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Sample programs for different higher education settings (E2)
Scenario #3: A two-semester sequence consisting of a math content course and a math methods course for elementary pre-service teachers

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Key characteristics of this scenario

Scenario 3: A two-semester sequence consisting of a math content course and a math methods course for elementary pre-service teachers

Overall goals of the courses: Math content course: Help students review mathematical content relevant for the elementary curriculum, focusing on identifying the "big ideas" within the major areas of mathematics. Math methods course: Introduce prospective elementary teachers to current recommendations for school mathematics, and more specifically to instructional practices and strategies consistent with the NCTM Standards.

Participants: Mostly students enrolled in an elementary teacher preparation program, although each course is also open to interested in-service elementary teachers.

Program structure: Each course is a semester-long and consists of 14 weekly meetings of 2 1/2 hours each, plus weekly assignments and a few major take-home projects. A full-fledged field experience is not included in either course, although as a final project in the math methods course all participants are expected to design and implement a series of lessons informed by the pedagogical principles learned in the course.

Professional development main characteristics:

Math content course: The course begins with some activities intended to elicit participants' beliefs about mathematics and introduce new perspectives about this discipline (framework component 1). The main part of the course consists of "modules" of 2-3 sessions each, each devoted to developing/revisiting a "big mathematical idea." Two of these modules are designed around experiences as learners based on our illustrative units; the sessions on tessellation are intended to develop the study of shapes and their characteristics, while the sessions on area focus on the notions of area and variable (framework components 2, and part of 3). The course concludes with an independent inquiry (framework component 7.2) and some written assignments and activities designed to elicit participants' reflections on how their beliefs about mathematics changed as a result of the course (framework component 8).

Math methods course: The course begins by providing images of the kind of mathematics instruction it is designed to promote and making connections with the participants previous experiences as learners, by watching the video of a classroom experience based on our tessellation unit and reading the Area story as well as other vignettes of innovative instructional experiences (framework component 4). In the next couple of sessions, participants are asked to examine these classroom experiences, as well as their experiences as learners in the math content course, to begin to identify characteristics of teaching mathematics through inquiry, examine the theoretical foundations of this approach, derive some implications for planning and assessment, and also making connections with the current recommendation for school mathematics (framework component 5). Participants then move to examine issues about children's thinking and learning, starting with an analysis of some implementation of the illustrative units they are familiar with and then consider other areas of mathematics as well; issues about affective aspects of learning mathematics and diversity are also addressed (not part of the framework, but important if this is the only mathematics education course for most participants). Issues about planning inquiry experiences are then revisited by both discussing the process of planning inquiry units and introducing instructional materials and resources that can help them put into practice what was learned in the course so far (framework component 7). The next series of lessons is devoted to interactive presentations, where small groups of participants report on a project where they examined the learning and teaching of specific areas of mathematics (once again, not part of the framework, but important if this is the only mathematics education course for most participants). The course concludes with the presentation of the lessons participants have developed, as well as with some written assignments and activities designed to elicit their reflections on what was learned in the course and its implications for them as future mathematics teachers (framework components 7.5 & 8).

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Weekly agendas and assignments for the math content course
Lesson 1:
  • Orienting participants to the program: information about the course goals and organization, and their rationale
D1.1
  • Rethinking "What is math?"
D1.4
Hw. 1:
  • Journal entry
D1.2
  • Survey on math beliefs
D1.5
  • Readings on the nature of mathematics
Lesson 2:
  • Brief follow-up discussion on readings
  • 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 plus the personal investigation of one the conjectures raised)
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
    • Beginning to explore conjectures about tessellations independently (in small groups)
D2.1.6
Hw. 3:
  • Journal entry
D1.2
  • Fully develop and report in a poster the results of the group's exploration of a conjecture
D3.1
  • Reading an essay on the mathematical idea of "shape"
Lesson 4:
  • Tessellation experience as learner -- part III:
    • Group presentations and discussions
D2.1.6
  • Reflecting on the experience as learner: examining what was learned about shapes, and possibilities for further learning on this "big idea"
D3.3
Hw. 4:
  • Write an essay summarizing key things learned about "shapes" and explaining their relevance in mathematics
Lesson 5:
  • 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. 5:
  • 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
Lesson 6:
  • 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 - what was learned about the notions of area and variables, and possibilities for further learning in these areas
D3.3
Hw. 6:
  • independent project: develop area formula for some non-standard figure of your choice
D2.2.4
  • readings from the NCTM Standard (geometry and measurement)
D3.3
  • follow-up problems involving variables in a variety of other situations
  • follow-up readings on variables
  • Final project of developing an independent inquiry on the topic of their choice is assigned (due at the end of the course)
D7.2
Lessons 7-12 and related assignments:
  • Other series of 2-3 sessions on key ideas within other areas of mathematics
Lesson 13:
  • Time for students to meet with a partner to share preliminary results from their inquiries and receive feedback, while also having the opportunity to discuss their project with the instructor
D7.2
Hw. 13:
  • Written report on independent inquiry due
D7.2
  • "What have I learned" paper (participants' written final reflection)
D8.2
  • Fill in course evaluation questionnaire
D8.1
Lesson 14:
  • Course evaluation (forms + open discussion)
D8.1
  • Brief presentations on the independent inquiries (as celebration of students' accomplishments)
D7.2/
D8.3

