Kyle Luz from Eisenhower High School in Utica emailed me about some frustration he was having with his kids learning about the accelerating particle model.
Here is my response.
Here is the theme of this email: when we were teaching in a more traditional style the kids didn't really understand acceleration then either but our teaching didn't put us in a position to even know it!
Most teachers (at times myself included) exist in persistent state of denial about how much their students know and are able to do. With a traditional model we teach and then give homework, go over the homework, and then quiz. The students who do well "really must have paid good attention" and the students who did poorly "just didn't get it" or "didn't apply themselves". The students are to blame and we just go about the business of teaching. We don't know (along the way) what they know and are able to do and frankly many teachers really don't want to. We don't even give ourselves an opportunity to find out! This is not necessarily all true - I'm stereotyping to make a point.
With the modeling method we are constantly into the kids business of learning! We are constantly finding out what they know and don't during white board creation when we visit their small groups, during white board discussion in large groups, during challenges (practicums) when they are forced to apply their knowledge, all of the time! Because the focus is on the students and not on the teacher they have to express their knowledge on a daily basis not just on quizzes.
This, however, doesn't mean that they "get it" in fact it just highlights the fact that acceleration is the HARDEST topic of study that they will encounter! Until I started really working with kids I didn't know how challenging this was for them. And even if kids can draw the correct graphs I don't know if they get acceleration. That's why we do motion maps also.
Let's talk about the graphs. How hard are these?!?!?! Impossible, seriously. But the fact that the kids cannot interpret these graphs is not necessarily a function of your class. It is a deficiency built of years of mediocre math and science education. This is a huge problem for all kids in all schools. That is why the ACT science section (which is just interpreting graphs) is such a good assessment of kids reasoning abilities. Knowing this and I mean really knowing this gives us a huge advantage over other teachers. We now know what the kids can and cannot do and have the tools to help them do better!
Your situation is not unique, however. Yesterday we were doing a challenge where they were given a ball bearing and a ramp and a buggy. They took whatever measurements they wanted and the challenge was, when given a spot on the ramp from which to release the ball could they get the ball to hit the buggy at the end of the ramp. Some kids jumped in and knew that they needed the acceleration of the ball and the speed of the buggy. However, I visited one group who told me they were looking for the "speed of the ball on the ramp". I'm like, but doesn't the ball speed up on the ramp? Blank stares. Seriously?
After years of this, however, I kind of know where the kids are going to struggle so I'm not too surprised and I'm finally not in denial about how hard it is and how they really don't get it. Consider this statement, "Fast cars have fast accelerations." I don't think there is a student out there who would dispute this, however, aren't there huge issues with this statement! The kids naturally confuse the value of a with the change in that value - in this case its velocity and acceleration. But all of their lives the two have been inseparable!
1. They really have never gotten acceleration on a conceptual level that would allow them to do more than solve problems.
2. It is way harder than advertised!
3. Living in denial about what you students know and is so much easier and acknowledging their failings does turn one's hair white (or whiter).
4. The kids don't understand these things because of cultural misunderstandings.
But, there is hope. Helping kids learn this stuff in the context of real learning is WAY better than not. Even though they all might not get it, they will develop skills that will take them far into the future. And they are engaged, and they like it, and you have a good relationship with them; all positives! We never know how long it will take anyone to learn something. That is why some of us have our kids assess and reassess and re-reassess. It given them multiple opportunities to show what they have learned. But that is a conversation for another time.
This will help until we get to unbalanced forces and ask kids to remember acceleration and they look at you like you're speaking Greek!
The original email is below.
Funny you send out an email when I need a quick boost in my teaching. I had a Unit 3 test scheduled today, but after the review exercise I gave out yesterday, felt that students were not ready. So, going against report cards telling me when to give a test, I gave a short quiz today and will test next week after some more work. The quiz was a v vs. t graph from a 2000 APB exam. Lots of positive and negative velocities and horizontal lines. Things I feel we covered and practiced and talked about. (I am still talking too much, but I'm only a rookie).
My student did not seem to do as well as I thought. They could not identify a zero velocity on a v vs. t graph as where it crosses the x-axis and most told me where it was horizontal. I can understand the misconception and will work to change it next week, but I had about 5 of 35 tell me that the cart NEVER had a velocity of zero!? How do I deal with that? And after using and practicing "area" to determine a displacement, when the question asked where the "final position" of the cart would be if it had started at 2.0 m at t=0, it was like I asked them the question in latin.
It avoid any more of my hair turning white, can you tell me? Do you, after 15 years of skillful modeling, still have students get through a unit and not have a clue of what was done? I have a sketch of that mythical outcome graph you showed from your book last month to keep me motivated, but hope you a second to give another boost.
Thanks, see you at the zoo,Kyle