Discourse and Discourse and Mathematics: Mathematics: Get Connected!Get Connected!

Rosann Hollinger and Bernard Rahming

Milwaukee Public Schools

April 27, 2012

NCTM Annual Meeting

Philadelphia

Learning IntentionLearning Intention

We Are Learning To… deepen our understanding of structures/conditions that lead to

productive math talk in the classroom.

Success CriteriaSuccess Criteria

We will know we are successful when we can…

describe productive talk moves that

promote discourse, andexplain how to integrate some of

the ideas raised today into our classroom/school practice.

Alignment of Principles of Formative Assessments

to the Learning Team Continuum of Work for Mathematics

Principles of Assessment for Learning

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(1) Prior to teaching, teachers study and can articulate the math concepts students will be learning. (2) Teachers use student-friendly language to inform students about the math objective they are expected to learn during the lesson.

(3) Students can describe what mathematical ideas they are learning in the lesson. (4) Teachers can articulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments (CABS), and fits within the progression of student learning.

(5) Teachers use classroom assessments that yield accurate information about student learning of math concepts and skills and use of math processes. (6) Teachers use assessment information to focus and guide teaching and motivate student learning.

(7) Feedback given to a student is descriptive, frequent, and timely. It provides insight on a current strength and focuses on one facet of learning for revision linked directly to the intended math objective. (8) Students actively and regularly use descriptive feedback to improve the quality of their work.

(9) Students study the criteria by which their work will be evaluated by analyzing samples of strong and weak work. (10) Students keep track of their own learning over time (e.g., journals, portfolios) and communicate with others about what they understand and what areas need improvement.

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Learning Targets

Stage 2 Align State Framework

and Math Program

Stage 3 Common CABS

Stage 4 Student Work on CABS

Stage 5 Descriptive Feedback

on CABS Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.

Develop meaning for the math embedded in the targets and alignment to state standards and descriptors and to the school’s math program.

Provide a measure of consistency of student learning based on standards/descriptors and targets.

Examine student work to monitor achievement and progress toward the targets and descriptors.

Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.

Note: Even though the continuum and principles of assessment are described as stages, each previous stage needs to be continuously embedded in subsequent stages. Each stage highlights the focus or foreground for professional development and classroom practice as schools and teachers move along the continuum.

References: The MMP assessment principles are adapted from the work of Rick Stiggins and colleagues

Chappuis, S., Stiggins, R., Arter, J., & Chappuis, J. (2005). Assessment for learning: An action guide for school leaders (2nd ed). Portland, OR: Assessment Training Institute.

Connecting Discourse to Connecting Discourse to AssessmentAssessment

“ Classroom discourse provides a supportive context for students to share partial understandings and misconceptions, and instructionally embedded assessment allows teachers to gather information about students’ partial understandings or misconceptions and to further investigate students’ intended meaning through additional probing, guiding and reframing of questions.” Webb (2004)Webb, David. (2004)  Enriching assessment opportunities through

classroom discourse.  In Romberg, T (ed) Standards-based Mathematics Assessment in Middle School.  NY:  Teachers College Press,  p. 170

Classroom DiscussionsClassroom Discussions Using Math Talk to Help Students LearnSuzanne H. Chapin, Catherine O’Connor, Nancy Canavan

Anderson

“… we believe that the ways we used talk in the classroom helped these students make their thinking public; it helped students to explicate and elaborate their reasoning; it allowed them to model, build on, and add to the development of complex ideas; and in at least some cases, it provided a socially grounded motivation to learn.”

Wisconsin Common Core Wisconsin Common Core Standards for MathematicsStandards for Mathematics

ROSANN

Standard 3: Construct viable arguments and critique the Standard 3: Construct viable arguments and critique the reasoning of others.reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They 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. Mathematically proficient students are also 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. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Productive Talk MovesProductive Talk Moves 1. Revoicing: Teacher repeats some or all of what the

student has said. Students verify what was said.

2. Repeating: Asking students to restate someone else’s

reasoning.

3. Reasoning: Asking students to apply their own reasoning to someone else’s reasoning.

4. Adding on: Prompting students for further participation.

5. Waiting: Using wait time.

In action …In action …

Think: individual time to think through

promptPair: small group (use graphic

organizer)Share: whole group reporting out

What’s the Story?

The number of cars in a school parking lot changes as time passes during a school day. These graphs show two possibilities for the way the number of cars might change over time.

Graph 1 Graph 2

Describe the “story” each graph tells about the school parking lot. Which graph shows the pattern you expect?

How could you label the graph you chose so that someone else would know what it represents?

Productive Talk Productive Talk FormatsFormats

Whole-Class Discussion Small-Group Discussion Partner Talk

Conditions need to be Conditions need to be right!right!Classroom cultureGround rules for respectful and courteous talkWhat do you have to do to bring out

productive talk?

TroubleshootingTroubleshooting

The same few students do all the

talking.

I’m falling behind in my curriculum.

Focusing Discourse with Focusing Discourse with QuestionsQuestions

Which questions might be helpful if

your lesson design looked like this:

Launch, Explore,

Summarize

Implementation IdeasImplementation Ideas

As you think about what you know

about discourse, how might you plan

to have this practice become part of

your classroom/school culture?

Success CriteriaSuccess Criteria

We will know we are successful when we can…

describe productive talk moves that promote discourse, and

explain how to integrate some of the ideas raised today into our classroom/school practice.