Scenario 1: A first-year program for teachers involved in a “local systemic change” project

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Sample programs for different in-service settings (E1)
Scenario #3: A program for volunteer teachers which takes place during the school year and focuses on rethinking the teaching and learning of geometry/measurement informed by an inquiry perspective.

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Key characteristics of this scenario (repeated from the main text for your convenience)

Agendas of the first set of professional development sessions, taking place BEFORE the implementation of the first illustrative inquiry unit

Agendas of the second set of professional development sessions, taking place AFTER the implementation of the first illustrative inquiry unit

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Key characteristics of this scenario

Scenario 3: A program for volunteer teachers which takes place during the school year and focuses on rethinking the teaching and learning of geometry/measurement in middle school informed by an inquiry perspective.

Overall goals: To empower individual teachers to: rethink their beliefs and practices in a spirit of inquiry while focusing on the topic of geometry/measurement; begin to actually change the way they teach geometry/measurement and revise priorities in their current geometry/measurement curriculum.

Participants: In-service and pre-service teachers responsible for mathematics instruction at grades 6-8. Participants are encouraged to attend with a colleague from the same school, if at all possible.

Program structure: The program consists of eight two-day sessions (Friday + Saturday), taking place monthly over the course of the school year. In addition, all in-service teachers are expected to teach one of the illustrative units in the first half of the school year, plus another "innovative" unit in geometry/measurement based on a unit developed by an NSF-funded curriculum series later in the year, as well as to undertake a few other smaller field experiences as assigned during the program. All pre-service teachers are expected to pair up with an in-service participant and be participant-observers during their field experiences (see description of activity D4.3 for more detail). In-class support is not provided, although facilitators are available for ad-hoc meetings with participants who want to discuss their preliminary plans for the inquiry unit to be implemented in their classes.

Professional development main characteristics: The main experiences comprising the week-long Summer Institute described in Section B.2 are rearranged over the first four series of two-day meetings, so as to prepare the participants for their first "experience as teachers." More specifically:

first 2-day meeting: mostly devoted to the "experience as learners" on Tessellation and related activities (framework components 1-4);
second 2-day meeting: mostly devoted to the "experience as learners" on Area and related activities (framework components 1-4);
third 2-day meeting: devoted to articulating what it means to teach mathematics through inquiry and engaging participants in the planning of their first "experience as teachers" (framework components 5-6);
fourth 2-day meeting: continuing to support the participants' planning of their first inquiry experience, with a special focus on assessment (framework components 5-6).

The participants are then given the opportunity to implement their first inquiry unit, and later come back together to share on these experiences and begin to move beyond the illustrative units (framework components 6-8). Relevant NSF-funded curriculum series are used extensively at this point to inform the participants' rethinking of the geometry strand of their curriculum -- thus going even beyond the scope of our framework.

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Agendas of the first set of professional development sessions, taking place BEFORE the implementation of the first illustrative inquiry unit

Preliminary assignments to 1st two-day session:

Getting oriented to the program -- reading description of program structure and expectations
D1.1

Tessellation experience as learner -- preliminary assignment
D2.1.2

Session 1 (scheduled in late August, before the beginning of school)

Friday:

Getting oriented to the program -- staff and participants' introductions; reminder of program structure and expectations (with special attention to the first "experience as teacher") (1/2 h)
D1.1/
D6.1

Presentation on results and recommendation of TIMSS report, with speial attention to middle school geometry, followed by a brief discussion (1 h)
D1.2

Rethinking "What is math?" (1h)
D1.4

Tessellation experience as learner -- part I (3 h):

Introduction
D2.1.1

Interpreting a definition of tessellation
D2.1.2

Developing conjectures about tessellations
D2.1.3

hw:

Journal
D1.3

Tessellation experience as learner -- assignment (including reading on definition)
D2.1.4

Saturday:

Tessellation experience as learner -- part II (2 1/2h):

Reflecting on mathematics and definitions
D2.1.4

Modeling how to test a conjecture
D2.1.5

Exploring conjectures about tessellations independently
D2.1.6

Reflection on the Tessellation experience as learner: "Walk down memory lane" (with special attention on highlighting differences among learners) (1 1/2h)
D3.1

