Elementary Mathematics Learning Community Dialogue 2

1. Elementary Mathematics Learning Community Dialogue 2 Office of Academics and Transformation Division of Mathematics November 2012 NOTE: One of the goals of this presentation is to discuss data driven decision making, and the instructional implementation of data analysis. For this reason, at the actual presentation, some slides with Interim Assessments items were shown. However, such slides have been deleted from this power point presentation version due to test security. Slides with answers to activities conducted with participants were also deleted due to availability of this power point prior to conducting the PD session.

2. AGENDA • Puzzles, Patterns, Learning in Context • What is Problem Solving? • Metacognitive Behaviors • What Do Good Problem Solvers Do? • Effective Instructional Procedures for Teaching Math Problem Solving • QMBA Item Analysis (K-2) • Will CCSSM Matter in Ten Years? • Instructional Coaching Cycle

3. Puzzles, Patterns, Learning in Context • Maria saved $24. She saved 3 times as much as Wayne.

4. Two interpretations of Division Thomas H. Parker and Scott Baldridge

5. When we know the original amount and the number of parts, we use partitive (sharing) division to find the size of each part. We use “division to find the number in each group.” Thomas H. Parker and Scott Baldridge

6. When we know the original amount and the size or measure of one part, we use measurement division to find the number of parts. Sarah made 210 cupcakes. She put them into boxes of 10 each. How many boxes of cupcakes were there? We use “division to find the number of groups.” Thomas H. Parker and Scott Baldridge

7. Partitive or Measurement Divison? • Millie has 15 cookies. She puts 3 cookies in • each bag. How many bags can she fill? • Millie has 5 bags of cookies. Altogether she has15 cookies. There are the same number of cookies in each bag. How many cookies are in each bag? Measurement Division Partitive Division Adapted from Cognitively Guided Instruction, University of Wisconsin-Madison, 1992

8. Partitive or Measurement Divison? • Manuel has 24 pencils. They are packed 6 pencils to a box. How many boxes of pencils • does he have? • Manuel has 6 boxes of pencils with the same number of pencils in each box. Altogether, he has 24 pencils. How many pencils are in each box? Measurement Division Partitive Division Adapted from Cognitively Guided Instruction, University of Wisconsin-Madison, 1992

9. Einstein is quoted to have said : “if he had one hour to save the world he would spend fifty-five minutes defining the problem and only five minutes finding the solution”.

10. What is Problem Solving? Problem solving is a process and skill that you develop over time to be used when needing to solve immediate problems in order to achieve a goal. University of South Australia

11. New Research • You're at a big group dinner and it's time to pay up, to divide the total and multiply a certain percentage for the tip. How many people tense up and say something like, "Oh, I'm so bad at math"? • Fear of math is everywhere - in the adult world where there aren't official pop quizzes, and in schools where the next generation of scientific problem-solvers are struggling with homework. • Researchers report in a new study in the journal PLOS. One that this anxiety about mathematics triggers the same brain activity that's linked with the physical sensation of pain. Elizabeth Landau - CNN.com Health Writer/Producer

12. Metacognition • Several research studies have concluded that metacognitive processesimprove problem solving performance. (Artzt & Armour-Thomas, 1992; Goos & Galbraith, 1996; Kramarski & Mevarech, 1997) • Metacognitionis also believed to help students develop confidence to attempt authentic tasks (Kramarski, Mevarech, & Arami, 2002), and to help students overcome obstacles that arise during the problem-solving process (Goos, 1997; Pugalee, 2001; Stillman & Galbraith, 1998). Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model by AsmamawYimer and NeridaF. Ellerton

13. What is metacognition? Metacognitionis defined as "cognition about cognition", or "knowing about knowing." It can take many forms; it includes knowledge about when and how to use particular strategies for learning or for problem solving. Wikipedia

14. Categories of Cognitive and Metacognitive Behaviors: • Engagement: Initial confrontation and making sense of the problem. • Transformation-Formulation: Transformation of initial engagements to exploratory and formal plans. • Implementation: A monitored acting on plans and explorations. • Evaluation: Passing judgments on the appropriateness of plans, actions, and solutions to the problem. • Internalization: Reflecting on the degree of intimacy and other qualities of the solution process. Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model by AsmamawYimer and NeridaF. Ellerton

15. Problem solving and Metacognition “Without metacognitive monitoring, students are less likely to take one of the many paths available to them, and almost certainly are less likely to arrive at an elegant mathematical solution.” Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model by AsmamawYimer and NeridaF. Ellerton

16. Problem Solving Mathematical problem solving is a complex cognitive activity involving a number of processes and strategies. Problem solving has two stages: problem representation problem execution Successful problem solving is not possible without first representing the problem appropriately. Appropriate problem representation indicates that the problem solver has understood the problem and serves to guide the student toward the solution plan. Students who have difficulty representing math problems will have difficulty solving them. Math Problem Solving for Upper Elementary Students with Disabilities by Marjorie Montague, PhD

17. Visualization A powerful problem-solving strategy… Math Problem Solving for Upper Elementary Students with Disabilities by Marjorie Montague, PhD

