I’ve posted about the demonstration of the volumes of matching cones and cylinders in the past. Today, part of my workday was spent looking for “digital resources” related to this relationship. I found some great stuff, and I found some of the horrible pieces I came across in the past.
So here’s the deal. We expect middle school students to know the relationship between the volumes of a prism and a pyramid with matching heights and base areas. I came across a couple of videos that were inspiring. The films’ presentations were reminiscent of a magician’s: Behold! Be curious! Be amazed!
The better clip I found (linked at the bottom of this post) was short – 1:19. No dialogue, just loud, brash music. The presenter showed off a pair of hollow plastic geometric figures; a cube and a square pyramid. He wordlessly demonstrated the bases and heights matched. He then filled the pyramid with darkly colored water, poured it into the cube, and set the empty pyramid in view. He filled a new matching pyramid with water and poured it into the cube, setting the empty pyramid next to the last one. Another matching pyramid is presented, filled, and as it is poured into the cube, the water level reaches the very top of the cube. We now see three matching pyramids arranged in a row, reinforcing the relationship without the need for any subtitles. I thought it was very simple and very nice.
The poorer examples managed to eliminate the wonder from this demonstration. I wish we would learn from our English-Language Arts colleagues and remember to “SHOW, don’t TELL.” Many presenters talked too much! The gave away the reveal. No flourish, just droning. Some of them marked the prism with marks 1/3 of the way along its height, squelching any curiosity. In the best example of this weakness, a teacher went over the formulas for volume of a prism and volume of a pyramid, then told the class, “since many of you have trouble getting that, we’re going to look at a demonstration that shows this relationship.” Look, if you know they have trouble grasping the dry context-less formulas, why didn’t you start with the demo!? How much more engaging to involve the students! “Can we guess the volume of the pyramid?” “How many pyramids do you think will fit in the prism?” “Now do you want to change your guess?” “How can we be sure we’re exact and not just ‘pretty close?'”
This is a great piece of mathematics. The Egyptians knew the relationship between these volumes. We can prove it today with calculus, but how did the Egyptians know? How can our middle school students know? The best video I found was 1:19. Do we really not have time to SHOW before we TELL?
It also occurred to me how most teachers just don’t have the time to really study and think about their pedagogy. A Professional Learning Network and/or support staff is such a benefit to our craft and to our students’ learning. Just sayin’.