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Discourse and Mathematical Argumentation in the Classroom. Wednesday, June 6, 2012. Computing seems to be an instructional priority despite the fact that the field of mathematics goes far beyond procedures. At its core, mathematics involves exploring , arguing , and justifying .

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Discourse and mathematical argumentation in the classroom

8 standards for mathematical practice
8 Standards for Mathematical Practice fact that the field of mathematics goes far beyond procedures.

  • Make sense of problems and persevere in solving them.

  • Reason abstractly and quantitatively.

  • Construct viable arguments and critique the reasoning of others.

  • Model with mathematics.

  • Use appropriate tools strategically.

  • Attend to precision.

  • Look for and make use of structure.

  • Look for and express regularity in repeated reasoning.

Discourse that promotes conceptual understanding by elham kazemi
Discourse that Promotes fact that the field of mathematics goes far beyond procedures.Conceptual Understanding by ElhamKazemi

  • 3 things that are clearer to you regarding discourse, mathematical argumentation, and sociomathematical norms

  • 2 connections to your own classroom

  • 1 question or point you would like to discuss further

Kazemi s main points
Kazemi’s fact that the field of mathematics goes far beyond procedures. Main Points

Discuss in pairs
Discuss in pairs… fact that the field of mathematics goes far beyond procedures.

Kazemi wrote that “press for learning was measured by the degree to which teachers

  • emphasized students’ effort

  • focused on learning and understanding

  • supported students’ autonomy

  • emphasized reasoning more than producing correct answers.”

Discourse and mathematical argumentation in the classroom

My research study
My Research Study classroom?

  • Mathematical Context: Arithmetic Properties

  • Goals:

    • Identify and describe the characteristics of students’ mathematical arguments related to the arithmetic properties

    • Quantify growth when instruction promoted mathematical argumentation

  • Two Fourth-Grade Classrooms

    • One had more opportunities for argumentation and an emphasis on explaining and exploring.

    • One followed the traditional textbook and worksheets.

Depth of knowledge
Depth of Knowledge classroom?

Traditional Textbook Tasks

Modified-Lesson Tasks

If you take any number and multiply it by zero, you will always get a number larger than 100. Do you agree or disagree? Explain.

5 + 1 = _____ + 5

“What should go in the blank so that the following number sentence is true? Who can explain why their answer is correct?”

Teacher moves and sociomathematical norms
Teacher Moves and classroom?Sociomathematical Norms

Language Frames

(Ross, Fisher, & Frey, 2009)

  • I believe _____ (statement) because _____ (justification).

  • Based on _____, I think _____.

    • I noticed _____, when _____.

    • I disagree with ____ because ____.

Sentence Starters (Loper and Baker, 2009)

  • What do you think?

  • What is your claim?

  • Why do you think that?

  • What is your evidence?

  • My claim is…

My teacher moves
My Teacher Moves classroom?

I had 23 teacher moves but only six of them occurred before mathematical arguments:

  • repeats or restates

  • invites ideas or observations

  • invites students to agree or judge

  • prompts for justification, explanation, or convincing

  • prompts for elaboration or clarification

  • gives a false claim

Facts about my teacher moves
Facts about my Teacher Moves classroom?

  • The most commonly used teacher move (repeating or restating) did not occur before many arguments.

  • The teacher move that most frequently occurred before a student argument was a prompt for justification or explanation (about 65%) even though it was not a common teacher move overall (occurring only about 7 % of the time).

Mathematical errors
Mathematical Errors classroom?

  • What are some ideas about teacher moves for a mathematical error introduced by a student?

    • What have you done in the past?

  • What are your ideas about introducing false claims?

What are the students reactions to my false claim what could i have done next to follow up
What are the students’ reactions to my false claim? false claim?What could I have done next to follow up?

Did including mathematical argumentation make a difference in student learning
Did including mathematical argumentation make a difference in student learning?

Pre- and Post-Assessment Data

Individual interview assessments with students in both classrooms focused on:

  • Correctness

  • Computational vs. Number Pattern Strategies

  • Recognition of a Property

Correctness in student learning?

Pre and post assessment results summary
Pre- and Post- Assessment Results Summary in student learning?

Some students in both classrooms showed improvement on the assessment.

Students in the focus classroom applied their understanding of properties more frequently than in the contextual classroom.

Students in the focus classroom applied more number pattern strategies to the assessment tasks.

Discussion points
Discussion Points in student learning?

  • What are the benefits and disadvantages of including mathematical argumentation? What could be done to alleviate the disadvantages?

  • How can you include mathematical argumentation in your knowledge package topic?

Depth of knowledge and standards for mathematical practice
Depth of Knowledge in student learning?and Standards for Mathematical Practice

  • In order to teach at higher levels of the DOK framework, we need to be including mathematical argumentation and justification.

  • Mathematical argumentation is one of the 8 Standards for Mathematical Practice.

  • What are the characteristics of tasks aligned with standards for mathematical practice, high DOK levels, and mathematical argumentation?


Homework in student learning?

  • Read What exactly do “fewer, clearer, and higher standards” really look like in the classroom? Using a cognitive rigor matrix to analyze curriculum, plan lessons, and implement assessment.

    Karin K. Hess, Dennis Carlock, Ben Jones, John R. Walkup

  • Reflection