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Developing a Technology and Geometry Rich Mathematics Methods Course


Developing a Technology and Geometry Rich Mathematics Methods Course. Dr. Daniel Miller ... Teaching Secondary Mathematics: A Focus on Geometry and Technology ... – PowerPoint PPT presentation

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Title: Developing a Technology and Geometry Rich Mathematics Methods Course

Developing a Technology and Geometry Rich
Mathematics Methods Course
  • Dr. Daniel Miller Millikin University damiller_at_mai

A New Vision
  • Breath v. Depth
  • Technology
  • Mathematics
  • Research based
  • Standards based

Starting Point The Current Course
  • 3-hour
  • Senior level
  • 20 hours field experiences hours
  • At student teaching placement
  • Course Description
  • Covers all content for grades 6-12 mathematics

  • NCTM 2000
  • Geometry The Forgotten Strand
  • Glenda Lappan (1999)
  • TIMMS, 1996 NAEP, 1998
  • Royal Society / Joint Mathematical Council
    working group (RS/JMC, 2001)
  • identifies geometric constructions as a
    fundamental concept
  • Their suggestions included increasing the amount
    of geometry taught to a level of 25 of the total
    time reserved for mathematics.

  • NCATE, 2001
  • Professional Standards for the Accreditation of
    Schools, Colleges, and Departments of Education,
    National Council for Accreditation of Teacher
    Education Washington, DC.
  • ISTE, 1999
  • Standards for Basic Endorsement in Educational
    Computing and Technology Literacy, Available
    on-line http//
  • ISTE Standards numbering is used through the rest
    of the presentation

Vision for a New Course
  • As articulated in the Illinois Content Area
    Standards for all Teachers (ISBE, 1996)
  • undergraduate teacher programs "will ensure that
    teachers are prepared to take full advantage of
    the learning potential of technology and
  • Specifically, this course hopes to develop
    technology skills that enhance students' learning
    while increasing both content and pedagogical
    content knowledge of geometry

Target expectations of NCATE (2001) for
pedagogical content knowledge
  • Teacher candidates reflect a thorough
    understanding of pedagogical content knowledge
    delineated in professional, state, and
    institutional standards. They have in-depth
    understanding of the subject matter that they
    plan to teach, allowing them to provide multiple
    explanations and instructional strategies so that
    all students learn. They present the content to
    students in challenging, clear, and compelling
    ways and integrate technology appropriately

1.2.1 use productivity tools for word processing
Word documents for each construction were
developed for handouts and instructions
1.2.2 apply productivity tools for creating
multimedia presentations
PowerPoint documents for both in-class and
on-line instruction
1.1.4 use imaging devices such as scanners,
digital cameras, and/or video cameras with
computer systems and software 1.2.8 observe
demonstrations or uses of broadcast instruction,
audio/video conferencing, and other distant
learning applications 2.2.5 identify, select,
and integrate video and digital images in varying
formats for use in presentations, publications
and/or other products
Videos of constructions using traditional tools
were then converted from .avi to .mov for cross
platform and Internet use
2.2.1 use advanced features of word processing,
desktop publishing, graphics programs and
utilities to develop professional products
2.4.5 identify examples of emerging
programming, authoring, or problem solving
Geometer Sketchpad files using built-in
1.2.4 use computers to support problem solving,
data collection, presentations, and decision
making 3.1.4 design and practice methods and
strategies for teaching problem-solving
principles and skills using technology resources
Geometer Sketchpad files using minimal functions,
i.e. simulation of compass and straightedge
1.3 Application of Technology in Instruction
Produced an integrated teaching unit using many
of the developed components
Student Presentations of Completed Lessons
  • 2.4.7 use a computer projection device to support
    and deliver oral presentations
  • 3.1.6 practice methods and strategies for
    teaching technology concepts and skills in a lab
    and classroom setting

A Call for Participation
  • Secondary Methods Textbook Development
  • Teaching Secondary Mathematics A Focus on
    Geometry and Technology

Chapter 1 Standards and Research
  • Geometry and Technology Standards
  • NCTM
  • MAA
  • ISTE
  • State
  • Research on Technology Based Teaching
  • Academic Achievement
  • Research on the Teaching Geometry
  • Van Hiele Model

  • Chapter 2 Presentation Technologies
  • Basics of Productivity Tools Presentation
  • Word
  • Acrobat
  • PowerPoint
  • Scanners / Digital Cameras
  • Photo Editor
  • Movie Editor
  • Basic File Management and Conversions
  • Basic Web Design
  • Netscape Composer
  • FrontPage

Chapter 3 Integrating Calculators and
Computers Computer Algebra Systems (CAS)
Analytical Geometry Transformational
Geometry Programming Calculator BASIC LOGO

Chapter 4 Spreadsheets Exploring
Transformation Programming
Chapter 5 Dynamic Geometry Software Sketchpad
Basics Advanced Constructions
Chapter 6 Geometric Probability Modeling
Dynamic Events Based in Geometric Conditions
Chapter 7 Other Geometries and
Representations Vectors 3-Space Finite
Non-Euclidean Projective Hyperbolic Ellipti