Philosophy of Teaching

Philosophy of teaching: Elizabeth Little

elizabethlittle@berkeley.net

My own journey in mathematics is a necessary ingredient to understanding the teacher I have become. I was not a math-whiz or star student as a child. Even worse, I did not like school. I was quiet, shy and forever day dreaming. We had tracked classes and I was in the lowest track for mathematics in elementary school. In junior high school, I changed districts and was tested for placement. I tested into advanced level mathematics. I was stunned. I was bewildered and intimidated in a class where students were eager, inquisitive, and motivated. I had none of the student skills needed to be such a learner. I dropped out of the advanced class.

In high school I found that I could easily write an English paper, do science labs, or memorize history facts. I was unchallenged until I arrived in my math classes. Math was a perplexing mystery. I worked hard trying to make sense of the subject. At that time, math education was mostly a memorization of procedures without application, concept, or context. I was not satisfied. I worked painfully and slowly to wrestle understanding and meaning from numbers. By the time I went to college I was married with children and the director of my own preschool. I loved my math classes but again, it was left to me to put the material in the larger context of the subject and make conceptual sense of the work. It was a task I enjoyed immensely.

I have been a middle grades math teacher since 2001. Over the years I have developed a teaching philosophy based on the following three principles:

1. All students want to learn.

2. Basic math understanding is necessary for modern life.

3. Conceptual understanding and problem-solving skills are paramount in mathematics.

When faced with my students, I remember my own lack of student skills and confidence that made me drop out of advanced math in seventh grade. Before teaching any math, I teach children how to be engaged, confident students. We start each year with an online game called Game About Squares. There are no directions, no prizes, no sounds. You do not need to know English or be a math whiz or quick, or a computer nerd to play well. You just click around and find out what works and what doesn’t. Through experimentation and mistakes, you build your own knowledge.

After the game I ask students to tell me how to be successful at the game. This is what they inevitably come up with:

· You just have to start.

· Try stuff to see if it works.

· The only way to learn the game is by making mistakes.

· Use the “redo” button until you get it. There is no penalty for starting over.

· Notice patterns and use what you have learned.

· Have fun.

· Go slowly.

· Ask a friend for help if you’re stuck.

· Keep trying.

After writing their ideas on poster paper, I put a new title on their list, “How to Succeed in Math.” We leave the poster up all year and refer to it often. Through this activity and others like it, the students begin to relax and rely on themselves as competent learners.

The inevitable question: “Why do we have to learn this stuff?” Is one that I am eager to answer. I tell the students, “I want to you to be able to do your life.” Middle school math is the math of everyday life: figuring paychecks, buying a house, evaluating credit deals, calculating discounts, measuring for carpet, doing taxes, understanding data, voting, reading charts, and problem solving. Life is a word problem!

One of my favorite activities that leads to deep mathematical discussions and learning does not focus on the math at all. In fact, I don’t teach during this activity, but often hear, “Wow, I learned so much today!” after these lessons. I divide students into random groups of four and hand out a group-worthy task, that is, something no student could solve on their own but is within reach of a hard-working group. One resource I use is the Formative Assessment Lessons from the Mathematics Assessment Project available on the MARS (Mathematic Assessment Resource Service) website. Instead of teaching the math I teach students how to interact. I silently walk around the classroom, listening to, and observing groups. I post reflections of what I see and hear. If the observation is of a behavior helpful to the group, I put a happy face by it, if not, a sad face. Students are keen to get as many happy faces as possible (their points for the assignment) and will correct their behavior accordingly.

Example of one group’s reflections:

Group off to a quick start, reading the problem to each other (Happy Face)

Students all leaning in and focused (Happy Face)

Off topic conversation (Sad Face)

“I don’t understand, could you explain?” (Happy Face)

Group engaging in polite math argument (Happy Face)

“I think…because…” (Happy Face)

By teaching students how to disagree politely, state a case, accept and give help, be kind leaders, invite each other to speak, listen to each other, and put the group’s successes before their own, the math gets done. It doesn’t just get done, it gets done on a deeper level than I could ever achieve teaching 30 students at once. Students learn to cooperate in a way that they will most likely have to use in their work place of the future. At the end of the period the students have pulled together and triumphed over challenging material. They emerge confident, connected, supported, and capable.

Finally, I am very happy with the direction math education is going in the United States. With the adoption of the Common Core Standards of Mathematics we have moved away from rote memorization toward a deep conceptual understanding of how math works, and why it is useful. Certainly, there is a place for memorization for example, the times tables but for the most part, if one understands how math works, there is little memorization needed. I am very comfortable with the Common Core Standards (CCS), as it makes explicit what I had to glean for myself as a math student. For example, if one realizes that multiplication is simply repeated addition, and powers are simply repeated multiplication, then the order of operations becomes a natural and inevitable outcome rather than something nonsensical to be memorized with, “Please Excuse My Dear Aunt Sally.” (A mnemonic for remembering the order of operations.) It is upon a few fundamental principles, that all of mathematics rests. When students are given this key, they can move from strength to strength, discovering new and more complex ways to use math as a flexible tool to model and solve life’s problems.

I realize the irony in becoming a teacher, given my general dislike of school as a child. I marvel that I kept going back for the math even though I was dissatisfied with its presentation. I loved the math for itself. Not everyone needs to love math, but everyone needs to be able to do life. That’s why I teach.

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