There are a few occasions I have my math students told me that if they do not write the exact steps their day school teachers told them then their points will be deducted. I did not have the chance to clarify with their teachers but there were many students who have told me so I feel it is important to point out. Below is a few examples.
1. Solving equation
For example, to solve 3x + 3 = 2
The teacher insists that the students have to use the following method by minus 3 on both sides.
3x + 3 – 3 = 2 – 3
I teach a method with a bit "fast" way that is by moving 3 to the right which basically amounts to the same answer that is 3x = 2 - 3, the reason is 3 - 3 is always zero on the left side any way. It is shocking that there are many math teachers who do not seem to understand this "moving" method.
The same problem exists that the math teacher insists that when dividing a number the students are asked always do the following way, for example to solve 3x = 3, by writing "/3" on both sides without allowing mental math:
3x = 3
3x / 3 = 3 / 3
x = 1
In a simpler way, students can use mental math by "getting" or "seeing" x = 1 without writing "/3".
I am at loss on why the math teachers are not able to see they need to be flexible to allow students to use the method which students feel comfortable to work with and be able to get answers much quickly?
The problem of insisting on using the "subtraction" method is the equation will get much complicated when the students "always" have to subtract a variable or a number. For example, to solve 2 + 3 (x - 1) + (x - 2) = 3 (x – 4) + 3, it is much cumbersome that student has to subtract numbers in order to cancel the numbers on the left side of equation or subtract equations on the right side of equation.
2. Percent problems
A number can be converted to % by using the idea of proportion but the method of using proportion is not the only method, it surprises me that some teachers seem to insist that the only method can use is to use proportion when in fact a simple "backward method" is much easier to get answer especially when children later have to work on multi-step commission, discount or tax problems. What % of 75 gives 20. The 20 is a product so to get the % back, one just needs to use reverse method that is to use 20 divided by 75. 20/75 = 0.4 = 40%. Why teacher has to insist the proportion method?
What surprised me is not the math teacher should not ask students to use proportion to do % problems or should not ask student to use subtraction method to cancel variables or numbers; it is their attitude of insisting that their students can "only' use one method without allowing students to use other methods.
Students will learn math much better without being misled or at least being pointed out there are different methods to solve the same problem. The best is teacher can take an open view on different steps or methods students can use.
More details on various teaching ideas, please visit www.mathandchess.com.
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