Over the past couple of months I have been following a discussion about math zombies. It originated in the comments on Dan Meyer’s blog. It has been expanded upon with examples in several other blogs such as here, here, or here. I had previously been thinking about different mindsets in math class; how different people could sit in on the same class and come away with drastically different experiences. Now what I will be discussing in this post is the mindset of the person who sits in on the class, not the engagement of the person with the material of the class. For the purpose of this argument I am defining a mindset as how a person thinks about the material at hand and engagement would be how a person articulates that mindset.
From my personal experience here is how I would classify the mindsets of the students that come into my class.
- Wizards – Have you ever met that person that seems to “get” everything, that everything seems to come so easily? Wizards are those students that can perform a task that would make others struggle, to the point that sometimes it seems like magic. This is the student that usually craves projects or might want to initiate discussion. Every time a teacher asks questions about concepts, those “why” questions, the wizard is usually the first to volunteer an answer. (I got the idea for this name when my five-year-old grabbed a copy of our Pre-Calculus textbook and called it his wizard book. I thought it was appropriate since for some people math does seem magical, or at least like witchcraft.) For another good description view the difference between a good mathematician and a great mathematician.
- Survivors – The survivors are the students that do what they have to do to get through the class. They see much of their academic experience as gate keeping procedures. An example from my experience would be a student who was deciding what math he should take his senior year and couldn’t decide between Statistics and Pre-Calculus. As we looked at different math requirements at various colleges for his planned accounting degree we noticed that the requirement ranged from College Algebra to Statistics to Calculus I. All of the graduates can be qualified to take the CPA exam, so what is the difference in the specific math requirements? A survivor has realized that these courses function for the purpose of weeding out those students who will not put in the requisite work. As such, the course material itself is irrelevant, putting the student in the mindset of wanting to pass the course with the least amount of effort possible. Understanding is inconsequential since the material will not be needed for the end result.
- The Lost – Everyone has probably seen the lost before. These are the students who seem to randomly be guessing all the time. These are the students where a slight change from procedure can flummox them. These are the students who seem to have never mastered procedures from other classes, that cause the teacher to wonder, “how did they pass?” When they complete an assessment, they have no idea whether if the outcome will be good or bad.
- Delusionals – A delusional student has many of the characteristics of a survivor, except they are not aware of the superficial aspect of their learning. I often find these students will create an image of themselves based upon a grade and not on any sort of comprehension. They measure success upon GPA, class rank, and ACT scores. When they struggle in class, these students are often the first to ask for extra credit or blame the teacher for their struggles. If they achieve low ACT scores, they blame test anxiety or say that test scores don’t matter/ A delusional student will be eager to expunge the value and importance of a class, but then be unable to actually apply material to any sort of context. A delusional student dreads word problems, and will ask to do “actual math,” which means manipulate equations. They lack the ability to apply “school” math to the real world.
The problem with mindsets is that they are not easily measured. I find that I have to interact with my students to understand how they view math. The first thing I learned is that grades do not necessarily reflect a mindset. I have been fortunate enough to have been in every mindset on my list, albeit relying on the benefit of hindsight to come to that conclusion. I was delusional in high school, became lost during my sophomore year of college, slowly morphed into a survivor over the course of my junior year, and finally became a wizard after teaching for several years. This provides me the benefit to at least empathize with every student in my class to some extent.
Now as a teacher, I wonder how I could effectively reach each mindset. I wonder if I should be trying to encourage to students to change their mindset? I think of my presentation, am I modeling the type of mindset I want my students to have? What I have learned as a teacher is that I think heterogeneous classrooms strive for mediocrity. It’s not a numbers thing. I have had classes of two students and I have had classes of 25 students, and I have found that the most effective classrooms I have had the most homogeneous mindset. And I think that is because I can only effectively engage one mindset at a time, I can only teach from one perspective at a time. But homogeny ain’t cool, so what do I do?