Claims made by yourself or by others can be treated as dogma until you or the people making the claim provide evidence to back it up. Until then....stay skeptical.The point is simple and has practical uses in an infinite number of scenarios. Just a few I can think of: (note: none of these claims are thought of to be necessarily true--they are just claims I have heard or claims that I know others have heard)
- Doctor comes in and tells you that you have cancer
- You hear from a friend that your girlfriend is cheating on you
- The quality of education a school provides is based solely on the funding it receives
- low-income students will naturally have low academic scores
- Climate change is simply not true
- African-Americans can jump higher due to subtle physiological differences
- Females are better at multitasking than males
- Students learn better when the teacher accommodates for different learning styles
- water is made up of 2 atoms of hydrogen and 1 atom of oxygen
The list could literally go on and on. Regardless of the claim, each one requires evidence to back it up. For example, it may very well be true that when the doctor tells you that you have cancer that means you ACTUALLY have cancer, but we all know that no one is going to simply accept a life-threatening illness without SOME sort of evidence to back it up. It's not that I don't trust the doctor and it's not that I don't trust the the people who make the claim. It's the fact that ALL claims about reality require evidence, otherwise you're simply accepting things based on faith.
So what's the last straw that broke the camel's back that prompted me to write this?
The other day, in my high school chemistry class, we were trying to determine the thickness of aluminum foil. In order to do this, we needed to use our newly-derived equation from a mass vs. volume graph.
Density = mass / volume
Along with this, we needed to use an equation for volume:
Volume = Area * thickness
To solve for thickness, you need to know the area of the aluminum foil square and its volume. Area was no big deal, simply measure length and width and multiply them--cool. However, the problem arose when my students went to solve for volume using their original density equation. Keep in mind that I gave them the density of aluminum (2.7 g/cm^3) and they found mass on their own by putting it on a scale. When solving for volume, EVERY single lab group did the following thing:
Hopefully you can see the problem with this. So how does this tie in with what I've been saying about providing evidence for claims? Let me continue...
After giving a brief "algebra lesson" I tried to get the students to understand that you simply can't do this when trying to get the denominator by itself. So why did a bunch of 11th and 12th graders make a basic 8th grade algebra mistake? I think it was due to the years of mindlessly knowing that they can multiply the denominator by itself to get rid of it.....so why not carry the same logic to the numerator? Then this stupid thing came up......
I can't tell you how much I hate something like this. Any teacher of math or science has seen this and I absolutely hate it. It totally promotes a "no thought required" approach. The claims it makes are simple:
density = mass / volume
mass = density * volume
volume = mass / density
In this case, all claims provided by the triangle are true. But the reason they are true IS NOT because I, as a teacher, showed you this little triangle "trick". They are true for very basic mathematical reasons! In fact, if I really wanted to, I could provide a graph which plots density vs. volume and show them how to calculate the area under the curve and literally show them where something like mass = density * volume comes from. No matter the case, you can use proven rules of algebra to solve for ANY of the variables.
Interestingly enough, when I showed my students this triangle, their faces lit up and it was like I had given them a brand new present. Kids love it when you show them procedural or algorithmic ways of doing something--because it requires very little (if any) thought. However, if I require to you derive the density formula from a mass vs. volume graph (which we did) and then algebraically rearrange that equation to solve for any of the variables....I've asked too much of you.
It's not a matter of capability either. EVERY single one of my students is fully capable of doing all the things mentioned right above. I just don't want them to accept the fact that mass = density * volume or volume = mass / density just because they heard it from a teacher. I want them to know it because they can prove it using their own reasoning skills along with the math skills we have taught them.
Finally, the last thing I got into with my class as we took a little detour from chemistry class. I asked them, "what is pi?" Immediately, every single one of them responded with, "3.14159 blah blah blah". Some of them even know something like 7 decimal places....impressive! But then I asked them, "how do you know this is number or, better yet, where does this number even come from?" Not a single student had the slightest clue. They had been taught this number since they were young and not a single teacher had managed to take 10 minutes to allow them to plot a circle's circumference vs. its diameter and calculate its slope (which is the value for pi). "That's where this number comes from!" I said with a smile. They weren't too amused. By the way, it's not their fault....I didn't know this until I was 22 for the same reasons that they don't know it at their age of 17 and 18.
Do I really care THAT much that kids know where the value of pi comes from or that mass = density * volume? No....but don't miss the point. If we consistently leave out room for the students to naturally use their reasoning to investigate WHY things are the way they are or HOW things happen and just simply tell them the facts, then we as teachers are no different than a Google search. One of the cornerstones to a successful scientifically-literate democracy of people is the ability to reason. If we willingly inhibit this ability, we are not only hurting our students in terms of inhibiting growth of their own thinking skills, but we are robbing them of a much deeper understanding of the amazing universe around them.
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