Exploring Mathematics
using
Mathematical Treats
Dr. Michael Brennan,
Department of Mathematics
Cork Institute of Technology
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
1
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
2

Student question
``What exactly is
 ? ``
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
3
What is




?
3.14159265358979323846
22
7
or
355
113
Ratio of the circumference to the
diameter of a circle
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
4
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
5
Birthday Problem


How large does a group have to be
to guarantee a match?
How large does a group have to be
so that the chance of a match is
greater than 50%
Birthday Problem
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
7
Examples of Treats

Definition of Pi

Probability

Geometric Series
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
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1/4 + 1/16 + 1/64 + 1/256 + · · ·
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
9
Geometric Treats
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
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Sum of Series 0 < r < 1
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
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What is a Mathematical Treat?

Definition
A Mathematical Treat is an
educational resource, e.g.
puzzle,animation,story,image,game
that inspires and/or adds insight into
a mathematical idea.
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
12
Mathematical Treats
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
13
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
16
Use of Games Bloxorz
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
17
More Beginnings & Endings



CPU Blog
Psychological Principle Primacy-Recency
Dr. Lisa Bullard (Active Learning) LIT2009
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
18
Active Learning



Find Pi using a Glass
Homemade
Object
Create a Mobius
Strip
Devise Birthday
Analysis
Coin
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
Clock
Mug
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
Universal
Recycle Symbol
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
20
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
21
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
22
Painter’s Paradox

Gabriels Horn has
a finite volume and
an infinite surface
area
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
23
Useful Resources







Colleagues
MERLOT
Geogebra
Wolfram Alpha
Math Wikipedia
MathWorld
Maple Applications
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
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Endings...!





Use Sparingly*
Relevancy/Context
Encourage Engagement
Subjective
Reaction/Response
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
25
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
26
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
27
5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
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5th Annual Conference in Mathematics &
Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.
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