Professor Kathryn G. Shafer, Assistant Professor of Mathematics at Ball State University, has a long history with Logo, having taught with Logo since 1993. Her first experience was as a classroom teacher at Altamont Community Unit School Corporation in south central Illinois. At Altamont, Professor Shafer worked with sixth graders through high school students in regular math classes as well as in a gifted class of high school sophomores. Sixth graders learned the basics of a programming language while the sophomores learned about fractals.
Logo was used in geometry classes to discover the relationships between lines and angles. While working on a Logo assignment, students received immediate feedback on the success of their strategies by watching the turtle on the screen. In a Logo classroom, students control their learning. Prof. Shafer observed that when using Logo, students are highly motivated to work on mathematics during class and that Logo helped them learn geometry theorems and properties.
For five years at Bethel College and currently at Ball State University, Prof. Shafer has used Logo to teach future elementary teachers about polygons, the Pythagorean theorem, and trigonometry. Students complete Logo projects requiring the use of procedures, super procedures and recursion and must demonstrate understanding of the coordinate grid and turtle headings. Her current students were challenged to design an an entire city block with Terrapin Logo and Prof. Shafer recorded them for dynamic display on the web.
Calculating the area of a circle Another student developed a Logo project that illustrates how the formula for calculating the area of a circle may be derived by converting a circle into a parallelogram. Combining turtle graphics and Logo math, the project begins with a circle and successively breaks it into more and more parts until it becomes a parallelogram.
Prof. Shafer believes the use of Logo with preservice teachers pushes them towards a deeper understanding of mathematical concepts and reveals the overarching structure of mathematics. Use of Logo helps them see that testing, conjecturing, hypothesizing, deducting, proving, symbolizing and computing constitute the objectives of mathematics education and prepares them to use a Logo environment with their own future students to impart the same knowledge. She has developed an on-line Logo math course, available for credit or independent study, that embodies these concepts and provides a structured series of lessons for teachers themselves or to use with their students.
This course is a 4-week 12-lesson on-line Logo course that uses Logo to explore the basics of shape and measurement. The course is targeted for students in grades 6-10 and is a great resource for math teachers of that age group. It also works well for homeschooling and other independent study environments and provides a fun challenge for any adult learners.
Each lesson thoroughly explores a geometry and measurement concept, bringing it alive through interactive Logo programming. Lessons are sequential and each introduces new math vocabulary and Logo commands, building on what has already been learned. Completing the course builds a strong foundation in both Logo and geometry and allows students to create fun and colorful math-based projects.