D. DESCRIPTION OF FRAMEWORK COMPONENTS
2. Experiencing Inquiry as Learners
D2.1. Tessellation inquiry experience
List of materials available about the ENTIRE "Tessellation
inquiry experience":
- Logistics and scheduling information. (In-service program / Methods
course)
- Facilitator's plan:
- overview of the entire experience (In-service program
/ Methods course)
- "Teaching practices that support teaching mathematics
through inquiry" (Borasi & Fonzi, 1998)
- "Mathematical topics that can be pursued through
the study of tessellations" (Rose 1994) (available
in the booklet "Investigating tessellations to learn geometry: Supporting
materials for teachers")
- Instructional materials for the teacher educator
- Samples of participants' work:
- VIDEO of this experience: Exploring tessellations:
A professional development experience (about 110
minutes)
- Participants' feedback:
- responses to an anonymous questionnaire (In-service program
/ Methods course)
- sample of written reflections on various components
of the experience (written by the participants
as part of a "walk down memory lane" activity on this inquiry
experience -- see Section D3.1 for a description of this kind of reflective
session) (Methods course)
- excerpts from reflective journals after day 1 of the
Tessellation inquiry experience -- to show participants'
initial reactions to the experience (In-service
program)
D2.1.1 Introduction to the tessellation inquiry experience
List of materials available for the "Introduction
to the tessellation inquiry experience":
- Facilitator's plan (In-service program/ Methods
course)
- Instructional materials:
N/A
- Samples of participants' work:
- VIDEO -- this video segment shows how a facilitator
introduced the first "experience as learners" in a specific implementation
(see first few minutes of the video Exploring tessellations: A professional
development experience)
D2.1.2 Interpreting a definition of tessellation
List of materials available about "Interpreting
a definition of tessellation":
- Facilitator's plan (In-service program/ Methods
course)
- Instructional materials:
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see Section 1 of the video Exploring
tessellations: a professional development experience)
- selected examples of tessellation brought in by the
participants -- to give an idea of the variety
of these examples and the potential questions they could raise, and also
suggest examples of tessellations the facilitator may want to have available
to add to the class collection (In-service
program)
- final definition of tessellation the participants
agreed on (In-service program/
Methods course)
- newsprint summarizing the large group discussion (In-service program)
D2.1.3 Developing conjectures about tessellations
List of materials available about "Developing conjectures
about tessellations":
- Facilitator's plan (In-service program / Methods
course)
- Instructional materials:
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see the section entitled "Developing
conjectures" in the video Exploring tessellations: A professional
development experience)
- list of questions/conjectures generated by the participants
(In-service program / Methods course)
D2.1.4 Reflecting on mathematics and definitions
List of materials available about "Reflecting on
mathematics and definitions":
- Facilitator's plan (In-service program / Methods
course)
- Instructional materials:
- text of homework assignment (In-service program / Methods course)
- "What does it mean to study a geometric figure
mathematically?" (Borasi, 1992) (available in hard copy ONLY, in
booklet titled "suggested readings for the participants")
- Samples of participants' work:
- VIDEO -- this video
segment captures some participants' responses to Activity 2 in a specific
implementation of the tessellation inquiry experience (see the section
entitled "Reflecting on definitions and mathematics" within the
video Exploring tessellations: A professional development experience)
- Artifacts from the discussion of mathematics and definitions
(In-service program)
- Excerpts from participants' written reflections
(Methods course).
D2.1.5 Modeling how to test conjectures about tessellations
List of materials available about "Modeling how
to test conjectures about tessellations":
- Facilitator's plan (In-service program / Methods
course)
- Instructional materials:
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see section entitled "Modeling
how to test conjectures" in the video Exploring tessellations:
A professional development experience)
- participants' suggestions for how to test conjectures
(In-service program)
- sample of small group work on the conjecture "All
triangles tessellate" (In-service
program)
D2.1.6 Exploring conjectures about tessellations independently
List of materials available about "Exploring conjectures
about tessellations independently":
- Facilitator's plan (In-service program / Methods
course)
- Instructional materials:
- text of homework assignment (Methods
course )
- handout with list of questions/conjectures generated
by the participants (In-service program/Methods course)
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see section entitled "Exploring
conjectures independently" in the video Exploring tessellations:
A professional development experience)
- sample of small group work on conjectures of their
choice (In-service program/Methods course)
D2.2. Area inquiry experience
List of materials available about the ENTIRE "Area
inquiry experience":
- Information about scheduling and other logistics (In-service program / Methods
course)
- Facilitator's plan:
- Instructional materials:
- Samples of participants' work:
- VIDEO of this experience: "Developing area formulas:
A professional development experience" (about
100 minutes)
- Participants' feedback:
D2.2.1 Introduction to the area inquiry experience
List of materials available about the "Introduction
to the Area inquiry experience":
D2.2.2 The "fish activity": Computing the
area of a complex figure
List of materials available about the "Fish activity":
- Facilitator's plan (In-service program / Methods
course)
- Instructional materials:
- "Fish"
slide (photocopy ready - use
the "BACK" button on your browser to return here)
- "Fish"
handout (photocopy ready - use
the "BACK" button on your browser to return here)
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see the segment entitled "Computing
the area of a complex figure" within the video Developing area
formulas: A professional development experience)
- examples of participants' approaches to computing
the area of the "fish" (In-service
program)
- strategies to compute area recorded on newsprint (Methods course)
- issues about area raised by participants during discussion
(In-service program)
D2.2.3 The "diamond activity": Modeling how
to develop an area formula
List of materials available about the "Diamond
activity":
- Facilitator's plan (In-service
program/ Methods course)
- Instructional materials:
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see the segment entitled "Modeling
how to develop an area formula" within the video Developing area
formulas: A professional development experience)
- newsprint recording the key steps followed in creating
an area formula (In-service program/Methods course)
D2.2.4 The "star activity": Developing area
formulas independently
List of materials available about the "star activity":
- Facilitator's plan (In-service
program / Methods course)
- Instructional materials:
- Samples of participants' work:
- VIDEO -- this video segment can provide an image
of how the experience played out in a specific implementation and how the
participants responded to the activities (see the segment entitled "Developing
area formulas independently" within the video Developing area formulas:
A professional development experience)
- star posters created by different groups (In-service program)
D2.2.5 Rethinking the math of area
List of materials available about "Rethinking the
math of area":
- Facilitator's plan (In-service program/ Methods
course)
- Instructional materials:
- Samples of participants' work:
- sample of participants' initial reflections on the
"thought-provoking questions" about area -- to show how difficult it is for teachers to engage in this kind
of mathematical discussion without some support (Methods
course)
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