A project of the
Vermont State Mathematics Coalition
Bring
college and university mathematicians to your classroom!
Choose a topic which would be of interest to your students.
Contact the presenter directly by phone, fax, email, or postal mail.
Check for prerequisites, if any.
There is no charge for this service. The presenters give of their own time, and they cover their own travel expenses.
For more information contact:
John Devino
Phone: 8028635403
Email:
devino13@comcast.net
George Ashline
Saint Michael’s College
Phone: (802) 6542434
Email:
gashline@smcvt.edu
I have much faculty consultant experience in grading AP Calculus Free Response questions, and I would be willing to answer questions that any AP Calculus teachers may have about that.
“Correlation Properties and Applications”
Through an activity and examples, we investigate properties of scatter plots and correlation in context, leading to a discussion of the correlation coefficient and challenges inherent in attempting to find causal links between variables. If time and technology permit, students can explore the online Correlation Guessing Game.
Prerequisite: Familiarity with the concepts of the mean and standard deviation of a variable (also, twovariable statistics calculators are helpful)
“An Introduction to Bias and Margin of Error”
Through an initial activity, we explore the potential impact of bias in statistical analysis. We can also consider how bias may arise in survey questions and ways that it can be reduced. In another activity, we can consider different types of error that may impact a survey or experiment and the meaning of margin of error.
Prerequisite: Familiarity with averages, percentages, and surveys
“Exponential Functions in Snowflakes, Carpets, and Paper Folding”
Through constructions of initial stages of several fractals, students can explore and represent underlying patterns using exponential functions. Other examples of exponential functions and their properties can be discussed. If time permits, students can play the Chaos Game to “create” the Sierpinski Triangle.
Prerequisite: Familiarity with exponents and functions
James R. Bozeman
Lyndon State College
Phone: (802) 6266489
Fax:
(802) 6269770
Email: james.bozeman@lsc.vsc.edu
"What Your Math Teacher Never Told You"
The talk introduces topics not normally taught in high school which could be. Ex: (a+b)^{2} = a^{2} + b^{2}; triangles whose angle sum does not equal 180 degrees; pieces of paper with only one side; bottles with no inside/outside.
Prerequisite: A little algebra and geometry.
"The Mathematics of DNA"
Through handson demonstrations and technology, students will discover the formula which describes DNA’s threedimensional conformation.
“Applied Geometry  Nearly Convex Sets and the Shape of Legislative Districts”
In this talk we develop a method for deciding how close a polygonal planar set is to being convex. We introduce 'nearly convex' sets and then 'nicely shaped' legislative districts. Those districts which are not nicely shaped may indicate improper gerrymandering in the redistricting plan.
Priscilla Bremser
Middlebury College
Phone: (802) 4435555
Email: Bremser@middlebury.edu
“William R. Hamilton and the Quaternions”
In 1843, while strolling across a bridge in Dublin, Hamilton had a flash of insight and discovered the Quaternions, a new number system he had been searching for 15 years. What did he hope his discovery would do, why did it fail, and why was it nevertheless a major contribution in mathematical history?
Prerequisites: None
Length
40 or 80 minutes
“Symmetry”
What do wallpaper patterns, prints of M.C. Escher, and molecular structure have to do with mathematics? We will discuss what symmetry means to mathematicians.
“The Mathematics of Change Ringing”
Change Ringing is the art of ringing a set of bells in specific sequences. It started in England, where it is still popular, and is practiced invarious places around the world. In this session we will discuss the history of this art as well as the mathematical principles involved. Students will get a chance to practice on handbells. This presentation is appropriate for middle school and high school.
Joanna EllisMonaghan
Saint Michael’s College
Phone: (802) 6542660
Email:
jellismonaghan@smcvt.edu
Willing
to do multiple classes at one location.
"Cops and Routers"
Use of graph theory to explore a patrol officer‘s beat, a security officer‘s camera locations, or find route for snowplowing or postal delivery
"Instant Insanity"
A
handson introduction to mathematical modeling with graph theory.
"Networks and Graphs"
The above model intercommunications, relationships, and conflicts. We will explore a variety of applications from: the internet, the stock market, classroom scheduling, power grids, the Kevin Bacon game, computer chips, social circles, and DNA.
"To Knot or Not"
Is
your shoelace really knotted? How can you tell? A gentle introduction
to knot theory.
"Geometry in the Real World"
Where
does math come from”? We will see some of the new math in
network theory being developed today as well as some of the critical
applications driving its creation. In particular, we will see new
mathematical theory created for DNA origami and tile assembly used
for biomolecular computing, nanoelectronics, and cuttingedge
medicine. We conclude the talk by showcasing examples of what
mathematicians do in real life, and how some of the top jobs use
mathematical skills.
