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.
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.
Contact Information
- Name: Kathryn G. Shafer
- Position: Assistant Professor of Mathematics
- School: Ball State University
- Location: Muncie, IN
- Address: Robert Bell 432, Muncie, IN 47306
- Email: kgshafer432@gmail.com
- Website: http://www.k12actionmath.com/
- Tags: Logo, Coding, Indiana
- Age: College