## COURSES & MATERIALS

Materials

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Lessons via PowerPoint

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·        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