Section E1: Scenario #2: A one-year program to introduce volunteer teachers to an inquiry approach to mathematics instruction, with more limited funding

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Scenario #2: A one-year program to introduce volunteer teachers to an inquiry approach to mathematics instruction, with more limited funding

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

Agendas of the summer institute

Agendas of the follow-up meetings

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Key characteristics of this scenario

Scenario 2: A one-year program to introduce volunteer teachers to an inquiry approach to mathematics instruction, with more limited funding

Overall goals: To empower individual teachers to: rethink their beliefs and practices in a spirit of inquiry, begin to actually change their classroom instruction, make concrete plans to pursue the process of instructional innovation thus initiated.

Participants: In-service and pre-service teachers responsible for mathematics instruction, at grades 4-10. Participants are encouraged to attend with a colleague from the same school, if at all possible.

Program structure: The program consists of a 1-week Summer Institute, 10 half-day monthly meetings during the following school year, and field experiences without classroom support. All in-service teachers are expected to teach one of the illustrative units at the very beginning of the school year, plus another "innovative" unit later in the year. All pre-service teachers are expected to pair up with an in-service participant and be participant- observers during their two inquiry unit (as outlined in activity D4.3).

Professional development main characteristics: The week-long Summer Institute is devoted to developing a shared vision of teaching mathematics through inquiry, and centers on the participants' experiences as learners of both illustrative units and the reflections developed around these experiences (framework components 1-5) -- much along the lines of the summer institute described in Section B.2. Some additional experiences are interspersed during the week to introduce participants to planning and assessment issues so as to empower them to develop on their own a first plan for their first inquiry unit. The follow-up meetings are scheduled monthly to provide a forum to discuss the on-going field experiences, some opportunities to receive feedback and support in planning these experiences (especially in consideration of the fact that the program can not provide in-class support), begin to move participants beyond the illustrative units, and help them reflect on the whole experience (framework components 6-8).

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Agendas of the summer institute

Preliminary assignments:

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

Making connections with math reform -- preliminary readings
D1.2

Survey on participants' math beliefs
D1.5

Tessellation experience as learner -- preliminary assignment
D2.1.2

DAY 1 (Monday):

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

Learning disabilities awareness session (F.A.T. City video) (1 1/2h)
D3.2

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

Tessellation experience as learner -- part I (2h 30'):

Introduction

D2.1.1

Interpreting a definition of tessellation

D2.1.2

Developing conjectures about tessellations

D2.1.3

HW #1:

Journal
D1.3

Tessellation experience as learner -- assignment
D2.1.4

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

DAY 2 (Tuesday):

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" (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

HW #2:

Journal
D1.1

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

DAY 3 (Wednesday):

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

Reflecting on the Tessellation experience as learner focusing on learning differences among adult learners, and implications for teaching in inclusive classrooms (1 1/2h)
D3.2

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 #3:

Journal
D1.1

Area experience as learner -- assignments
D2.2.5

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

DAY 4 (Thursday):

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

Area inquiry experience II (2 1/2 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

First session on assessment (1 h)
D5.3

HW #4:

Journal
D1.1

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

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

Identify teaching strategies modeled in the Summer Institute -- preliminary assignment
D3.4

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

DAY 5 (Friday):

Follow-up discussion on readings from the Area supporting materials for teachers (1/2 h)
D6.2

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

Reflecting on the teaching practices modeled in the Summer Institute (1 h)
D3.4

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 of facilitators circulating in the room (2 h)
D6.4

Testimonial from teachers who have been in the program, sharing their insights about their first year as inquiry teachers and providing tips for "survival" (1 h)
D6.3

Soliciting feedback on the program: evaluation questionnaire (1/2 h)
D8.1

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Agendas of the follow-up meetings

FOLLOW-UP PROJECT-WIDE MEETINGS:

Note: This schedule assumes that all follow-up meetings take place in the third week of the month

1. August meeting

Participants share and refine their plans for their first inquiry unit in small groups with facilitators (3 1/2 h)
D6.4

Hw: journal entry; develop a preliminary plan and assessment tools to evaluate students' learning as a result of the illustrative unit D1.2/
D6.7

2. September meeting

Informal sharing on the on-going field experiences (1 1/2h)
D6.6

Raising and addressing assessment issues with respect to the participants' plan for their first inquiry unit (2 h)
D6.4/
D5.3

Hw: journal entry; collect significant samples of student work from the implementation of the illustrative unit, to be examined at the meeting; be prepared to share one positive thing and one concern from implementing the illustrative unit D1.2/
D6.7

3. October meeting

Round robin sharing on the first field experiences (2 h)
D6.6

Small group in-depth examination of representative samples of student work brough in by each participant to better assess what they learned (1 1/2 h)
D5.3

Hw: journal entry; select a few topics around which you could develop a second inquiry unit; read the essay "Planning a new inquiry unit: A case-study" D1.2/
D7.1/
D7.5

