Dec 14, 2018

Math from 3 to 7:

Jul 12, 2018

Before I started a new job I had myself read: 1. So good they can't ignore you 2. Deep work 3. Mythical man-month 4. Power of habit

Now I am reading Tools of titans by Tim Ferris. I never thought I would get into the genre of self-improvement books, but it seems I like these :-) Even though I am conscious about the fact, that I am applying maybe 10% of the books advice :P

Another thing I am reading is Math from three to seven [1], mostly because I would like to discuss math with my 4yo daughter one day, preferably sooner rather than later, because I find math discussions immensely fun :-D Maybe I will even start a math-circle :-)


Mar 04, 2018

Why do you think (paraphrased) “I think secondary school mathematics should focus on solving non-obvious problems” has anything to do with “proving P ≠ NP” per se? I’m obviously not suggesting that we should assign famous unsolved research problems to secondary students. I would instead hope we could assign students a variety of problems taking them between 10 minutes and a few weeks to solve (at their current level of skill), with emphasis placed on smart problem-solving efforts rather than on sorting students based on who gets the most right answers.

Most American undergraduate differential equations courses are taught as a list of recipes with little room for thought. Rather comparable to elementary school arithmetic drills frankly, though obviously involving more built up preparation.

However, it is possible to assign difficult problems to students at any level from age 3 onward (see for an example of real mathematics instruction for preschool students; for primary students look up the work of Dienes; at the middle school level I think some Russian programs are pretty good etc.). It just takes more work for teachers to provide feedback about student solutions to such problems, it’s less amenable to grading by rote (and therefore not easy to check via standardized tests), and it takes more significant focus/attention/decisionmaking by teachers from moment to moment (and ideally more teacher background preparation). The students learn the subject more deeply, enjoy the process more, and learn significantly more transferrable skills.

Porting a graphics engine from one platform to another very similar platform (after having ported many other software projects between the same pair of platforms) or baking a cake just like all the others you have baked before might take nothing more than skillful application of well-established procedures, but making a new graphics engine in the first place (assuming it does something novel) or inventing a recipe for a new type of cake definitely takes problem solving skills.

Feb 13, 2018

Not quite the same kind of tool but you might enjoy