Watching the video of a middle school inquiry unit on tessellations (1h)
D4.1

Acquainting participants with the supporting materials for the illustrative units -- first introduction to these materials (1/2h)
D6.2

Presentation and brief discussion of the first field experience task: designing and implementing a "What is math?" activity with their students during the first days of the school year

Tasks to be performed before Session 2:

Journal
D1.1

Designing and implementing a "What is math?" activity with their students during the first days of the school year

Making connections with math reform -- follow-up readings
D1.2

Acquainting participants with the supporting materials for the illustrative units -- extensive reading assignment from the Tessellation booklet
D6.2

Session 2 (mid-September)

Friday:

Brief follow-up discussion of the readings on school mathematics reform (1/2 h)
D1.2

Sharing on the results of the first field experience task (1 h)

Follow-up discussion on readings from the Tessellation supporting materials for teachers, with the participation of teachers who have already taught the unit (1h)
D6.2/
D6.3

Area experience as learner -- part I (3 h)

Introduction
D2.2.1

Fish activity
D2.2.2

Diamond activity
D2.2.3

Star activity (begins)
D2.2.4

hw:

Area experience as learner -- assignments
D2.2.5

Reading from the story of a middle school unit on Area
D4.2

Saturday:

Follow-up discussion on the readings from the Area story (1/2h)
D4.2

Area inquiry experience II (3 h)

Star activity (continues)
D2.2.4

Rethinking the math of area
D2.2.5

Reflecting on the goals of an area unit (1 1/2 h)
D3.3

Presentation and brief discussion of a second "field experience task" (1/2 h)

Tasks to be performed before Session 3:

Journal
D1.1

Second "field experience task"

Acquainting participants with the supporting materials for the illustrative units -- extensive reading assignment from the Area booklet
D6.2

Identifying common elements of inquiry units -- preliminary assignment
D5.1

Identify teaching strategies modeled in the first two sessions -- preliminary assignment
D3.4

Make a tentative decision about which illustrative unit will be implemented as the first field experience

Session 3 (mid-October)

Friday

Sharing on the results of the second field experience task (1 h)

Follow-up discussion on readings from the Area supporting materials for teachers, with the participation of teachers who have already taught the unit (1 h)
D6.2

Identifying common elements of inquiry units (1 h)
D5.1

Brief discussion about what it takes to plan the implementation of one of our inquiry units (1/2 h)
D6.4

Initial planning session for the first field experience -- in small groups by unit and grade levels, and with the support of the "flexible plans" in the supporting materials for teachers and facilitators who will be circulating in the room (2 h)
D6.4

hw:

continue to develop the plan for your unit
D6.4

Saturday:

Time for groups and/or individuals to continue to plan their unit, with opportunities for support and feedback by facilitators and peers (2 h)
D6.4

Time for questions/answers with teachers who implemented the illustrative unit (1 h)
D6.3/
D6.4

Time for groups and/or individual to continue to plan their unit, with opportunities for support and feedback by facilitators and peers (1 1/2 h)
D6.4

Reflection on the process of planning, sharing strategies and insights (1 h)

Tasks to be performed before Session 4:

Journal
D1.2

Complete in writing your preliminary overall plan for the implementation of an illustrative unit
D6.4

Follow-up readings on inquiry
D5.1

Identify teaching strategies modeled in the professional development program -- preliminary assignment
D3.4

Preliminary readings on assessment
D5.3

bring in a "good" assessment tool you have been using to be shared, along with representative examples of students' responses
D5.3

Session 4 (early November)

Friday:

Use readings on inquiry as a frame to engage in a reflection on the teaching practices that can support teaching mathematics through inquiry, beginning with identifying the practices modeled in the professional development program (1 1/2 h)
D3.4

Participants share and revise their preliminary plans in small groups, informed by previous discussion and readings (1 1/2 h)
D6.4

First discussion on assessment, focused on the need to develop appropriate assessment for the unit participants are planning and with the goal of identifying issues and setting goals for the next activity (1/2 h)
D5.3

Small group in-depth analysis of the assessment tools and sample of students' responses brought in, with final sharing of insights gained from this activity (1 1/2 h)
D5.3

hw:

