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.

The Redo & Portfolio Organization

After students have completed and corrected their assignments, they often have a false sense of security about the material. The “redo” is a sure fire way of authentically assessing knowledge of the subject area. Later, ample time before testing, the student should “redo” the problems they got incorrect from scratch. If they complete the problem, with no assistance, they can be confident they have learned the concept. However, if still incorrect, the solution is restudied and the problem is placed at the bottom of the “redo” list and must be addressed again, at a later time.

When the student completes all of the problems on the “redo” list, they should feel extremely secure about the topic. This learning style is best if the “redos” are organized in a portfolio with specific markings, loggings and sections created by the student. This method also alleviates a phenomenon known as test anxiety.

Make It Real & Tell Me A Story

Although most topics in mathematics are tangible, many feel even the straightforward subject matter is abstract. The classic question “When am I going to use this?” is a valid point that warrants consideration. If you asked me to perform a ludicrous task in which I found no relevance in my life, would I have enthusiasm to complete it? I don’t think so.

How can we fault our youth if we can relate to their questioning and confusion? By “making it real”, the student can take a particular topic and incorporate it into their everyday lives.

For example, if I needed to find the volume of a rectangular prism, a “real life’ interpretation can be filling up my fish tank with water. With this method of learning, a student does not rely on memorization, but learns to apply concepts in their life, which were formally abstract. This method of learning works best when incorporated into a story-like setting. When a student “tells a story”, the problem in turn becomes more real, important and solvable.

Sing It

Perhaps some educators might be averse to singing in the classroom, but not in mine. The art of music is universal, as mathematics, and is a perfect medium to learning. When a student creates or mimics formulas through song, they absorb the difficult without thought or memorization. It is somewhat similar to the way they blindly learn lyrics to a song, or hum the catchy melody of a commercial.

One of the most difficult formulas nearly all students must memorize is the quadratic formula. Within fifteen minutes, I taught my students, an awful but contagious little ditty, and they all knew the formula. Most remember it for life, and return years later boasting about their accomplishments. Teachers can encourage students to create their own tunes for different formulas to ease their pain of memorization.

Study Groups & As The Student Teaches

I assessed very early in college, the necessity of working with others to assist my learning progress. Every mind collects data differently so it would be logically to collaborate to exchange thoughts and ideas. Far be it for me to expect each student in my class to understand exactly what I teach and the way I present the material.

In study groups, students can openly discuss their strong and weak areas amongst their peers. They are more apt to be honest with individuals their own age, and less fearful to express their lack of understanding. The most effective and reinforcing part of a study group is the learning that occurs when the roles reverse, and the student teaches.

Everyone has something to contribute, from the weakest to the strongest. Peer study groups work at all levels across all disciplines so why not develop the skill and knowledge of these groups at a young age. As the saying goes, “together we stand, and sometimes divided we fall.”

Teaching is a labor of love, and there is no greater high than witnessing the dormant light in a student turn on when they learn. Yes, many still argue the subject, especially much of high school mathematics, is useless in everyday life. On the surface, I would have to agree, but it is the transparent learning that has purpose.

Our brains are just organs inside of our bodies, and much like our muscles, need to be exercised and nourished. Different mathematics ignite various parts of the brain. A person becomes more aware, and well rounded. The exercises many perform in the gym, at face value, seem absurd, but they work.

Our goal as educators, parents and students are to embrace different methods of learning like the “circle of learning” to help us work out our brains and become all that we can be.