1.9 lbs lbs lbs. HOW MUCH DOES EACH BALL WEIGH?

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1 HOW MUCH DOES EACH BALL WEIGH? 1.9 lbs lbs lbs. W I L L I A M S ) 1 Adapted from Van de Walle, Bay-Williams, Lovin, & Karp, 2014; Maida, 2004

2 Critical Thinking through the CCSS Standards For Mathematical Practice Critical Thinking with the Common Core Murfreesboro, TN Jennifer M. Bay-Williams University of Louisville June 5, 2013

3 THAT S ME! W I L L I A M S ) 3

4 OUR AGENDA Basics of the Standards for Mathematical Practices: Where to Find Them Test Yourself Understanding the Standards for Mathematical Practices: Mini-Vignettes Infusing the Standards for Mathematical Practices: High Potential Tasks Grade-level Lessons Adapt-a-Tasks W I L L I A M S ) 4

5 Basics W I L L I A M S ) 5

6 Posted on the overview page for every grade level! W I L L I A M S ) 6

7 TEST YOURSELF I M P L E M E N T I N G T H E M AT H E M AT I C A L P R AC T I C E S ( B Y J. B AY- W I L L I A M S ) 7

8 The Standards for Mathematical Practice Standards for Mathematical Practice W I L L I A M S ) 8

9 The Standards for Mathematical Practice Standards for Mathematical Practice W I L L I A M S ) 9

10 SMP: 4-Model with mathematics W I L L I A M S ) 10

11 SMP: 5 Use appropriate tools strategically W I L L I A M S ) 11

12 SMP: 6-Attend to precision W I L L I A M S ) 12

13 Understanding W I L L I A M S ) 13

14 Mathematical Practices: Mini-Vignettes Select a card and read the scenario to your table. Discuss which Mathematical Practice is represented in the scenario. W I L L I A M S ) 14

15 Negotiate! W I L L I A M S ) 15

16 Mathematical Practices: Mini-Vignettes SMP 1 - D SMP 2 - H SMP 3 - A SMP 4 - E SMP 5 - B SMP 6 - F SMP 7 - C SMP 8 - G W I L L I A M S ) 16

17 What is it about teaching that influences I M P L E M E N T I N G T H E student conceptual M A T H E M A T I C A L P R A C T Iunderstanding? C E S ( B Y J. B A Y - W I L L I A M S ) 17

18 1.Allowing students to struggle with important mathematical ideas 2. Making mathematical relationships explicit I M P L E M E N T I N G T H E M A T H E M A T I C A L P R A C T I C E S ( B Y J. B A Y - W I L L I A M S ) 18

19 MAKING MATHEMATICAL RELATIONSHIPS EXPLICIT Treat mathematical relationships between ideas, facts, and procedures in an explicit and public way Remind students of the main point of the lesson and how it connects to previous and future learning Discuss the mathematical meaning that underlies a procedure Question students about how different solution strategies are similar to or different from each other Discuss the ways in which mathematical concepts build on each other (Hiebert & Grouws, 2007) W I L L I A M S ) 19

20 EXPLICIT INSTRUCTION DIRECT INSTRUCTION W I L L I A M S ) 20

21 Making mathematical relationships explicit Allowing students to struggle with important mathematics 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. CONNECTING RESEARCH AND MATHEMATICAL PRACTICES W I L L I A M S ) 21

22 Infusing W I L L I A M S ) 22

23 HOW MUCH DOES EACH BALL WEIGH? 1.9 lbs lbs lbs. W I L L I A M S ) 23 Adapted from Van de Walle, Bay-Williams, Lovin, & Karp, 2014; Maida, 2004

24 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. Opportunity for Mathematical Practices to Develop? W I L L I A M S ) 24

25 Which of these shapes has been partitioned into fourths? Explain why or why not. From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 25

26 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. Opportunity for Mathematical Practices to Develop? W I L L I A M S ) 26

27 ONE UP, ONE DOWN When you add 7 + 7, you get 14. When you make the first number 1 more and the second number 1 less, you get the same answer = = 14 Is this true for 5 + 5? Is it true for other addition problems? What else do you notice about this pattern? From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 27

28 ONE UP, ONE DOWN What happens when you change addition to multiplication? 7 x 7 = 49 8 x 6 = 48 What can you find out about this pattern? Why is this true? Explore individually and then with a partner or group. From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 28

29 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. Opportunity for Mathematical Practices to Develop? W I L L I A M S ) 29

30 CONJECTURES If you multiply any number by 2, the answer is even. From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 30

31 CONJECTURES If you take half of one factor and double the other factor, the answer is the same. From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 31

32 CONJECTURES If you take half of one factor and double the other factor, the answer is the same. From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 32

33 CONJECTURES If you double one factor, the answer is double. From Elementary and Middle School Mathematics: Teaching Developmentally (8E) W I L L I A M S ) 33

34 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. Opportunity for Mathematical Practices to Develop? W I L L I A M S ) 34

35 In Your Group: 1. Solve the task 2. Discuss how you might implement the task 3. Decide on which MPs to emphasize (and how) Gr. 3: Quilt Making Gr. 4: Counter Counts Gr. 5: Decimal Displays W I L L I A M S ) 35

36 Take your grade-level task with you. Find 1 person from a different grade level. Share (x 2): The Task Which Math Practice(s) you selected How you will press on the selected Math Practice(s). Move Share-Share-Move W I L L I A M S ) 36

37 THINK What is your elevator talk to respond to the question How do the Standards for Mathematical Practice support critical thinking? W I L L I A M S ) 37

38 IN A NUTSHELL What idea(s) will you take back with you? W I L L I A M S ) 38

39 QUESTIONS? W I L L I A M S ) 39