Begin thinking about how what has been learned today can apply to your plan to assess students' learning as a result of the illustrative unit
D5.3/
D6.4

Saturday:

Time for small groups and/or individuals to develop appropriate assessment tools for their units (3 h)
D6.4

Large group sharing and discussion of effective assessment tools for the illustrative units (1 1/2 h)
D5.3/
D6.4

Teachers who implemented the units discuss their experiences of planning and evaluating them, as well as other tips for the participants (1 h)
D6.3

Tasks to be performed before Session 5:

Journal
D1.2

Complete plan and implement the illustrative unit
D6.4

Collect artifacts from students' work and bring a representative selection to class
D6.7

Readings on geometry

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Agendas of the second set of professional development sessions, taking place AFTER the implementation of the first illustrative inquiry unit

Session 5 (early February)

Friday:

Round robin where participants share their experiences teaching an illustrative unit (2 h)
D6.6

Small group in-depth examination of the student work brought in, to determine what students' learned from these experiences (1 1/2 h)
D6.7

Sharing what students' learned, with special attention to geometry, and discussion of the significance of this learning in light of the readings on geometry done for homework (1 h)

Brief presentation to introduce the NSF-funded curriculum series that are going to be used as resources to continue to rethink the teaching of geometry/measurement, followed by the opportunity to begin to peruse some materials (1 h)
D7.3

hw:

follow-up readings about the NSF-funded curriculum series
D7.3

Saturday:

Examining in-depth a geometry unit from one of the NSF-funded curriculum series (including some experience as learner, readings from the instructional materials and reflections on the mathematical content of the unit) (4 h)
D7.3

Brief presentation of the focus of the other geometry/measurement units in the same series, followed by time to look at the materials and then a decision by each participant about which unit s/he will examine before the next meeting (1 1/2 h)
D7.3

Tasks to be performed before Session 6:

Journal

Read and examine in depth the chosen geometry unit, and be prepared to give a brief report on this unit to the rest of the group

Session 6 (late February)

Friday:

Participants' brief presentations on the unit they examined (2 1/2 h)

Discussion on the new goals and priorities reflected by the choices made by that curriculum series (1 h)

Small group brainstorming, followed by a large group sharing and discussion, on how these units could be used as reasources and taught in a spirit of inquiry (1 1/2 h)
D7.4

Brief introduction of another curriculum series (1/2 h)

hw:

Follow-up readings about the second curriculum series

Saturday:

A similar series of experiences around a unit plus discussions and a presentation of the entire geometry/measurement strand in the series by the instructor (5 h)

Time for participants to peruse the materials (1 h)

Tasks to be performed before Session 7:

Journal

Select a unit (from either curriculum series) and implement it in one of your classes

Session 7 (March)

The entire two-day session is left open for participants, in small groups or individually, to work on the unit they have chosen to implement it in their classes

Tasks to be performed before Session 8:

Journal

Implement the selected unit; collect artifacts to support a presentation to the rest of the group

Prepare a written reflection on the experience in the program

Session 8 (June)

Friday:

The entire day is organized as a "mini-conference" where participants present on their field experiences, open to other people from their schools

Saturday:

Rethinking the teaching of geometry in middle school -- synthesis of the insights gained (2 h)

Revisiting the recommendations of NCTM Standards and TIMSS report in light of the previous discussion (1 h)

Implications for participants' future teaching of geometry -- small group brainstorm how they would plan their geometry curriculum for the next year, and then share highlights with the rest of the group (2 h)

Final reflections and ideas for next steps (1/2 h)

Celebration (1/2 h)

