The Circle of Learning

In my ten years as a high school mathematics teacher, one of my most frustrating teaching experiences was discovering student’s inability to know how to study. Over the years, I developed what I call “the circle of learning”. It is a technique students use to learn how to retain their subject material.

Math can be tedious and let’s face it – down right boring. Books dealing with this subject matter, could sell as a sleep aide. I beg to differ. On the average day, my classroom is upbeat and full of laughter. I want to give parents and students the opportunity to bring that environment in their homes. As an educator, I have explored many learning techniques. However, never did a concept such as “the circle of learning” come across my desk. The idea is really quite straightforward.

In an average classroom, the following occurs:

1. Instruction: A student gets instruction from a teacher or professor. They sit in a classroom, take notes, hear lecture and often complete examples on the topics they were taught.
2. Homework: Problems are assigned reflecting the day’s work, which enable a drill and practice of the material.
3. Checking: Students correct their homework and learn their mistakes.
4. Extra Help/Tutors: Students attend extra help sessions or meet with tutors to gain a better understanding of the material.

The Learning

Here is where the breakdown usually occurs. Frequently, the student believes they understand the material, and perhaps are ready for the exam. However, this is not always the case.

How often have I heard a student says these words?

1. “I thought I knew the material.”
2. “I knew it when you went over it in class.”
3. “I blanked out during the test.”
4. “I studied for three hours and I just don’t get it.”
5. “How do you study for math anyway?”
6. “I hate math.”
7. My personal favorite complaint I hear year after year.
8. “When are we going to use this?”

The problem is simple. Students did not complete the circle of learning. Maybe they understood the material practiced, but were they be sure it was learned? Should we wait for a test to find out if learning actually took place? No, it is far too risky.

Many students cannot complete their circle of learning with traditional teaching style and memorization. I have developed and used several techniques including the “redo”, “portfolio organization”, “make it real”, “tell me a story”, “sing it”, “study groups”, and my favorite “as the student teachers” to address these problems. I also attempt to answer the provocative question as to math’s purpose in their lives.