Sometimes when you are teaching, you have to simplify a problem so that students can understand the concepts involved. I will explain. When I was a teacher, I was trying to explain to my Honors Class (I think chemistry, might have been physics. It’s been awhile) how to do a unit conversion using a method called dimensional analysis. It’s a pretty common way of solving equations that is used in the physical sciences.
I first learned the dimensional analysis when I was in the Navy at NucField A school and at Nuclear Power School. It’s handy for solving a lot of things. Dimensional analysis is a method for solving various problems that, once mastered, allows for the rapid solution to unit conversions, various physical problems (like Ohm’s law), medication dosage calculations, and more. It reduces calculation errors and is a very handy skill to have. I use this method all the time to calculate drug dosages, and used it as a firefighter to calculate hose pressures and other useful numbers.
I was teaching it to my students by giving the students a list of things I wanted converted from one item to another. The worksheet that I gave them was a list of problems that were easy to solve, but included the following instruction:
Show all of your work, including the proper setup of the dimensional analysis method. Your work is part of your answer, and any problem that does not include the showing of your work in the proper format will be marked as incorrect and will receive no credit.
The questions were things like:
- Convert a $5 bill to nickels
- How many toes would 22 people have?
- How many legs would 123 ants have? (they each have 8 legs)
So one of my students answered:
And promptly got a zero for a grade. Yes, the math was correct, but I wasn’t looking for the mathematical solution, but a solution that showed me that he had mastered the method of dimensional analysis. Anyone with fourth grade understanding of arithmetic can tell you that 22 people have 220 toes. I knew that they could do simple math, because it was a requirement to have already passed Algebra and Geometry as a prerequisite to even be in my class. This was an honors course where students could receive college credit at the end of the course.
It was important that they understood the concept so when we went on to more complicated problems, they would have the skills needed to solve them. It wasn’t about the math of that particular problem, it was about knowing HOW to use dimensional analysis. That way, when you get a problem that goes like:
A sample of calcium nitrate, Ca(NO3)2, with a formula weight of 164 g/mol, has 5.00 x 1027 atoms of oxygen. How many kilograms of Ca(NO3)2 are present?
The problem can be solved without too much difficulty. The easy problems were not a test of math ability, they were a means of learning a new method for applying math skills that the student already has. A “learn to walk before you try to run” sort of thing.
The child’s parent wrote me and demanded that he receive full credit because he got the correct answers. I tried pointing out the instructions and explaining the reasons behind showing your work. No go. The parent argued that “in the real world” no one cares how you got the answers, just that you ended up with the correct answers. I tried pointing out that, this being school, demonstrating that you have mastered the method is more important than getting the correct answer. The parent continued to argue and demanded that the student receive credit. I refused. They even told me that they would get a lawyer involved. I told them “good luck finding anyone that will support you not showing your work on math homework, when the instructions clearly required it.” Then I told them if lawyers were to be involved, I would be happy to give them my attorney’s number, and their attorney could call mine to arrange a meeting. They hung up on me.
So the parents went to the principal. Nope. They went all the way to the school board, to no avail. The parent finally pulled the kid out of my class and put them into a low level environmental science class.
In this case, the parent did the child no favors.
EDIT: I am editing this to give an example of how dimensional analysis works. Here is the example:
Convert 1 week into seconds:
*Terms on the top AND bottom of the equation cancel out, leaving: (1*7*24*60*60s)/1=604,800 s