1. Moving beyond “Fidelity of Implementation” Some Thoughts about Mathematics Curriculum and Teacher Professional Development Moving beyond “Fidelity of Implementation”: Some Thoughts about Mathematics Curriculum and Teacher Professional Development Ed Silver MSU ExCITE Conference November 20, 2008

2. Fidelity of Implementation

3. What is fidelity? Merriam-Webster  The quality or state of being faithful [semper fidelis] Synonyms: allegiance, fealty, loyalty, devotion  The degree to which an electronic device (record player, radio, television) accurately reproduces its effect (as sound or picture) [Is it live or is it Memorex?]

4. Why Might Fidelity Matter? Did it work? [ WWC ] Did they REALLY do “it”? [ faithfulness ] Did THEY really do “it”? [ reproducibility ] Did they really do “IT”? What is/was “IT”? Student core materials? Student core materials? Student supplemental materials? Student supplemental materials? Teacher support materials? Teacher support materials? With what planned modifications? With what planned modifications? With what emergent modifications? With what emergent modifications?

5. Stances toward fidelity of implementation  Fidelity is an absolute necessity  Fidelity is an unrealistic expectation, but one can assume that sources of variation are randomly distributed  Alternate view: Variability (infidelity) might be an object of study rather than an annoyance or an irrelevance

6. Similarities and Differences in Multiple Instances of a Lesson Similarities  Same lesson  Positive about the curriculum  Involved students in answering questions, sharing solutions  Worked with colleagues Differences  Role of teacher (leading vs. facilitating)  Types of questions asked  Who judged correctness?  Extent to which students were allowed to struggle  Move toward a generalization

7. The Mathematical Tasks Framework Tasks as set up by teachers Tasks as they appear in curricular materials Tasks as enacted by teacher and students Student learning Stein, Grover & Henningsen (1996) Cognitively demanding tasks were sometimes not set up as intended and often not enacted in that way Cognitively demanding tasks were sometimes not set up as intended and often not enacted in that way

8. High-Level Tasks Can (and Often Do) Evolve during a Lesson  Maintain high-level demands  Decline into procedures without connection to meaning  Decline into unsystematic and unproductive exploration  Decline into absence of mathematical activity Stein, Grover, & Henningsen (1996); Stein, Smith, Henningsen & Silver (2000)

9. 9 Enactment Affects Student Learning High SET UP ENACTMENT STUDENT LEARNING Low High Low, but... Moderate

10. Temporal Phases of Curriculum Use Intended Curriculum Written Curriculum (materials) Enacted Curriculum Student learning Stein, Remillard & Smith(2007) Teachers are key agents in shaping the transformations Teachers are key agents in shaping the transformations Students, School contexts, and policies also play a role Students, School contexts, and policies also play a role

11. Some questions that might be worth asking  When is “it” usable? What conditions support or impede sustainable effective use of “it”?  How do components of “it” interact in the work of teachers and students? [A. Castro]  Under what conditions do students learn from “it” what “it” affords an opportunity to learn? [G. Stylianides]  What do teachers learn from “it”?  How do slowly changing phenomena (personal beliefs, customary practices, organizational norms) afford and constrain the pace and depth of adoption (of effective utilization, of assimilation and accommodation) of “it” ?

12. Role of Curriculum Materials in Instruction

13. Three views of mathematics curriculum materials in U.S.  Curriculum materials as intervention  Curriculum materials as invention  Curriculum materials as detention

14. What do they imply?  How does curriculum as invention interact with the usability of curriculum materials as interventions?  Must curriculum as intervention lead to curriculum as detention?  What do these views suggest that we need to understand better about the teacher-curriculum interface?  And so on...

15. Curriculum Materials and The Instructional Triangle Silver, Ghousseini, Charalambous, & Mills (in press) Curriculum implementation plateau associated with teachers having an underdeveloped: (a) conception of their role as active mediators of the interaction between students and content through the tasks found in the mathematics curriculum materials; and (b) repertoire of instructional strategies to use in shaping and facilitating students’ learning of mathematics content through their engagement with curriculum materials

16. Using “Reform” Curriculum Materials Well Some Instructional Challenges

17. 17 MTF Draws Attention to the Key Role of the Teacher Tasks are important, but teachers also matter! Tasks are important, but teachers also matter! Teacher actions and reactions … Teacher actions and reactions … influence the nature and extent of student engagement with challenging tasks, influence the nature and extent of student engagement with challenging tasks, affect students’ opportunities to learn from and through task engagement. affect students’ opportunities to learn from and through task engagement.

18. 18 Among the Things We Have Seen in Our Work Some instructional challenges Some instructional challenges Identifying mathematical goals of a lesson Identifying mathematical goals of a lesson staying focused and basing instructional decisions on mathematical goals staying focused and basing instructional decisions on mathematical goals Identifying and using evidence of student learning Identifying and using evidence of student learning Scaffolding students’ thinking rather than telling “how to do it” Scaffolding students’ thinking rather than telling “how to do it” Judging when, how, and for how long to allow students to struggle Judging when, how, and for how long to allow students to struggle Incorporating multiple solution strategies Incorporating multiple solution strategies

19. 19 Instructional Challenges: Multiple Solutions What’s involved in using multiple solutions in the classroom ? What’s involved in using multiple solutions in the classroom ? Anticipating solutions Anticipating solutions Choosing solutions Choosing solutions Sequencing solutions Sequencing solutions Handling errors Handling errors Keeping the mathematical goal in mind throughout Keeping the mathematical goal in mind throughout

20. Three additional thoughts  Don’t neglect Lesson Planning/Preparation – undervalued and understudied as a part of instruction  Sustained improvement efforts are needed – Lesson Study or TRGs based on CMP?  What are the trade-offs of PD focused on specific curriculum materials vs. key aspects of teaching?