Getting Kids to Talk Math! Mathematical Discourse

Lesson 1 Traditionalist Math Versus Reform Math Objective: To understand the difference between the traditionalist approach to teaching mathematics versus the reform mathematics approach to teaching mathematics. Outcome: Teacher participants will use Graffiti Walls to compare and contrast the two approaches to teaching mathematics.

2 Truths and a Lie Activity

Curriculum Outcomes Folder Organization KWL Chart

Video One Discussion Questions: Video One Link Questions: o Why do you think this teacher feels the way she does? o Do you agree or disagree with her? o What changes do you think this math teacher has seen over her years of teaching?

Reform Mathematics Movement vs. Traditionalists NCTM Process Standards CCSS Practice Standards

Video Two Discussion Questions: Video Two Link Questions: o Why do you think this teacher feels the way she does? o Do you agree or disagree with her? o What changes do you think this math teacher has seen over her years of teaching?

Graffiti Wall Activity

Reflection

Extension of Learning Participants can explore The Hunt Institute’s videos that were designed to explain Common Core Math Standards. -Link to The Hunt Institute’s YouTube channel- https://www.youtube.com/channel/UCF0pa3nE3aZAfBMT8pqM5PA 2. Participants can read the following article about traditionalist math ideology and reform math ideology- http://www.usnews.com/news/special-reports/articles/2014/02/25/the-common-core-math-standards-content-and-controversy

Lesson 2 National Council for Teaching Mathematics Framework Objective: To know the components of NCTM’s framework for teaching mathematics. Outcome: Each teacher participant will present the definition of one of the five (a different one for each participant) standards by adding their own slide(s) to the collaborative PowerPoint presentation.

problem solving reasoning and proof communication connections representations.

Jigsaw Activity Resources Standards_and_Positions/PSSM_ExecutiveSummary.pdf http://www.nctm.org/flipbooks/standards/pssm/index.html Pages 52-67,182-206,402 2. https://mathequality.wordpress.com/2012/06/26/nctm-process-standards-for-mathematics/

Group PPT Use graphic organizer notes to share what you’ve learned with your group. Work together to create a PPT about the process standards. Share your PPT with peers and facilitator.

Extension of Learning Analyze how the curriculum that is used in your district stacks up against the standards. Does the curriculum for math that is being used hinder or help the implementation of the process standards? Record at least two lessons of yourself teaching. Use the Lesson Analysis Form to assess the use of the process standards in your lessons. Ask a trusted colleague to help you assess the lessons.

Reflection

Lesson 3 NCTM’s Communication Standard Objective: To know the meaning of and components of the NCTM’s communication standard. Outcome: Teacher participants will analyze the four components of NCTM’s communication standard by participating in a think-pair-share activity.

Think-Pair-Share Activity Discussion Questions: o What is communication? o What is the function of communication? o How do we see and hear our students communicating? o How do we see and hear one another communicating?

Vygotsky’s Theory of Social Learning

4 Components of NCTM’s Communication Standard “Organize and consolidate their mathematical thinking through communication; Communicate their mathematical thinking coherently and clearly to peers, teachers, and others; Analyze and evaluate the mathematical thinking and strategies of others; Use the language of mathematics to express mathematical ideas precisely” (NCTM, 2000).

4 Components of NCTM’s Communication Standard In Our Classrooms Use the graphic organizer to record the ideas generated during class. Record at least two examples of how we could see/hear evidence of the communication standard in our classrooms.

Extension of Learning Create a dialogue between a student and a teacher or between students that shows the components of the communication standard. The dialogue could take many forms. It could be written, drawn, recorded, created digitally, etc.

Reflection

Lesson 4 Expectations in a Math-Talk Community Objective: To understand the development of a culture of a math-talk community in the mathematics classroom. Outcome: Teacher participants will develop their own set of expectations to use in their classroom in order to set up their students to successfully participate in a math-talk community.

Readings/Resources o What does the research say the benefits of discussion in mathematics class are? By Michelle Cirillo o What are some strategies for facilitating productive classroom discussions? By Michelle Cirillo o Creating cultures of participation to promote mathematical discourse by Cory A. Bennett o Creating Math Talk Communities by Erin L. Wagganer http://www.scholastic.com/teachers/top-teaching/2014/01/math-talk-101

Pre-Reading Activity Survey the texts and brainstorm questions you think the texts were designed to answer. Share at least one question with the group.

