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Summer Workshop Plans


PRIME Summer Institute, Peoria Illinois

submitter: PRIME Mathematics Project, K-5
published: 10/05/2000
posted to site: 10/05/2000

PRIME Summer Institute, Peoria Illinois

A collaborative program between Illinois State University and Peoria School District #150

Overview of our summer, 2000 institute for teacher development

Teachers in our project attended a one-week course (2 sem hr grad credit).
  • June 5-9, 2000,
  • June 12-16, 2000, or
  • June 19-23, 2000.

Our summer institute focused on the geometry and measurement strands from Investigations in Number, Data and Space, next year, year 2 will focus on number and operations, and year 3 on data analysis and change.

Two major components characterized the week-long summer sessions: (1) Learning mathematics through investigations; and (2) Analyzing teaching and learning through video clips, case studies, and student. Teachers analyzed the development of the mathematical ideas within and across grade levels, technology integration, alternative assessment strategies, and features of the modules themselves (e.g. choice time activities, Teacher Notes, Dialogue Boxes, 10-Minute Math). Teachers carried out and practiced leading activities within the curriculum from Investigations Units in the grade level they most often teach. They also engaged in mathematical extensions of those content ideas, especially through the use of the Bridges curriculum.* Individually, in small groups, and in grade-level large groups, they reflected on instruction and content, discussing their own responses and reasoning as well that of students presented through video clips, case studies, and work samples.

Focus questions guided our discussion toward the themes for our project. The themes were:

  • Building task-focused lessons around substantial tasks,
  • good questioning practices,
  • ways of engaging students in the mathematics as active participants and discussants.

What follows is our specific response to each of the questions addressed to LSC projects:

a) We provided one-week workshops, with an additional assignment for developing lesson plans to integrate that content area into their planning cycle for the upcoming year, and to carry out a sample lesson and assessment for sharing at an upcoming round of grade level meetings in October, 00.

b) In all, 330 teachers attended our workshops, nearly all the classroom teachers and special education teachers teaching K-5 students in the district.

c) Goals: We focused this summers' workshops around geometry and measurement, phase I of three phases to bring in units from the Investigations in Number, Data and Space curriculum as tools for teaching in this district. Next summer we expect to work on units focusing on number and operations, and the last summer of our project will focus on data and representations. Our intent was to demonstrate the development of geometry and mathematics content appropriate to each grade level by teaching through tasks rather than by the typical skills and procedures approaches observed in this district at present. We focused on three themes: using good tasks, asking good questions to determine students' ways of thinking about the mathematics, and promoting student initiative and involvement in investigating, communicating and justifying their ways of doing mathematics.

We used the Investigations curriculum (NSF curriculum for K-5 mathematics) to illustrate task-based pedagogy and contextual instruction in mathematics. A typical day in our workshop began by working through a particular sample unit from the curriculum, following the sessions and developing the interaction between assessment and investigation of concepts through examples and activities. For example, a grade 4 plan is shown below:

d) We offered professional development focused on the Investigations in Number, Data and Space curriculum since it is a primary means for us to address substantial tasks and questioning practices.

e) We employed the professional development materials entitled "Bridges to Classroom Mathematics" as a primary tool for developing teachers' knowledge of mathematics, especially geometry and measurement this summer.

Grade 4 Teachers

DAY 1 Session Outline

(8:00 - 9:30)
Introduction 15 mins. Presenter
Investigation I: Session I, II from Seeing Solids and Silhouettes
(p.4) Making Buildings -student sheet #1
  • What kind of language do students use to communicate about 3-D spatial relationships?
  • How do students understand and interpret drawings of 3-D cube configurations?
    30 mins. Interlocking cubes: 65 cubes per pair (2 bags of 65 per group)
    Discussion: In groups (5 minutes)
    As a class (10 minutes)
    Teacher's note
    (p.8) Interpreting 2-D Diagrams of 3-D Shapes
    10 mins. Individual read, then as group discussion, then class.
    (p.10) Building from Quick Images. 2, 4, 5, 7, 10, 11, 12

    Reflection: When constructing cube buildings from memory, what kinds of mental images do students use to organize their thinking? Do they mentally decompose the building into smaller units, counting cubes in different parts of the building? Do they look for simpler geometric shapes or see the image as a whole object? How many times do students need to see an image flashed before they can successfully reproduce the cube configurations shown?

    35 mins. O/H sheets of 3D images to be flashed for 3 seconds. Teachers to build. 45 seconds. Reflash for 3 seconds and 45 seconds. Flash and leave for revision and correction.

    Focus on Geometry CONTENT
    (9:30 - 11:15)
    Focus: Ways of Describing Symmetry Among 2D and 3D objects: Rotational and Reflective Symmetry. (Extending the material in the Mathematical Thinking unit for Grade 4, Investigations, and developing material from Bridges to Classroom Mathematics curriculum)
    (11:55 - 2:00)
    Investigation II: Exploring Geometric Silhouettes (Sessions I, II, III, IV)
    Sessions I, II
    (p. 16) What are Silhouettes?
    20 mins.
    • O/H Geometric solids
    • 6 sets of Geometric solids
    • 1 set per six students
    Activity and Reflection: (p.18) Matching Solids and Silhouettes -SS #4
    (p.20) What Can You See from Here? Landscape I SS #5
    30 mins.
    • Interlocking cubes: 65 cubes per pair (2 bags of 65 per group)
    • O/H SS#'s 4,5
    Teacher Note:
    (p.28) Good Thinking Doesn't Always Result in "Correct" Answers
    10 mins. Individual read, then as group discussion, then class.
    Sessions III, IV
    Activity and Reflection:
    (p.31) Drawing a Building's Silhouettes -SS #10
    (p.33) Drawing Before Building - SS #12
    (p.34) Drawing Before Building - SS #14
    30 mins.
    • Interlocking cubes: 65 cubes per pair (2 bags of 65 per group)
    • O/H ss# 10, 12, 14
    Teacher Note: (p.38)Integrating Three Views: How Students Try to Do It 10 mins.
    • Individual read, then as group discussion, then class.
    Investigation III: Writing How To Instructions
    Activity and Reflection
    (p.45) Writing Good Instructions
    25 mins.
    • Interlocking cubes: 65 cubes per pair (2 bags of 65 per group)
    • Two sets of instructions per group to be exchanged between groups. One group to present on O/H
    • Blank transparencies 2-3 for group presentation