MATH COMMUNICATIONS Created for the Georgia – Alabama District By: Diane M. Cease-Harper, Ed.D 2014

Warm-up Directions: 1.Work with the peers at your table 2.Use graphics, diagrams, words, pictures, etc., to show your ideas on this topic. 3.Topic: Communication and Math Time Limit: 5 minutes Communication and Math

Oral Language Explain Writing Number Sentence Math Journals Explain Demonstrate Solution Strategies Steps Process Mistakes Steps Labels Answer with a sentence Collaboration Vocabulary Relationships Thinking Draw a Picture Solution Predict Invent Retell Demonstrate Reflect Feelings Attitude Communication and Math Strategies Response to Literature Reading Listening Develop written and oral skills Handwriting Vocabulary

Goals  I want my students to be able to:  Communicate with their peers and their teachers.  Communicate the steps/strategies used to solve a problem.  Communicate their mistakes and how they can correct mistakes.  Answer questions about how they reached the answer.  Communicate a good understanding of the topic.  Analyze the problem, find an appropriate method for solving, and then communicate the steps with the teacher or their peers.  I do not want my students to:  See a math problem and write an answer.

Why Oral Communication in Math is Important As the thinking of the students is exposed, teachers not only begin to understand the thought processes, strengths, and limitations of a particular student, they also begin to shape future instruction.

Types of Oral Communication  Uni-Directional Communication ( weakest) Teacher tends to dominate discussions by lecturing, asking closed questions, and allowing few opportunities for students to communicate their strategies, ideas, and thinking.  Contributive Communication Interactions between students and between students and teacher in which conversations are limited to assistance and sharing  Reflective Communication Students share ideas, strategies, and solutions with peers and teacher as springboard for deeper investigations and explorations  Instructive Communication This type of communication can result in a modification in the students’ mathematical understanding

Opportunities for Communication Be aware of the opportunities for helping students to communicate about math.  Solving real world problems  Solving word problems  Vocabulary development  Literature Connection  Gathering, representing, and interpreting data.  Working with partners  Small group with adult facilitator  Small group without adult facilitator  Teacher modeling thought process  Students sharing thought process in whole group, small group, partners.

Five Ways to Get Students Talking  Revoicing  “I hear you saying this is an odd number.”  Deep thinking and powerful reasoning do not always correlate with clear verbal expression.  Restate what the child is saying using mathematical verbiage  Students restating other students thinking  “Can you repeat what he just said in your own words”  Gives other students another rendition of the first students thinking  Valuable for students whose first language is not English.  Students come to realize that others are listening to what they say and make efforts to communicate effectively.  Apply their reasoning to someone else’s reasoning.  “Do you agree or disagree and why?” and “Can you tell us why you agree (disagree)?  Teacher does not state her position, but rather uses talk to elicit respectful discussion of ideas.  Teacher conveys correct understanding only when students are not able to convey

Five Ways to Get Students Talking  Prompting students to further participation  “Would someone like to add on?”  Begin with revoicing and move to prompting others to contribute to the discussion  Using Wait time  “Take your time … we’ll wait”  Wait 10 seconds after asking a question to call on someone.  Allow student who has been called on to formulate his/her answer.  Second language learners will need more than the typical 10 seconds to answer.  When only the same children are raising their hands to volunteer an answer wait time should be increased.

Written Communication

Why Written Communication Math is Important  When writing, thoughts become clearer  discover exactly what you are thinking.  Students explain and give examples of their understanding of concepts  Students make connections to real-life applications of the math they are learning  Multiple skills used – writing, drawings, graphs to explain their thinking.  Requires students to organize, clarify, reflect on, explore, and extend their ideas

Examples of Math Writing Assignments  Exploring number concepts through Number of the day.  Journal-chronological record of what is being covered in math  Aid to solving math problems by writing what they were thinking as they arrived at a solution  Write about specific math concepts before formal, during, and/or after lessons  Creative Writing

Suggestions: How to Add Writing as a Component of Math Instruction  Teach how to write about what you think.  Modeling  Encourage students and give prompts that they can choose from.  Positive reinforcement  Daily topics  Free Choice - Idea file  Have students write solution strategies to share with the class. Check attitudes  Reflection

Math Journals  Two basic types  Writing about Mathematical Ideas  Mathematical Understanding  Blended Model  Benefits  Experience in making connections in words, pictures, numbers, and manipulatives.  Verbal knowledge, mathematical knowledge, personal experience, and visual ideas merge as connections to mathematical ideas are made.  Encourages both oral and written communication

Write About Mathematical Ideas  Explain in your own words what subtraction means. (familiar first)  Explain what is most important to understand about fractions  What do you know about angles?  What does measurement mean to you?

Explaining How do you know? Whether students are talking or writing about their mathematical learning, the most valuable question that a teacher can ask is “How do you know?”

Use Writing in Math “Students who have opportunities, encouragement, and support for… writing in math reap dual benefits: They communicate to learn mathematics and they learn to communicate mathematically.” NCTM Principles and Standards 2000 Informs teacher Increases math vocabulary Offers extended learning opportunities Allows time to process Helps students think Writing in Math

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