Ball State University
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.
Another student developed a Logo project that illustrates how the formula for calculating the area of a circle can 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 developed an on-line Logo math course that embodied these concepts and provided a structured series of lessons for teachers themselves or to use with their students.
|Name||Kathryn G. Shafer|
|Position||Assistant Professor of Mathematics|
|School||Ball State University|
|Address||Robert Bell 432, Muncie, IN 47306|
|Tags||Logo, Coding, Indiana|