Once, in a course on learning and the brain, we learned that empathy is visible in infants. So, I thought that implied that empathy is innate and doesn’t change. Even my recent investigation into Mindset (Dweck, 2009) didn’t shake this belief because I didn’t make the connection. I don’t think of empathy as something you learn, but if Mindset is to be believed, everything can be learned. There were two news items about this today:
Occasionally, students ask me questions about why math works the way it does. This doesn’t happen enough, in my opinion, but it does happen. The latest is why, when we perform synthetic substitution, do we use the number as it is, but in synthetic division, there’s some sign trickery. I have an answer for this. It’s not super complicated either, but whenever I’ve given the explanation in the past it’s been frustrating and incomprehensible to students. So, I don’t know if it is worth the time it takes to do that, and that kind of understanding is not necessary for skill performance. But then, what am I doing? If we don’t care about understanding or make that kind of tradeoff of “well, they don’t really need to know this” that feels like the opposite of mathematics education. I’m pretty good at explaining things like this, so I don’t think it’s me. There is such a thing as developmental readiness and that’s what’s happening here. I think.
What do you do when explanations are over the students’ heads? Is that just a normal thing that resolves itself with further mathematics study and we shouldn’t worry about it? I find “that’s just how it works” a completely unacceptable response.
I’m thinking that one way to escape GERM is to go to Canada. Alberta is moving towards the Finnish model, right? I seem to remember that. Any advice would be great. The problem is that I have an 8 year old’s view of looking for a job because I’ve only had to do it twice in my life. It turns out that you can’t just apply to the government of Canada and have them place you in a school and I guess find you a place to live.
On the other hand, the best way to escape GERM would be to go to Finland itself.
The author at the link below talks a bit about items from the 6th grade assessments where she goes to school. Here’s a test item and her take on it (the not boldfaced part is her.)
If “Nasser of the Shaduf had been written in the third person, the reader would probably have learned less about which of the following?
a) Nasser’s childhood
b) Nasser’s sisters
c) how Nasser felt about working the shaduf
d) how his father felt about Nasser
I think they’re all a little bit wrong.
homegirl is 12
For about 4 months, I’ve thought that there needs to be some kind of balancing force to keep modern ed “reformers” in check. Even they themselves ought to recognize the importance of a debate where their propositions are not the only ones. This is the value of competition of ideas. But it’s all very one-sided right now.
For example, what group is contesting the Common Core State Standards? There are individuals here and there expressing reservations, but many more groups have gotten on board without, as far as I can tell, any decision making process. This is not to say that the CCSS are a bad thing, but the debate is important. What group is contesting the notion that more hours over more days will improve the quality of education for students?
Unions are probably the easiest objection to this post. But if you follow the links above, or pay any attention at all, you can forget about unions taking any kind of position here. The exception is the CTU, which is where I got the phrase “better school day.” Here‘s someone talking about better school days to give you an idea if you’re not familiar.
I’m probably not as informed as I think, but I’m working on it. Any comments with information are appreciated.
Some things I’ve found since writing this post:
Super Teacher Tools
Maybe the neatest site I’ve seen for whole class math games.
At a meeting earlier this week, some of the other math teachers were saying that they didn’t teach their kids about the LCM or how to choose a variable to eliminate when solving systems by linear combination. I was stunned. Instead of using the LCM, they said they told the kids to always swap the x coefficients and multiply, being sure to make one equation positive and the other negative. Let’s leave aside the sloppiness of the language here for a minute. I can’t really imagine using an approach geared to the lowest level students. It doesn’t seem fair to everyone else to present material that ignores what ought to be prior knowledge, and after all “Algebra 2” means something.
But they went on to say that students picked up on the variations on their own.
So, this is a dilemma: should I present a severely dumbed-down approach, hoping that students will make the extensions themselves, or be more comprehensive in my presentation?
If I’m serious about students deciding what and how and how much they will learn, I have to be willing to take the risk of them being lazy. So I did that today. The thing is that they’ve seen this before, in Algebra 1. So, I don’t know how it would have worked with a class that had not seen the technique before. Luckily (hah) I have an Algebra 1 class too, and can try it there later this year.