Materials
Lessons via
PowerPoint
·
A lesson to
demonstrate the conceptual meaning of division involving fractions
·
A lesson to demonstrate
why the Euler’s Formula for polyhedral works for an orthogonal pyramid
·
A lesson to demonstrate the
meaning of the slope of a line
·
A lesson to show the
connection between the Simpson’s paradox and weighted average
Lessons
using Clickers and PowerPoint
·
A lesson to address
“multiplication makes bigger; division makes smaller” misconceptions
·
A lesson with
problems on conceptual understanding of fractions
·
A lesson with
problems on measurement concepts
·
A lesson with
problems on algebraic equations
Virtual Manipulatives using GeoGebra to
Highlight Co-variation of Quantities and Invariant Relationships
·
Invariant product for this
ballot-counting problem:
There were a large number of election ballots to be counted manually in a city
in 1980. The major of the city expected a team of 25 people to take
approximately 8.4 hours to count all the ballots. Let p represents the number of people in the team and h represent the number of hours it took
the team to count all the ballots. Write an equation and draw a graph to show
the relationship between h and p.
·
Invariant ratio for this
two-different-candles problem:
Two different candles, P and Q, lighted at the same time were burning at
different, but constant, rates. When candle P had burned 16 mm, candle Q had
burned 10 mm. Let p represent the
number of millimeters candle P has burned when candle Q had burned q mm. Write an equation and draw a graph
to show the relationship between p
and q.
·
Invariant difference for
this two-identical-candles problem:
Two identical candles, A and B, lighted at different times were burning at the same
constant rate. When candle A had burned 20 mm, candle B had burned 12 mm.
Let a represent the number of millimeters candle
A has burned when candle B had burned b
mm. Write an equation and draw a graph to show the relationship between a and b.
·
Invariant sum for this
one-candle problem:
A candle is burning at a constant rate. When it has burned 30 mm, its height is
75 mm. Let h represent the candle’s
height when it has burned x mm. Write
an equation and draw a graph to show the relationship between h and x.
A Java
Applet for the Two-Candle Problem
·
A
collection of Java applets to
illustrate how a graph represents the co-variation between the height of a
burning candle and time.
List of
Mathematics and Mathematics Education Courses
MATH 2303: Mathematics for Preservice
EC-4 & 4-8 Teachers (1. Number
Systems, Arithmetic Operations)
Fall 2006, Spring 2007
MATH 2304: Mathematics
for Preservice 4-8 Teachers (2. Shapes &
Measurement)
Fall 2007
MATH 3305: Mathematics
for Preservice EC-4 Teachers (3. Fractions, Ratios
& Proportions, Measurement, Algebra)
Spring 2009
MATH 3308: Mathematics
for Preservice 4-8 Teachers (3. Rational Numbers,
Ratios & Proportions, Algebra)
Spring 2007, Fall 2007, Spring 2008, Fall 2008
MATH 3309: Mathematics
for Preservice 4-8 Teachers: Generalists
(Co-variations & Functions)
Fall 2010, Spring 2011, Fall 2011, Spring 2012
MATH 4302: Mathematics for Preservice
4-8 Teachers: Math Specialists (Capstone Course)
Spring 2010, Spring 2011, Spring 2012
MATH 5360: Introduction
to Research in Mathematics Education I
Fall 2008, Fall 2009, Fall 2011
MATH 5360: Introduction
to Research in Mathematics Education II
Fall 2009
MATH 5370: Seminar
for Mathematics Teachers in M.Ed. Program (Quantitative Reasoning)
Spring 2008, Summer 2008, Spring 2009
MATH 5370: Seminar
for Mathematics Teachers in M.Ed. Program (Algebraic Reasoning)
Fall 2010
MATH 5396: Graduate
Research
Summer 2011
The most productive form of learning is
problem solving.
Albert Koestler
Updated on Feb 17, 2012