**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