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Sample programs for different higher education settings (E2)
Scenario #1: A semester-long course on teaching mathematics through inquiry

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

Weekly agendas and assignments

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Key characteristics of this scenario

Scenario 1: A semester-long course on teaching mathematics through inquiry

Overall goals of the course: Introduce in-service as well as prospective mathematics teachers to an inquiry approach to mathematics instruction.

Participants: Mostly secondary math and elementary in-service teachers pursuing advanced degrees and secondary math and elementary pre-service teachers enrolled in a teacher preparation program. Other educators with an interest in an inquiry approach also welcomed.

Program structure: A semester-long course including weekly meetings of 2 1/2 hours (for a total of 14 sessions), weekly assignments, a few major take-home projects and a field experience. The field experience is conducted by participants either in pairs (consisting of a classroom teacher and either a colleague at the same grade level or a prospective teacher) or individually (option for classroom teachers only), and consists of developing a plan for an inquiry unit for a specific class -- with the hope that such a unit would be implemented later in the year.

Professional development main characteristics: The course begins with some activities intended to provide an image of what teaching mathematics through inquiry means and begin to challenge participants' beliefs about mathematics and its teaching (framework component 1). The next 3 sessions are devoted to "experiences as learner" around the Tessellation illustrative unit, followed by some reflective sessions and the viewing of the video on the implementation of the same unit in a 6th grade class (framework components 2-4). Participants are then asked, in small groups, to prepare a preliminary plan for implementing this unit in the class of one of the group members; these plans are then shared with the large group in a "poster session," followed by a discussion on what it takes to plan inquiry units (part of framework component 6). This is followed by another cycle of experience as learner, reflections on this experience and analysis of implementations of the same unit in a classroom setting focusing on the Area unit (framework components 2-4). In preparation for a discussion of the principles and foundations of an inquiry approach -- as well as other constructivist-based approaches -- students then read/view several other examples of instructional innovation as well as more theoretical articles about constructivism and inquiry (framework components 4-5). Participants are then assigned the task of designing an inquiry unit for an actual math classroom. In preparation for this experience, practical issues about implementing an inquiry approach across the curriculum are addressed by both examining the process of planning new inquiry units and acquainting participants with existing resources such as the new NSF-funded curriculum series developed for various grade levels (framework component 7). The course concludes with a presentation -- in the form of another "poster session" -- of the plans produced by the participants, as well as some written assignments and activities designed to elicit reflections on what was learned in the course and its implications for mathematics instruction (framework component 8).

