Assessment for Learning Mathematics: Developing eyes to see and ears to hear student thinking

1. Assessment for Learning Mathematics: Developing eyes to see and ears to hear student thinking presented by Mary Lou Kestell Student Achievement Officer, Literacy and Numeracy Secretariat

2. Assessment for Learning Mathematics

3. Learning Goals In this session, coaches will discuss and share strategies for getting teachers to • focus on student actions and voices rather than the behaviours of teachers • develop eyes to see and ears to hear student thinking • set study goals related to the work they do in the classroom • use assessment today to plan instruction for tomorrow • decompress their knowledge of division and be open to processes that honour “student generated algorithms” Job-embedded professional learning approaches: • Co-teaching • Coaching • Teacher inquiry / study Setting learning goals

4. Components of CIL − M Inquiry/Study focuses on a unit of study that teachers will be teaching: • Day 1 – Overview of CIL and observation lesson • Day 2 – Learning materials pedagogy study #1 • Day 3 – Learning materials pedagogy study #2 • Day 4 – Research lesson; analyzing and sharing student work samples and assessment for learning results from unit of study/inquiry • Day 5 – Research report development – electronic Dufferin-Peel CDSB; Huron Perth CDSB; London DCSB; Waterloo RDSB Collaborative planning

5. CIL-M : Collaborative Inquiry for Learning Mathematics for Teaching • Co-teaching – makes it possible for teachers to engage in teaching as collaborative problem-solving • Coaching – involves teachers in collaborative processes in which they refine, reflect, conduct research, expand on ideas, build skills and knowledge and problem solve in order to improve student learning and achievement • Teacher Inquiry / Study – engages teachers in working on dilemmas and difficult situations that will appear in every teacher’s practice LNS Coaching binder

6. Un-learn, Learn and Re-learn Making changes to the complex, internalized skills, beliefs and knowledge of classroom teachers is recognized as difficult and time-consuming. We teach as we were taught. There is a great deal of unlearning to do. Philippa Cordingley

7. Who are we coaching? My Thirteenth Year : A Memoir by Samantha Abeel. (2003). New York, NY: Scholastic

8. The activity, the intervention, the study group, the reading … Teachers passions… Teachers are willing to engage if • they think “it” will help them enhance student learning • the links between what they do and its effect on the learner are made explicit • there is a sense of hope that engagement will help them to make a difference G. Thomas and R. Pring

9. Sustained Problem Solving prevails… Research and evidence-informed practice is, at its heart, a learning process for practitioners which is underpinned by the same pedagogical principles that operate in classroom practice. If practitioners are to use evidence, they need to work together to interpret it and reflect upon its significance for their own particular context. G. Thomas and R. Pring

10. Sustained Problem Solving prevails… Such practice means making decisions and taking action to take learning forward – effectively a process of sustained problem solving. Problems in education are context-specific, because they depend upon chance and dynamic combinations of • learner starting points • teacher skills and understanding • school and socially driven constraints • learning expectations G. Thomas and R. Pring

11. We’re all in the together… • Our students – rather than my students • Our classrooms – rather than my classroom • Our schools – rather than my school • Our region – rather than my board Michael Fullan

12. Change only happens when it happens in the heart of the teacher … Fourth, … Our idea is to put the teacher and the student in the learner’s seat, supported by a surrounding system that requires and enables focused instruction. … what is the role of the coach? Breakthrough, 2006 pg 45 Michael Fullan

13. Informal Math Knowledge • Describe some different ways you have used division in your daily life over the past few days. • Use one sticky note for each example and be ready to share.

