Module 7: Research -Based Math Teaching Strategies

1. WASHINGTON STATE 21st Century Grant Project Core/Time/Digital October 2016 Module 7: Research-Based Math Teaching Strategies Marcy Stein, PhD University of Washington Tacoma

2. Learning Targets Participants will: • Strengthen CCSS math content knowledge in teaching strategies to build procedural fluency with math facts. • Discuss strategies for integrating the 4-step formative assessment processinto instruction: (1) Clarify intended learning; (2) Elicit evidence; (3) Interpret evidence; and (4) Act on evidence.

3. The 3 Shifts in CCSSM-Math • Focus strongly where the standards focus • Coherence: Think across grades and link to major topics within grades • Rigor: In major topics, pursue with equal intensity: • Conceptual understanding • Procedural skill and fluency • Application RTI Conference August 21, 2013

4. RIGOR Conceptual understanding Procedural skill and fluency The standards call for speed and accuracy in calculation. Students must practice core functions, such as single-digit multiplication, in order to have access to more complex concepts and procedures. Fluency must be addressed in the classroom or through supporting materials, as some students might require more practice than others. Application

5. National Math Panel(NMP) Executive Summary Main Findings and Recommendations • Curricular Content • Learning Processes • Teachers and Teacher Education • Instructional Practices • Instructional Materials • Assessment • Research Policies and Mechanisms

6. NMP Recommendations Learning Processes (8) 10. “To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills.” 11. “Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall of addition and related subtraction facts, and of multiplication and related division facts. It also requires fluency with the standard algorithms for addition, subtraction, multiplication, and division. Additionally it requires a solid understanding of core concepts, such as the commutative, distributive, and associative properties.”

7. NMP Recommendations 27. “Explicit instruction with students who have mathematical difficulties has shown consistently positive effects on performance with word problems and computation. Results are consistent for students with learning disabilities, as well as other students who perform in the lowest third of a typical class.”

8. RELATIONSHIP TO CCSS CCSS.Math.Content.1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

9. RELATIONSHIP TO CCSS CCSS.Math.Content.2.NBT.B.5 • Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. CCSS.Math.Content.2.NBT.B.6 • Add up to four two-digit numbers using strategies based on place value and properties of operations. CCSS.Math.Content.2.NBT.B.7 • Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

10. RELATIONSHIP TO CCSS CCSS.Math.Content.3.NBT.A. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

11. Instruction for Math Facts I. Conceptual Activities II. Relationship Activities III. Mastery Activities

12. I. Conceptual Understanding Concrete Models Drawings Numbers Lines Using the Smarter Balanced Digital Library

13. II. Relationship Activities Three types of relationship activities: Series Saying Three Number Fact Families Tricks: +9 same as +10-1

14. Series Saying 6 + 2 = 8 6 + 3 = 9 6 + 4 = 10 Important alternative to using fingers...

15. Three Number Fact Families  __6__ + __2__ = __8___ __2__ + __6__ = __8___ __8__ - __2__ = __6___ __8__ - __6__ = __2___ Promotes conceptual understanding of the relationships between addition and subtraction

16. Integration and Extension 2 + 4 = 6 4 + 2 = 6 6 – 4 = 2 6 – 2 = 4

17. Integration: Number Family Rules 2+4=6 4+2=6 6-2=4 6-4=2 2 4

18. Integration: Word Problems First: graphically represent the word problem. Then: determine how to write the number problem.

19. Problem Solving - Comparisons S is 15 more than B. B is 77. What number is S? 77 15 B S 15 + 77 = 92

20. Problem Solving - Comparisons Fran was 14 years older than Ann. 14 A 13 F Ann was 13 years old. 14 +13 27 How many years old was Fran?