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Agendas of the first set of professional development sessions, taking place BEFORE the implementation of the first illustrative inquiry unit
Preliminary assignments to 1st two-day session:
Getting oriented to the program -- reading description of program structure and expectations	D1.1
Tessellation experience as learner -- preliminary assignment	D2.1.2
Session 1 (scheduled in late August, before the beginning of school)
Friday:
Getting oriented to the program -- staff and participants' introductions; reminder of program structure and expectations (with special attention to the first "experience as teacher") (1/2 h)	D1.1/ D6.1
Presentation on results and recommendation of TIMSS report, with speial attention to middle school geometry, followed by a brief discussion (1 h)	D1.2
Rethinking "What is math?" (1h)	D1.4
Tessellation experience as learner -- part I (3 h):
Introduction	D2.1.1
Interpreting a definition of tessellation	D2.1.2
Developing conjectures about tessellations	D2.1.3
hw:
Journal	D1.3
Tessellation experience as learner -- assignment (including reading on definition)	D2.1.4
Saturday:
Tessellation experience as learner -- part II (2 1/2h):
Reflecting on mathematics and definitions	D2.1.4
Modeling how to test a conjecture	D2.1.5
Exploring conjectures about tessellations independently	D2.1.6
Reflection on the Tessellation experience as learner: "Walk down memory lane" (with special attention on highlighting differences among learners) (1 1/2h)	D3.1
Watching the video of a middle school inquiry unit on tessellations (1h)	D4.1
Acquainting participants with the supporting materials for the illustrative units -- first introduction to these materials (1/2h)	D6.2
Presentation and brief discussion of the first field experience task: designing and implementing a "What is math?" activity with their students during the first days of the school year
Tasks to be performed before Session 2:
Journal	D1.1
Designing and implementing a "What is math?" activity with their students during the first days of the school year
Making connections with math reform -- follow-up readings	D1.2
Acquainting participants with the supporting materials for the illustrative units -- extensive reading assignment from the Tessellation booklet	D6.2
Session 2 (mid-September)
Friday:
Brief follow-up discussion of the readings on school mathematics reform (1/2 h)	D1.2
Sharing on the results of the first field experience task (1 h)
Follow-up discussion on readings from the Tessellation supporting materials for teachers, with the participation of teachers who have already taught the unit (1h)	D6.2/ D6.3
Area experience as learner -- part I (3 h)
Introduction	D2.2.1
Fish activity	D2.2.2
Diamond activity	D2.2.3
Star activity (begins)	D2.2.4
hw:
Area experience as learner -- assignments	D2.2.5
Reading from the story of a middle school unit on Area	D4.2
Saturday:
Follow-up discussion on the readings from the Area story (1/2h)	D4.2
Area inquiry experience II (3 h)
Star activity (continues)	D2.2.4
Rethinking the math of area	D2.2.5
Reflecting on the goals of an area unit (1 1/2 h)	D3.3
Presentation and brief discussion of a second "field experience task" (1/2 h)
Tasks to be performed before Session 3:
Journal	D1.1
Second "field experience task"
Acquainting participants with the supporting materials for the illustrative units -- extensive reading assignment from the Area booklet	D6.2
Identifying common elements of inquiry units -- preliminary assignment	D5.1
Identify teaching strategies modeled in the first two sessions -- preliminary assignment	D3.4
Make a tentative decision about which illustrative unit will be implemented as the first field experience
Session 3 (mid-October)
Friday
Sharing on the results of the second field experience task (1 h)
Follow-up discussion on readings from the Area supporting materials for teachers, with the participation of teachers who have already taught the unit (1 h)	D6.2
Identifying common elements of inquiry units (1 h)	D5.1
Brief discussion about what it takes to plan the implementation of one of our inquiry units (1/2 h)	D6.4
Initial planning session for the first field experience -- in small groups by unit and grade levels, and with the support of the "flexible plans" in the supporting materials for teachers and facilitators who will be circulating in the room (2 h)	D6.4
hw:
continue to develop the plan for your unit	D6.4
Saturday:
Time for groups and/or individuals to continue to plan their unit, with opportunities for support and feedback by facilitators and peers (2 h)	D6.4
Time for questions/answers with teachers who implemented the illustrative unit (1 h)	D6.3/ D6.4
Time for groups and/or individual to continue to plan their unit, with opportunities for support and feedback by facilitators and peers (1 1/2 h)	D6.4
Reflection on the process of planning, sharing strategies and insights (1 h)