Prerequisite: Grade 6 and up
Length of
Presentation: 20 min to 2 hours (longer versions may have some hands
on activities).
Janel Hanrahan
Lyndon State College
Phone: (802) 6266370
Email:
janel.hanrahan@lyndonstate.edu
“Mathematics and the Atmosphere”
Our planet is surrounded by a thin fluid envelope of gasses called an atmosphere, and its state at any given time is known as weather. The behavior of this fluid is described by mathematics, and atmospheric science concepts naturally lend themselves to inclass mathbased activities at many levels. For this activity, we will measure properties of the air with handheld meteorological instruments to compute the weight of the air in the classroom. Depending on the individual class needs, we will further explore the properties of our fluid atmosphere in the context of algebra, exponentials, graphing, and/or calculus.
Grade level: Middle school or above
Length:
40 – 80 minutes
Karla Karstens
University of Vermont
Phone: (802) 8787322
Email:
karla.karstens@uvm.edu
“The Mathematics of Sharing: Getting Your Piece of the Pie”
Your family inherits some artifacts that need to be distributed among all the relatives, or you want to divide a pizza among friends. How can you accomplish this so everyone involved gets a fair share? Principles of fair division lead to the solution of this class of problems.
Prerequisite: Middle School level
or above
Length 40 – 50 minutes
Gerard T. LaVarnway
Norwich University
Phone: (802) 4852325
Fax:
(802) 4852333
Email: lavarnwa@norwich.edu
“Cryptology: The Art and Science of Secret Writing”
An introduction to cryptology will be given. The history of cryptology will be discussed from the time of Caesar to the present. Various ciphers will be demonstrated. The mathematical foundations of ciphers will be discussed.
Prerequisite: Grades 9 –
12
Length 40 – 50 minutes
Daisy McCoy
Lyndon State College
Phone: (802) 6266260
Email:
daisy.mccoy@lsc.vsc.edu
Travel Limitations: Northeast Vermont
"The Magic of Nine"
There are a number of special properties of the number 9. This session will look at these properties and other properties of our number system such as "casting out nines" and doing number tricks.
Prerequisite: Can be adapted
to various levels.
Length of
Presentation: 40 – 80 minutes
"Math Like an
Egyptian"
Four
thousand years ago the Egyptians were writing numbers and doing
mathematics. Try out some of the computational methods they used and
look at some of the problems they did.
Prerequisite:
Multiplication and Fractions
Length of Presentation: 40 to 80
minutes
Travel Limitations: Northern or Eastern Vermont
“Mayan Mathematics”
The Mayan numeration system, the first to develop the concept of zero, will be investigated. Pictures of monuments will be used to identify the numerals. Mayan arithmetic and the development of a calendar will also be covered.
Grade Level: Adapted to 3 – 12
Michael Olinick
Middlebury College
Phone: (802) 4435559
Fax:
(802) 4432080
Email: molinick@middlebury.edu
"Cryptology: The Mathematics of Making and Breaking Secret Codes"
Mathematics provides the answer
"The NearSighted Fly: A Topological View of the Universe"
Length of Presentation: 40 – 80 minutes
Darlene M. Olsen
Norwich University
Phone (802)
4852875
Email: dolsen1@norwich.edu
"Maximizing the Flight Time of a Paper Helicopter"
The mission is to design a paper helicopter that remains aloft the longest when dropped from a certain height. Various combinations of design factors contribute to the flight time.
Response surface methodology (RSM) is a statistical technique that explores optimization through experimentation. Three tools in RSM are design of experiments, multiple regression, and optimization. These tools will be used to explore efficiently the combination of design factors that will improve the performance of the paper helicopter.
Grade Level: 10 –
12
Length 30 – 45 minutes
“Mathematical Ties to Tying Neckties”
Did you ever ask the question of how many possible ways there are to tie a necktie? Furthermore, what factors determine an aesthetic tie knot? This problem can be answered using mathematics. We will discover the mathematical ways for describing how to tie necktie knots. We will also classify knots according to their size and shape.
High School level
Length
45 minutes
Rob Poodiack
Norwich University
Phone: (802) 4852339
Email:
rpoodiac@norwich.edu
"Paradoxes in Probability"
In certain games, our intuition will tell us one thing, when probability calculations clearly tell us to do another. We will investigate the effect of human nature on probability using: “Let’s Make a Deal” and the Hershey’s Kiss Challenge. If time permits, we’ll engage in a series of threeway duels (“truels”).
Prerequisite: At least Algebra
Length of
Presentation: 45 – 75 minutes


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