex Theakston, & Rachael Todd (Heather Bosman, Lorraine Males, Faith Muirhead)

• NSF• AB members: Ryota Matsuura, David Pimm,

Mary Schleppegrell, Ed Silver, Peg Smith, Randy Phillipp

• Evaluation team: Horizon• Classroom teachers who have allowed us to use

their classroom observations as the basis of these materials (NSF, Grant #0347906, Herbel-Eisenmann, PI)

Mathematics Discourse in Secondary Classrooms (MDISC): A Case-Based PD Curriculum•How can teachers’ and students’

purposeful attention to discourse contribute to productive and powerful mathematical experiences for students?▫Productive: How does discourse in the

classroom help construe students’ understandings of mathematics?

▫Powerful: How does discourse in the classroom help with developing students’ identities as people who can know and do mathematics?

•The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

MDISC Timeline

Project Timeline

Design & External Review Field Testing Large-Scale Publication &

Internal & Revision & Revision Pilot Dissemination

Review & Revision

Phase I Phase II Phase III Phase IV Phase V

2009-2010 2010-2011 2011-2012 2012-2013 2013-2014

Overview of materials• Setting the stage: building community, exploring

beliefs, and noticing beginning aspects of classroom discourse

• Constellation 1: Evidence, Explanations & Tacit Expectations (focus on students)

• Constellation 2: Teacher Discourse Moves and opening up classroom discourse (focus on teachers)

• Constellation 3: Planning for productive and powerful discourse

• Constellation 4: (Focus: launch & explore stages)• Constellation 5: (Focus: summarize & assessment)• Capstone and cycles of action research

Overview of Presentation

•Key discourse constructs shaping the materials (Beth)

•Overview of a subset of materials (Mike)•Observations from small groups

(Michelle)•Comments & discussion (Ryota)

Key constructs: Language and language learning

Beth Herbel-EisenmannMichigan State University

Beginning point: “Talk Moves” (Chapin, O’Connor & Anderson, 2003)

•using appropriate wait time [Wait Time]; •Revoicing, •asking students to explain someone else’s

reasoning [Restating], •prompting students to participate in

substantive mathematical conversations [Prompt]; and

•having students apply their own reasoning to other people’s reasoning [Apply]

Teacher Discourse Moves (TDMs)• Inviting student participation •Waiting•Revoicing•Asking students to revoice•Probing a student’s thinking•Creating opportunities to engage with

another’s reasoning

Why not focus on just these TDMs?• Previous work focused on

elementary

• Are somewhat pedagogically generic

• Provide a tool for focusing attention

• Secondary teachers wanted more mathematical substance to the discourse readings

• Don’t focus attention on increasing sophistication of mathematical discourse

• Don’t necessarily help with considering when, why, or how to use these TDMs

•Mathematically proficient students…▫… justify their conclusions, communicate them

to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose.

▫…able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.

▫…try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose... (CCSS)

Considering why, when & how: Systemic

Functional Linguistics (Halliday & colleagues)

•Not a ‘transformational’ view of language, which suggests that children are born with a genetic blueprint for language learning

•Learners learn to use language for a range of purposes--how adept they become at controlling language and understanding the purposes (consciously or not) is dependent on the contexts in which learners find themselves

Register•The set of grammatical and lexical features

that realize a specific context (Halliday & Hasan, 1989)

•Mathematics register:▫The meanings that belong to the language of

mathematics (the mathematical use of natural language, that is; not mathematics itself) and that a language must express if it is being used for mathematical purposes. (Halliday, 1978, p. 195)

▫Not only about how mathematical terms are used but also characteristic phrases and certain modes that are acceptable (Pimm, 1987)

Developing Math Register: Mode Continuum (Gibbons, 2003, 2004, 2006, 2008, 2009)

•Can serve as a mechanism for teachers and teacher educators to analyze mathematical talk and support the deliberate development of the mathematics register

•Focuses on gradations of communication between spoken and written mode of communication

•Movement from context-dependent language to more abstract and discipline-based use of language

Imagine how language might be used as…•Students engage with trying to generalize

the division of exponential expressions that have the same base

Consider how language changes as…

•a small group of students work at their desks to try to figure out how to generalize the division of exponential expressions that have the same base;

•one student from that group is asked to describe the solution to other students after the groups worked on the task;

•a student might write up a formal explanation; and

•textbook explanation

Supplementing Gibbons: How language relates to mathematical representations

•Classroom Generated Language (“slantiness”)

•Bridging Languages▫Contextual Language (“dollars per mile”)▫Transitional Mathematical Language (“the

steepness,” “what it goes up by”)•Official Mathematical Language (“slope”)

(Herbel-Eisenmann, 2002)Not a linear progression, rather teachers & students need to move back and forth across the mode continuum. The decisions about when, how, and why to move back and forth must be informed by what the teacher knows about the students with whom she works…

Attending to mathematics register alone is not sufficient!

Interpersonal function of language is also important…

Productive… and Powerful!

Positioning…the ways in which people use action and speech to

arrange social structures… recognizes that there can be multiple kinds of conversation happening in any mathematics classroom, each of which assigns fluid roles to the participants. (Wagner & Herbel-Eisenmann, 2009)

• People can position themselves &/or others• Not necessarily intentional

Who is considered knowledgeable in my classroom? About what (e.g., procedures? concepts?)? Who is considered a struggling learner? What does it mean to know mathematics in this classroom? What is emphasized, thinking processes or doing processes? Do we generate mathematics collaboratively or is it something that is mostly done individually?

•What: ▫TDMs: a place to focus teacher’s

attention•When, how, & why:

▫Mathematics register & mode continuum: productive

▫Positioning: powerful

Applying the constructs in our work

Mike SteeleMichigan State University

Why not focus on just these TDMs?

• Previous work focused on elementary

• Are somewhat pedagogically generic

• Provide a tool for focusing attention

• Secondary teachers wanted more mathematical substance to the discourse readings

• Don’t focus attention on increasing sophistication of mathematical discourse

• Don’t necessarily help with considering when, why, or how to use these talk moves

Goals of Constellation 1• Explore criteria & assumptions related to

evaluating student work• Examine student written solutions and other

contributions with nuance associated with the Mode Continuum

• Use student written work and other contributions to think about what students know and what we are not sure students know

• Examine student discourse with respect to positioning and mathematical dispositions

• Identify factors that open up & close down student discourse

Constellation 1 Activities

1. Reflective Questions2. Solve Triangle Area and Perimeter Task3. Create an Imagined Transcript4. Examine Student Work5. Compare Two Classroom Cases6. Analyze Classroom Video7. Looking Back/Looking Forward

Constellation 1 Activities

1. Reflective Questions2. Solve Triangle Area and Perimeter Task3. Create an Imagined Transcript4. Examine Student Work5. Compare Two Classroom Cases6. Analyze Classroom Video7. Looking Back/Looking Forward

The slides around activities 1.4 and 1.5 are omitted……because they don’t make sense without the work session activities. If you’re interested in piloting the materials, contact Beth (bhe@msu.edu), Mike (mdsteele@msu.edu), or Michelle (mcirillo@udel.edu).

Observations from small groups

Michelle CirilloUniversity of Delaware

Comments & Discussion

Ryota MatsuuraSt. Olaf’s College

Discussion Questions• In what ways do you see these activities

helping to achieve the goals we described?•How might these activities help spur change

(through field experiences or action research) to secondary mathematics classroom discourse?

•What do you see as the challenges of engaging teachers in reflecting on their classroom discourse?

•Looking ahead, what kind of evidence would convince you that teachers changed their thinking and classroom discourse practices?