1. Improving Mathematical Number Sense & Technology Integration Teacher Quality Grant Peyton Forest Elementary Atlanta Public Schools Atlanta, GA July 23, 2013 Teacher Quality Grant Peyton Forest Elementary Atlanta Public Schools Atlanta, GA July 23, 2013

2. Exit Cards What does this program include? What resources/manipulatives/materials will we receive? How often are students assessed? How do you implement, introduce, change, and manage centers? How is this applicable for 3-5 th grade? What assessments would be given in upper elementary classrooms?

3. Last Night’s Homework Using a summarizing strategy present and reflect using the following questions as a guide. What was the article about? What implications does this article have for students at your grade level? In what ways might this article help you think differently about math instruction? Is there anything else you would like to add?

4. The Importance of Mathematical Tasks “There is no decision that teachers make that has a greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in studying mathematics.” Lappan and Briars, 1995

5. Mathematical Tasks

6. The Importance of Mathematical Tasks “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, Smith, Henningsen, & Silver, 2000 Stein, Smith, Henningsen, & Silver, 2000

7. The Importance of Mathematical Tasks “The level and kind of thinking in which students engage determines what they will learn.” “The level and kind of thinking in which students engage determines what they will learn.” Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human,1997 Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human,1997

8. Martha’s Carpeting Task Martha was recarpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? Stein, Smith, Henningsen, & Silver, 2000, p. 1 Stein, Smith, Henningsen, & Silver, 2000, p. 1

9. The Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits. If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? How long would each of the sides of the pen be if they had only 16 feet of fencing? How long would each of the sides of the pen be if they had only 16 feet of fencing? How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it. Stein, Smith, Henningsen, & Silver, 2000, p. 2 Stein, Smith, Henningsen, & Silver, 2000, p. 2

10. The Mathematical Tasks Framework

11. Break Time!! 10 Minutes

12. Your Turn... Xmania Work with your group. Record your findings in an organized way. Be prepared to share your work.

13. Lunch! During this time, please read through pages 26-27 of the Introduction to the Assessment Series in your notebook.

14. Assessing Math Concepts Hiding Assessment

15. Hiding Assessment “Children who are able to subtract with ease and efficiency know the parts of numbers and see the relationship between composition and decomposition of numbers and addition and subtraction.” (Richardson, p.26)

16. Goals To find out which number combinations the child knows by determining if they can tell the missing part of a number without having to figure it out.

17. Grade Required Fluency K Add/Subtract within 5 1 Add/Subtract within 10 2 Add/Subtract within 20 & Add/Subtract within 100 (pencil & paper) 3 Multiply/Divide within 100 & Add/Subtract within 1,000 4 Add/Subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division & Multi-digit decimal operations 7 Solve px + q = r, p (x + q) = r 8 Solve simple 2 x 2 systems by inspection 9-12 Algebraic manipulation in which to understand structure. Writing a rule to represent a relationship between two quantities. Seeing mathematics as a tool to model real-world situations. Understanding quantities and their relationships.

18. Critical Learning Phases Figures out missing parts of numbers when unknown Knows missing parts without needing to figure them out Uses addition to solve subtraction

19. Internalizing How do we know when a child has internalized a number? What are some key ideas about how children develop strategies for adding and subtracting? What strategies did you notice Aliyah using? Some good references in the AMC Hiding Assessment book: pp. 26 - 27 pp. 33 - 34 Teacher: asks self what mastery/proficiency really looks like and means plans for progressions of levels of understanding spends the time necessary to gain the depth of the understanding becomes flexible and comfortable in own depth of content knowledge Teacher: asks self what mastery/proficiency really looks like and means plans for progressions of levels of understanding spends the time necessary to gain the depth of the understanding becomes flexible and comfortable in own depth of content knowledge

20. View the Video of the Hiding Assessment Look at the Critical Learning Phases of the Hiding Assessment in your handout. As you view the video take notes about the interview. What does the student prove to you that she knows? What are the next steps?

21. Documenting The Assessment AMC Hiding Assessment in your Assessment Kit Part One What you need Goals Procedure Part One: Hiding Objects Summarizing Instructional Needs

22. Documenting The Assessment AMC Hiding Assessment in your Assessment Kit Part Two What you need Goals Procedure Part Two: What If? Summarizing Instructional Needs

23. The Indicators For Part One For Part Two In general, 4 levels: A - Ready to Apply P - Needs Practice I - Needs Instruction N - Needs Prerequisite

24. Children must be strong with both the cubes and the ‘what if’ questions. If a child knows 5, would you assume they know 4 and 3? You can go back and check those, but we usually assume this. After 5, it is usually necessary to check each and every number. Some interesting things happen between 6 and 10! Sometimes children will know the even number combinations better than the odd number combinations.

25. Video 7 View the video again This time, using the online Hiding Assessment Student Interview

26. Hiding Assessment Your Turn

27. Partner Practice Choose a partner. Using all the materials, conduct an assessment with your partner. Be sure to record your partner’s responses. Switch roles.

28. More Video Practice Watch and score the assessments of: Video 8 Video 9 Video 10 Video 11 Afterward, discuss in your group: What thoughts came to you as a teacher while you watched the interviews? What kinds of information can you learn as an interviewer?

29. Children’s Progress with Combinations Progress is much slower than you think. Even if you’re doing all the right things and giving them all the best experiences and practice... It isn’t fast. At the end of 1st grade: most children have internalized facts through 5 or 6. At the end of 2nd grade: most children have internalized facts through 8. It takes until the first part of 3rd grade for most children to have internalized facts to 10 and be really solid.

30. Hiding Assessment Data

31. AMC Reports

32. Hiding Assessment Part 1

33. Hiding Assessment Part 2

34. Using Your Data What is the one thing preventing this child from moving 1 level higher - on this assessment and in their daily work?

35. AssessmentAssessment ObservationObservationDataData InstructionInstruction The information you gets tells you what you need to do for your students. What you learn can truly guide your instruction. The Assessments are the Beginning, NOT the End

36. Brown Book Walk

37. Homework Read Helping Teachers Connect Vocabulary and Conceptual Understanding Never Say Anything a Kid Can Say Number Talks Implementing Number Talks - Helpful Hints Consider the following as you read: What about this article is important for you to share with your colleagues? How do the ideas in this article connect with CCSSM? AMC? In what ways does this article make you think differently about your classroom? Be ready to share your thoughts.