Tasks to be performed before Session 4:
Journal	D1.2
Complete in writing your preliminary overall plan for the implementation of an illustrative unit	D6.4
Follow-up readings on inquiry	D5.1
Identify teaching strategies modeled in the professional development program -- preliminary assignment	D3.4
Preliminary readings on assessment	D5.3
bring in a "good" assessment tool you have been using to be shared, along with representative examples of students' responses	D5.3
Session 4 (early November)
Friday:
Use readings on inquiry as a frame to engage in a reflection on the teaching practices that can support teaching mathematics through inquiry, beginning with identifying the practices modeled in the professional development program (1 1/2 h)	D3.4
Participants share and revise their preliminary plans in small groups, informed by previous discussion and readings (1 1/2 h)	D6.4
First discussion on assessment, focused on the need to develop appropriate assessment for the unit participants are planning and with the goal of identifying issues and setting goals for the next activity (1/2 h)	D5.3
Small group in-depth analysis of the assessment tools and sample of students' responses brought in, with final sharing of insights gained from this activity (1 1/2 h)	D5.3
hw:
Begin thinking about how what has been learned today can apply to your plan to assess students' learning as a result of the illustrative unit	D5.3/ D6.4
Saturday:
Time for small groups and/or individuals to develop appropriate assessment tools for their units (3 h)	D6.4
Large group sharing and discussion of effective assessment tools for the illustrative units (1 1/2 h)	D5.3/ D6.4
Teachers who implemented the units discuss their experiences of planning and evaluating them, as well as other tips for the participants (1 h)	D6.3
Tasks to be performed before Session 5:
Journal	D1.2
Complete plan and implement the illustrative unit	D6.4
Collect artifacts from students' work and bring a representative selection to class	D6.7
Readings on geometry

Agendas of the second set of professional development sessions, taking place AFTER the implementation of the first illustrative inquiry unit
Session 5 (early February)
Friday:
Round robin where participants share their experiences teaching an illustrative unit (2 h)	D6.6
Small group in-depth examination of the student work brought in, to determine what students' learned from these experiences (1 1/2 h)	D6.7
Sharing what students' learned, with special attention to geometry, and discussion of the significance of this learning in light of the readings on geometry done for homework (1 h)
Brief presentation to introduce the NSF-funded curriculum series that are going to be used as resources to continue to rethink the teaching of geometry/measurement, followed by the opportunity to begin to peruse some materials (1 h)	D7.3
hw:
follow-up readings about the NSF-funded curriculum series	D7.3
Saturday:
Examining in-depth a geometry unit from one of the NSF-funded curriculum series (including some experience as learner, readings from the instructional materials and reflections on the mathematical content of the unit) (4 h)	D7.3
Brief presentation of the focus of the other geometry/measurement units in the same series, followed by time to look at the materials and then a decision by each participant about which unit s/he will examine before the next meeting (1 1/2 h)	D7.3
Tasks to be performed before Session 6:
Journal
Read and examine in depth the chosen geometry unit, and be prepared to give a brief report on this unit to the rest of the group
Session 6 (late February)
Friday:
Participants' brief presentations on the unit they examined (2 1/2 h)
Discussion on the new goals and priorities reflected by the choices made by that curriculum series (1 h)
Small group brainstorming, followed by a large group sharing and discussion, on how these units could be used as reasources and taught in a spirit of inquiry (1 1/2 h)	D7.4
Brief introduction of another curriculum series (1/2 h)
hw:
Follow-up readings about the second curriculum series
Saturday:
A similar series of experiences around a unit plus discussions and a presentation of the entire geometry/measurement strand in the series by the instructor (5 h)
Time for participants to peruse the materials (1 h)
Tasks to be performed before Session 7:
Journal
Select a unit (from either curriculum series) and implement it in one of your classes
Session 7 (March)
The entire two-day session is left open for participants, in small groups or individually, to work on the unit they have chosen to implement it in their classes
Tasks to be performed before Session 8:
Journal
Implement the selected unit; collect artifacts to support a presentation to the rest of the group
Prepare a written reflection on the experience in the program
Session 8 (June)
Friday:
The entire day is organized as a "mini-conference" where participants present on their field experiences, open to other people from their schools
Saturday:
Rethinking the teaching of geometry in middle school -- synthesis of the insights gained (2 h)
Revisiting the recommendations of NCTM Standards and TIMSS report in light of the previous discussion (1 h)
Implications for participants' future teaching of geometry -- small group brainstorm how they would plan their geometry curriculum for the next year, and then share highlights with the rest of the group (2 h)
Final reflections and ideas for next steps (1/2 h)
Celebration (1/2 h)