Here's the book on math teaching lessons, and although it's in Russian, you can get an overall idea of the level of math involved by skipping through the pages: http://www.mccme.ru/free-books/57/davidovich.pdf
It describes a 4-year program, from 8 to 11 grade of russian school, for kids from 13-14 to 16-17 years old respectively.
Your two points are really the same point. The reason that people don't understand what mathematicians do, is because we've been referring to calculation as mathematics our whole lives. If we did a better part separating the two out earlier, people would understand which part mathematicians work on.
The Lego Friends theme doesn't have firefighters because it is focused on social relationships, not overcoming conflict. It doesn't have to be a girl vs boy thing (although it is undoubtedly targeted toward girls to compete with other non--confrontational toys that have proved popular with girls), it is just part of the theme. Ninjago doesn't have firefighters either.
I think it is great that Lego has developed a theme that isn't focused on physical confrontation. I have three girls who play with Lego and they request a mix of sets. For Christmas, they requested sets from Friends, Lord of the Rings, and Ninjago. My four year old got a Chima set. They don't see it as a girl vs boy thing.
I'm not convinced on the marketing part. How is a lifeguard post or a ranch more social and less conflicting than firefighters or construction workers ?
Now, if I was heavily into buying Lego bricks, I'd also mix from the different sets to have more situations, and my kid doesn't really care if his toys are action figures or dolls.
I don't think "social" is the selling point. If I just look at "all buildings", only very few of them seem to be about actual work. It's more about having fun in exclusive locations with loving animals.
As a mathematician, how much time do you spend studying proofs written by other people?
I'm genuinely curious, because I think that if I wanted to be a novelist, I would spend a lot of time reading novels before trying to write one. I feel like we never have children read the great "literature" of mathematics, but then expect them to write their own proofs and are surprised when they hate it.
I literally study the proofs of others every working day, for at least a few hours a day. But I am a young mathematician and still inexperienced with research.
I imagine that once you are a professor you can spend less time studying the details of proofs because you can generate them on your own once you understand the big picture. But even so this depends on your field (combinatorics folks, for example, REALLY spend a lot of time studying proofs).
I think you're absolutely right that math has to be motivated. A lot of the effort to motivate it is to provide problems that students understand relate to the real world. Most of them come across as contrived.
You hit on a good concept with the idea of incorporating the history of math. I'm working on a Geometry curriculum that does just that. Understanding math in the context of a grand story of mankind trying to understand the world around us is a lot more interesting than as a set of received wisdom that must be memorized.
I would love to see more math material along these lines, but there isn't much out there, and it takes a long time to produce. I've been working on mine for around 6 months and am just up through looking at how the discovery of incommensurable lengths influenced Plato's philosophy. The idea is to work through the history and philosophy in parallel with Euclid's Elements, relating points back and forth where possible.
I've tried teaching a history of math class to local homeschool kids along those lines, focusing on Egyptian - Greek history, with some success. It takes a lot of research and work though.
Yeah, absolutely. In fact, I'd say that it's just as important that students receive confirmation of this history and motivation in their other subjects. For example, in various history classes, we learn about kings and wars and important philosophers. But we rarely learn about mathematicians and why their contributions were important, of if they were polymaths, we discuss their non-mathematical contributions, but omit their mathematical ones entirely.
Then in writing and literature we spend endless hours on appreciating tiny non-relevant symbols, but don't read something like Ringworld and spend part of a session calculating and relating the size of it. Conversely, in Math class, writing a paper on the history and influence of Platonic solids or similar would have been an interesting break and let kids struggling with crunching numbers take an interest and shine a little.
Or imagine a math course that analyzes things like agricultural output from Roman times to modernity, involving geometry, arithmetic, algebra, percentages (taxes to the king!), nutrition, etc. Extend out to how greater agricultural output per unit land produces surpluses that enable people to take up other labors like politics or art or music.
Off the cuff examples that would need more careful thought, but hopefully the idea is sound.
Bringing math into other non-math subjects, and bringing arts into non-art subjects I think helps prop up what students see as isolated subject "silos" that have nothing to do with anything.
Literature and history courses mutually reinforce each other, and math and science course mutually reinforce each other, but there's a tremendous gap between these two groups of courses where they don't reinforce each other.
This really needs to end because it all is connected and builds relevance for students.
I'm still struggling with how to handle this. On the one hand, it makes a lot of sense for it to be public. On the other, I've given up a lot to spend time developing it (including going part time on my day job), and I would love to be able to devote more time to it, which would require making some money off of the material in some way.
I've been thinking about doing a kickstarter, but I'm interested in exploring other models. I don't have a ton of time, and I'm always torn between spending time trying to figure out how to publish/market/exploit the material versus spending the hundreds of hours reading history and math and trying to actually write the curriculum. So far I've just been punting on it till I get this first course done.
I don't have a lot of knowledge, but there are websites that allow for the monetization of lesson plans. Maybe workbooks and videos to help teachers present the materials?
I do think a kickstarter would definitely help as would getting it out in other teacher's classrooms to get earlier feedback.
Just checked out your site, it is like you are brother from different mother. Awesome stuff. I have a project I am working on that I will ping you with to get your feedback, I think you will like it.
ESR is being extremely condescending and patronizing. I don't consider that friendly or helpful. He's giving tons of hand-wavy pop psychology in response to a technical issue on which he's out of his depth. His "experience" was not with anything the size and complexity of the Linux kernel and was not particularly relevant. He does like to set himself up as the wise old mentor to people who don't really want or need to listen.
Linus wisely declined to respond to this extremely condescending comment by someone who was out of their depth and didn't clearly understand the issue at hand.
He didn't ask whether it was an honorable, noble thing to do, he asked whether they were "obligated" to do it. Once you are obligated to do something, it is no longer honorable or noble just to do it. Your uncle stood out because he went beyond what he was coerced to do.
