Goals/Agenda. Norms 5/30/13. Book Study: Number Talks by Sherry Parrish
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1 Book Study: Number Talks by Sherry Parrish HELPING CHILDREN BUILD MENTAL MATH AND COMPUTATION STRATEGIES Grades 2 5 Wednesday, June 5 th Facilitated by: Christine Roberts croberts@ers.tcoe.org Goals/Agenda Welcome Overview Sample Number Talks Videos Routine Teacher s role Student expectations Supporting the Common Core State Standards Next Steps Wrap Up Norms 1
2 Number Talks Calculate the following mentally. Be prepared to share strategies aloud Classroom Clip: 2.1 Number Talks: Video Watch the video showing a Second Grade addition Number Talk. Discuss (with your elbow partner): What is the teacher s role in the number talk? What features of this video would you like to see in your classroom? 5 Why Number Talks? The practice of number talks is one of the most powerful vehicles I know for helping students learn to reason with numbers and make mathematically convincing arguments, for building a solid foundation for algebraic reasoning, and for teaching mathematics as a sensemaking process. If all teachers make this shift in their practice, it would represent a profound advancement in mathematics education. - Ruth Parker 2
3 What are Number Talks? u Classroom conversations around purposefully crafted computation problems that are solved mentally. u The problems are designed to elicit specific strategies that focus on number relationships and number theory. u Students are given problems in either whole- or smallgroup settings and are expected to mentally solve them accurately, efficiently, and flexibly. u By sharing and defending their solutions and strategies, students have the opportunity to collectively reason about numbers while building connections to key conceptual ideas in mathematics. Rationale for Number Talks 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. Accuracy, Efficiency, and Flexibility Accuracy denotes the ability to produce an accurate answer; efficiency refers to the ability to choose an appropriate, expedient strategy for a specific computation problem; and flexibility means the ability to use number relationships with ease in computation. 3
4 Focusing on the Mathematical Process, NOT Answer Getting Students are asked to defend or justify their answers to prove their thinking Students have a sense of shared authority in determining whether an answer is accurate Teacher is not ultimate authority Wrong answers are used as opportunities to unearth misconceptions Students investigate their thinking and learn from mistakes Mistakes play an important role in learning and provide opportunities to question and analyze thinking, bring misconceptions to forefront, and solidify understanding, pages My Favorite No The Teaching Channel: The Teaching Channel, Number Talks: Video Teacher Interview Watch the video showing a Teacher Interview. Discuss (with your face partner): How does the teacher feel about Number Talks? How have Number Talks influenced her classroom and her teaching? 12 4
5 Number Talks Articles Choose one of the articles to read. Stand-Up, Hand-Up, Pair-Up Share your thoughts and questions after reading the article. 13 Tulare County Office of Education Number Talks Calculate the following mentally Classroom Clip: 3.1 As you watch the video, consider: What evidence in the video supports student understanding of place value? How do the student s strategies exhibit number sense? Which strategies were more accessible to you: More challenging to follow? How are accuracy, flexibility, and efficiency interwoven in the students strategies? 5
6 What Are Number Talks? Key Components of Number Talks 1) Classroom environment and community 2) Classroom discussions 3) The teacher s role 4) The role of mental math 5) Purposeful computation problems Overview Mental math problems posed Students are given think time and indicate a solution and multiple strategies Students share solutions and explain their thinking Encourages students to communicate about math The teacher acts as a facilitator and his/her primary function is to question students in order to guide the discussion 6
7 Routine Daily, 5-15 minutes Consistent location Students in close proximity, seated on the floor or in chairs Easy visibility for teacher and students Teacher records student thinking on the whiteboard and/or chart paper Problem or string of problems are posed Students are given think time Teacher facilitates a conversation around the problem(s) posed that day Number Talks Hand Signals o Teach the Hand Signals o I have an answer (Thumb up in front of chest) o I agree ( hang ten back and forth) o I disagree (hands back and forth by ears or in front of body) Classroom Discussions Teacher writes problem on board and give students time to solve the problem mentally. Once students find an answer, they are encouraged to continue finding efficient strategies while others are thinking. Students indicate when they are ready with a solution by quietly raising a thumb against their chest. They indicate they have other approaches by raising another finger for each solution. 7
