A Glenn County Professional Development Day

1. Common to the Core A Glenn County Professional Development Day 9.23.2013

2. Promoting Discourse in the Mathematics Classroom Rita Nutsch GCOE-Mathematics Coordinator

3. “People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others.” f       ~Pascal

4. The importance of mathematical discourse • “Through mathematical discourse in the classroom, teachers “empower their students to engage in, understand and own the mathematics they study.” • (Eisenman, Promoting Purposeful Discourse, 2009)

5. Misconception • There is a misconception that the shift toward the use of classroom discourse in teaching mathematics means that the teacher simply presents the problem and then stands aside while students discuss and solve it . • The teacher’s instructional role is perceived as “don’t tell the answer.” • (Chazan and Ball 1995).

6. The Teacher’s role is to: • Anticipate student responses to challenging mathematical tasks • Monitor students’ work on and engagement with the tasks • Select particular students to present their mathematical work • Sequence the student responses that will be displayed in specific order • Connect different students’ responses and connect the responses to key mathematical ideas “How to Get Students Talking!” Lisa Ann de Garcia

7. Five Practices for Improving Quality of Discourse in mathematics Classrooms • Stetting up a supportive environment • Engaging students in discourse • Practicing the art of questioning • Using student thinking to propel the discussion • Orchestrating the discourse • Modified from “How to Get Students Talking!” Lisa Ann de Garcie

9. NCTM • 93% of teacher questions are knowledge based focusing on recall of facts. • The National Council for Teachers in Mathematics encourages teachers to increase student participation by “posing questions that elicit, engage, and challenge student’s thinking.”

10. Eight Mathematical Practices

11. Mathematical Practice #3: Construct viablearguments and critique the reasoning of others • Mathematically proficient students: • • understand and use stated assumptions, definitions, and previously established results in • constructing arguments. • • make conjectures and build a logical progression of statements to explore the truth of their • conjectures. • • analyze situations by breaking them into cases, and can recognize and use counter examples. • • justify their conclusions, communicate them to others, and respond to the arguments of others. • • reason inductively about data, making plausible arguments that take into account the context • from which the data arose. • • 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. • • 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. • • determine domains to which an argument applies. • • listen or read the arguments of others, decide whether they make sense, and ask useful • questions to clarify or improve the arguments.

12. Two ways to introduce and engage students in Mathematical Discourse • Number Talks • Estimation180.com

13. Number Talks- What are they? • Goal: The goal of a number talk is to build number sense and computational fluency while practicing communicating mathematically, justifying answers, and critiquing the reasoning of others. • Computational fluency: having an efficient and accurate method for computing Principal and Standards for School mathematics, NCTM, Reston, VA 2000, p.152

14. Why do Number talks? • It allows children the opportunity to engage in rich meaningful conversations. • Students have a chance to share and explain strategies. • Justify answers • Build Number Sense and Fluency • Mental Math

15. NuMber talks! • Done daily • Separate from your other math block • 10-15 minutes • Meaningful conversations • No pencil and paper • Does not replace your current math curriculum • Small group or whole group

16. Number Talk Format • Present the problem • Allow for quiet think time • Thumbs up when ready • Students share their answers • Teachers record all possible solutions • Students share their strategies

17. Ready to do some Math?

18. 59 + 13

19. 116 + 118

20. 32 × 15

21. For Number talks to be successful we need to: • establish a safe classroom climate & protocol • make early problems accessible and rewarding • limit daily time to 10 – 15 minutes; occasionally extend to investigate ideas • model mental mathematics routinely ourselves • vary approaches: calculation, stories, tiles, games; individual, partner, group • allow ownership & pursue students’ ideas • involve all children • assess mental math skills • - Katy Early

22. Estimation180.comAndrew Stadel

23. Why Estimate? • Estimation is a process that is used constantly by mathematically capable adults, and that can be mastered easily by children. It involves an educated guess about a quantity or a measure, or an intelligent prediction of the outcome of a computation. • The growing use of calculators makes it more important than ever that students know when a computed answer is reasonable; the best way to make that decision is through estimation. • Equally important is an awareness of the many situations in which an approximate answer is as good as, or even preferable to, an exact answer.

24. Estimation 180.com comments • Students think critically with justifications • Using context clues, background knowledge, or reasoning skills have all been developed by a simple 5 minute warm-up.  • -John Stevens • There's reasoning behind every estimate (not guess).Find out what that reasoning is! DON'T let student reasoning go untapped! • Students cite evidence to justify answers.

25. How many almonds in the cup? • http://www.estimation180.com/day-6.html

27. -Jonathon Long

29. How many almonds in a new container?

31. How many tissues in the package?

33. How many tissues in the box?

34. In Conclusion … • Participating in a mathematical community through discourse is as much a part of learning mathematics as the conceptual understanding of mathematics itself. • As students learn to make and test conjectures, question and agree or disagree about problems, they are learning the essence of what it means to do mathematics.

35. Questions/comments/ideas/Thoughts?