I’ve started to critically reflect on all the rewards systems I’ve ever used. Including every single grade my students have ever earned.
I am currently reading Punished by Rewards by Alfie Kohn. The basic premise that Kohn makes is that “rewards” as we know them (token economies, grades, etc.) are not only ineffective, but can even be detrimental to the growth of students. Often times, teachers, including myself, use these systems because they “work” and rarely question them. (In fact, this is true for many things that we take for granted.) I have been relating this reading directly to my classroom economy that I have instituted in my class for several years, along with the many other positive reinforcement strategies that I have come across through the years. But even more drastically, I have begun to question every grade that I have ever assigned to an assignment or report card. Grades are essentially rewards for the work that students complete.
Instead of focusing on reinforcement strategies, which only focus on what students do, I could allow systems and feedback to drive my classroom practices. Instead, this would focus on who students are and what they actually understand.
I spent four days this week on a deserted island with my precalculus students.
It all started when I read this post by Sue Vahattum. If you’re looking for a good exponential modeling activity, I’d check it out. She explains it pretty well on her blog, so I’ll just recap my experiences this past week.
The basic premise is that you present your students with a scenario where the entire class has been shipwrecked on a deserted island. Suddenly there is a murder and one member of the class is the culprit. The class will need to use body temperature and logarithmic equations to determine the time of death and, eventually, the murderer. Here’s the handout I gave my students that frames it all. Of course, you would customize the names to the students in your class.
UPDATE 1/9/17: Improved handouts and storyline are here.
This is the second time I’ve done this activity, and both times it’s been a total hit with the kids. It’s pretty engaging, out of the ordinary, and totally applicable to the curriculum. To get into the spirit of the activity, I come in wearing sandals, shorts and sunglasses during first couple of days and they enjoy that. Besides, we are on a tropical island. They work in groups and I use this whole thing as a culminating activity to my exponential/logarithmic functions unit. The modeling goes beyond just a simple regression, of which a data table can be put into their graphing calculator. What is great here is that the modeling contains a vertical shift in the function, so they have to do the modeling by hand. To tie into their unit assessment, I also will include a problem on their exam relating body temperature and time of death.
The only hiccup this year came on the third day when they couldn’t actually find the murderer! The students overlooked a detail related to the time intervals and we had to conclude on a fourth day. Since I was actually “murdered” on the third day, I couldn’t help them (which was perfect to assess mastery). This actually made it even more dramatic as they had to wait the entire weekend to figure out who the murderer was! Oh, by the way, before the activity I did secretly “choose” a student who could play a good murderer before we started – and he consented to this part in the activity. No one in the class knew who it was beforehand, so when he was revealed at the end he could come up with a little skit as to why he did it. It was a fun touch.
I have a Regents prep course (basically students that need to pass a New York State math exam in order to graduate) that I have been teaching all semester. These students are about six weeks away from the exam. I’ve decided to adopt a new structure to help them get over the hump of passing it. These kids are a challenging bunch, but their attendance is solid and they have good attitudes.
Every Monday, starting this past Monday, I will give them a simplified mock Regents exam. This will essentially be a diagnostic: it will not effect their final report card grade. My students usually buy into this pretty well. I will use the results of this assessment to identify which concepts we will focus on for Tuesday, Wednesday, Thursday, and Friday. During these days my co-teacher I will reteach and review these concepts, pretty much one concept a day to keep it simple and bite size. The following Monday we will repeat this process with an exam and using the rest of the week to tackle four more concepts (hopefully not needing to repeat those that we had previously relearned).
This targeted, structured, data-driven approach is something I’ve been seeking for this class for a little while. I’m consistently using data analysis for all my classes and I knew I was going to take this approach with them, I just didn’t know how it would look. Now I do.
After looking at the data from today’s exam a short time ago and mapping out the concepts for the week, I am really excited for the benefit this structure could provide my students.
Concepts for the first week:
1. Identifying trigonometric ratios from a given right triangle
2. Translating verbal statements into mathematical expressions
3. Basic operations on polynomials
4. Writing equations of lines and their graphs
I attended Math for America’s Master Teachers on Teaching event last night. If you’re not familiar with it, it’s essentially a Ted-ED style event where math teachers give presentations on topics that they are passionate about. One of my biggest takeaways had to deal with technology and how I address how my students use it.
There were some awesome presentations and one that stood out to me was Patrick Honner’s talk about the shortcomings of technology as it relates to teaching and learning. A couple examples that Patrick pointed out were the TI-84’s inability to accurately represent continuity (asymptotes) and Desmos’s failure in representing holes in polynomial functions. Normally, technology allows beautiful, helpful representations of mathematics, but in all of these instances technology utterly fails to do this. Patrick encouraged the audience to embrace these types of pitfalls as teachable moments that could enable deeper understanding of the concepts.
This whole discussion reminded me of something that happened in my class a while back. Once during an exam, I witnessed a (precalculus) student enter “1 + 2” into their calculator as they solved a problem. In the moment, I almost laughed out loud (and afterwards I did). The next day when I handed back the exam, I brought my observation up to the class. The guilty student openly took ownership of the act and said:
“Mr. P, on an exam, you never know!”
This example is slightly different than the ones Patrick highlighted, but it nonetheless brings attention to my students’ increasing dependency on technology. This connects with what was Patrick’s concluding point: our students blindly and inherently trust most all technologies they use – more so than they trust their own intuition. Combining this with technology’s pitfalls, and I see a recipe for disaster: students wholeheartedly trusting a flawed tool.
This means that I have a crucial responsibility to transform student reliance on technology into teachable moments that enable deeper understanding. It also means that if my students blindly trust technology and all it’s shortcomings and fail as a result, I have also failed.