In my Make Your Own Dragster unit, middle school students first calculate the velocity of a non-geared up robot car, in this case Riley Rover. They take three time measurements on a ten foot course. I observed that students do not have a common sense, deep understanding of the mathematics. My thesis is that this comes from years of largely doing calculations on worksheets removed from any real world context.
Example 1 – Average of 1.73, 1.73, 1.173
Students used calculator, made a mistake and got an answer that was not 1.73 and did not notice a problem. If students had an understanding of what average means, they would know that they did not need to calculate and the answer is 1.73.
Example 2 – Average of 2.78, 2.50. and 2.30
Students got an answer of 7.20 and did not notice a problem. Students with a conceptual understanding of average should have seen that their answer was not reasonable and the average should be 2 point something.
Example 3 – Students write answers like 2.434566 ft/sec and do not notice an issue.
Students should know that the measurement variation and errors make digits beyond one decimal point meaningless.
Of course, it was a great opportunity to discuss all these examples with the class.
Engineering really makes mathematics meaningful, useful, and ties it to the real world. The danger of years of mathematics education largely out of context is that students focus on getting the calculations right and not really understanding the concepts behind the calculations.