Number Talks: Strengthen Students’ Mathematical Reasoning

1. Number Talks: Strengthen Students’ Mathematical Reasoning • Sara Baranauskas • K-6 Math Coordinator • Regional School District #6 • Robin Moore • K-6 Math Specialist • James Morris School, RSD#6

2. About Us…. Robin Moore K-6 Math Specialist, James Morris School 12 years Grades 1 and 5, 2 years Math Specialist Email:rmoore@rsd6.org twitter: @rmoore628 Sara Baranauskas K-6 Math Coordinator,Regional School District No. 6 15years Grades 5and 6, 3years Math Coordinator Email:sbaranauskas@rsd6.org twitter:@sarabara13

3. Today’s Purpose To provide teachers with an instructionalstrategy that isgroundedin developing students’ mathematical reasoning and conceptual understandings rather than just teachingrules and procedures without understanding of numerical relationships.

5. What is Mathematical Reasoning? As one of the five Process Standards (NCTM 2000), reasoning (and proof ) is an essential part of acquiring and using mathematics. More than a means by which to confirm whether a solution is correct, mathematical reasoning involves exploring the mathematics at hand; generating, implementing, and evaluating conjectures; as well as justifying our thinking and actions as we engage in mathematics. Simply put, mathematical reasoning is about making sense of the mathematics in our world as well as making mathematical sense of our world. Nurturing Mathematical Reasoning, Jennifer Thom, Teaching Children Mathematics, Nov 2011

6. Focus Questions • How can Number Talks develop students’ mathematical reasoning? • How do Number Talks align to the Common Core Mathematical Practices and Content Standards?

7. What is a Number Talk? A number talk is a quick (10 min)classroom routine used todevelop computational fluency that promotes students to: •Clarify thinking. • Investigate and apply mathematical relationships. • Build a repertoire of efficient computationalstrategies. • Make decisions about choosing efficient strategies for specific problems. • Consider and test other strategies to see if they are mathematically logical. • Build connections between key conceptual ideas.

8. Key Components of a Number Talk • Classroom environment and community • Classroom discussions • The teacher’s role (facilitating vs. teaching) • Purposeful computation problems • The role of mental math

9. Classroom Discussions • Problem is posted for all students to solve mentally. • Wait time is critical! • Multiple strategies are encouraged. • Discrete signals to indicate solution and strategies. • Students share, discuss, justify and critique strategies and solutions. • Mistakes are an opportunity for learning- wrong answers are used as springboards to address misconceptions.

10. Classroom Discussions cont’d Benefits of sharing and discussing computation strategies Students have the opportunity to: Clarify their own thinking. Consider and test other strategies to see if they are mathematically logical. Investigation and apply mathematical relationships (connections) Build a toolkit of flexible and efficient strategies. Make decisions about choosing efficient strategies for specific computation problems. Number Talks: Helping Children Build Mental Math and Computation Strategies, Sherry Parrish, 2010

11. The Role of Mental Math The KEY COMPONENT of any Number Talk Focus on number relationships and use these relationships to develop flexible, efficient strategies to develop accuracy (fluency!) Mental math allows students to rely on what they know and understand about number and how they are inter-related. Leads to efficiency with numbers to avoid holding numerous quantities in their heads.

12. The Role of Mental Math cont’d Strengthens understanding of place value, rather than the discrete quantity of digits. Numbers initially written horizontally – encourages place value understanding. Both formats should be used once students are comfortable with flexible strategies.

13. Let’s Try It!! 59 + 13 Thumbs up indicates solution. Fingers extended signify strategy.

14. Our Number Talk What mathematical ideas did we share? How do these strategies encourage mathematical reasoning (number sense and the use of number relationships)?

15. A Third Grade Number Talk 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)

16. Let’s apply mathematical reasoning 1. These students share several addition strategies • Adding up in chunks • Decomposing by place value • Making landmark or friendly numbers. How are these strategies similar and different? • How could you help students connect among strategies they share? Taken from Number Talks, Parrish

17. The Content Standards Computational Fluency Number Talks are within the domains of Operations and Algebraic Thinking Numbers and Operations in Base Ten Numbers and Operations – Fractions But Number Talks can also be within any domain of the Common Core content standards.

