I was just reviewing the searches for my blog and I found that someone had typed in “Why do people hate math?”
My feeling is that perhaps people do not hate it so much as fear it or are intimidated by it. Our culture (western) is so dominated by the verbal we learn to think in words and feelings perhaps before anything else. Mathematics is simply another language for explaining and interpreting the phenomena in the world. However, it is a very straight forward and logical language that has rules, that often elude us because we are not taught these rules properly in school.
Serendipitously, I’m currently working on developing a course on teaching algebra to middle school students, both the SME (Subject Matter Expert) and myself decided that one of the biggest obstacles to really getting math, let alone algebra, is the proper development of “Number Sense.” If I could explain what number sense means to myself and the other ‘verbal’ people out there, I’d probably start by saying that Number Sense may be analogous to being able to understand the basic rules of structure in language. (Maybe, I need a better analogy. Anyone else out there want to help?) Here is a simple, simple comparison.
Word Sense: I know that a sentence must have a subject and a verb. I know that the verb tense/form must agree with the nature of the subject (I am, you are, he is, etc.)
Number Sense: (Or maybe number babbling) I know that when I add two positives together I get a positive. Conversely, I know that when I add two negatives I get a negative. When I add a negative and a positive… I’m really combining or matching the negative and positive and combining them. After you combine these pairs that each equal zero I take them away – and I’m left with the remainder of the greater number (either positive or negative). Oh, heck… just look at the picture I drew.
If I were asked to explain this using pictures the first time, I think the concept would have sunk it a lot faster. I’ll bet dimes to dollars, if you were taught math more than 40 years ago all they did was simply put a set of problems in front of you. Maybe with the help (if you were lucky) of an astute teacher, they would explain what was happening in the problems or the pattern of solutions. But generally you were expected to figure it all out on your own. I didn’t learn math 40 years ago, but still, that’s how I felt it was taught. I went through the mechanics of solving the problems without really learning the rules of the language of mathematics.
Since, I didn’t understand the rules I could really only solve the simplest level problems in algebra. I sort of got the concepts, but as I moved into advanced algebra and calculus I’d often get lost. I was the “Queen of Partial Credit” on quizzes and tests. In the end in Calculus I barely scraped by with a C-. I could blame adolescent hormonal binges I was experiencing at the time, but looking back, I think that if I really sat down with the teachers and tried to understand math (from my own terms) I might have been able to do much better. I don’t think I really found the language of mathematics meaningful until I started applying it to my work in the form of ratios and proportions. Hexidecimal values and understanding the concepts of arrays and tables. But isn’t that the challenge that most teachers face, we must really coax the understanding and application of knowledge from our students regardless of who they are.
When I was actually teaching in the classroom, I really tried to understand how my students were perceiving a concept or what their general understanding or lack of understanding was. I really did try with certain complex subjects to relay the information to them in various ways or even ask them to explain why they thought they didn’t understand something. This morning at breakfast, my husband and I were talking about the difficulties of designing really good instruction. He puzzled about why it is so hard to teach… it doesn’t seem that hard, he said. More, it shouldn’t be hard to capture all that needs to be taught in writing. Yes, I explained, it’s easy to capture content int he form of raw concepts and information, but it’s the getting the student to understand and apply these things that is the hardest part. You can teach any monkey* to take a test, but getting people to make something with what they learn… that’s another challenge. I explained that teaching is an art that require not just book smarts and knowledge… it requires heart and the ability to read people and adjust your teaching to their needs.
*My apologies to all monkeys out there.