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.
D.C. charter schools expel students at far higher rates than traditional public schools
Charter schools need the ability to remove students who endanger the safety of the other kids. I think that’s true. Also students who make the classrooms less conducive to learning. So far so good.
Well, no duh. Do charters have some magic urgency to what they’re doing that the rest of us in actual public schools don’t? If a charter operator took over an entire school district, without the possibility of expulsion, they’d end up recreating the public school system that they replaced. Without the ability to choose your enrollment, all of the high powered expectations go out the window:
- no excuses
- zero tolerance
- 30+ students per class with direct instruction every day
Towards the end of the article, there is some talk about charter heads setting up an alternative school as an alternative to expulsion. So it begins.
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:
Micro rewards have weird effects on decisions
How would you implement micro rewards for wrong steps in a classroom? The idea would be to either have students get savvy enough that they didn’t take the reward automatically or else learn from the experience of receiving a reward that was short-term good and long-term bad. The easy answer is candy. Like, “I’ll give you a piece of candy if you eliminate 13x instead of 2x” when 2x is the right thing to do. The extension and real lesson here is that sometimes people are trying to get you to do something that’s better for them than you by offering you a short term reward. This article is really about game design, but it has instructional implications.
It’s easy to see the implications of rewarding correct steps. This is shaping. But even that is questionable according to the paper in the linked article. The paper concludes that when someone is rewarded for correct steps, their learning is not transferable to novel problems, only to identical or very similar problems.