Studying Coaching Moves

1. Studying Coaching Moves Toronto July 4, 2007

2. Working Hypothesis • Skillful teachers can guide greater numbers of students to deeper, more robust levels of learning • Skillful teaching is learnable and complex • Coaching is one professional learning opportunity that can impact this

3. Teaching Requires • An understanding of the content to be taught and its connections to related ideas and applications in the world • An understanding of how people learn and the capacity to diagnose what they know • An understanding of how to make the content accessible to learners--pedagogical content knowledge

4. What is the Purpose of Content-Focused Coaching? • To develop, improve, and refine professional judgment as it relates to teaching in a particular content area utilizing available resources (e.g. curriculum materials; standards; assessments)

5. Coaching Focuses on the Instructional Core • Lesson planning habits of mind, instructional strategies and methods designed to foster students learning a particular subject (Pedagogical Content Knowledge)

6. What is Pedagogical Content Knowledge? • PCK are all the things we learn to do to make mathematics accessible to people who are learning mathematics. • PCK is different from and in addition to understanding mathematics.

7. Pedagogical Content Knowledge In Math • Making Math Accessible to Learners • Using and Analyzing Representations • Using and Inventing Notation • Generating Simpler and More Complex Versions of Problems • Asking Mathematical Questions and Thinking of Special Cases • Adapted from Deborah Ball

8. Pedagogical Content Knowledge • Knowledge mathematics teachers draw on or use in practice • Knowledge related to or underlying content assessed at grade level • Mathematics that is NOT held by or taught to students at grade level (e.g. what comes before; what is the trajectory through the grades) • Adapted from Patricia Campbell, University of MD

9. Pedagogical Content Knowledge • Knowledge of students’ understanding of or thinking about mathematics • Identify or write a problem to reveal whether a student has a specific misconception • Describe a common misconception held by students that leads to student error

10. Pedagogical Content Knowledge • Knowledge related to the teaching of mathematics • e.g. Identify or describe how connected mathematical ideas (or typically sequential prerequisite/subsequent mathematical ideas) can be taught simultaneously • Patricia Campbell, University of Maryland

11. Pedagogical Content Knowledge • Identify or describe “big ideas” that typically are fundamental to understanding a specific math idea • Patricia Campbell, University of Maryland

12. Coaches Offer Assistance • It is not enough for coaches to limit themselves to eliciting teacher reflection and offer no direct assistance • Coaches need to provide substantive contributions that will impact the quality of the lessons and create opportunities for teachers to learn from practice.

13. What do coaches do? • Coaches assist teachers by way of coaching moves. • Moves that invite teacher contributions • Respect and take into account teacher’s knowledge and underlying beliefs

14. What do coaches do? • Coaches assist teachers by way of coaching moves. • Moves that provide direct assistance • Based on coach’s knowledge of teacher’s plans and understand of the lesson • Genuine co-constructions

15. What specific moves might coaches employ? • Observe a lesson and give feedback • Teach a lesson in order to demonstrate specific teaching method • Coteach a lesson • Intervene in classroom talk

16. What specific moves might coaches employ? • Suggest lesson designs • Assess student learning • Explain content • Raise questions • Inject explanations relative to the how, what, why of teaching

17. How does a coach know what to focus on in coaching conversations? • Fostering student learning • Supporting the professional development of teachers

18. A Framework for Lesson Design and Analysis(adapted from Staub 1999, 2001)

19. What do coaching conversations focus on? • What is the curricular content to be learned by the students? • In order to state the learning in a lesson specifically, teachers must know-thoroughly-the particular content and how it relates to the standard

20. What do coaching conversations focus on? • How is the content to be taught? • The teachers repertoire of methods and strategies determines the number of potential teaching moves he or she has to choose from.

21. What do coaching conversations focus on? • Why is the specific content to be taught? • Why will it be taught in this particular way?

22. Cardinal Rule in Lesson Design • Do the activity before you teach it. • Do the math in order to analyze the “what” • What is the mathematics in this lesson? • Concepts • Strategies • Skills

23. Concepts • Fractions with different names can be equivalent • To compare fractions the whole must be the same • The greater the denominator the smaller the piece.There is a relationship between the size of the piece and the number of pieces.

24. Concepts • Two fractions that relate to the same whole can be compared to each other. One half is twice as big as one fourth of the same whole. • Fractions can be thought of as division.

25. Concepts • Unlike fractions can be combined. • When the numerator and the denominator match, the fraction equals one whole.

