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/