Reading Activity Participants will each read one of the readings for the lesson. While reading the participants will use sticky notes (placed in the text next to important findings) to keep track of their thoughts on the reading, focusing on the objective for the lesson. Participants will then share what they found to be valuable in each reading with their group. The sticky notes will be used to guide what exactly they share.

Post Reading Activity Discussion Questions: o What is a math talk community? o Why is it important to set up a math talk community? o What about your current classroom environment already displays the presence of a math talk community?

Establish Math-Talk Community Expectations

Critique Math-Talk Community Expectations

Extension of Learning Teacher participants can create an addition to their staff webpage (already acquired through our district) to communicate their expectations to students, parents, and community members. Teacher participants can involve their students in the display of the expectations in the classroom. Student input will be taken in order to decide how expectations for their math talk community will be created and displayed.

Reflection

Lesson 5 Productive Use of Incorrect Answers Objective: To understand the development of a culture of a math-talk community in the mathematics classroom. Outcome: Teacher participants will create a role-play scenario which illustrates research based strategies that use incorrect answers to aid students’ learning.

Reflection Reflect on the image to the right. Write your ideas down and be ready to share your reflection.

Brainstorm How are incorrect answers used in your classroom? What do you hear students saying? What do you see students doing?

Read How are incorrect answers used in your classroom? What do you hear students saying? What do you see students doing?

Role Play Scenario

Extension of Learning Create a pamphlet, poster, or chart about how to use incorrect answers to promote student learning in math. Their audience for this product is parents.

Reflection

Lesson 6 The Teacher’s Role in a Math Talk Community Objective: To understand the development of a culture of a math-talk community in the mathematics classroom. Outcomes: · Teacher participants will investigate the role of a teacher in a math-talk community. Teacher participants will create a response to the question on the group discussion board and will critique their peer responses on the discussion board.

A teacher is...

Investigate the Readings

Discussion o Share ways in which you see yourself taking on the roles of a math talk community teacher already. o Share ways that you could improve your role as a teacher of a math talk community by setting at least two goals for yourself.

Discussion Board Prompts Visit our Google Classroom to participate in the discussion for this lesson. Initial Post: Share ways in which you see yourself taking on the roles of a math talk community teacher already. Share ways that you could improve your role as a teacher of a math talk community by setting at least two goals for yourself. 2 Response Posts: Tell your colleague something you have in common. Tell your colleague something you learned from their post. Provide your colleague with an idea (or ideas) of how to grow toward their goal.

Extension of Learning Watch the video and write down possibilities for the teacher’s ideas to be implemented in your classroom. https://www.teachingchannel.org/videos/peer-learning-between-students 2. Participants can access the following articles for further reading about creating a math talk community. http://gettingsmart.com/2015/10/talking-math-6-strategies-for-getting-students-to-engage-in-mathematical-discourse/ http://gettingsmart.com/2015/09/talking-math-how-to-engage-students-in-mathematical-discourse/ http://teachersnetwork.org/ntny/nychelp/Professional_Development/facilitator.htm

Reflection

Lesson 7 What is a Math Talk Community Scale? Objective: To understand Hufferd-Ackles’ math-talk community scale. Outcome: Teacher participants will analyze the the math-talk community scale designed by Hufferd-Ackles’ et al (2010).

What is a math-talk community? Write Around Activity

The work of Hufferd-Ackles, Fuson, & Sherin

Simplify the Information for... Parents Students Teachers

Extension of Learning Create a bulletin board for the main hallway in our building displaying what a math-talk community looks like in our school. The audience is parents and students. Create a video explaining the components of a math-talk community and the math talk community table from the article. The audience is math teachers in our district.

Reflection

Lesson 8 Application of the Math Talk Community Scale Objective: To understand Hufferd-Ackles’ math-talk community scale. Outcome: Teacher participants will apply the math-talk community scale designed by Hufferd-Ackles’ et al (2010).

Every Teacher Can Improve

Math-Talk Community Reflection & Discussion

Design A Plan

Extension of Learning Participants can involve their students in their plan. Student input can be used to add ideas to the plan. Participants can implement their plan over time and ask a colleague to help them evaluate the environment using the math talk community scale.

Reflection