8 Classroom Discussions Continued The quiet form of acknowledgement allows for more student think time at the same time as challenging students that already have an answer. All answers- correct and incorrect- are recorded. Students share strategies and justifications with peers. Benefits of Sharing and Discussing Computation Strategies Students have the opportunity to: 1. Clarify their own thinking. 2. Consider and test other strategies to see if they are mathematically logical. 3. Investigate and apply mathematical relationships. 4. Build a repertoire of efficient strategies. 5. Make decisions about choosing efficient strategies for specific problems. Sample Number Talk Calculate the following mentally. Be prepared to share strategies aloud
9 Classroom Clip: 32 As you watch the video, consider: What evidence in the video supports student understanding of place value? How does each strategy foster number sense and the use of number relationships? Which strategies were most accessible to you? More difficult to follow? Choose one of the strategies to model with the open number line. How could this be an effective tool for your students? Teacher and Student Roles in Number Talks Roles and Participation Teacher s role Planning - be purposeful in the selection of problems Facilitating Questioning Recording answers/student thinking Accepting accept and record answers/explanations without confirming or denying Student participation All students work to find an answer Signal that they have an answer and if they have multiple strategies Share and explain their thinking Defend their thinking Inquire about the thinking of others 9
10 The Teacher s Role Teacher's role shifts from being sole authority in giving information and confirming correct answers Teacher is facilitator, questioner, listener, and learner Guide students to ponder and discuss examples that build upon teacher s purposes. How did you get your answer? By changing my question from What answer did you get to How did you solve this problem? I was able to understand how they were making sense of mathematics. Teacher Responsibilities Plan problems with a purpose/goal in mind Pose the problem(s) for the day Record student responses to reflect how they were explained (not the teacher s interpretation) Practice notation to represent student thinking accurately Provide the structure and procedures to facilitate the Number Talks Post sample prompts to helps students structure their explanations or questions in front of the class Be aware of the equal sign and use it properly Choosing Purposeful Problems Craft problems that guide students to focus on mathematical relationships. Teacher s goal and purpose should determine the numbers and operations that are chosen. Discuss: How might you work together to select and plan for number talks? 10
11 Number Talks are a Purposeful Vehicle to: Make sense of mathematics Develop efficient computation strategies Communicating mathematically Reasoning and proving solutions Sample Number Talk and Video Classroom Clip 5.3: 16 x 35 As you watch the Number Talk, consider: 1) What procedures are in place that allow students to share their thinking? 2) What opportunities exist for the teacher to informally assess student understanding? 3) How is student communication encouraged and valued? 4) How would you describe the teacher s role during the number talk? 11
12 Developing Student Strategies and Supporting all Learners Developing Accountability with Students 1) Ask students to use finger signals to indicate the most efficient strategy. 2) Keep records of problems posed and the corresponding student strategies. 3) Hold small-group number talks throughout each week. 4) Create and post class strategy charts. 5) Require students to solve an exit problem using the discussed strategies. 6) Give a periodic computation assessments to monitor growth. Supporting Students Use this time to make informal observations and interactions. Provide appropriate wait time to ensure that the majority of the students have accessed the problem. Validate student thinking by accepting all answers. Encourage student communication throughout the number talk. 12
