Math By The Plug and Chug Method

Many school students learn to do math by what I call the “plug and chug” method, where they mechanically perform calculations without really understanding what they are doing.    I formed this opinion based on my interaction with hundreds of college students, many of whom did not understand basic algebraic concepts.   While such a  mechanical approach might get many students  through state mandated standardized tests,   they are functionally “illiterate” when it comes to applying basic math to real life situations.  I provide two examples of this problem:  one, a personal experience involving  a 7th grader, and the other, rather shocking, involving a highly paid expert witness.

 Late last December, to test if a  7th grader understood percentages, I asked him this question: How many dollars will you have to give me, if you have $200 and you owe me 12% of that amount?  He could not answer that because he did not understand the concept that percentage is based on 100.  So, 6% means 6 every 100, to be proportionally adjusted for numbers smaller and larger than 100. For example, 6% of 50 and 200 would be 3 and 24 (oops, 12, thanks to a sharp-eyed reader) respectively (no calculator is needed).

Next, I asked him the same question amenable to the “plug and chug” method: Calculate 12% of $200. Using his calculator, he mechanically converted 12% in his mind to 0.12,  and multiplied it with 200 to give the correct answer of $24.

 The second example deals with an accident reconstruction expert who has trouble converting fractions to decimals. Given that the scaling factor   is 20 feet to an inch, he just could not convert 3 and 3 /16 inches  to the corresponding length in feet, using a calculator.   He kept saying that he needed formula sheets to do this straightforward calculation.

These examples emphasize the dire need to explain fundamental mathematical concepts, especially  early in students’ educational training.   Math teachers everywhere, please take note.