COURSES & MATERIALS

 

 

Materials

·        Voting ABCD Card

 

 

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

·        A lesson involving burning candles for students to make connections between proportion (a/b = c/x) and algebra (y = mx)

·        A lesson involving fencing three sides of a rectangle to introduce co-variation of quantities, functions, domain, range, graphs, and optimization

·        A lesson involving two real-life problems to help students understand the conceptual idea behind addition of functions and multiplication of functions

 

 

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