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> solve 10 generic and meaningless problems using this formula I used to think this too, even when I started teaching. But I think if you look at a (modern?)

> solve 10 generic and meaningless problems using this formula I used to think this too, even when I started teaching. But I think if you look at a (modern?) textbook you'll see that those problems are not actually generic. They are often designed problems that are trying to help you gain insights as you solve them. Each problem is probably demonstrating a different interesting pattern, if you are looking for that. Admittedly, students are not taught what to look for in those problems and if the text book as "answers to odd problems" in the back of the book, then there are probably 2x the number of problems necessary. I teach HS Computer Science and I have to teach about division with ints and doubles. It would be nice if I could just explain the rules and give 2 or 3 examples and be done with it... but it turns out I have to have them work through lots of "generic and meaningless problems" 10 / 5 5 / 10 10 / 10 10 / 3 3 / 10 10 / 5.0 10.0 / 5 10.0 / 5.0 10 / 3.0 10.0 / 3 10.0 / 3.0 10 / 10.0 10.0 / 10 10.0 / 10.0 Each of those problems demonstrates a different "edge case". Towards the end there are some repetitive ideas I could leave off (once they know that double/int, int/double, double/double all evaluate to a double it may be overkill to keep repeating those patterns, but...) If I don't have them work through each of those problems, it is likely that at least one student will pick up the wrong pattern and run into problems in their labs when they encounter those patterns. That being said, I think the biggest problem with math education (in the US) is that many Elementary teachers would probably rank their Mathematics skill as one of their lowest skills. I personally know an elementary school teacher (with a master's degree) that took her last Math class her Junior year in high school. I met her in her college Math credit course which was a Computer Science survey course where we listened to talks by researchers and wrote 1 page papers about what they were researching.. I know she's a great teacher, but she just doesn't have the math background to teach more than "these are the steps to do math, follow them to get the answer."

dorchadas 5y ago
> That being said, I think the biggest problem with math education (in the US) is that many Elementary teachers would probably rank their Mathematics skill as one of their lowest skills. Absolutely yes. I'm a secondary level math/physics teacher, and I've come to the conclusion that the problem truly stems from elementary level teachers who don't understand the math and just teach rote steps. Then, when things diverge from those rote steps (usually around fractions, negatives and variables, from what I've seen), that's where you really start to lose students. The teachers themselves have no underlying grasp of the material and what it actually means, so of course they can't really impart that to the student (especially multiplying/dividing fractions and doing operations with negatives). Then it just compounds in middle school and by the time they get to high school it's a huge mess.

dorchadas 5y ago

> That being said, I think the biggest problem with math education (in the US) is that many Elementary teachers would probably rank their Mathematics skill as one of their lowest skills. Absolutely yes. I'm a secondary level math/physics teacher, and I've come to the conclusion that the problem truly stems from elementary level teachers who don't understand the math and just teach rote steps. Then, when things diverge from those rote steps (usually around fractions, negatives and variables, from what I've seen), that's where you really start to lose students. The teachers themselves have no underlying grasp of the material and what it actually means, so of course they can't really impart that to the student (especially multiplying/dividing fractions and doing operations with negatives). Then it just compounds in middle school and by the time they get to high school it's a huge mess.