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Five Major Reasons That Talk Is Critical to Teaching and Learning • Talk can reveal understanding and misunderstanding. • Talk supports robust learning by boosting memory. • Talk supports deeper reasoning. • Talk supports language development. • Talk supports development of social skills. Strategies for Encouraging High-Quality Student Interaction The Use of Rich math tasks • Tasks with multiple solutions and/or strategies • Opportunities to explain and justify their strategies and reasoning • Tasks with simple operations and simple solutions with provide little or no opportunity to engage. Justification of Solutions • Encourage productive argumentation and justifications in class discussions • Justify strategies, not recount procedures Students Questioning One Another • Provide students with higher-order question prompt cards with a range of higher-order questions • Use question stems that could be applied to current content such as “how are ... and ... similar?” Use of guidelines for math-talk • Explain: “This is my solution/strategy….” “I think _______ is saying that …” ▫ Explain your thinking and show your thinking. ▫ Rephrase what another student has said. • Agree with reason: “I agree because…” ▫ Agree with another student and describe your reason for agreeing. ▫ Agree with another student and provide an alternate explanation. • Disagree with reason: “I disagree because …” ▫ Disagree with another student and explain or show how your thinking/ solution differs. • Build on: “I would like to build on that idea…” ▫ Build on the thinking of another student through explanation, example, or demonstration. • Go Beyond: “This makes me think about…” “Another way to think about this is…” ▫ Extend the ideas of other students by generalizing or linking the idea to another concept. Teach as Facilitator Accountability & Assessment • Hot Seat Questioning: teacher calls on one student to summarize another student’s thinking. • Secret Student: Teacher selects on secret student. If that student is on task when the teacher checks on him/her the whole class gets a point. • Mini White Boards • Thumbs Up, Thumps Down • ADCD Cards/Corners • Exit Passes with “Why” Questions • Group Quiz Productive Partners How students can be expected to act during partnered academic discussions 4 L's • Look at your partner • Lean toward your partner • Lower your voice • Listen attentively Sample Strategies for Precision Partnering How teachers can present partnered discussion expectations to students • Students will be split into A/B partners, consider ability when pairing. • Discuss prompt/question ▫ Students will read answer to their partner. Should be read with expression. ▫ Teacher will indicate when it is time for different partner to share. ▫ Listen to partner's idea, make eye contact and have a pleasant facial expression. Write down partner's idea. • Students are expected to always be on task. If students have extra time, they will share a second answer or simply repeat their first. ▫ . Be an “Idol” not “Idle”, if students are not on task, they will be the first group called on to report out in the whole group discussion. • Whole class discussion (various structures for student accountability) Sample Discussion Sentence Starters • To share new ideas... ▫ What if we tried __________________________? ▫ I have another approach to the problem. ▫ How about _________________? ▫ Here's another possibility. We could _________________? • To disagree respectfully... ▫ That is a good approach to the problem, but what about _________________? ▫ I understand what you're saying but __________________? ▫ I am not sure that will work because __________, what if we tried _________? • To help clarify ideas... ▫ Could you explain what you mean by (other person's idea here) ? ▫ Could you explain that another way? ▫ What part of the problem is hard to understand? ▫ What can we do (what do we need to know) to clear up our confusion? • To summarize ideas already shared... ▫ I hear you saying ___________, is that right?(Name) suggested that _______________. ▫ What do the rest of you think? ▫ I like (Name)'s idea that _________________. Number Talks • The order of number talks has been selected based on the problems simplicity and its ability to elicit conversation: • Middle Grades – 5 Days of simple algorithms – focus on 1 talk move per day. Week 1: • Algorithms – beginning with simple problems for your grade level, moving towards inequalities and comparisons. Number Talk Talk Move 3.4 + 5.7 = practice respectful/attentive listening positions 14.6 – 12. 8 = practice repeating partners response 6.3 – 2.7 = listening, repeating and sharing out partners response Number Talks • Equalities – with out variables initially. With variables (missing values) next. • Number Lines – Bars, grids and graphs • Verbal – number trains • Number Translations – models • Creating a 6-10 minute ritual each day. Repeating, practicing and modeling the communication expectations will go a long way in opening up shy students, E.L. students and unfocused/unmotivated students. Number Talks • Series of number talks with a common theme across grade levels (primary, upper elementary, middle school) • Rich enough to produce continued discussion • Emphasis is on reasoning of understanding, not solving the problem – “defend work” • http://www.sandi.net/page/33501 EXAMPLE: Number line theme K -2 Defend the placement of a whole number on a number line 3-5 Defend the placement of a fraction on a number line 6-8 Defend the placement of rational numbers on a number line Sample Number Talk • Alex says that 5/8 is always to the left of ½ on a number . Cecilia says 5/8 is always to the right of ½ in a number line. Who is correct and why? 0 ½ 1 Resources • Articles & Information ▫ www.mathsolutions.com • Number Talks ▫ http://www.sandi.net/page/33501