Math

1. Math PLUS Promoting Learning and Understanding for Students in Mathematics Leadership for High Quality Teaching and Learning

2. Welcome and (Re)introductions • Kim Estes, GRREC Math Consultant • Gary Houchens, WKU Department of Ed. Admin., Leadership, & Research • Other new faces

3. Today’s Agenda 1. Review of MathPLUSgrant components 2. Goals for Leadership Session/Big Picture 3. Data Collection/Debrief homework assignment 4. Explore the scope, audience, and purposes of student assessment - Concept Maps 5. Review research findings on the role of assessment in supporting student learning - Jigsaw Reading 6. Consider formative assessment practices that benefit student learning - Partner Quiz Lunch 12:00-12:30 7. Reflecting on Assessment Feedback 8. Homework

4. NORMS • Set cell phones to vibrate. • Check email during lunch. • Participate and contribute fully. • Create safe environment for sharing. • Respect ideas of others. • Use rule of two feet

5. Math PLUS Grant Components • 1. Content PD through new common standards 23 days of content and standards-based PD around Common Core and content needs as determined by PRAXIS II

6. Math PLUS Grant Components • 2. Authentic learning communities Lenses on Learning One-On-One Coaching School level PLC

7. Math PLUS Grant Components • 3. Thinking strategies PD via the Denver-based Public Education & Business Collaborative

8. Math PLUS Grant Components • 4. Coaching Teachers and leadership teams Planning/Pre-brief Observation Reflecting/Debrief

9. Math PLUS Grant Components • 5. Demonstration sites Schools will become demonstration labs for high-quality math instruction and assessment

10. Goals for Leadership Sessions • For participants, individually, to expand their notions of: • The mathematical knowledge and dispositions students need to have to be mathematically literate in today’s world • The learning opportunities that need to be created in order to make significant mathematics accessible to all students • For building teamsto move their educational systems and classrooms forward in a state of continuous improvement in mathematics instruction and achievement and support the work of teachers engaged in the teacher portion of the MathPLUS grant.

11. The Big Picture • Learning about the characteristics of high-quality math instruction • Learning the NCSM PRIME Leadership framework for leading high-performing math programs in your schools • Increasing administrator confidence regarding instructional leadership of the school’s math program

12. More of the Big Picture • Assembling a collaborative building/district-level team for leading math improvements. • Building team capacity for using data to inform instruction and develop a meaningful, long-term math improvement plan. • All this facilitated through face-t0-face sessions at GRREC, team work back home, and on-site coaching.

13. Support Material PRIME Leadership Framework PRinciples and Indicators for Mathematics Education Leaders Based upon four essential principles of leadership: 1. Equity 2. Teaching and Learning 3. Curriculum 4. Assessment

14. Last Year’s Focus • Day 1 – Content (Algebra) • Day 2 - Characteristics of High Quality Instruction

15. Last Year, continued • Sources of data for evaluating your school’s math program • Team-based approach to observing math lessons- each team’s DATA assignment includes an observation of a math lesson

16. DATA Collection Reminders • When observing lesson, goal is not to judge. • Intent of observation is to consider how students were making sense of the mathematics and how the teachers worked with student ideas and thinking processes in these lessons. • Explain to teacher that you are conducting this observation as part of an assignment for a seminar in which you are enrolled.

17. DATA Collection Assignments Teams are taken through a structured process for collecting, analyzing and interpreting data for the purpose of identifying current strengths and weaknesses in their mathematics program.

18. Steps to Success 1. Take intellectual risks when needed to explore complicated issues, new ideas, and new mathematics. 2. Complete the individual and team assignments between each session. 3. Meet as a mathematics leadership team between each session to discuss team DATA assignment.

19. For your DATA assignment you were asked to do the following: 1. Observe a mathematics lesson (using the Secondary Lenses on Learning Observation and Reflection Guide), then reflect with the others who observed the same lesson. 2. Obtain a copy of any problem/task used during the lesson. 3. Meet as a team to discuss the lesson and to identify the cognitive demand of tasks used during the lesson.

20. Working with Team Data Among the tasks collected: • Identify the cognitive demand of each task. • Categorize each task along a scale from 1 to 4 where 1= low level & 4= high level. (Note that all tasks could be the same level.) Write level of each task on separate post-it note. • Place each of the post-it notes at the appropriate position on the chart paper along the horizontal axis (cognitive demand)

21. Reflecting on your Classroom Observations: Identify the following: • One or two areas of strength that became evident when your team considered your classroom observations • One or two areas that will be important to develop • Which component of instruction will be especially important for your mathematics program improvement plan to address.

22. Essential Question for Today • How Can Assessment Support Learning and Instruction? This session offers participants the opportunity to: • Explore the scope, audience, and purposes of student assessment • Review research findings on the role of assessment in supporting student learning • Consider formative assessment practices that benefit student learning.

23. Assessments • Discuss at your table the various assessments typically used in education.

24. What is a “Concept Map?” • A technique for visualizing the relationships among different concepts. • A diagram showing the relationships among concepts. • A technique development by Joseph Novak at Cornell University as a means of representing the science knowledge of students.

