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Push for Basics in mathematics
by Christine Haight Johnson
Pershing County, Nevada
Thank you, thank you, thank you, Seattle. I was energized to read about your Push for Basics in mathematics referred to in a Nov. 14, 2006 New York Times article. For years some of us have been saying the same thing. Maybe now that more people are speaking out we perhaps will begin to make a difference.
I am a math teacher in a small high school in Nevada. My classes range from Proficiency Math to Math 96 at the Community College. While not a mathematician by formal training I think of myself rather as a mathlete I enjoy solving math problems.
Over the past twelve years I have watched my students stagger and fall behind more each year in math. My lesson plans and goals for the classes have to be lowered by eliminating some of the chapters or assignments. Why? Some of the blame must go to block scheduling, which means students go to a class every other day for 80 minutes instead of every day for 50 minutes. There is no consistency or daily routine for learning with this kind of schedule. In education classes in college we were taught that 20 minutes is the average amount of time a student can concentrate. Block schedules mean I lose 100 minutes of teaching time every two weeks yet am still trying to teach the same amount as if there were 50 minutes a day.
Additional blame for lowering class learning standards is the fact that I have to teach or re-teach the basics or even introduce them for the first time. Students in grade schools (the ones I soon will be getting) are getting fuzzy math, often confused, perhaps purposely, with fuzzy logic. Fuzzy math emphasizes process over content. Fuzzy logic deals with reasoning approaches used in higher physics where one must deal with complex sets of probabilities. The two fuzzies are not equivalent and should not be linked.
Kids taught fuzzy math are inundated with new terms, definitions, concepts, etc. The result too often plays out like my exchange with one fifth-grade student when I asked what she learned in her (fuzzy) math class. We learned about ratios and statistics, she said proudly. I said great, now can you tell me what three times twelve is? She couldnt tell me without using a pencil and paper and taking way too much time. Many of my students havent learned or cant remember adding, subtracting, multiplying and dividing with fractions, decimals, or even integers. So, we re-teach.
I keep telling my students that practice makes perfect or better yet, practice makes permanent (working problems over and over again until it becomes easier). Math does not get harder it just gets longer. We still add, subtract, multiply and divide. But, the problems may involve more than one of these operations.
For example: 6x-5 = 3x-10
SUBTRACT 3x from both sides
6x-53x = 3x103x
And you get 3x5 = -10
ADD 5 to both sides
3x5+5 = -10+5
And you get 3x = -5
DIVIDE both sides by 3
3x / 3 = -5 / 3
And you have the answer x = -5 / 3
If these arithmetic operations are not understood this problem could be very difficult. An algebra problem may take much paper and writing when figuring out the answer. But, you solved the problem . the mystery. And, you should feel great. Just like practicing to make a basket at basketball practice. You make a point, a couple of points, and then a three-pointer. ]]]
The children we teach have developing minds. They need a strong foundation in math to be successful as they grow. For example: How can you read words if you dont know the alphabet? Here is my mathematical way of explaining the sequence:
c+a+t = cat letters to words
yellow + cat = yellow cat words to phrases
The + yellow cat + sleeps. words and
phrases to sentence
sentences to paragraph
paragraphs to story/article/book
So, 1+1=2, then to subtraction, multiplication, and division to algebra, to geometry, to algebra II, to trigonometry, and then to calculus.
Math can be fun. If you know the basics, like practicing with training wheels, the rest becomes easier and easier. The training wheels come off very quickly, and you are ready to adventure on to rougher terrain.
My hope is that together we can get our children and students back on the solid path to success in math.
Christine Haight Johnson teaches math in Pershing County, Nevada.