In an earlier post I wrote about the mantra for my precalc class. The general idea is that the process of learning begins with a surface level understanding, followed by some confusion, and finally a deeper level understanding. Calcdave used a great illustration of the idea in his Diary of Infinity. I think I stumbled upon another application this weekend.
I’m currently reading a book called Mindset by Dr. Carol Dweck. In the book, Dr. Dweck (I love that name by the way) distinguishes between two different mindsets – the idea that ability is an unchangeable vs the idea that people can improve with practice. According to her, “In one world – the world of fixed traits – success is about proving you’re smart and talented. Validating yourself. In the other – the world of changing qualities – its about stretching yourself to learn something new. Developing yourself.” In other words, people with a fixed mindset approach every challenge as a test of their innate abilities, while people with a growth mindset approach challenges as an opportunity to improve oneself. I believe that this ties in very well with the precalc mantra in my classroom.
For example. Suppose a student scores a 20% on a test. I used to struggle with what to say to that student. My canned response now goes something like this:
Just because you failed this test does not mean it’s the end of the world. What it means is that you are in the confusion stage when it comes to understanding this concept. In a way, that is a good thing, as it means you’re well on your way to a deeper understanding. We now have some very valuable information as to how we can proceed in this class and help you emerge from your confusion with a mastery of this concept.
I feel as though this viewpoint is advantageous in a few ways. It doesn’t place the blame on the student or imply that the student is somehow defined by his 20%. Instead, it takes a perspective that the 20% is a launching pad for improvement and a natural part of understanding mathematics. The fact that a student is confused does not mean that he or she is a failure – a score on a test proves nothing about the student. It means he/she has an opportunity to learn something new and a lot of room to grow.
(I also feel as though the growth mindset ties in very well with standards based grading, but thats a whole other story.)
Great alignment of theory and practice! BTW, I mentioned that I had a “fixed growth mindset” today…it confused a few folks…I was hoping for a laugh, but my Brit-esque humor is too dry for many.
I wish that we had read about these mindsets during the summer, and had shared what we knew with our students! I feel like Dweck’s work gives us both the language and strategies that we could have used to with some of our more challenging students. I am glad that you are able to apply it to your current classes and, definitely, to your own practice.
This makes me think. And it’s an uncomfortable frustrating feeling. Thing is, I’ve been doing the “test results aren’t a reflection of your worth, they’re just an opportunity for further growth within this limited field” for the last two years. I’ve given tons of reassessments, and I’ve tried to cater to students’ needs.
Then I read a bit about Hofstede’s cultural value dimensions and how in exactly those countries where students do very well in Math (I’m talking east Asia, Russia, etc) values go the opposite way of what I was doing. There, the strong student is the prescriptive norm. Failure is — failure. It does reflect on worth, whatever “worth” really means. And I think maybe that way students identify more with school progress and therefore put in more effort. Also, teaching is much more authoritarian and not as soft and friendly as I’ve aimed at in the past.
Now I’m trying a tougher surface, and let students feel the disappointment and frustration of poor results instead of making them think differently about it etc. Well, it’s an uncomfortable fit but does seem to have some pleasant side effects. They try much more on their own before asking me for help, for one. But I think student evaluations of me will be lower this year.
FYI here is some decent info on the Hofstede cultural value dimensions as applied to education. http://fuhu.dk/filer/FBE/Arrangementer/Denmark%20Unlimited%20080508/FBE_geert_hofstede_teaching_learning.pdf
I definitely generalize considerably when I talk about my reaction to students’ low achievement. Of course one should treat things on a case by case basis, and there are students who need to be knocked down a peg, reprimanded for a lack of preparedness, and feel a sense of disappointment. However, those are not the students I generally worry about. I worry about the kid that sits for 40 minutes writing nothing down with the excuse that she ‘just doesn’t get math’ or the heart breaker… the kid that tells me “I don’t understand it! I did all the homeworks, helped other students, and then on the test I can’t remember it at all!” The ones who are already unconfident in their math ability are the ones I feel the need to reassure. In a way I’m cheating by using a summative test as a formative assessment. On the other hand, nothing is set in stone and the students have numerous opportunities to relearn concepts and improve their grade.