Today, I tried my best not to let some bad (untimely? unfortunate?) curricular elements harm the well-being of my class and the students who come to it. The way I see it is this: It is a high priority of my job to protect my students from any undue or unnecessary harm to their sense of self-worth and ability, especially those that will function as serious liabilities for their learning in this course and beyond.
Today, in my flipped class, students were sent back to a computer, which then proceeded to blast away at their self-worth by asking questions that never should have been asked. For example, groups were asked by a computer how to find x-component of displacement from an x-component of velocity vs. time graph. Out of the 16 groups that I observed (8 in my class and 8 in another class), only 1 group was even in the ballpark of understanding what the question was asking. In the class I observed, I only knew this because I visited each group and listened and watched. When the instructor asked, “Did everything make sense? Does anybody have any questions?”, not a single student spoke up. In my class, I knew this because every group of students knew it was their job to share with the class what was confusing. They raised their hands and called me over. I had already set the tone that we are here to learn and that confusion is where learning lies. I was and am proud of them for having the courage to stick up for their right to learn and not to just click through some computer problems that were completely incomprehensible to them. I had to explicitly tell them afterward that they could not have been expected to understand everything, rather that those exercises are merely fore-shadowing the things you will need to come to understand.
Let’s back track, a little bit. Before class, several students asked me to meet with them before class to discuss some problems they were working on. I think the problem was about a person running 3 m/s for 30 minutes, and they were supposed to find the distance.
This is what the students had done:
3 m/s / (30 minutes / 60 seconds) =
I asked them what they did and why. And they said, “we divided because we saw that the seconds was in the denominator [pointing to the s in the m/s], and we figured we had to convert to seconds somehow. But we weren’t sure exactly how to do it.”
OK. So I decided to ask a simple question, “How far does it go in one second?” Someone answered 3 meters. OK, well, how far does it go in 2 seconds? Someone said 6 meters. Now I asked, why? Someone said, its 3 times 2. I said, “Yeah, and it’s also 3 + 3. He traveled 3 meters in the first second and another 3 meters in the second second”. Then, I asked how far it would go in 10 seconds. It was certainly not automatic for them to say 30 meters, suggesting to me multiplication by 10s was not at their finger tips. So, then I asked them how far would it go in a whole minute, and they were able to eventually figure out that it must go 60 * 3 m/s. And then it wasn’t easy (but neither hard) for them to realize that is must be 3 * 60 * 30.
This. this stuff is ground zero for these students–quantities, rates, and ratios. Jumping to finding the area under a curve is absurd (a bit too quick to the gun?)
Let’s talk again about computer problems. Students had another question where there was written description of a motion–on object moving toward the origin, then going slower in the same direction, then stopping, then going faster in the same direction and moving through the origin. They had to pick out the right graph. Many students were struggling with this as can be expected, so I asked the following question to several groups, “Can you show me where x = 0 is?” Some students pointed to the center at (0,0), while most pointed to vertical axis.
Once again, interpreting graphs and reasoning across written and graphical representations is tough stuff, but no one had even invited them to the playground. These students were confused about why the “x” was on the y-axis and were (understandably) confusing the origin of coordinate systems with the (0 second, 0 meter) location on our position vs time graph. Total stuff I expect to see, depending on the population.
So afterwards, I took a poll. I asked them to talk with their group about, “Where x=0 is?”. After they talked, I asked for ideas, and four ideas came up. It is the vertical line (axis). It is the point (0,0). It is the horizontal axis line. It is arbitrary and could be any horizontal line. Someone brought up the fact that when you zoom in a graphing calculator, the horizontal line shown isn’t always zero. I simply just wrote up their suggestions as they gave them and I asked for why someone might think this. I then sent them back to their groups to discuss what they thought it should be after hearing all the ideas. All the groups came back saying it should either be the horizontal line of the axis or it could be any horizontal line if it isn’t labeled. We ended up deciding that you should always label your axes, but if you find one that isn’t labeled, it’s a safe bet that the axis represents the zero value.
I was already “waaaay behind”. Note here that I didn’t say, my students were waaay behind. I think my students were probably now a little less behind than students in the other class, but the my INSTRUCTIONAL timing was behind. I refuse to leave my students behind, and that’s why I shouldn’t be allowed to teach certain courses.