Report

Protocols and Procedures for Fostering Mathematics Discourse - Elementary Sep 16, 2013 (2:00 pm - 2:50 pm) Outcomes • Participants 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. Mathematics Discourse Agenda • Background and rationale • Experience a variety of Number Talks • Consider implications for implementation of mathematics discourse. • Closing Mathematics Discourse Enhancing Instruction for CCSSM “FAL” MiniUnit with Formative Assessments Number Talks Upgrading Units Mathematics Discourse Hand Signals • • • • • • • Solution Strategy Question Comment I agree Integers Fractions Mathematics Discourse Hand Signals • Solution • Agree • Strategy • Integers • Question • Fractions • Comment REASONING AND EXPLAINING 1. Make sense of problems and persevere in solving them 6. Attend to precision OVERARCHING HABITS OF MIND CCSS Mathematical Practices 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Mathematics Discourse Four Goals for K-2 Number Talks • Developing Number Sense • Developing fluency with small numbers • Subitizing • Making Fives and Tens • Number Conservation Number Talks -Sherry Parrish Mathematics Discourse Mathematical Thinking • • • • Counting All Counting On Known Facts Derived Facts – Decomposing – Recomposing Duality, Ambiguity, and Flexibility in Successful Mathematical Thinking Research by Eddie Gray and David Tall, 1994 Mathematics Discourse Understanding Math Discourse • Talk Formats – Whole-Class Discussion – Small-Group Discussions – Partner Talks Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003) Mathematics Discourse Understanding Math Discourse • Talk Moves – Revoicing • So you’re saying the top number in a fraction is called the numerator. – Repeating • Can 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) Mathematics Discourse Understanding Math Discourse • Talk Moves (continued) – Reasoning • Do you agree or disagree and why? – Adding On • Please add onto Jimena’s strategy. – Waiting • Please take some quite think time. Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003) Mathematics Discourse Number Talks • A planned daily routine for whole‐class instruction • Number Sense (eﬃciency, accuracy & ﬂexibility) • Generalized Arithmetic-conceptual understanding • Reasoning and Problem Solving • Mental Mathematics • Preview-Review-Conceptual Understanding Mathematics Discourse Number Talks and Time • Number Talks (about 10 minutes) • Mini-Lesson (10 to 20 minutes) • Lesson (more than 20 minutes) Mathematics Discourse Number Talk Examples – – – – – – – – – Dot Patterns Rekenreks Five and Ten Frames Mental Math Number Strings True/False Statements Dilemmas Spatial Reasoning What’s My Rule? Mathematics Discourse Norms “No one is as smart as all of us are together.” • Respect • Individual think time • Everyone participates • Everyone helps • Leave no one behind • Be positive • Technology courtesy Mathematics Discourse 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. Mathematics Discourse REASONING AND EXPLAINING 1. Make sense of problems and persevere in solving them 6. Attend to precision OVERARCHING HABITS OF MIND CCSS Mathematical Practices 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Mathematics Discourse Lenses to Consider During Professional Development Sessions Learner Lens Teacher Lens Mathematics Discourse Dot Talk How many dots do you see? How did you see them? Mathematics Discourse Dot Talk I saw ______dots. I grouped the dots…. I also saw ___ dots, but I grouped the dots differently. I … Mathematics Discourse Dot Talk How many dots do you see? How did you see them? Mathematics Discourse Dot Talk Mathematics Discourse Rekenrek DVD K.2 Mathematics Discourse Five Frames Mathematics Discourse Ten Frames Mathematics Discourse Ten Frames How many dots do you see? How did you see them? Mathematics Discourse Ten Frames How many dots do you see? How did you see them? Mathematics Discourse Mental Math 26 + 27 Mathematics Discourse Mental Math 32 x 15 Mathematics Discourse Number String (Mental Math) 7+6 8+7 14+13 25+26 Mathematics Discourse Number String (Mental Math) 3 x 50 3 x 100 3 x 149 Mathematics Discourse Number String (Mental Math) 35 x 8 70 x 4 140 x 2 Mathematics Discourse True/False 7=4+3 True or False? Why? Mathematics Discourse True/False 17-16= 9-8 True or False? Why? Mathematics Discourse True/False 8 x 7= 8 x (5+2) True or False? Why? Mathematics Discourse True/False 15 x 24 = 30 x 12 True or False? Why? Mathematics Discourse True/False Mathematics Discourse Dilemma Kirsten says that 9 is the missing number in 5= -4 David says that 1 is the missing number in 5= -4 Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above. Mathematics Discourse 10-5+4 Dilemma Kirsten says that 9 is the missing number in 5= +4 David says that 1 is the missing number in 5= +4 Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above. Mathematics Discourse Dilemma David says that 10-5+4 is equal to 9 Kirsten says that 10-5+4 is equal to 1 Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above. Mathematics Discourse Order of Operations Grouping Symbols ( ), { }, [ ], I I Exponents Multiplication/Division Division/Multiplication Addition/Subtraction Subtraction/Addition Mathematics Discourse Spatial Reasoning How many cubes? How do you see them? What is the surface area? Mathematics Discourse Spatial Reasoning Math Talk How many cubes? How do you see them? What is the surface area? Mathematics Discourse What’s My Rule? In Out 1 5 3 2 3 7 5 4 Mathematics Discourse What’s My Rule? Input Output 1 5 3 2 5 25 15 10 Mathematics Discourse What’s My Rule? X Y 1 5 3 2 0 4 2 1 Mathematics Discourse Number Talk Examples – – – – – – – – – Dot Patterns Rekenreks Five and Ten Frames Mental Math Number Strings True/False Statements Dilemmas Spatial Reasoning What’s My Rule? Mathematics Discourse Number Talks and Time • Number Talks (about 10 minutes) • Mini-Lesson (10 to 20 minutes) • Lesson (more than 20 minutes) Mathematics Discourse Table Talk • Have 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? Mathematics Discourse 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? Mathematics Discourse 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? Mathematics Discourse Outcomes • Participants 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. Mathematics Discourse Closing • Thank you! • [email protected] • http://goo.gl/ylgKi for K-2 Resources • http://goo.gl/F58uB for 3-5 Resources Mathematics Discourse