Presentation on theme: "Jefferson County Schools K-5 Math Back to School Conference"— Presentation transcript:
1 Jefferson County Schools K-5 Math Back to School Conference Number Talks: Strengthen Students’ Mathematical ReasoningJefferson County Schools K-5 Math Back to School Conference
2 K-5 Math Survey Depth of Knowledge Small Group Instruction Number Talks
3 Today’s PurposeTo provide teachers with an instructional strategy that is grounded in developing students’ mathematical reasoning and conceptual understandings rather than just teaching rules and procedures without understanding of numerical relationships.
4 OutcomesParticipants will deepen their understanding of mathematics discourse, including some background and rationale.Participants will experience Number Talks and consider how they might be used as part of a daily routine.
5 Focus QuestionsHow can Number Talks develop students’ mathematical reasoning?How do Number Talks align to the Common Core Mathematical Practices and Content Standards?
6 Table TalkHave you implemented Number Talks as part of your daily routine? What were some of the benefits and challenges?When in your daily routine could you incorporate the use of Number Talks?
7 Number Talks A planned daily routine for whole‐class instruction Number Sense (eﬃciency, accuracy & ﬂexibility)Generalized Arithmetic-conceptual understandingReasoning and Problem SolvingMental MathematicsPreview-Review-Conceptual UnderstandingCecilio
8 Curriculum Leadership Council 2011-2012 CLC December 6, 2011Norms“No one is as smart as all of us are together.”RespectIndividual think timeEveryone participatesEveryone helpsLeave no one behindBe positiveTechnology courtesy
9 Four Goals for K-2 Number Talks Developing Number SenseDeveloping fluency with small numbersSubitizingMaking Fives and TensNumber ConservationNumber Talks-Sherry ParrishCecilio
10 The Teacher’s RoleTeacher as facilitator, questioner, listener and learner – NOT teller and explainer.Crafts purposeful problems.Supports discourse to deepen mathematical understanding and knowledge and keeps discussion focused on the important mathematics.Assists students to learn how to structure their comments and wonderings in a meaningful and natural manner.Asks open ended questions – from “What answer did you get” to “How did you get your answer?” and “Why did you choose your strategy?”
11 Hand Signals Solution Agree Strategy Question Comment Curriculum Leadership CouncilCLC December 6, 2011Hand SignalsSolutionStrategyQuestionCommentAgree*
12 Understanding Math Discourse Talk MovesRevoicingSo you’re saying the top number in a fraction is called the numerator.RepeatingCan you repeat what Miguel said in your own words?Classroom Discussions: Using Math Talk to Help Students Learn-S. Chapin, C. O’Connor, N Anderson (2003)
13 Understanding Math Discourse Talk Moves (continued)ReasoningDo you agree or disagree and why?Adding OnPlease add onto Jimena’s strategy.WaitingPlease take some quite think time.Classroom Discussions: Using Math Talk to Help Students Learn-S. Chapin, C. O’Connor, N Anderson (2003)
14 WHAT the students are learning 1st HalfPractice Standards:HOW the students are learning2nd HalfContent Standards:WHAT the students are learning
15 CCRS Mathematical Practices REASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of othersOVERARCHING HABITS OF MIND1. Make sense of problems and persevere in solving them6. Attend to precisionMODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategicallySEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated reasoning
16 K-2 Number Talk in Jefferson County Watch the number talk.Refer back to the Key Components. What do you notice?- Classroom environment and community- Classroom discussions- The teacher’s role (facilitating vs. teaching)- The role of mental math- Purposeful computation problems(Think-Pair-Share)
21 How many dots do you see? How did you see them? Dot TalkHow many dots do you see? How did you see them?Intent: Participants will experience a Dot Talk.Talking Points:Explain to participants that we will now model a dot talk.Please note that this is an animated slide.
22 Mental MathAfter a 20% discount, the price is 80% of the original price. So 80% of the original price is $140. What is the original price?
28 Kirsten says that 10xy-5xy + 4xy equals xy Dilemma Number TalkKirsten says that 10xy-5xy + 4xyequals xyDavid says that 10xy-5xy + 4xy equals 9xyExplain the mathematical reasoning that both David & Kirsten used to simplify the expression above.*Introduce Dilemmas as a type of number talk*What could come before and after this number talk. Give rationale.28
29 How many cubes? How do you see them? What is the surface area? Spatial ReasoningHow many cubes? How do you see them? What is the surface area?
30 TransformationsRotate the figure 90˚ clockwise. What are the new coordinates of point A?
34 Number Talk Examples Dot Patterns Mental Math Number Strings True/False StatementsDilemmasSpatial ReasoningWhat’s My Rule?Error Analysis and CoachingCecilio
35 Math Block •Balance procedural understanding and conceptual understanding •Balance whole group and small group •Balance teacher directed and student-focusedDebriefGuided Math/Learning TasksNumber TalksMini-Lesson
36 Socio-mathematical Norms Errors are gifts, they promote discussion.Share a second sentence to connect your thoughts.The answer is important, but it is not the math.Build on the thinking of others.Ask questions until ideas make sense.Think with language and use language to think.
37 Questions Teachers Might Ask Who would like to share their thinking?Did someone solve it a different way?Who else used this strategy to solve the problem?How did you figure it out?CecilioIntent: Participants will review possible questions teachers may ask of their students during a number talk.Talking Points:These questions are just a few questions a teacher would ask.The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)
38 Questions Teachers Might Ask What did you do next?What did you need to know?Why did you do that? Tell me more.Which strategies do you see being used?CecilioIntent: Participants will review possible questions teachers may ask of their students during a number talk.Talking Points:These questions are just a few questions a teacher would ask.The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)
39 “ Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules.”Why Talk About Math
40 3, 2, 1, Exit Ticket3 Things you will do to prepare to implement Number Talks in your classroom2 Things you discovered about Number Talks1 Question you still have