Many moons ago, when I was a younger version of myself struggling through math, I learned about pi. Actually, I remembered that pi was 3.1415 and there was like one kid in my class that could count out to about 50 decimal places for pi. He was super smart. I knew that pi was some sort of ratio, but why it was that ratio never made any sense. I realized that all of my math equations for circles used pi. So, if I was gonna work with a circle, I would use pi. If I wasn't working with a circle, then I wouldn't use pi.
Skip forward to the older version of myself.
When I started teaching, I realized that I didn't have a true understanding of why pi is important. So, I took it upon myself to go learn about pi and I had a pretty huge OMG moment when I realized that pi was in fact 3.14 radians. Holy Math Book! Shut the front door! Half a circle was only 3.14 radians...thus it was π!
It hit me that referring to pi as only 3.14 was tragically dangerous because people like me didn't know that the number was referencing 3.14 radians. The lack of units gave the number no true purpose!!!! I wondered, did other people NOT know this as well?
So, I decided to ask my students the following question: "What is pi?" Here are some of their answers.
- half a circle
- a ratio of something
- has something to do with circles
- you need the circumference to find it
- apple pie is delicious
I then asked, "3.14 whats? What are the units? Is it 3.14 elephants? 3.14 hamsters?"
Silence. It was an uncomfortable silence...as if to say, "Seriously? Units for pi?"
I had everyone draw a circle. We identified that the circle is 360 degrees. Half a circle is 180 degrees. We identified that a radian was about 57.2 degrees. I then drew 3 radians in our circle, side by side and asked the kids how much was left over in the half circle. It took a moment but I heard some kids finally say, "0.14?" The gasps were everywhere! I literally heard one kid say, "Oh my God! No way!" I had my evidence that my own students didn't even know what the 3.14 represented.
I then asked the group, "If we refer to half a circle as π, what would we refer to the entire circle?" Everyone said, "2π." I said, "Awesome. How many radians are in a full circle." The class quickly responded "6.28!" They finally got it!
Here is my point. Numbers without context, without units, without application will mean NOTHING to our students. I can't think of a more common constant in math than pi and not one single student in my many years of teaching has been able to tell me the units for pi. I hammer on units! I need the kids to realize that numbers in physics have a meaning, a purpose!
I'm not pointing fingers here, but clearly there needs to be a conversation between math and science teachers about the importance of units...because the only people ultimately effected are the students.
I challenge any teacher who facilitates a math or science class to ask their students, "What is pi?" See if ANY of them realize that there are units associated with pi. Would love to hear about everyone's findings.