4. November meeting

Participants briefly share the topics/themes they are considering for their second inquiry unit (1/2 h)
D7.5

Follow-up discussion of the essay on the process of planning an inquiry unit, drawing concrete implications for the participants' planning of their second inquiry unit (1 h)
D7.1

Learning strategies for using instructional resources effectively (1 h)
D7.4

Small groups begin discussing ideas about their second inquiry unit (1 h)
D7.5

Hw: journal entry; develop a preliminary overall plan for the second inquiry unit D1.2/
D7.1/
D7.5

5. January meeting

Participants briefly identify the units they have been working on (as a basis to form compatible small groups) and reflect on the process of planning these units (1 h)
D7.5/
D6.6

Planning session to share and revise participants' plans for the second unit, and benefit from facilitators' feedback (2 1/2 h)
D7.5

Hw: journal entry; finalize plan for the second inquiry unit; readings on teaching mathematics through inquiry D1.2/
D7.5/
D5.3

6. February meeting

Informal sharing on the on-going second field experience (1 1/2 h)
D7.5

Analyzing classroom vignettes from an inquiry perspective -- group experience to revisit what it means to teach mathematics through inquiry (2 h)
D5.2

Hw: journal entry; readings on assessment; bring in a "good" assessment tool you have been using to be shared (along with representative examples of students' responses) D1.2/
D7.5/
D5.3

7. March meeting

Informal sharing on the on-going second field experience (1 1/2 h)
D7.5

Assessment issues are concretely revisited through the in-depth examination in small groups of the examples of assessment tools and students' responses participants have brought in, and a final sharing and reflection (2 h)
D5.3/
D6.6

Hw: journal entry; try to conclude the implementation of the second inquiry unit and collect artifacts in preparation for a presentation that will take place at the last meeting D1.2/
D7.5/
D6.7

8. April meeting

Informal sharing on the on-going field experiences (1/2 h)
D7.5

Examining in-depth a 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) (2 1/2 h)
D7.3

Hw: journal entry; half of the participants prepare to set up posters and stations with artifacts from their implementation of the second inquiry experience; choose a unit of interest from a relevant NSF-funded curriculum and read it, thinking about how it could be used in your classroom D1.2/
D7.5/
D8.2

9. May meeting

Poster presenters briefly announce the topic of their units; other participants circulate around the room asking questions and examining artifacts (2 h)
D7.5

Discussion on potential and possible uses of the units from NSF-funded materials examined by the participants for homework (1 1/2 h)
D7.3

Hw: journal entry; prepare a written reflection on your experiences in the program; the other half of the participants prepare to set up posters and stations with artifacts from their implementation of the second inquiry experience D1.2/
D7.5/
D8.2

10. June meeting

Poster presenters briefly announce the topic of their units; other participants circulate around the room asking questions and examining artifacts (2 h)
D7.5

Final reflections on the program and possible next steps (1 h)
D8.1

Informal gathering with refreshments (1/2 h)
D8.3

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Agendas of the summer institute
Preliminary assignments:
Getting oriented to the program -- reading description of program structure and expectations	D1.1
Making connections with math reform -- preliminary readings	D1.2
Survey on participants' math beliefs	D1.5
Tessellation experience as learner -- preliminary assignment	D2.1.2
DAY 1 (Monday):
Getting oriented to the program -- staff and participants' introductions; reminder of program structure and expectations (with special attention to the first "experience as teacher"), making connections with math reform (1h)	D1.1/ D6.1/ D1.2
Learning disabilities awareness session (F.A.T. City video) (1 1/2h)	D3.2
Rethinking "What is math?" (1h)	D1.4
Tessellation experience as learner -- part I (2h 30'):
Introduction	D2.1.1
Interpreting a definition of tessellation	D2.1.2
Developing conjectures about tessellations	D2.1.3
HW #1:
Journal	D1.3
Tessellation experience as learner -- assignment	D2.1.4
Making connections with math reform -- follow-up readings	D1.2
DAY 2 (Tuesday):
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" (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
HW #2:
Journal	D1.1
Acquainting participants with the supporting materials for the illustrative units -- reading assignment from the Tessellation booklet	D6.2
DAY 3 (Wednesday):
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
Reflecting on the Tessellation experience as learner focusing on learning differences among adult learners, and implications for teaching in inclusive classrooms (1 1/2h)	D3.2
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 #3:
Journal	D1.1
Area experience as learner -- assignments	D2.2.5
Reading from the story of a middle school unit on Area	D4.2
DAY 4 (Thursday):
Follow-up discussion on the readings from the Area story (1/2h)	D4.2
Area inquiry experience II (2 1/2 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
First session on assessment (1 h)	D5.3
HW #4:
Journal	D1.1
Acquainting participants with the supporting materials for the illustrative units -- readings from Area booklet	D6.2
Identifying common elements of inquiry units -- preliminary assignment	D5.1
Identify teaching strategies modeled in the Summer Institute -- preliminary assignment	D3.4
Make a tentative decision about which illustrative unit will be implemented as the first field experience
DAY 5 (Friday):
Follow-up discussion on readings from the Area supporting materials for teachers (1/2 h)	D6.2
Identifying common elements of inquiry units (1 h)	D5.1
Reflecting on the teaching practices modeled in the Summer Institute (1 h)	D3.4
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 of facilitators circulating in the room (2 h)	D6.4
Testimonial from teachers who have been in the program, sharing their insights about their first year as inquiry teachers and providing tips for "survival" (1 h)	D6.3
Soliciting feedback on the program: evaluation questionnaire (1/2 h)	D8.1

