Math Ed 5031: Teaching Mathematics: Geometric Structures

Course Syllabus, Spring 2000

Do one of:

  • Work all problems in LTG: Chapter 15 to hand in.
  • Work half the problems in each section of LTG: Chapter 15 to hand in. and LTG page 221. Work 1-4 and generate another question like these. (Spend no more than 1/2 hour one each of 1-4 - if you don't get it, record your work and go on.)

    • DATE

    TOPIC

    READING DUE

    WRITING DUE

    REFLECTION DUE

    1/19

  • Introduction , course requirements
  • What is geometry
  • What do you know about geometry?

    •  

     

     

    1/24

  • What is geometry, revisited
  • State and National Standards for geometry
  • LTG: Chapter 2
  • SMM: Shape, Space and Measure, pp. 4-17
  • PSSM:
    • Ch. 3: Standard 3: Pk-12
    • Ch. 6: Standard 3: 6-8
    • Ch. 7: Standard 3: 9-12
  • C&E:
    • Grades 5-8: St. 12
    • Grades 9-12: St. 7 & 8
  • Compile an annotated list of at least 5 web sites that would be helpful for geometry teachers. Report your list electronically at the class web resource list.
  • Write a two to three page summary and reaction paper to your readings. Answer such questions as: Why is geometry important for students? What is important content for middle and high school geometry classes? What has changed from C&E to PSSM?
  • C: Describe your geometry learning experiences - good and bad. How can your memories help you be a good teacher?
  • P: Describe your practicum placement. What text series are they using? How can you use your practicum to help you learn all you can about teaching geometry?

    • 1/26

  • Van Hiele model
  • Habits of Mind
  • Dynamic geometry tools
  • GMP: Chapters 1 and 2
  • LTG: Chapter 1
  • EDC: Implementation Guide, pp. 16-23: Mathematical Habits of Mind and Program Philosophy (Implementation guide is at the bottom of the home screen)
    		•
  • Students are studying the concept of area. Describe what van Hiele levels 0, 1, and 2 would look like. Describe a set of activities that would help students move from level 1 to level 2 using the five phases of learning in the van Hiele model. Bring 4 copies of your paper to class.
  • C: Where would you place yourself on the van Hiele level structure when you took geometry in high school? Where are you now?
  • P: How do the students at this practicum assignment differ from those in your fall assignment? How does that affect the teaching?

    • 1/31

  • Problem Solving and Problem Posing
  • Sign up for group project in new curriculum
    		•
  • LTG: Chapters 6 and 7
  • Conjecturing article handed out in class on Wednesday
  • At least one article reviewon using technology or problem solving in geometry. Be sure to bring a copy of your review to class.
  • Proof of falsity of statement 2e on "test"
  • Work any 5 problems from Chapter 7 without looking at the hints. Describe how you worked each problem and how you would use each in the classroom
  • C: Reflect on the computer activity in class on Wednesday
  • P: Continue to reflect on your practicum experience

    • 2/2

  • Inquiry
  • Conjecture
  • NWREL Inquiry Book, pp. 2-15 (skip8-10)
  • Begin reading Flatland: remember it is a social satire -- raising awareness of inequities in Victorian England
    		•
  • Outline inquiry reading.
  • Solve the surfer problem: locate a point on the interior of an equilateral triangle such that the sum of the distances from the point to the three sides is a minimum.
    		•
  • C : Reflect on the class activities on Monday
  • P: Are you seeing attention to problem solving in your observations? In what way?

    • 2/7

  • Reasoning and Proof
  • LTG: Chapter 5
  • Stallings Article
  • PSSM:
    • Ch. 3: Standard 7: Pk-12
    • Ch. 6: Standard 7: 6-8
    • Ch. 7: Standard 7: 9-12
  • C&E:
    • Grades 5-8: Standard 3
    • Grades 9-12: Standard. 3
  • At least one article reviewon inquiry, proof, or conjecturing. Articles are available from the instructor.
  • Outline PSSM and C&E readings -- highlight the main points in each section
  • Problem set: 1-4

    •  NOTE: Reflective Journals will be collected today and returned on Wednesday.

    2/9

  • A Case Study
  • Harvard Case Study (postponed)
    		•
  •  Problem set: 5-8
  • Outline answers to assigned discussion questions on case study(postponed)

    •  

    2/14
  • Proof in Geometry
  • Review all previous reading

    •  

  • At least one article reviewon inquiry, proof, or conjecturing
  • Write paper on proof
    		•  
    2/16  
  • GMP Chapter 10
  • Harvard Case Study
  • Outline answers to assigned discussion questions on case study
  • Problem set: 9-12
    		•  
    2/21
  • Geometry Connections
  • 3-D and 4-D
  • Coordinate Geometry
  •  Finish Flatland
  • LTG: Chapter 15 and 18
  • GMP: Chapter 6
  • At least one article reviewon connecting geometry to other areas of mathematics
  • Problem set: 13-16
    		•   
    2/23
  • Geometry in NSF Integrated Curricula

  • No new reading
  • IMP: Stacey, Jeff, LoriLa, Liz
  • CMP:Leif, Ryan, Jen, AndreaB, Tina
  • STEM:Luke, Kip, Tom, AndreaA
  • Core+: Mike, Miriam, LoriLu, Tracy
  • Arise: Eoin, Jenny, Chris
    		• Prepare, in groups of 4-5, a presentation tracing geometry in one of the NSF curricula. Include overview of the curriculum, including philosophy and instructional model. Prepare handout with an outline of your main points.  
    2/28
  • Geometry in NSF Curricula, rescheduled
    		• 20 minute presentations. Be sure to keep to the time limit. Details can be included on the sheets you hand out.    

    3/1

    Microteaching I

    Johnson I

    Prepare a 20 minute lesson that you will each teach in class to 4 of your colleagues.

    Do Activities 14-15 in GMP, then using what you learned from Flatland, construct a 4-dimensional cube. Bring your results to class.

    At least one article review(any geometric topic)

    Problem set: 17-20 Concept map of unit plan

     

    3/6

    Flatland Revisited

    Questioning techniques

    Catching up on the problems

    Review questioning in Johnson book

    At least one article review

    What do you think of Johnson's way of dealing with homework?How else can you keep homework correcting from overwhelming you?

    3/8

    Microteaching the NSF Curricula, completed

    Extracurricular mathematics

    No new reading

    Problem set: 21-24

    What is the hardest part of questioning for higher order thinking? What can you do to keep improving your questioning techniques?

    3/11

    Make-up 3/6 or 3/13

    At St. Olaf, for those who miss 3/6 or 3/13: 9-11:15

     

     

    3/13

    Setting the Stage for Conjecturing and Proof

    Fractal geometry

    Review Stallings-Roberts Article

    Preliminary Outline of Unit Plan

    At least one article review

    Problem set: 25-26

     Could you conduct a class in the manner described by Stallings-Roberts?

    3/15

    Fractal Geometry

    Graph Theory on the web

    GMP: Chapter 9

    GMP: Activity 6

    Watch video on new geometry

     

    3/20

    Graph Theory

    SSM: Discrete Math, pp. 4-14, 22-23, 60-67

     

    There was a time when many teachers did not want to teach geometry. Now it is often a desirable teaching assignment. How do you account for the change?

    3/22

    Final Exam

     

    Portfolio,

    Unit Plan

     

    Revised 2/29/00

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