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Sample programs for different in-service settings (E1)
Scenario #1: A first-year program for teachers involved in a "local systemic change" project with adequate funding

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Key characteristics of this scenario

Scenario 1: A first-year program for teachers involved in a "local systemic change" project with adequate funding

Overall goals: Developing a shared vision for school mathematics consistent with the most recent calls for reform and begin to make instructional changes informed by such a vision. After completion of the program, teachers will be expected to participate in additional professional development (for ex: learning to use one of the new NSF-funded curriculum series such as Investigations in numbers, data and space [TERC, 1996] or Mathematics in context [University of Wisconsin, 1998]).

Participants: All those responsible for students' math learning in the schools participating in the project -- that is, all the mathematics teachers in these schools, special education teachers and teacher aids responsible for mathematics instruction, math tutors, and representatives from administration and parents.

Program structure: The program consists of a 2-week Summer Institute, 5 day-long follow-up meetings during the school year, and supported field experiences. All those responsible for mathematics instruction 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 other participants are expected to be participant observers in some of these experiences. A mathematics teacher educator is assigned to each participating school as "school facilitator" for 10-15 hours a week, with the role of supporting participants' field experiences and promoting collaboration among participants in the same school.

Professional development main characteristics: The first week of the Summer Institute (intended for all participants) 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. The second week of the Summer Institute is intended only for those participants responsible for mathematics instruction. These participants will be supported in planning their first inquiry unit on Tessellation or Area, while also further exploring the principles and implications of teaching mathematics through inquiry (framework components 5-6). The follow-up meetings are scheduled at critical points during the following school year to provide opportunities for sharing on the on-going field experiences and to begin to discuss how teaching mathematics through inquiry can be extended beyond the two illustrative units by learning to plan new inquiry units and becoming familiar with innovative curriculum series (framework components 6-8).

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Agendas of the first week 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, making connections with math reform (1h)
D1.1/
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 (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
  • Beginning to reflect on implications for 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
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 1/2h)
D5.1
  • Beginning to learn about resources available to support instructional innovation: presentation on new NSF-funded curriculum series (1 h)
D7.3
  • Reflecting on the teaching practices modeled in the Summer Institute (1 1/2h)
D3.4
  • Soliciting feedback on the program: evaluation questionnaire (1/2 h)
  • Teachers from the same school meet to coordinate their choices for field experiences (1/2 h)
D8.1

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Agendas of the second week of the summer institute
SUMMER INSTITUTE (second week)   
DAY 6 (Monday): READING DAY
  • Follow-up readings on inquiry
D5.1
  • Extensive readings from the booklet for the unit chosen for classroom implementation
D6.2
  • Begin to sketch a plan for the chosen unit
D6.4
HW #6:
  • Journal
D1.3
DAY 7 (Tuesday):
  • Follow-up discussion on the readings on inquiry (1 h)
D5.1
  • Discussion on the process of planning inquiry units (2 h)
D6.4/
D7.1
  • Sharing of preliminary plans/ideas (in groups by units); developing list of questions to ask "experts" (1 1/2 h)
D6.4
  • Testimonials of teachers who taught the units/ question/answer session (1 h)
D6.3
  • Continue developing your plan for the unit
D6.4
DAY 8 (Wednesday): PLANNING DAY
  • Time for individuals and pairs to work on their plans, with the support of facilitators and expert teachers (5 1/2 h)
D6.4
HW #8:
  • Complete a first draft of your overall plan for the unit
D6.4
  • Readings on assessment
D5.3
DAY 9 (Thursday):
  • Sharing in small groups on the plans created (1 1/2h)
D6.4
  • Assessing inquiry experiences (2 h)
D5.3
  • Examining student work (2 h)
D5.3
HW #9:
  • Journal
D1.1
  • Begin to develop assessment tools for your unit
D6.4
  • Time for individuals and pairs to work on their assessment tools, with the support of facilitators and expert teachers (2 1/2 h)
D6.4
  • Sharing of assessment tools created in small groups (1 1/2h)
D5.1
  • Reflection on the process of planning and designing assessment (1 h)
D7.3
  • 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:  
1. Sharing on the implementation of the first illustrative unit (Late October, just after participants concluded this field experience)
  • Round-robin sharing of the concurrent field experiences (2h)
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
  • Discussion of selected issues and concerns raised by the participants (1h)
D6.6
  • School-based groups discuss ideas for next field experience and possible school efforts towards reform (1h)
1. On the process of planning a new inquiry unit (November)
  • Characterizing elements of teaching mathematics through inquiry revisited (after preliminary reading assignment) (1/2 h)
D5.1
  • An in-depth look at the process of planning an inquiry unit based on the case-study on planning the Olympics unit (1h)
D7.1
  • Participants' independent inquiries on the mathematics of a sport of their choice -- in pairs or small groups (1 1/2 h)
D7.2
  • Whole group brainstorming on the overall plan for an inquiry unit on the mathematics of sports (1 h)
D7.1
  • Small groups begin to plan their own unit on the mathematics of sports (1 1/2h)
D7.1/
D7.5
  • Reflections on the process of planning inquiry units (1/2 h)
D7.1
1. Learning about resources to support instructional innovation (December)
  • Time for informal sharing on on-going field experiences (1 h)
D6.6
  • Brief introduction to NSF-funded curriculum series (1/2 h)
D7.3
  • 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) (3 h)
D7.3
  • Discussion about possible uses of the resources provided by the instructional materials examined (1 h)
D7.3/
D7.4
  • Time for the participants to peruse available materials from several curriculum series (1h)
D7.3
1. Revisiting what it means to teach mathematics through inquiry and its implications for assessment
  • Analyzing classroom vignettes from an inquiry perspective -- group experience to revisit what it means to teach mathematics through inquiry (1 1/2 h)
D5.2
  • Brief discussion to identify issues about assessment that participants have been struggling with (1/2 h)
D5.3
  • Participants bring in examples of assessment tools they have been using, and samples of students' responses, and examine these in-depth in small groups (2 h)
D5.3/
D6.6
  • Issues about assessment revisited in light of what was learned from the previous activity (1 h)
D5.3
1. Concluding session (May -- at conclusion of the field experience)
  • Interactive presentations of participants' second inquiry unit (4 h)
D6.6/
D8.3
  • Final reflections on the program (1 h)
D8.1
  • School-based small groups meet to discuss plans for the future (1 h)
D8.3

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