25. Concept Map: Individually • Create a concept map, list, or outline that summarizes the range of student assessments used in your school. • Include information about the purposes of, and audiences for, each type of assessment.

26. Concept Map: Team • Share maps, lists, and outlines with other building team members. • Make revisions (using a different color writing tool) based on comparisons and discussion of how various assessments are used in your building setting and who the audience is for the information.

27. Black & Wiliam, Inside the Black Box (1998) • Meta-analysis of 250 studies from several countries. • Concluded that formative assessment, properly used, leads to significant learning gains (.4 to .7 SD gain) • 25 percentile points on the ITBS • 4 ACT score points

28. Working Inside the Black Box Questions posed • Is there evidence that improving formative assessment raises standards? YES • Is there evidence that there is room for improvement? YES

29. Why Improve? • The assessment methods teachers use are not effective in promoting good learning • Grading practices tend to emphasize competition rather than personal improvement • Assessment feedback often has a negative impact, particularly on low-achieving students, who are led to believe they lack “ability” and so are not able to learn

30. Jigsaw Reading 3.2 pg. 102 – 115 Number 1 – 7 #1 – Questioning #2 – Feedback through Grading #3 – Peer Assessment and Self-Assessment #4 – Formative Use of Summative Tests #5 – Underlying Issues #6 – The Big Idea #7 – What You Can Do

31. Working Inside the Black Box (Reading 3.2, pp. 99-116) • Black, et. al (2004) • Define formative assessment: “An assessment activity can help learning if it provides information that teachers and their students can use as feedback in assessing themselves and one another and in modifying the teaching and learning activities.”

32. Formative Assessment:Two Key Ideas • The target audience for data from formative assessment is both the teacher and the student. • The information gleaned from data must be “actually used to adapt the teaching work and to meet learning needs.”

33. Formative Assessment:Beyond Exit Slips & Ungraded Quizzes • Questioning • Feedback • Peer Assessment & Self-Assessment • The Formative Use of Summative Assessments

34. Questioning • Lengthen wait time • Allows for more complex questions and for students to express provisional thinking • Use questions that make visible student thinking – answer and explanation • Redirect and extend student thinking

35. Peer and Self-Assessment • Make opportunities for peer- and self-assessment a regular part of instruction. • Use clear learning targets and rubrics available to students for judging their own work. • Use targets to guide all phases of instruction and encourage students to monitor their own progress.

36. Formative Use of Summative Tests • Allow students to develop their own test questions and solutions. • Through peer and self assessment, let students identify how their work might be improved and revise their answers. “A student’s lack of learning at any given point is never the end, but rather the starting point for the next level of learning.”

37. Feedback • Shift toward descriptive, non-evaluative feedback: • Use written tasks and oral questions that make student thinking visible • Offer comments that let students know what was done well, what still needs improvement, and guidance on how to make improvements • Give opportunities for students to improve

38. 10 minute BREAK

39. Formative Assessment: Partner Quiz • During this activity you will: • Engage in a partner quiz as a student • Analyze the task for its algebra • Analyze the experience of participating in a partner quiz for what students and teachers can learn about students’ knowledge of algebra.

40. Partner Quiz: Outline • Select partners. • Work Question 1 of the task individually. • Discuss Question 1 with partner. • Make revisions (as needed) based on your partner conversation. • Complete Question 2 with your partner.

41. The Supermarket Carts Task The task shows a drawing of a single supermarket cart and of as et of 12 nested supermarket carts. The drawings are 1/24 the real size. • Create a rule that will tell you the length of the storage space needed when all you know is the number of supermarket carts to be stored. Show how you built your rule: explain which data you used and tell how you used it. • Now show how you can figure out the number of carts that can fit in a space s meters long.

42. The Supermarket Carts TaskScoring Rubric See handout 3.j

43. Sample Student Work: Student A (Annabel)

44. Sample Student Work: Student A (Annabel), continued

45. Sample Student Work: Student B (Brandt)

46. Sample Student Work: Student C (Charlie)

47. Partner Quiz: Debrief Questions • What could a teacher learn about a student’s knowledge of linear patterns from this quiz? How could this activity help a teacher adjust instruction? • How could this partner quiz enhance student learning? How would you rate its cognitive demand? • How does this activity make the learning goals and performance expectations clear to students? • How does the partner quiz shift assessment from assessment OF learning to assessment FOR learning? • How would a student who has struggled with math in the past feel about his or he chances of success on this type of assessment?

48. LUNCH 12:00 – 12:30

49. Written Feedback from Teachers Assume the role of a teacher who is reviewing student papers from the Supermarket Carts partner quiz. Draft feedback of the type described on pages 99-116. In deciding what feedback to offer Student C, consider the goals of the task and identify the following: • What math skills or concepts does this student seem to understand? What evidence can you point to? • What math skills or concepts does this student still need to learn? What evidence can you point to?

50. Reflecting on Feedback When you have completed your comments on the student paper, consider the following questions: • How is this approach to providing feedback similar or different from your understanding of current practices? • How might a student, particularly one who has struggled with math in the past, feed about his or her chances to be successful given this type of feedback?