1. Kristie J. Newton, Temple University Jon R. Star, Harvard University

2.  We would like your ideas here – what do you look for to determine if a professional development experience was effective?  In particular, when examining teachers’ practices for evidence that they are using new knowledge and skills, what do you look for?

3.  Level 1: Participants' reactions  Level 2: Participants' learning  Level 3: Organization support and change  Level 4: Participants' use of new knowledge and skills  Level 5: Student learning outcomes

4.  Did participants effectively apply new knowledge and skills?  Examined through questionnaires, interviews, direct observation, video

6.  Introduce teachers to comparison as a tool for fostering algebraic understanding and flexibility  Train teachers to use curriculum materials designed to help them include comparisons  Assist teachers in finding ways that the materials could be easily implemented in their classrooms

7.  Worked Example Pairs Side-by-side presentation Topics covering Algebra I  Three Phase Model Understand Compare Make Connections

8.  Practice-based PD - an approach that aims to situate mathematics teacher learning within the profession of teaching (Silver, 2009; Smith, 2001)  Professional Learning Tasks - tasks that utilize artifacts of teaching to engage teachers in aspects of their work

9.  Solve and discuss mathematical problems  Watch and discuss videos  Model Teaching Activity Write a lesson plan Teach the lesson to a "class" of fellow teachers Discuss the demonstration lesson as a group

11.  Silver (2009) noted that empirical evidence is lacking for many theoretical claims about the effectiveness of PLTs. In particular, there is a critical need to better understand how learning from PLTs might transfer to the classroom.

12.  We seek feedback on our framework.  We are interested in participants' ideas for alternative frameworks.  We aim to have a discussion about alternative PLTs and ways that their effectiveness can be (or has been) explored in teachers' practices.

13.  Identify accurate, appropriate, and sufficient indicators of use.  Specify dimensions of quantity and quality.  Determine if adequate time has been allowed for relevant use to occur.  Allow for sufficient flexibility for contextual adaptations.

14.  Quantity Worked Example Pairs (WEPs)  Quality Order of Three Phase Model Integrity of Three Phase Model Clear takeaway Classroom discourse

15.  Usually: Use of one or more WEPs constitutes the majority of the lesson.  Sometimes: A substantial amount of time is devoted to the WEPs, but they constitute the minority of the lesson.  Rarely: Little or no class time is spent using the WEPs.

16.  Ideal: The teacher used all three phases and they were used in the proper order.  Acceptable: Only two phases were addressed, but these phases are used in the correct order.  Unacceptable: The teacher did only one phase, or the teacher did the phases out of order, such as “Compare” before “Understand.”

17.  Ideal: The teacher asks relevant, additional follow-up or probing questions that substantially build on the questions provided in the WEP.  Acceptable: The teacher touches on the instructional aim of all three phases.  Unacceptable: The teacher skips a phase or fails to touch on the instructional aim of all three phases.

18.  Ideal: The takeaway is clear and written down or presented visually for the students.  Acceptable: At the end of the WEP portion of the class, there is a clear, explicit statement of the main takeaway(s) of the WEP.  Unacceptable: A partial summary statement is given, with the omitted parts constituting an important part of the rationale of the WEP; a summary statement is absent; the summary statement captures a takeaway that is different from the intended takeaway.

19.  Ideal: The teacher and students are engaged in mathematical conversation during multiple phases, including the Make Connections phase.  Acceptable: The teacher and students are engaged in mathematical conversation only during the Make Connections phase.  Unacceptable: Discussion does not involve both teacher and students, does not occur during Make Connections, or involves students in minimal ways (e.g., with “yes” or “no” answers).

22.  Indicators of Use Worked Example Pairs (WEPs) Order of Three Phase Model Integrity of Three Phase Model Clear takeaway Classroom discourse  Goal for discussion Feedback on framework Alternative frameworks Other PLTs, explorations of their effectiveness

23. Kristie Newton Temple University kjnewton@temple.edu