About Lsquared

My high school chemistry teacher nicknamed me L² since both my first and last initials at that time were 'L'. The name stuck and I signed all of my high school math, physics, and chemistry papers that way. When I started this website I still used the name even though my initials no longer warrant it.

I have a master's degree in mathematics with many years of teaching experience at the college level and many more years of tutoring experience at various levels. I want my students to learn how to think about math instead of memorizing procedures. I also want my students to learn to play with ideas and discover mathematical properties and procedures on their own. I am developing software to help facilitate both necessary basic skills as well as play to figure out concepts. I am now testing some programs with some high school and college students and getting feedback from other teachers and their students so I can make adjustments and further improvements to the software. My own students give me the best feedback since I am there with them while they are using the software.

I have many ideas for projects and many projects already available that I want to develop further. Here is a listing of some things that are in the works:

The Unit Circle: There are several projects related to the unit circle already posted. I have current plans to develop the Unit Circle Symmetries program further to get students thinking about the symmetries on the circle in a larger variety of situations

Vectors: Many semesters students have troubles with the topic of vectors. Thus I created a lab environment where they can do experiments and discover properties for themselves, so that hopefully the concepts will stick with them better. This was first done during the spring semester of 2006 and it seemed to be successful. The program is called the Vector Drawing Board and I am continuing to add features to it, so that it will be useful in a larger variety of situations.

Alien Arithmetic: I used to have some static worksheets related to Alien Arithmetic on this website. The idea of the worksheets was that we use base ten for counting since we have ten fingers. If we were to meet an alien with eight fingers, then he might be using a counting system similar to ours except in base eight. Now there is an alien arithmetic program where students can build the alien's hands and then work in the base counting system according to how many fingers the student gave his or her alien. I continue to work on this program since it is used every November for Lansing Community College's Science and Math Elementary Exploration. I plan to create levels for next November so that it will be easier for kids at a variety of grade levels to find things in the program that they are ready to handle. The program can also be challenging for adults since most adults are not used to thinking in other base counting systems. I also plan to bring in manipulatives to help students calculate answers with counting blocks. You can print the counting blocks from this site using card stock paper or sticker paper so that you can then put the blocks on foam or cardboard to make it easier to manipulate them.

Conic Sections: I started a project involving conic sections a during the spring of 2005. In this project, you can click and drag some foci around and see how an ellipse and a hyperbola change as you move things around. You can also adjust the constant that is involved with the ellipse and hyperbola. I plan to add more parts to this project so students can also learn about eccentricity and the directrix. I would like to also show the relationship between the definitions of the conics in a plane and their definitions involving the intersection of a plane and a cone.

Trianlges: I enjoy teaching solving triangles with a visual approach, but have found that some students have a hard time drawing a triangle using the given information. I plan to make a program to help students learn to draw and visualize the given information so that they can then solve for the rest of the triangle parts and feel confident that they have the right number of solutions.

Angles and Sides in Quadrants: Students often have troubles figuring out how to draw an angle and given sides from information given such as sin θ < 0 and tan θ = -5/2. There is also a variety of other situations that lead to making this kind of drawing. I am currently brainstorming program ideas to help students learn to work through the steps needed to get the right picture and then solve their problem.

Trig Graphs: There are two programs related to trig graphs right now. On one program you are given a random equation and you determine the scales and then make the graph. This program needs a bit more work so that the program will accept any graph that is correct. Currently if you are graphing a transformed sine function, you have to select the sine shape. The program needs to be set up so you can select the cosine shape also and then transform it to the correct graph.

Talk to Course Management: Last summer I learned how to make all of my Flash™ programs talk to Course Managements systems such as Angel™ and Blackboard™ so that when a program is placed inside one of these systems, scores can be entered automatically into the gradebook. I used the SCORM standards to achieve this task. This summer, I plan to study and experiment further so that I can also make the program record other kinds of results and use the SCORM standards in a larger variety of situations.

This page last updated: June 11, 2018