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The American math curriculum is so strangely rigid, coming from a foreign perspective. pre-Algebra, Algebra-I, pre-Calculus, Calculus I, Geometry etc etc. So many fields of mathematics are interrelated, teaching them in such a segregated way is very strange (at the low introductory level e.g. all of high school).
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Sep 11, 2015 16:48
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tsa posted:You do learn about the inter-relations, you would know that if you actually attended school here. Focusing on one thing as a primary topic is the best way to educate though, it's very difficult for people just learning this stuff to appreciate the relations without having a solid base. Point being that it often makes sense to spend a small amount of time developing skills in one area of maths, go to another topic, spend a small amount of time developing skills in that area, return to the first area applying skills from the second for further development etc. Even if aspects of other classes are brought in, I don't get the impression that an algebra class pauses algebra content to spend time on geometry content that'll be relevant etc. If that's a wrong impression, well then the class names are stupid  A solid base is super important, but I think that base should be developed in parallel rather than sequentially.
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Sep 11, 2015 17:02
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Jack of Hearts posted:What solution are you proposing? Ending all advanced classes? It's a difficult problem, and there's no one solution. Teaching a range of material in class (in terms of material complexity) is extremely difficult and requires a lot of resources. But as soon as you track, you end up with students in the "dumb" classes beginning to massively resent school (their perspective is that they are "dumb" and the school has given up on them by making them second class students; why should they bother putting in effort?), and the students in the "smart" classes. I have a fair bit of teaching experience because I'm getting my PhD, but it's difficult to generalize to secondary schooling because I teach some of the objectively smartest and hardest working students in the world. Also some of the most privileged. But there's still sometimes a noticeable spectrum of abilities. What I've had great success with is doing a flipped classroom (material delivered online, at home etc), with in class sessions focusing on giving people individual attention for the questions and problems they have. Without the need to teach the general material itself in the limited time I have, I can teach to particular students' progress while having everyone in a room together (where peers can assist each other). Of course, this approach has serious problems at the secondary schooling level since it requires students to be willing to participate in the flipped side of the classroom while at home / outside of school. Since family support of education and actually having the time to do this sort of thing varies so drastically with socioeconomic status, it's hard to argue that a similar sort of process implemented in secondary schools wouldn't disproportionately benefit wealthier students. But it's one way to keep students in the same class. You simply can't keep everyone in the same class AND teach the same material to everyone. It's maddening for a gifted student to go at the pace of people who are struggling (and vice versa). But it's worth doing everything possible to keep them in the same class; because the people who are considered gifted changes all the god drat time. A major problem with tracking is that it assigns students a label; they are either dumb, or they are smart. That label affects their perception of themselves and their schooling. It's so easy for kids with high ability who struggle with a basic early concept to give up on their education (even if, had they persevered, they would find themselves to be extremely capable). Even for the kids who'll never excel academically, that brand is tied so deeply to their concept of self-worth and the value of their education that it screws them up for life.
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Sep 13, 2015 05:17
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Gifted students can also become terrors if they get bored in school, which happens when material is too easy for them. They can also become incredibly lazy if they can coast by on natural talent, resulting in them not developing the necessary learning skills required to cope when they are ultimately challenged.
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Sep 13, 2015 23:04
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PT6A posted:I agree very strongly with your point about self-teaching One needs to be careful with this; intelligence or ability isn't the same thing as knowledge. A gifted student can't know what they don't know. It's very easy for students to self-learn terrible habits, or miss out on critical fundamentals, or allocate their time poorly etc etc. So any "self-learning" should still have a fairly substantial amount of supervision.
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Sep 21, 2015 00:57
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