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Title: InterMath Professional and Cognitive Development through Problem Solving and Technology http://www.intermath-uga.gatech.edu/


1
InterMath Professional and Cognitive Development
through Problem Solving and Technology http//www
.intermath-uga.gatech.edu/
  • Evan Glazer
  • Learning and Performance Support Laboratory
  • University of Georgia
  • eglazer_at_coe.uga.edu

http//www.arches.uga.edu/eglazer/NECC2001.html
2
Overview
  • My Background
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
3
Background
  • Doctoral Candidate in IT at UGA

http//www.intermath-uga.gatech.edu/
4
Baptism Bulldawg Style
5
Background
  • Doctoral Candidate in IT at UGA
  • InterMath - problem solving with TEMIs.

http//www.intermath-uga.gatech.edu/
6
Under the direction of Jim Wilson and others
http//www.intermath-uga.gatech.edu/
7
Background
  • Doctoral Candidate in IT at UGA
  • InterMath - problem solving with TEMIs.
  • Taught high school mathematics in Glenview,
    Illinois

http//www.intermath-uga.gatech.edu/
8
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9
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10
You might be a real teacher if...
  • You grade papers in the car, during commercials,
    in faculty meetings, in the bathroom, and (at the
    end of the six weeks) have been seen grading in
    church.
  • You have a disjointed neck from writing on boards
    without turning your back on the class.
  • You are written up in medical journals for the
    size and elasticity of your kidneys and bladder.

http//www.intermath-uga.gatech.edu/
11
You might be a real teacher if...
  • You have been timed gulping down a full lunch in
    2 minutes, 18 seconds. Master teachers can eat
    faster than that.
  • You know it is better to seek forgiveness than to
    ask permission.
  • You buy Excedrin and Advil at Sam's.
  • You know secretaries and custodians run the school

http//www.intermath-uga.gatech.edu/
12
You might be a real teacher if...
  • You hear the heartbeats of crisis always have
    time to listen know you teach students, not just
    a subject and you are absolutely
    non-expendable.

http//www.intermath-uga.gatech.edu/
13
Background
  • Doctoral Candidate in IT at UGA
  • InterMath - problem solving with TEMIs.
  • Taught high school mathematics in Glenview,
    Illinois
  • Web-based development since 1993.

http//www.intermath-uga.gatech.edu/
14
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15
Background
  • Doctoral Candidate in IT at UGA
  • InterMath - problem solving with TEMIs.
  • Taught high school mathematics in Glenview,
    Illinois
  • Web-based development since 1993
  • I have a passion for working with kids, teaching,
    learning, mathematics, and running

http//www.intermath-uga.gatech.edu/
16
Mathematicians have the unique talent of
determining how fast they are running, and how
much faster they need to run by the end of the
race in order to set a personal record.
http//www.intermath-uga.gatech.edu/
17
Unflattering portrait How one child perceives
mathematicians
Source http//www.thetimes.co.uk/article/0,,2-613
52,00.html
18
Background
  • Doctoral Candidate in IT at UGA
  • InterMath - problem solving with TEMIs.
  • Six years of teaching high school mathematics in
    Illinois
  • Web-based development since 1993
  • I have a passion for working with kids, learning,
    mathematics, and running
  • Research and writing interests include
    communities of practice and technology
    integration.

http//www.intermath-uga.gatech.edu/
19
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20
Available September 1, 2001
Greenwood Publishing
21
About InterMath
  • What is InterMath?
  • Who is involved in InterMath?
  • What is the rationale for InterMath?
  • What are the goals of InterMath?

About InterMath Professional Development Cognitive
Development
http//www.intermath-uga.gatech.edu/
22
What is InterMath?
  • A five year, NSF-funded Internet-based
    professional development project
  • A community of middle school mathematics teachers
    and administrators
  • An effort to strengthen teachers conceptual
    understanding
  • A program that uses technology to explore problem
    solving situations
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
23
A Sad Excuse for Problem Solving
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

24
A Consequence of Bad Problems
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

25
Who is Involved?
  • LPSL - UGA (Hannafin, Wilson)
  • Research scientists, SMEs, Web and curriculum
    developers
  • CEISMC - Georgia Tech (Ohme)
  • Web designers and technical support
  • Workshop Participants
  • Middle school teachers/administrators and
    instructors at UGA, Kennesaw State, Valdosta
    State, and state INTECH centers.
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
26
Rationale for InterMath
  • New approaches to teaching and learning
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

27
Learning over the Past 50 years
Teaching Math in 1950 A logger sells a
truckload of lumber for 100. His cost of
production is 4/5 of the price. What is his
profit?
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

28
Learning over the Past 50 years
Teaching Math in 1960 A logger sells a
truckload of lumber for 100. His cost of
production is 4/5 of the price, or 80. What is
his profit?
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