18. Visualization

19. Problem Solving READ the problem for understanding. PARAPHRASE the problem by putting it into their own words. VISUALIZE or draw a picture or diagram. HYPOTHESIZEby thinking about logical solutions. ESTIMATE or predict the answer. COMPUTE. CHECK. Math Problem Solving for Upper Elementary Students with Disabilities by Marjorie Montague, PhD

20. Instructional Procedures The content of math problem solving instruction are the cognitive processes and metacognitive strategies that good problem solvers use to solve mathematical problems. ~Marjorie Montague Math Problem Solving for Upper Elementary Students with Disabilities by Marjorie Montague, PhD

21. Problem Solving Effective instructional procedures for teaching math problem solving! Math Problem Solving for Upper Elementary Students with Disabilities by Marjorie Montague, PhD

22. Instructional Procedures • Explicit Instruction • Sequencing and Segmenting • Drill-repetition and Practice-review • Directed Questioning and Responses • Control Difficulty or Processing Demands of the Task • Technology • Group Instruction • Peer Involvement • Strategy Cues • Verbal Rehearsal • Process Modeling • Visualization • Role Reversal • Performance Feedback • Distributed Practice • Mastery Learning Math Problem Solving for Upper Elementary Students with Disabilities by Marjorie Montague, PhD

23. Part A A restaurant makes a special seasoning for all its grilled vegetables. Here is how the ingredients are mixed: 1/2 of the mixture is salt 1/4 of the mixture is pepper 1/8 of the mixture is garlic powder 1/8 of the mixture is onion powder When the ingredients are mixed in the same ratio as shown above, every batch of seasoning tastes the same. Study the measurements for each batch in the table. Fill in the blanks so that every batch will taste the same. The Charles A. Dana Center at the University of Texas at Austin and Agile Mind, Inc.

24. Answers The Charles A. Dana Center at the University of Texas at Austin and Agile Mind, Inc.

25. Part B A restaurant makes a special seasoning for all its grilled vegetables. Here is how the ingredients are mixed: 1/2 of the mixture is salt 1/4 of the mixture is pepper 1/8 of the mixture is garlic powder 1/8 of the mixture is onion powder The restaurant mixes a 12-cup batch of the mixture every week. How many cups of each ingredient do they use in the mixture each week? The Charles A. Dana Center at the University of Texas at Austin and Agile Mind, Inc.

26. Answers The Charles A. Dana Center at the University of Texas at Austin and Agile Mind, Inc.

27. Interim Assessments Edusoft Reports • Performance Band Report (Question Groups) • Item Analysis per Period

28. 2012-2013 Benchmark Analysis

29. Performance Band Report

30. Item Analysis

31. Edusoft Guides • Guide to Creating Interim Assessment Reports by Sub-Groups (All, Ethnicity, Ed Program, and ELL) • Guide to Performance Band, Item Analysis, and Item Response Reports • Edusoft Sub-Group (Demographic) Selection

33. Item Specifications Benchmark Clarifications • Explain how the achievement of the benchmark will be demonstrated by students for each specific item type. In other words, the clarification statements explain what the student will do when responding to questions of each type.

34. Item Specifications Content Limits • Define the range of content knowledge and degree of difficulty that should be assessed in the items for the benchmark. • Benchmark content limits are to be used in conjunction with the General Content Limits identified for each grade level in the Specifications. The content limits defined in the Individual Benchmark Specifications section may be an expansion or further restriction of the General Content Limits by Grade Level specified earlier in the Specifications.

35. Item Specifications

36. Item Specifications • MA.4.A.6.6

40. QMBA: Grades K – 2 (CCSSM) • Performance Band Reports • Item Analysis

44. Only three questions above 50% correct!

45. What are the Instructional Implications?

46. Re-teaching MA.4.A.6.6 • Resources • Instructional Strategies • Differentiated Instruction

47. Re-teaching MA.4.A.6.6 • GO Math! Resources

48. About Mini Bats and How to Use Them Interim assessments are a formative assessment that informs whether the student attained an understanding of the standards taught in the quarter. Fall Interim assesses Quarter 1 concepts. Winter Interim assesses Quarter 2 concepts. Mini BATs are mini benchmark assessments that assess whether, after remediation, a student has gained an understanding of the concepts of a benchmark he/she showed weakness on the Interim. Quarter 1 Mini BATs- are used during Quarter 2 based on remediation needed as per Fall Interim Assessment results. Quarter 2 Mini BATs- are used during Quarter 3 based on remediation needed as per Winter Interim Assessment results. Quarter 3 Mini BATs- can be used either in Quarter 3 or 4. Quarter 4 Mini BATs- can be used in Quarter 4.

49. Other Assessment Resources

50. SAT-10 Dailies • The SAT-10 Dailies is an instructional tool developed to help teachers reinforce instruction on basic mathematics concepts taught to students, using items that also reflect the content and process clusters measured by the Stanford Achievement Test-10. • The daily practice provides opportunities for both multiple-choice and student constructed responses during the school year leading up to the week of testing. • Suggested Usage: • Dailies should be used each day of the week, only one practice sheet per day. • Dailiesare recommended to be used during the transition time into the mathematics instructional block; preferably during the first five minutes of class. During such time, students answer the questions in 3 minutes or less and the teacher briefly reviews responses. • Effort grades may be assigned. Teachers should not assign a grade to Dailiessince they do not represent the students’ understanding of the concept(s) of the day’s lesson.