21. Problem Solving - Sequence of Events Mark gathered some nuts before lunch. After lunch he gathered 66 more pounds of nuts. At the end of the day, he had 121 pounds of nuts. How many pounds of nuts did he gather before lunch? 66 121 121 -66 55

22. Problem Solving - Classification A hotel is going to buy 112 pieces of furniture. It needs to buy 57 couches. The hotel will buy chairs for the rest of the furniture. How many chairs will the hotel buy? 57 112 112 -57 55

23. Integration Workers planted fir trees and maples in two parks—Rock Park and Wilson Park. They planted 128 fir trees in Rock Park. The total number of maples planted in both parks was 543. In Rock Park, they planted 17 more maples than firs. A total of 400trees were planted in Wilson Park. What’s the total number of trees that were planted? Were more maple trees planted in Rock Park or Wilson Park? In which park were more trees planted?

24. Integration - Tables

25. Integration Workers planted fir trees and maples in two parks—Rock Park and Wilson Park. They planted 128 fir trees in Rock Park. The total number of maples planted in both parks was 543. In Rock Park, theyplanted 17 more maples than firs. A total of 400trees were planted in Wilson Park. What’s the total number of trees that were planted? Were more maple trees planted in Rock Park or Wilson Park? In which park were more trees planted?

26. Integration 128 17 Firs 145 Maples

27. Integration 128 17 Firs 145 Maples

28. Teaching Formats Format: Series Saying • Part A: Reading Statements • Part B: Reading Statements with Answers Erased • Part C: Saying Statements • Part D: Random Fact Drill

29. Teaching Formats Format: 3-Number Fact Number Families • Part A: Structured Board Presentation • Part B: Discrimination Practice • Part C: Supervised Worksheet Practice

30. Sequence of Instruction

31. Sequencing Introduction of Facts Cumulatively introduce facts Separate similarfacts Teach easier facts first Teach relatedfacts together Reverse of specific series taught soon after initial series

32. III. Mastery Activities Programs for Fact Memorization include: 1. A specific performance criterion 2. Adequate allotted time 3. Intensive practice on new facts 4. Systematic practice on previously introduced facts 5. A record keeping system – Formative Assessment 6. A motivation system

33. 1. Performance Criterion Oral criterion: saying an entire fact every 2 seconds Writtencriterion: 2/3 rate at which student is able to write digits

34. 2. Adequate Allotted Time Approximately 10-15 minutes per day Preferably, time in addition to math instructional time Before school, during lunch recess, after school etc.

35. 3. Intensive Practice Instruction of new facts using relationship activity Oral practice on new facts Written practice on new facts

36. 4. Systematic Review 1. Written fact practice worksheet divided in half • Smaller number of facts to master at once Top half: Practice on new facts – current set and two previously introduced sets Bottom half: Current fact set presented twice; practice on previously introduced sets

37. 5. Formative Assessment Recording Keeping

38. 6. Motivation Integrate with formative assessment/record keeping system Motivation comes with success!

39. Two Fact Mastery Programs Homogeneous Group Program Teacher Led – Group Oral Practice Materials Pretesting Timed test Record keeping/Motivation

40. Two Fact Mastery Programs Heterogeneous Group Program Partner Practice Materials: folders for each student Pretesting Timed Test Record keeping/Motivation Modifications

41. Practice takes time… Tutoring Before/After School Intervention time Homework Club

42. Compare/Contrast Traditional Programs • Not teacher-directed • Length of time to mastery • Not cumulative +1s, +2s, +3s Effective Programs • Teacher-directed (Oral practice) • Quicker mastery of smaller sets • Cumulative introduction and review

43. The Devil is in the Detail… When people say that the devil is in the detail, they mean that small things in plans and schemes that are often overlooked can cause serious problems later on. http://www.usingenglish.com/

44. Full Disclosure From: Designing Effective Mathematics Instruction (2006) Stein, Kinder, Silbert, and Carnine Math Facts Chapter – 4th edition Teaching Formats Specific Recommendations Fact Mastery Worksheets mstein@uw.edu