14. Examples of Division in Our Daily Lives Activating Prior Knowledge • The person with birthday closest to today’s date starts. • Place one sticky note on the chart paper and describe your use of division. • Continue adding notes to the chart paper. • add to an existing column if your example of division was similar • create a new column if your example was different. Same / Different

15. What is / Where is Knowledge? Constructivism works from the premise that our understanding of knowing is greatly impoverished if it ignores the wealth of unformulated knowings that are enacted in every moment of our existences. Most of the time, we don’t know what we know. Brent Davis

16. Unpacking our Knowledge Our knowledge as adults is often compressed (Ball and Bass, 2000). In fact, we have worked for years to compact and streamline our mathematical knowledge. This compression of knowledge is central to the discipline of mathematics; however, “knowing mathematics sufficiently for teaching requires being able to unpack ideas and make them accessible as they are first encountered by the learner, not only in their finished form.” Unpacking Division to Build Teachers’ Mathematical Knowledge, Teaching Children Mathematics, NCTM. May 2005

17. Grade 4 Expectations

18. What does this mean? Examples of Division in Our Daily Lives Activating Prior Knowledge • Why do we care? • What has it got to do with teaching math through problem solving? • What does it have to do with assessment for learning?

19. The Teacher as Consciousness of the Collective Teaching cannot be about zeroing in on predetermined conclusions. It can’t be about the replication and perpetuation of the existing possible. Rather, teaching seems to be more about expanding the space of the possible and creating conditions for the emergence of the as-yet unimagined. Brent Davis

20. … consciousness of the collective … Complexivist teaching is not about prompting a convergence onto pre-existent truths, but about divergence into new interpretive possibilities. The emphasis is not only on what is, but also what might be brought forth. It comes to be a participation in a recursively elaborative process of opening up new spaces of possibility by exploring current spaces. Brent Davis

21. It’s about working as a collective to build knowledge so all students can experience success!

22. Let’s do math Aneeshia is making decorations for a picnic. She is tying balloons together in bunches of 4. How many bunches of 4 balloons can Aneeshia make with 77 balloons?

23. Working Conditions • Organize yourselves in groups of 4 or 5 (number off 1, 2, 1, 2, 1, … and move into two groups) • In each group, the person with the greatest number of years in education becomes the observer • Observers meet me at the front of the room • Everyone else follow these directions …

24. Challenge – In how many ways can you represent your solutions? • Work with your group. • Use manipulatives and chart paper. • Re-presenteach solution on 1/4 of a sheet of chart paper. • Make your thinking explicit. • Develop many different solutions and re-present each – one per sheet. • Be prepared to share your solutions. Aneeshia is making decorations for a picnic. She is tying balloons together in bunches of 4. How many bunches of 4 balloons can Aneeshia make with 77 balloons?

25. Simulating bansho … Observers lead this discussion… • Place all solutions – from all groups – on the table • Group any two or more solutions that represent the same mathematics (e.g., drawings of groups of 4; arrays; algorithms; skip counting) • Add to the display of thinking about this problem

26. Bansho at HPCDSB

27. Japanese bansho What students need to do and think about • coherent flow of the lesson • students see the logical connections among all parts of the lesson • shows lesson progression, the incorporation of student ideas and conclusion reached Connections and progression of lesson • students can always check detail on board • if lost, they can get back on track • can refer each other to what is on the blackboard to help each other Makota Yoshida, google Developing Effective Use of the Blackboard through Lesson Study (2002)

28. Bansho as Collective Think-pad Contrasting and discussing ideas students present • various student ideas are presented and the display becomes a place for students to discuss the presented ideas • similarities and differences in ideas are determined • merits of using a certain method are discussed • students develop new ideas or questions they want to investigate • discussion is carried out based on the ideas presented by students

29. Assessment for Learning CIL-M teachers reported, Bansho is the most effective tool I’ve ever used to • identify the range of student understanding • allow access for all students to use their informal knowledge to solve problems • prompt learning as ideas bump up against each other • identify overlapping zones of proximal learning • assist in identifying starting points for instruction

30. Examine and discuss student work • What does this student work tell you about what the students know? • What does it tell you about what the students can do? • Are there models of student-generated algorithms here?