29
Learning over the Past 50 years
Teaching Math in 1970 A logger exchanges a set
"L" of lumber for a set "M" of money. The
cardinality of set "M" is 100. Each element is
worth one dollar. Make 100 dots representing the
elements of the set "M". The set "C", the cost
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

of production contains 20 fewer points than set
"M". Represent the set "C" as a subset of set
"M" and answer the following question What is
the cardinality of the set "P" of profits?
30
Learning over the Past 50 years
Teaching Math in 1980 A logger sells a
truckload of lumber for 100. His cost of
production is 80 and his profit is 20. Your
assignment Underline the number 20.
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

31
Learning over the Past 50 years
Teaching Math in 1990 By cutting down
beautiful forest trees, a logger makes 20. What
do you think of this way of making a living?
Topic for class participation after answering the
question How did the forest birds and
squirrels feel as the logger cut down the trees?
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

32
Learning over the Past 50 years
Teaching Math in 2000 A company outsources all
of its loggers. The company claims that
contracting workers will Ultimately save them on
expenses for benefits and salaries when demand
for their product is down. The union requests
that you take a closer look at historical
employment, salary, benefits, and contracting
data located on the web. Was outsourcing a good
move? Use a cognitive tool like a spreadsheet
or simulation to develop and support your
reasoning.
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

33
Rationale for InterMath
  • New approaches to teaching and learning
  • Insufficient content background in teacher
    training programs
  • Resilient and pervasive beliefs about
    teaching mathematics
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
34
Is this what mathematics teaching is about?
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

35
Rationale for InterMath
  • New approaches to teaching and learning
  • Insufficient content background in teacher
    training programs
  • Resilient and pervasive beliefs about teaching
    mathematics
  • Escalating demands for teachers and
    little support
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
36
Teacher Support
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

37
Rationale for InterMath
  • New approaches to teaching and learning
  • Insufficient content background in teacher
    training programs
  • Resilient and pervasive beliefs about teaching
    mathematics
  • Escalating demands for teachers and little support
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development
  • Difficulty attaining learning standards

http//www.intermath-uga.gatech.edu/
38
Georgia Test Scores
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

39
The Truth
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

40
Compared to the Nation
  • Georgia drops to 50th in nation in SAT scores
  • State Board of Education's goal of reaching a
    1,000 mean score by 2001 is all but dead.
    -Savannah Morning News
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
41
Goals for InterMath
  • Promote innovative practices
  • Revitalize teaching by modeling and applying
    innovative approaches
  • Support reform of mathematics teaching and
    learning
  • Establish a human and technological support
    infrastructure
  • About InterMath
  • What is InterMath?
  • Who is involved?
  • Rationale
  • Goals
  • Professional Development
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
42
Professional Development
  • Participant Selection
  • Workshop Procedures
  • Our Use of Technology
  • Additional Contributions

About InterMath Professional Development Cognitive
Development
http//www.intermath-uga.gatech.edu/
43
Participant Selection
  • Underserved schools will receive priority
  • Schools where mathematical technologies are
    available
  • Teams of middle-school teachers and
    administrators
  • About InterMath
  • Professional Development
  • Participant Selection
  • Workshop Procedures
  • Use of Technology
  • Additional Contributions
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
44
If you can teach middle school, then you can
teach anyone.
  • About InterMath
  • Professional Development
  • Participant Selection
  • Workshop Procedures
  • Use of Technology
  • Additional Contributions
  • Cognitive Development

45
Workshop Procedures
  • 100 hours of training
  • 45 hour workshop, 55 hour follow along
    development course
  • Development of portfolio using a web page
  • Write-ups of investigations
  • Development of technology lessons
  • Ongoing support system
  • Human (experts, community)
  • Electronic (listserv, bulletin board, email)
  • Documents (tutorials, guides)
  • About InterMath
  • Professional Development
  • Participant Selection
  • Workshop Procedures
  • Use of Technology
  • Additional Contributions
  • Cognitive Development

46
InterMaths Use of Technology
does not focus on finding answers.
  • About InterMath
  • Professional Development
  • Participant Selection
  • Workshop Procedures
  • Use of Technology
  • Additional Contributions
  • Cognitive Development

47
InterMaths Use of Technology
  • Cognitive tool for building ideas, organizing
    thinking, solving problems, and exploring
    patterns
  • Multiple technologies promote multiple
    representations
  • Provides new learning opportunities
  • About InterMath
  • Professional Development
  • Participant Selection
  • Workshop Procedures
  • Use of Technology
  • Additional Contributions
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
48
Additional Contributions
  • Evolving database of investigations
  • Teacher resources and lesson plans
  • Discourse through electronic communities
  • About InterMath
  • Professional Development
  • Participant Selection
  • Workshop Procedures
  • Use of Technology
  • Additional Contributions
  • Cognitive Development

http//www.intermath-uga.gatech.edu/
49
Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