13 Developing Strategies Discuss with your partner at least four different strategies to solve How will you teach alternate strategies to students? Sample Number Talk Calculate the following mentally. Be prepared to share strategies aloud Number Talks: Video Classroom Clip: 3.1 Discuss: How does the teacher s recording of each strategy provide access for all students? Which strategies are easiest for you to understand? Which strategies are more challenging to follow? What mathematical concepts are being addressed during the number talk. How did the teacher bring these ideas to the forefront for the class? 13
14 Supporting English Learners According to David Foster, mathematics director, founder of the Silicon Valley Mathematics Initiative for the Noyce Foundation, Number Talks are one of the most important routines you can implement in order for EL students to be successful in mathematics. The key is in how you record student responses. Tulare County Office of Education Come se suma?/how do we add? A Number Talk in Spanish from Inside Mathematics: Inside Mathematics, insidemathematics.org OA Progression K, Counting and Cardinality; K-5, Operations and Algebraic Thinking, page 6, 14
15 8 Common Addition Strategies 1. Counting All 2. Counting on 3. Doubles/Near-Doubles 4. Making Tens 5. Making Landmark or Friendly Numbers 6. Compensation 7. Breaking Each number into its Place Value 8. Adding Up in Chunks 43 Number Talks Calculate the following mentally. Try to use multiplication strategies. 12 x 15 Multiplication and Division Strategies Repeated addition or skip counting Partial products Breaking factors into smaller factors Making a landmark or friendly number Doubling and halving Repeated subtraction or sharing/dealing out Multiplying up Partial quotients Proportional reasoning 15
16 Number Talks Calculate the following mentally. Be prepared to share strategies aloud Number Talks Calculate the following mentally. Be prepared to share strategies aloud Number Talks Video Classroom Clip: 5.4 Discuss: How did this particular sequence of problems help students use number relationships to solve the problems? What student confusions and misunderstandings surfaced with the array model? How did the teacher navigate the discussion to build understanding about multiplication, division, and array model? 16
17 Content Teacher Learning Student Math Assessment Collaborative The Silicon Valley Mathematics Initiative 5/30/13 Number Talks Anticipate possible student strategies and how they might be recorded Supporting the CCSS for Mathematics True/False with Justification? 7 = 4 + 3? = 3 + 5? 9 = 16-7? 16-7 = OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, = 2 + 5, = The Silicone Valley Mathematics Project 17
18 NUMBER TALKS: RELATIONAL THINKING = = = = The Silicone Valley Mathematics Project The Standards for Mathematical Practice Mathematically proficient students: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Tulare County Office of Education Mathematical Practices - Discuss What are some of the ways that the Mathematical Practices Standards are demonstrated through Number Talks? Talking Chips 1. The teacher provides a discussion topic and think time. 2. Any student begins the discussion, placing one of his/her chips in the center of the table. 3. Any student with a chip continues discussing, using his/her chip. 4. When all chips are used, teammates each collect their chips and continue the discussion using their talking chips (until the teacher stops the discussion). Tulare County Office of Education 18
19 Guess My Rule Extending Number Talks to Other Math Concepts from Inside Mathematics: org/index.php/5th6thgrade-guess-my-rule Inside Mathematics, insidemathematics.org Planning for Number Talks Identify grade level standards that require the type of mathematical thinking that Number Talks Promotes. Write several problems with your table group for your selected standards. Tulare County Office of Education Getting Started and Next Steps 19
20 Tips for Getting Started 1. Start with smaller problems to elicit thinking from multiple perspectives 2. Be prepared to offer a strategy from a previous student 3. It is okay to put a student strategy on the back burner 4. As a rule, limit to 5-15 minutes 5. Be patient with yourself and students as you incorporate Number Talks into your regular math time Next Steps What are your next steps in preparing Number Talks for next school year? What did you learn from today s session? What do you still need to learn? Tulare County Office of Education Resources 20
21 commoncore.tcoe.org Tulare County Office of Education Resources Questions/comments Resources: Numbertalks.pdf Domain/101/Math%20Documents/Routines/ mid_level_routinebank.pdf Tulare County Office of Education Resources TCOE Instructional Services TCOE Common Core Repository Christine Roberts Tulare County Office of Education 21
22 Please complete the feedback form and leave it on the back table. Feedback Have a great day! Tulare County Office of Education 22
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