31. Grade 4 Student Work

32. Grade 4 Student Work

33. Grade 4 Student Work

34. Grade 4 Student Work

35. Focusing on EVIDENCE has the potential to support teaching and learning precisely because it involves teachers in becoming learners again develops their understanding of how their students feel engages teachers in learning which provides models of learning for their students Evidence-based Practice G. Thomas and R. Pring

36. Requires sophisticated professional judgements about what the evidence means for: this group of learners with these expectations at this particular point in time Framed by teachers’ tacit knowledge and skills Must be insinuated into existing frameworks Supported by credible evidence that new approaches will enhance their students’ learning Processes must be made explicit and modelled to result in learning of any kind Tacit to Explicit Knowledge G. Thomas and R. Pring

37. Why Listening and Watching Matter • When you interact with another “culture”, you cannot assume that other people understand things the same way you do. • In fact, you should assume that they don't! Children have more in common with children of their same age from around the world than they do with people of different ages in their own families. “Anthropology” on the web

38. Personalization … • seeking to understand "the native point of view" remains fundamental to socio-cultural education • however, the idea of a single and homogenous “native” point of view has been called into question • the term "native" ignores the shifting identities and overlapping communities that people live in

39. Precision … • if we want to understand other people properly, we must see what their behaviours or words or concepts mean to them, not what they would mean to us.

40. Professional Learning … • Must be understood in terms of the specific demands that it makes on the practitioners’ own learning processes. • Learning has to build on and relate to previous knowledge, understanding and beliefs.

41. Assessment for learning is information gathered today about what needs to be done tomorrow. Assessment for Learning Assessment for learning … is about feedback on teaching and learning and using that feedback to further shape the instructional process and improve learning. • feedback to teachers enables them to focus their instruction • feedback to students enables them to monitor and improve their learning. Fullan et.al., Breakthrough

42. Job-embedded professional learning Waterloo Region DSB Principal Learning Teams

43. Turnkey – Daily professional learning on the part of every teacher What is needed: • Policymakers and educators need to understand what it means to be a learning teacher. • Ongoing learning for individuals paradoxically is, above all, relational. All learning that counts involves learning in context, that is, continuous improvement within the settings where we work. … the learning is by definition specific to the situation at hand; and it is, again by definition, shared. Michael Fullan, Breakthrough pg 86

44. The implementation curve … • Using change knowledge • Teachers are motivated by moral purpose • People begin to change their behaviours before they change their beliefs. • Shared vision and ownership are less a precondition for success than they are an outcome. • Learning in context is key. Michael Fullan, Breakthrough pg 88

45. "We can, whenever and wherever we choose, successfully teach all children whose schooling is of interest to us. We already know more than we need to in order to do that. Whether or not we do it must finally depend upon how we feel about the fact that we haven't so far." Ron Edmonds, founder of the Effective Schools Movement of the 1970s

46. Remember … If you make a change and it feels comfortable, you haven’t made a change. Lee Trevino

47. Remember … Never doubt that a small group of thoughtful and committed citizens can change the world. In fact, it has never happened any other way. Margaret Mead

48. Have a GREAT year!

49. References • Ball, D. (2000). Bridging Practices: Intertwining Content and Pedagogy in Teaching and Learning to Teach. Journal of Teacher Education. pp.241-247 • Ball, D. Hill, H. and Bass, H. (2005). Knowing Mathematics for Teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, pp. 14,16,17,20-22,43-46. • Davis, B., Sumara, D., and Luce-Kapler. R. (2000).Engaging Minds: Learning and Teaching in a Complex World. Mahwah, NJ: Lawrence Erlbaum Associates. • Davis, B. and Simmt, E. (2005). Mathematics-For-Teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, pp. 1-27. • De Groot, C.& Whalen, T. (2006). Longing for Division. Teaching Children Mathematics. NCTM: Teaching Children Mathematics, April 2006, pp. 410-418. • Fosnot, C.T. & Dolk, M. (2005). Exploring Soda Machines: A Context for Division. Portsmouth, NH: Heinemann. • Fullan, M. (2005). Leadership and Sustainability. Thousand Oaks, CA: Corwin • Fullan, M., Hill, P. & Crevola, C. (2006). Breakthrough. Thousand Oaks, CA: Corwin • Hedges, M., Huinker, D. & Steinmeyer, M. (2005). Unpacking Division to Build Teachers’ Mathematical Knowledge. NCTM: Teaching Children Mathematics, May 2005, pp.478-483. • Ma, L. (1999). Knowing and teaching elementary mathematics. NJ: Lawrence Erlbaum. Read Professional Resources