Communicating Mathematics
A Workshop by Dr. Kris Green
for Webster School District
Middle and High School Teachers
on March 22, 2000
Who Am I?
Assistant Professor in the MST Department
at St. John Fisher College
1999-2000 Project NExT fellow
Ph.D. in Applied Mathematics from
University of Arizona
B.S. in Engineering Physics from
University of Tennessee, Knoxville
Overview of the Workshop
Reasons for communicating mathematics
Theoretical perspectives on communicating
mathematics
Activities I use to encourage students to
communicate mathematics
My observations on effectiveness of these
Resources
Reasons for
Communicating Mathematics
NYS MST Learning Standards (explore, describe,
analyze, communicate)
The Work Force needs it (engineering teams,
publication and dissemination)
To make informed decisions (online trading,
phone services, etc.)
Easily incorporates new technologies (electronic
portfolios, desktop publishing, spreadsheets,
graphics applications)
Demonstrates mastery/points out weaknesses
Theoretical Perspectives
Algebra vs. Geometry
– Algebra is actually more Verbal/Linguistic
– Geometry is more Logical/Mathematical
Multiple Intelligences (Gardner)
– Writing provides more ways to bring the
verbal/linguistic intelligence into class with
support from the logical/mathematical and
visual intelligences (as well as the others to a
lesser degree)
Some of My Activities
Journal Writing
– Based on readings from the text or other
sources (MAA Resources for Calculus, v. 5)
– Includes information as well as “feelings” and
interpretations
– Involves a dialogue between student and myself
– Students are given questions to answer (these
are “big, important” questions)
More of My Activities
Class Reflections - standard questions to be
answered in journals after each class
– What was the most important thing you learned
today?
– What are you still confused about?
– Were you on time for class?
– Rate you participation in class (1-10). Why?
– What will you do to prepare for the next class?
More Activities
Writing Assignments
– What is Mathematics?
– Families of Functions
– Calculus Murder Mystery
– Synthesis of journal entries showing progress
Projects
– Essentially these are longer problem sets that
involve an application of the mathematics
More Activities
Exams (2-3 per semester, plus final)
– Q1: four “non-standard” multiple choice
questions
– Q2: four short answer/short calculation
– Q3: essay question - based on journals
– Q4 and Q5: free response, longer calculation
problems
Concept Mapping
More Activities
In class group work
– To derive properties of some objects (gradient)
– “Sketch the graph of a function which has as
many of the following properties as possible,
and then justify that your function has the
properties you claim it does.”
– Working as a class to build a graph (erf(x))
– Finding the shortest distance (geodesics)
– Explaining and evaluating the “Mystery
Number System”
More Activities
Two-column calculations
– Left 3/4 of page for computations (line by line)
– Right 1/4 of page for explanations of each
major step (reasoning, definitions, theorems,
etc)
Visual proofs in geometry
– (with Dr. Allen Emerson) to combine the visual
and logical/axiomatic approach to geometry
Even More Activities
Independent Study Project
– John is physically handicapped
– John has studied algebra, computer science
– Project
• Read some of the mathematics education literature
on the understanding of functions
• Write a paper that compares/contrasts these views
• Write a reflection on where his understanding falls
Observations
Journals have shown me where the
book/class/etc have caused confusion in the
use of an idea (integration as “giving back
the original function” or only applying to
“getting distance from velocity”)
Gets more students involved in the class -the Murder Mystery received many positive
comments
More Observations
These types of assignments are easily more
time-consuming to grade
“To check grammar or not to check
grammar, that is the question”
Often yields (pleasantly) surprising results
Resources for Math Reading
MAA Resources for Calculus, volume 5,
Readings for Calculus
The Mathematical Tourist, Ivars Peterson
Codes, Puzzles and Conspiracy, Dennis
Shasha
Flatland, Edwin Abbott
The Adventures of Penrose, the
Mathematical Cat, Theoni Pappas
Resources for How to Implement
Writing in Mathematics
Writing in the Teaching and Learning of
Mathematics, John Meier and Thomas
Rishel -- this book is okay for its purpose
Using Writing to Teach Mathematics, edited
by Andrew Sterrett -- not as good a resource
Other teachers!
Ideas for Good Writing
Assignments and Projects
Play on Words (the “Families of Functions”
project)
PRIMUS (Journal from the US military
Academy)
Mathematics Teaching in the Middle School
The Mathematics Teacher
Colleagues in Other Disciplines (History,
Science, Economics, Art, Music)
More Ideas
Any of the resources in the “Readings”
section
Scientific American (particularly the
“Mathematical Recreations” of Martin
Gardner)
Old Isaac Asimov’s Science Fiction
Magazine articles by Martin Gardner
More Ideas
The NYS MST Learning Standards
themselves (also the online resources)
Sample Web-based projects are available
from the “Virtual Teacher Resources” under
the MST homepage located at
http://home.sjfc.edu/~mst
Online computing resources are located at
http://www.mathwright.com/
Online Ideas
Chevron Corporation: under Educational
Programs at
http://www.chevron.com/community/frame.html
Discovery Channel School located at
http://school.discovery.com/
Exemplars materials can be viewed and
ordered from
http://www.exemplars.com/
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