Philosophy of education in mathematics

Philosophy of Education

Norma Cunningham

I am a nontraditional student and I am returning back to college due to a job loss. I have been given a second chance at obtaining an education. Since I have been attending college, I was accepted into the nursing program, but I turned it down. I did this because I remember my dream has always been to be a math teacher. Everyone knows teachers are not in the profession for the money, and that nurses make more money, so people may ask, why a teacher? Well, I remember when I was growing up, every time someone would ask me what I wanted to be, I always answered, a math teacher. Certain teachers that I have had in the past, and present, have helped me decide that I want to spend the rest of my life teaching math. Helping any age student to learn math gives me chills, because, like those teachers, I love solving problems and trying to figure out the right answers. Like John Travolta sang in Grease, "I've got chills, they're multiplying." Ever since I graduated in 1976, math has been my passion. I helped my children with their math throughout their education and also helped my older brother complete his college math while I was still in high school. Today, I still want to be a teacher -- but not just any teacher. I want to be one who reaches all of her students in a memorable way by following excellent teaching practices.

All children need to learn the basics of math in order to lead successful lives, not necessarily algebra or calculus, but definitely how to add, multiply, divide, subtract and yes, even problem solving. Problem solving which is observed in Maslow's hierarchy of needs involves various types of needs which are required to reach an individual's full potential, described as self-actualization (%% reference). Otherwise, to become everything that one is capable of becoming. This can be done by teaching the basics which would give them a solid foundation for their future. Just as a house needs a solid foundation to stand on children needs a solid foundation in math to be able to function in today's society. If people can't add or subtract, multiply or divide, they might not be able to know which deal at the grocery store is the best; a can of beans at three for a dollar or thirty five cents a can. Someone might ask a person who doesn't know their basic math skills if they would like to have five one dollar bills for their one ten dollar bill and believe it or not a person might trade thinking five one dollar bills are more than one ten dollar bill. This example can show students how important it is to learn math. Toni Morrison said, "If you can't count, they can cheat you. If you can't read, they can beat you" (Morrison, 1987). Without the basic knowledge of adding and subtracting there would be a great deal of cheating people out of what is rightfully his or hers.

Math education is particularly tricky because the dominant theory suggests that learning math is not a developmental problem but one of aptitude (Elmore, 2002). Thus, many students are left behind because they just don't "get it." Teachers have given up hope that they are actually capable of getting it, when the problem is that they're teaching abstract conceptual knowledge taken out of context (Brown & Duguid, 2002). Abstracting concepts that can be applied to many situations is a valuable skill, but it is students who should be doing the abstracting after learning the concept in context.

One way to teach math in context is by using a technique called Total Physical Response Storytelling (TPRS), the second generation of TPR. In this technique, if you are teaching fractions, say, you could give your students some measuring cups, ingredients (water or sand would do), and a recipe and ask them to make it -- but wait! You need to feed eight people and this recipe only feeds four! What do we do?! TPRS provides context, or scaffolding as Vygotsky put it, which helps them understand why they are doing what they are doing and why it is important (%% reference). The physical and visual aspects of TPRS help students retain the concept, and also transfer the concept to other situations. Some students may need to see the concept in several disparate contexts before they can make conceptual abstractions because they are not developmentally ready yet. I love seeing the smiling faces of children when they have solved a problem and when they pay for their purchases at Wal-Mart by themselves. Children need to learn how to involve math with their everyday lives and if they can realize this they might be able to enjoy learning math a little more. This is what TPRS can do.

The other main part of my teaching philosophy is what I like to call problem finding. This promotes the "higher order thinking" of Bloom's Taxonomy (Bloom, 1956). It's a metacognitive way to get students to think about how to transfer mathematical concepts to the world around them. Today's technology is the cure-all of education, but it does not always encourage students to think for themselves. I would like to be able to help children learn how to perform with their brains instead of being so dependent on a calculator -- to help children learn to think for themselves and be able to perform the basics of math and learn to enjoy math as much as I do.