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Studying Coaching Moves

Studying Coaching Moves. Toronto July 4, 2007. 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.

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Studying Coaching Moves

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  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.

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