26. Concepts • It is possible to split any fraction in half and to continue to do so forever. When you split a fraction in half, the denominator doubles. • Denominators can stand for the number of parts something was cut into or the number of times something was divided.

27. The Case of Dave Younkin • Coaching an experienced teacher--8 years teaching • Has taught grades K-3 • First year teaching grade 4 • First year using Investigations in Number Data and Space

28. The Class • 29 Students • Fourth Grade • Public School 234-- Manhattan • Heterogeneous grouping • Mixed socioeconomic status • Spring • Investigations In Number, Data, Space

29. Exploring Halves • Create designs on your geoboard paper that show one half. • The rules for this exploration: • You must use the entire area of the geoboard (16 square units) • Each half must be one contiguous piece--in other words you will end up with 2 pieces if you were to cut out the two halves • If using paper, lines between dots are straight

30. Exploring Fourths • Create designs on your geoboard paper that show four noncongruent fourths. • The rules for this exploration: • You must use the entire area of the geoboard • Each fourth must be one contiguous piece--in other words you will end up with 4 pieces if you were to cut out the fourths

31. Combining Fractions • Students construct ways of dividing a whole into a combination of halves, fourths, and eighths. They make drafts on small dot-paper squares…they write equations that reflect the relationships their designs illustrate. • (Investigations In Number Data and Space, Different Shapes, Equal Pieces, Grade 4.)

32. Combining Designs of Fractions

33. Introducing the Guide To Core Issues in Lesson Design • Please read over the guide. • What questions do you already include in your planning conversations? • What questions are new? • Which ones (5-7) are the most essential? • How might you use this in your work?

34. Guide to Core Issues in Mathematics Lesson Design • What are the goals and the overall plan of the lesson? • What is your plan? • Where in your plan would you like some assistance? • (Based on the teacher’s response, the coach focuses on one or more of the following ideas.)

35. Guide to Core Issues in Mathematics Lesson Design • What is the mathematics in this lesson? (I.e., make the lesson goals explicit) • What is your goal or goals? • What are the mathematics concepts?

36. Guide to Core Issues in Mathematics Lesson Design • Are there specific strategies being developed? Explain. • What skills are being taught in this lesson (applications, practice)? • What tools are needed (e.g., calculators, rulers, protractors, pattern blocks, cubes)?

37. Guide to Core Issues in Mathematics Lesson Design • Where does this lesson fall in this unit and why? (i.e., clarify the relationship between the lesson and the curriculum) • Do any of these concepts and/or skills get addressed at other points in the unit? • Which goal is your priority for this lesson? • What does this lesson have to do with the concept you have identified as your primary goal? • Which standards does this particular lesson address?

38. Guide to Core Issues in Mathematics Lesson Design • Which goal is your priority for this lesson? • What does this lesson have to do with the concept you have identified as your primary goal? • Which standards does this particular lesson address?

39. Guide to Core Issues in Mathematics Lesson Design • What are students’ prior knowledge and difficulties? • What relevant concepts have already been explored with this class? • What strategies does this lesson build on?

40. Guide to Core Issues in Mathematics Lesson Design • What relevant contexts (money, for example) could you draw on in relation to this concept? • What can you identify or predict students may find difficult or confusing or have misconceptions about? • What ideas might students begin to express and what language might they use?

41. Guide to Core Issues in Mathematics Lesson Design • How does the lesson help students reach the goals? (i.e., think through the implementation of the lesson) • What grouping structure will you use and why? • What opening question do you have in mind? • How do you plan to present the tasks or problems?

42. Guide to Core Issues in Mathematics Lesson Design • What model, manipulative, or visual will you use? • What thinking and activities will move students toward the stated goals? • In what ways will students make their mathematical thinking and understanding public?

43. Guide to Core Issues in Mathematics Lesson Design • What will the students say or do that will demonstrate their learning? • How will you ensure that students are talking with and listening to one another about important mathematics in an atmosphere of mutual respect? • How will you ensure that the ideas being grappled with will be highlighted and clarified?

44. Guide to Core Issues in Mathematics Lesson Design • How do you plan to assist those students who you predict will have difficulties? • What extensions or challenges will you provide for students who are ready for them? • How much time do you predict will be needed for each part of the lesson?

45. Viewing the Pre Conference • What issues from the guide are discussed in this segment? • How similar/different is this conversation from the ones you engage in with teachers? • Questions? Observations?

46. Viewing the Lesson • How did the preconference impact the lesson? • Comb the transcript to site evidence. • What concepts are students articulating? • Compare and contrast knowledge of students speaking to similar ideas.