18. What about the Practice Standards? MATHEMATICAL PRACTICE 1 Make sense of problems and persevere in solving them Mathematically proficient students explain to themselves the meaning of a problem and look for ways to solve it. apply a solution pathway rather than jumping right into a solution attempt. listen to the strategies of others and apply other approaches. Common Core Standards Initiative (2010)

19. Mathematical Practice 2 Reason abstractly and quantitatively Mathematically proficient students make sense of quantities and their relationships to each other. connect quantity to written symbols. attend to meaning of quantity, not just how to compute them. knowand flexibly compute using different properties of operations and strategies. CCSI (2010)

20. Mathematical Practice 3 Construct viable arguments and critique the reasoning of others Mathematically proficient students communicate clearly and articulate their ideas to others, their thinking becomes visible and their understanding deepens. follow the thinking of others and communicate why they agree or disagree their understanding often solidifies and strengthens. Math Sense: The Look, Feel and Sound of Effective Instruction, Moynihan (2012) CCSI (2010)

21. More Standards…. Mathematical Practice 6 Attend to precision Mathematically proficient students communicate to each other with precision. attempt to use clear definitions and discussion with others and within their own reasoning –their language is precise, their reasoning can be followed, their words and symbols are clear. Calculate accurately and efficiently. Math Sense: The Look, Feel and Sound of Effective Instruction, Moynihan (2012) CCSI (2010)

22. Example of Number Talk Progression Kindergarten-Subitizing/Partitioning Dot Images K.CC.B.5, K.OA.A.3

23. Number Talk Progression Kindergarten- Building to Ten using Ten Frames K.CC.B.5

24. Number Talk Progression cont’d… Grade 1- Making Friendly Numbers using Double Ten Frames 1.OA.B.4, 1.OA.C.5 1.OA.C.6

25. Number Talk Progression cont’d… Grade 1- Friendly Number Number Strings 2 + 5 + 8 1.OA.A.2, 1.OA.B.4 1.OA.C.6

26. Number Talk Progression cont’d… Grade 2- Making Friendly Numbers 9 + 14 13 + 8 + 7 49 + 27 2.OA.B.2, 2.NBT.B.5 2.NBT.B.9

27. Number Talk Progression cont’d… Grade 3 - Making Friendly Numbers 126 + 38 899 + 25 3.NBT.A.2

28. Number Talk Progression cont’d… Grade 4- Making Friendly Numbers 4 x 49 16 x 25 4.NBT.B.5

29. Number Talk Progression cont’d… Grade 5 - Making Friendly Numbers 840  25 756  24 5.NBT.B.6

30. Focus Questions • How can Number Talks develop students’ mathematical reasoning? • How do Number Talks align to the Common Core Mathematical Practices and Content Standards?

31. Resources The Common Core State Standards Initiative (2010) Moynihan, Christine (2012). Math Sense: The Look, Sound and Feel of Effective Instruction. Stenhouse. http://www.stenhouse.com/shop/pc/viewprd.asp?idProduct=9655 Parrish, Sherry (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies K-5. Math Solutions. http://store.mathsolutions.com/product-info.php?Number-Talks-pid270.html Thom, J (November 2011). Nurturing Mathematical Reasoning: do students physical actions and interactions precede sophisticated reasoning? Teaching Children Mathematics, 234-243.

32. Free Number Talks Resources • Article - Number Talks Build Numerical Reasoning: strengthen accuracy, efficiency and flexiblility…. http://www.mathsolutions.com/documents/NumberTalks_SParrish.pdf • Teaching Channel videos https://www.teachingchannel.org/videos/third-grade-mental-math https://www.teachingchannel.org/videos/third-grade-math-solutions • Math Perspectives http://www.mathperspectives.com/num_talks.html • Insidemathematics.com - Number Talks http://insidemathematics.org/index.php/number-talks • Implementing Number Talks Helpful Hints http://www.mathperspectives.com/pdf_docs/num_talks.pdf

33. DigitalResources Apps Subitize Tree, $.99 Quick Images, $.99 Counting Together, $1.99 Websites Math Coach’s Corner http://mathcoachscorner.blogspot.com/ Stanford Online - “How Children Learn Mathematics”, Spring 2014http://online.stanford.edu/

34. Free Formative Assessment Tools • Show Me – records voice and actions; saves to website for easy linking to websites, digital portfolios, etc • Educreations & Screen Chomp interactive whiteboard apps that records voice and actions • Three-Ring– take pictures, videos of students, write notes, add to students’ folders.