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Weekly agendas and assignments
Lesson 1:
Orienting participants to the program: brief video excerpts of an inquiry math classroom, information about the course goals and organization, and their rationale	D1.1
Rethinking "What is math?"	D1.4
Hw. 1:
Journal entry	D1.2
Readings of vignettes of inquiry math classrooms	D1.1
Readings on school math reform	D1.3
Lesson 2:
Brief follow-up discussion on readings	D1.1/ D1.3
Tessellation experience as learner -- part I:
Introduction	D2.1.1
Interpreting a definition of tessellation	D2.1.2
Developing conjectures about tessellations	D2.1.3
Hw. 2:
Journal entry	D1.2
Tessellation experience as learner -- assignment (including readings on the role of definitions in mathematics)	D2.1.4
Lesson 3:
Tessellation experience as learner -- part II:
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" (modeling)	D3.1
Hw. 3:
Journal entry	D1.2
Reflection on the Tessellation experience as learner: "Walk down memory lane" assignment	D3.1
Lesson 4:
Reflection on the Tessellation experience as learner: "Walk down memory lane" -- sharing and follow-up discussion	D3.1
Watching and discussing the video of a middle school inquiry unit on tessellations	D4.1
Introduction to the "Supporting materials for teachers" created for the Tessellation unit	D6.2
Hw.4:
Journal entry	D1.2
Follow-up readings from the Tessellation supporting materials	D6.2
Generate ideas about planning a tessellation experience	D6.4
Lesson 5:
Follow-up discussion on the readings from the Tessellation supporting materials	D6.2
First discussion on what it takes to implement inquiry units	D6.4
In small groups, participants begin the process of planning a Tessellation unit for the classroom of one member of the group, using the flexible plan as well as other documents provided in the "Supporting materials for teachers"	D6.4
Hw. 5:
Journal entry	D1.2
Conclude the preliminary plan for a tessellation unit; prepare a poster to be posted on the class walls for everyone to examine (containing the plan as well as a description of the classroom setting)	D6.4
Read the essay "Planning a new inquiry unit: A case-study"	D7.1
Lesson 6:
Poster session -- every group posts their plans for implementing the tessellation unit and participants go around the room examining them
Follow-up discussion about the process of planning inquiry unit, based on the previous experience as well as the reading of the essay	D6.4/ D7.1
Beginning to raise issues about assessing learning within an inquiry experience	D5.3
Hw. 6:
Journal entry	D1.2
(Individual) Revise the plans of your tessellation unit to include appropriate assessment	D6.4/ D5.3
Lesson 7:
Area experience as learner -- part I:	D2.2
Introduction	D2.2.1
Fish activity	D2.2.2
Diamond activity	D2.2.3
Star activity (preliminary group work)	D2.2.4
Hw. 7:
Journal entry	D1.2
Area assignments
continue working on the area formula of assigned star	D2.2.4
reflections on thought-provoking questions about area and reading of the essay "On the mathematics of area"	D2.2.5
readings from the Area story	D4.2
Lesson 8:
Area experience as learner -- part II:
Star activity (finalizing results + presentations)	D2.2.4
Rethinking the math of area (discussion)	D2.2.5
Reflecting on the experience as learner -- creating a "What have I learned" list	D3.3
Hw. 8:
Journal entry	D1.2
readings from the NCTM Standard (geometry and measurement)	D3.3
reading stories of inquiry/innovative math classes	D4.2
readings from the NCTM Teaching Standards	D5.1
Lesson 9:
Reflecting on the experience as learner -- focus on the goals of an Area inquiry unit and larger implications for rethinking the teaching of geometry	D3.3
Follow-up discussion on stories of inquiry math classes	D4.1/ D4.2
First identification of characteristics of an inquiry approach	D5.1
Hw. 9:
Journal entry	D1.2
Readings on constructivism and an inquiry approach	D5.1
Readings on school reform	D1.2
MIDTERM take-home exam (i.e, Analyze in writing a classroom vignette from an inquiry perspective) is assigned and due in 2 weeks	D5.2
Begin to think of possible topics for an inquiry unit for one of your classes (or the class of another participant)	D7.5
Lesson 10:
Follow-up discussion on the readings on constructivism, inquiry and school reform	D5.1/ D1.2
Process of planning new inquiry units revisited in the context of the assignment of planning an inquiry unit	D7.1
Small groups brainstorming on topics for their final project	D7.5
Hw. 10:
Journal entry	D1.2
MIDTERM take-home exam due	D5.2
Decide on topic for final project; begin an inquiry of your own on the mathematics to be covered in your unit	D7.2
Preliminary readings on NSF-funded curricula	D7.3
Lesson 11:
Time for students to share in pairs on the progress of their independent inquiry	D7.2
"Experience as learner" of an activity from one of the NSF-funded curricula	D7.3
Presentation on NSF-funded curricula at various grade levels	D7.3
Hw. 11:
Journal entry	D1.2
Follow-up readings on NSF-funded curricula	D7.3
Continue to work on the design of your inquiry unit	D7.5
Lesson 12:
Working session where groups continue to work on their plans and meet at designated times with the instructor for feedback	D7.5
Hw. 12:
Journal entry	D1.2
Complete written plan for the unit and prepare for a "poster session"	D7.5
Additional readings on inquiry	D5.1
Lesson 13:
"Poster session" -- every group posts their plans for a new inquiry unit and participants go around the room examining them (also as a celebration of students' accomplishments)	D7.5/ D8.3
Follow-up discussion on the units designed, and on the characteristics of inqiury units and the process of planning inquiry units	D5.1
Hw. 13:
Journal entry	D1.2
Reflect on teaching strategies modeled in the course	D3.4
"What have I learned" paper (participants' written final reflection)	D8.2
Fill in course evaluation questionnaire	D8.1
Lesson 14:
Discussion on teaching strategies that can support teaching mathematics through inquiry -- building on the strategies modeled in the course	D3.4/ D5.1
Course evaluation (forms + open discussion)	D8.1

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