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Weekly agendas and assignments for the math methods course
Lesson 1:
  • Orienting participants to the program: information about the course goals and organization, and their rationale
D1.1
  • Developing images of innovative mathematics instruction: watching the video of a classroom inquiry on tessellation
D1.4
Hw. 1:
  • Journal entry
D1.2
  • Readings of classroom vignettes (including Area story)
D1.1/
D4.2
  • Readings on school math reform
D1.3
Lesson 2:
  • Follow-up discussion on school math reform
D1.3
  • Follow-up discussion on tessellation video and stories of innovative math classes
D4.1/
D4.2
  • First identification of characteristics of an inquiry approach
D5.1
Hw. 2:
  • Readings on constructivism and an inquiry approach
D5.1
  • Readings on assessment
D5.3
  • Readings on school reform
D1.2
  • First major assignment: Analyze in writing a classroom vignette from an inquiry perspective (due in 2 weeks)
D5.2
Lesson 3:
  • Follow-up discussion on the readings on constructivism, inquiry and school reform
D5.1/
D1.2
  • Assessment activity
D5.3
Hw. 3:
  • First major assignment: Analyze in writing a classroom vignette from an inquiry perspective due
D5.2
  • Read essay "Planning a new inquiry unit: A case-study"
D7.1
Lesson 4:
  • Introduction of the final project -- designing and implementing a series of innovative math lessons
D7.5
  • Activity around planning a unit on Tessellation or Area, with the support of the "flexible plans" provided in the "Supporting materials for teachers"
D6.4
  • Learning how to plan a new inquiry unit
D7.1
Hw. 4:
  • Preliminary readings on NSF-funded curricula
D7.3
Lesson 5:
  • Introduction of group project on learning about the learning and teaching of specific math topics
  • Learning about resources to support instructional innovation: "Experience as learner" of an activity from one of the NSF-funded curricula for elementary schools
D7.3
  • Learning about resources to support instructional innovation: Time to examine materials from NSF-funded curricula for elementary school, as well as other instructional resources
D7.3
  • Developing strategies for using instructional resources effectively: discussion on how to use some of the materials reviewed to plan innovative math lessons/units
D7.4
Hw. 5:
  • Begin to work on projects
  • Preliminary readings on children's mathematical thinking and learning
Lessons 6-9 and related assignments:
  • Children's mathematical thinking and learning
  • Affective issues in mathematics education
  • Diversity and equity issues in mathematics instruction
Lesson 10:
  • Substituted with individual meetings with the instructor to receive feedback on preliminary plans of the innovative lessons designed
D7.5
Lessons 11-13 and related assignments:
  • Interactive presentations of group projects on the teaching and learning of specific math topics
Hw. 13:
  • Identify teaching strategies modeled in the course
D3.4
  • Written report on innovative lessons designed and taught in the form of a poster to be posted in the class for review
D7.5
  • Fill in course evaluation questionnaire
D8.1
Lesson 14:
  • Reflecting on teaching strategies modeled in the course
D3.4
  • "Poster session" on innovative lessons designed and implemented (also as celebration of students' accomplishments)
D7.5/
D8.3
  • Course evaluation (forms + open discussion)
D8.1
Hw. 14:
  • "What have I learned" paper (participants' written final reflection)
D8.2

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