Agendas of the follow-up meetings
FOLLOW-UP PROJECT-WIDE MEETINGS:
Note: This schedule assumes that all follow-up meetings take place in the third week of the month
1. August meeting
Participants share and refine their plans for their first inquiry unit in small groups with facilitators (3 1/2 h)	D6.4
Hw: journal entry; develop a preliminary plan and assessment tools to evaluate students' learning as a result of the illustrative unit	D1.2/ D6.7
2. September meeting
Informal sharing on the on-going field experiences (1 1/2h)	D6.6
Raising and addressing assessment issues with respect to the participants' plan for their first inquiry unit (2 h)	D6.4/ D5.3
Hw: journal entry; collect significant samples of student work from the implementation of the illustrative unit, to be examined at the meeting; be prepared to share one positive thing and one concern from implementing the illustrative unit	D1.2/ D6.7
3. October meeting

Round robin sharing on the first field experiences (2 h)	D6.6
Small group in-depth examination of representative samples of student work brough in by each participant to better assess what they learned (1 1/2 h)	D5.3
Hw: journal entry; select a few topics around which you could develop a second inquiry unit; read the essay "Planning a new inquiry unit: A case-study"	D1.2/ D7.1/ D7.5
4. November meeting
Participants briefly share the topics/themes they are considering for their second inquiry unit (1/2 h)	D7.5
Follow-up discussion of the essay on the process of planning an inquiry unit, drawing concrete implications for the participants' planning of their second inquiry unit (1 h)	D7.1
Learning strategies for using instructional resources effectively (1 h)	D7.4
Small groups begin discussing ideas about their second inquiry unit (1 h)	D7.5
Hw: journal entry; develop a preliminary overall plan for the second inquiry unit	D1.2/ D7.1/ D7.5
5. January meeting
Participants briefly identify the units they have been working on (as a basis to form compatible small groups) and reflect on the process of planning these units (1 h)	D7.5/ D6.6
Planning session to share and revise participants' plans for the second unit, and benefit from facilitators' feedback (2 1/2 h)	D7.5
Hw: journal entry; finalize plan for the second inquiry unit; readings on teaching mathematics through inquiry	D1.2/ D7.5/ D5.3
6. February meeting
Informal sharing on the on-going second field experience (1 1/2 h)	D7.5
Analyzing classroom vignettes from an inquiry perspective -- group experience to revisit what it means to teach mathematics through inquiry (2 h)	D5.2
Hw: journal entry; readings on assessment; bring in a "good" assessment tool you have been using to be shared (along with representative examples of students' responses)	D1.2/ D7.5/ D5.3
7. March meeting
Informal sharing on the on-going second field experience (1 1/2 h)	D7.5
Assessment issues are concretely revisited through the in-depth examination in small groups of the examples of assessment tools and students' responses participants have brought in, and a final sharing and reflection (2 h)	D5.3/ D6.6
Hw: journal entry; try to conclude the implementation of the second inquiry unit and collect artifacts in preparation for a presentation that will take place at the last meeting	D1.2/ D7.5/ D6.7
*8. April meeting*
Informal sharing on the on-going field experiences (1/2 h)	D7.5
Examining in-depth a 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) (2 1/2 h)	D7.3
Hw: journal entry; half of the participants prepare to set up posters and stations with artifacts from their implementation of the second inquiry experience; choose a unit of interest from a relevant NSF-funded curriculum and read it, thinking about how it could be used in your classroom	D1.2/ D7.5/ D8.2
*9. May meeting*
Poster presenters briefly announce the topic of their units; other participants circulate around the room asking questions and examining artifacts (2 h)	D7.5
Discussion on potential and possible uses of the units from NSF-funded materials examined by the participants for homework (1 1/2 h)	D7.3
Hw: journal entry; prepare a written reflection on your experiences in the program; the other half of the participants prepare to set up posters and stations with artifacts from their implementation of the second inquiry experience	D1.2/ D7.5/ D8.2
*10. June meeting*
Poster presenters briefly announce the topic of their units; other participants circulate around the room asking questions and examining artifacts (2 h)	D7.5
Final reflections on the program and possible next steps (1 h)	D8.1
Informal gathering with refreshments (1/2 h)	D8.3