Thursday, May 18, 2006
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When I saw the headlines of the Presidential Math Panel's report, I became very excited. The basic findings are exactly what I already knew existed. In fact, I could have written these same conclusions for half the money and in less than half the time.
I am a Virginia certified math and social studies teacher certified from 4th grade through dual enrollment (by summer 2009). My specialty is Algebra 1 and remedial math. My only claim to fame is regular 90%-100% pass rates on the Virginia Algebra 1 SOL overall and at least one class at 100% for several years in a row now. Since teaching at my current school, math scores have improved from 80% to 87% in the last two years.
Currently, elementary teachers say they teach fractions well and have scores to prove it. Secondary teachers claim, correctly, that rising students cannot do fractions. I have checked and the middle schools across the country are not feeding students stupid pills. So where does this problem originate?
In evaluating the problems addressed in the Panel's report, I looked at the history of math education. The problem began about the end of the 1950s to early 1960s. The change in math instruction was a trick called "cross multiplication". At first it was used on proportions which can be illustrated as fractions. Then it was applied to dividing fractions from right to left which gets a correct answer. Then super simple LCDs can be gotten by multiplying the denominators and "cross multiplying" the denominators with numerators.
Teachers who did not understand how to calculate a LCD would tell their students to "Try and Figure" what number both denominators go into evenly. There is no mathematical operation or law called "Try and Figure." This is not mathematics, it is mysticism. Students are expected to conger a LCD. No wonder they do not understand the mathematics of calculating a LCD. Therefore, they cannot apply this lack of understanding to more difficult problems, algebra, trigonometry and higher.
It is no longer just the teacher's fault. In a masters class teaching elementary and middle school teachers how to teach math, the term "cross multiply" was used in adding, subtracting, dividing fractions and proportions. This term is written into many textbooks as the "correct" methodology.
Why did teachers leave correct methods of instruction for "cross multiplying"? It is easier for many students to find answers to very basic fraction problems. However, these methods fall apart when applied to more difficult problems. Students remember the term "cross multiply" and try and cross multiply when adding, subtracting, multiplying and dividing fractions and sometimes even proportions.
So I worked to develop a solution to the problem as I saw it. Teachers need a simple method that they can understand and be able to teach. Students need a method they will understand that is also mathematically correct. In addition, many elementary students are very visual learners. Therefore, the method I developed is very visual. A side product has been improvement in special education students scores as well as their teacher's understanding of fractions. What I have developed can be used on 3rd grade fractions or calculus fractions - without change. I know of no other methodology of which this is true.
If teachers have a method they are comfortable with and understand which is mathematically correct and students can understand, they can then apply what they have learned to more difficult arithmetic and on into algebra and higher. This will lessen "math anxiety". People are not anxious about what they understand or anxious about that with which they are comfortable. Finally, this would go a long way to correcting the "broken" math education system mentioned by the Panel, in my humble opinion.
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I am a Virginia certified math and social studies teacher certified from 4th grade through dual enrollment (by summer 2009). My specialty is Algebra 1 and remedial math. My only claim to fame is regular 90%-100% pass rates on the Virginia Algebra 1 SOL overall and at least one class at 100% for several years in a row now. Since teaching at my current school, math scores have improved from 80% to 87% in the last two years.
Currently, elementary teachers say they teach fractions well and have scores to prove it. Secondary teachers claim, correctly, that rising students cannot do fractions. I have checked and the middle schools across the country are not feeding students stupid pills. So where does this problem originate?
In evaluating the problems addressed in the Panel's report, I looked at the history of math education. The problem began about the end of the 1950s to early 1960s. The change in math instruction was a trick called "cross multiplication". At first it was used on proportions which can be illustrated as fractions. Then it was applied to dividing fractions from right to left which gets a correct answer. Then super simple LCDs can be gotten by multiplying the denominators and "cross multiplying" the denominators with numerators.
Teachers who did not understand how to calculate a LCD would tell their students to "Try and Figure" what number both denominators go into evenly. There is no mathematical operation or law called "Try and Figure." This is not mathematics, it is mysticism. Students are expected to conger a LCD. No wonder they do not understand the mathematics of calculating a LCD. Therefore, they cannot apply this lack of understanding to more difficult problems, algebra, trigonometry and higher.
It is no longer just the teacher's fault. In a masters class teaching elementary and middle school teachers how to teach math, the term "cross multiply" was used in adding, subtracting, dividing fractions and proportions. This term is written into many textbooks as the "correct" methodology.
Why did teachers leave correct methods of instruction for "cross multiplying"? It is easier for many students to find answers to very basic fraction problems. However, these methods fall apart when applied to more difficult problems. Students remember the term "cross multiply" and try and cross multiply when adding, subtracting, multiplying and dividing fractions and sometimes even proportions.
So I worked to develop a solution to the problem as I saw it. Teachers need a simple method that they can understand and be able to teach. Students need a method they will understand that is also mathematically correct. In addition, many elementary students are very visual learners. Therefore, the method I developed is very visual. A side product has been improvement in special education students scores as well as their teacher's understanding of fractions. What I have developed can be used on 3rd grade fractions or calculus fractions - without change. I know of no other methodology of which this is true.
If teachers have a method they are comfortable with and understand which is mathematically correct and students can understand, they can then apply what they have learned to more difficult arithmetic and on into algebra and higher. This will lessen "math anxiety". People are not anxious about what they understand or anxious about that with which they are comfortable. Finally, this would go a long way to correcting the "broken" math education system mentioned by the Panel, in my humble opinion.
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