About InterMath Professional Development Cognitive
Development
http//www.intermath-uga.gatech.edu/
50
Rational of Workshop Activities
  • Intrinsically motivating
  • Appropriate level of challenge
  • Appeal to curiosity
  • Learner control
  • Realistic applications
  • Ownership of learning
  • Open-ended exploration
  • Generative extensions of investigations
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

51
Workshop Content
  • 14 topics under four categories
  • Algebra
  • Geometry
  • Number Concepts
  • Data Analysis
  • Adapted investigations from MTMS
  • Support materials
  • Guides and tutorials
  • Database of solutions
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
52
Investigation Criteria
  • Multiple cases can be investigated using
    technology.
  • Pre-Algebra students can rely on technology
    to investigate the situation.
  • The investigation promotes generalizability
    or can be used as a springboard for further
    exploration.
  • Multiple methods can be used to explore the
    situation.
  • Multiple solutions are possible.
  • The investigation is easy to start exploring.
  • The investigation can be modified for use in
    a middle school classroom.
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
53
Sample Investigation
Choose two numbers. Add them together and form a
Fibonacci-like sequence, starting with your
first two numbers, and ending with a total of
ten numbers. For example, if your first two
numbers are 3 and 5, then your third number is
8 (35), your fourth number is 13 (85), your
fifth number is 21 (813), and so on. Determine
a relationship using the seventh term and sum of
the terms of your sequence. Is this true for
every sequence of this nature? Explain.
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
54
Sample Investigation
To make a pen for his new pony, Ted will use an
existing fence as one side of the pen. If he has
ninety-six meters of fencing, what are the
dimensions of the largest rectangular pen he can
make? (Source Mathematics Teaching in the
Middle School, Nov-Dec 1994).
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
55
Sample Investigation
Quadrilateral ABCD is a rectangle with length to
width in the ratio of 3 2. AN and BM
are bisectors of angle A and angle B,
respectively. What is the ratio of the area of
the shaded region to the area of ABCD? Explain
your solution.
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
56
Teacher Write-Up
Determining which method to use in solving this
problem intrigued me. My students have been
studying rotations, dilations, and reflections
using a coordinate graph and triangles. This
seemed a good opportunity for me to show them
how these movements could be used to solve a
problem.
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
57
Creating Investigations What are some
issues?
  • Support
  • Familiarity with software
  • Motivation
  • Prior knowledge
  • Use of technology
  • Structure and hints
  • Self and Peer-evaluation
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
58
Teacher Lessons
Your employer has put you in charge of the
packaging for a new promotional item. If children
send in 10 proofs of purchase along with 1.95 to
cover shipping, they will receive a box of 125
cubic centimeters of SLIME! The packaging for the
slime should be in the shape of a rectangular
prism for easy mailing. What dimensions should
you give this package? Problem created by Kim
Seay, Dacula Middle School
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

http//www.intermath-uga.gatech.edu/
59
A Reflection
... it's a different story to hear from a
teacher "hey, I did this in my classroom, and
the kids did awesome with it, and you should see
what they did" than to hear somebody stand up at
a lecture and they say this is how you should
teach cause kids will do this and kids will do
that. Um, a lot of stuff sounds good in theory,
but you think, oh yeah, well how is that going to
happen? You know, how could you do that? ... I
think that since I have been able to do some of
it, and been able to get the type of reactions
from the kids, that makes me want to tell people,
you know, and show people, here you can do this
and it's really good.
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

60
Teacher Lessons
The bases on a baseball field are 90 feet apart
and form right angles. The pitchers mound is
60 ft and 6 inches from home plate. If the third
baseman is throwing the ball to the first
baseman, should the pitcher duck his head if he
is standing on the mound?
Problem created by Peggy Reigle, Athens Academy
  • About InterMath
  • Professional Development
  • Cognitive Development
  • Rationale of Workshop Activities
  • Workshop Content
  • Investigations
  • Teachers Activities

61
Next Steps
  • What we have achieved (years 1-2)
  • Design and development of workshop
    investigations and website
  • Workshops in Athens/Atlanta
  • Teacher development of write-ups and lesson plans
  • What we plan to achieve (years 3-5)
  • Implementation of workshops at various sites
    around Georgia
  • Ongoing support system of resources, tools, and
    people

62
Our Challenge Ahead
Our goal is to empower teachers with skills and
strategies to use technology in a manner where
mathematics is explored, learned, and applied in
meaningful, useful, and resourceful ways.
However, if we train teachers to use technology
solely based on our vision without being aware of
their learning and pedagogical needs, we may be
in for an unpleasant and unfortunate surprise...
http//www.intermath-uga.gatech.edu/
63
http//www.arches.uga.edu/eglazer/NECC2001.html
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