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December 17, 2017

[liveblog] Maarit Rossi on teaching math that matters

I’m at the STEAM ed Finland conference in Jyväskylä. Maarit Rossi, who teaches math teaching around the world, is talking on the topic: “AI forces us to change maths education.”

NOTE: Live-blogging. Getting things wrong. Missing points. Omitting key information. Introducing artificial choppiness. Over-emphasizing small matters. Paraphrasing badly. Not running a spellpchecker. Mangling other people’s ideas and words. You are warned, people.


Finnish teachers are doing a great, great job, she says. “But we are doing it too quietly.”


Education is too similar to industrial assembly lines. Students sit passively in rows. Students find math education to be boring, meaningless, and frightening. Typically this happens sometime in 5-7th grade. Teaching math has not changed in 100 years. It is a global problem.


Meanwhile, tech is changing really quickly. (She shows a photo from 1956 of workers shoving a 5 megabyte drive onto a truck.)

1956 5mb drive loaded onto truck

These days we are talking about personalizing math education. Easily available programs solve math problems. In the USA, people say the students are “cheating.” No, they’re being educated wrong. We need to be asking if we’re teaching students 10 critical skills, including cognitive flexibility, nebotiation, coordinating with others, emotional intelligence, critical thinking, creaetivity, complex problem solving, service orientation [and a couple of others I didn’t have time to copy down].


A modern math curriculum addresses attitudes, metacognition (e.g., self-regulation), skills, concepts, and processes. Instead, we focus on the concepts (e.g., algebraic, statistical, etc.).


A classroom has to be a safe place where you can make mistakes.


There are four pillars: practice, learning by doing, social learning, and interdisciplinary math. She gives some examples. Students estimate the price of a week’s shopping for a family of four. Maaritt has students work in groups of four. After that, they go to the nearest shop to find the actual prices; the students have to divide up the task to get it done in time. (You can have them do online shopping if there isn’t nearby shop.) Students estimate and round the numbers, tasks that are usually taught separately.


For higher grades, the students deal with real data from an African refugee camp. The students have to estimate how much food is needed to keep everyone alive for two weeks. “This is meaningful to them.”


It’s important for math to have double the lesson length. If it’s only one hour, it is not enough. “The students love it when they have the opportunity to think, to discover, to find themselves.”


Re-arrange the classroom. Cluster the tables rather than rows. The students can teach one another. “It is important that the feel successful.”


“And of course we use computers. And apps. And phones.”


“Math is also interesting because it can model many things.” If they have an embodied sense of a cubic meter, for example, they learn how to convert them to other measures. Or model the size of the solar system outside.


She has students estimate collections of objects, e.g. a bowl of noodles. Then they round. Then they count. Groups come up with strategies for counting, including doing it in ways that enable the count to be interrupted and resumed.


Physical exercise makes brains work better.

Classifying is important. She asks students to take sheets of paper and make the biggest triangle they can, and another of a different shape. They put all the triangles in the middle of the room. Then she asks them to see if they can cluster them by similarities.


“Students need to use their own language” rather than only hearing the teacher talk. This is how they learn to understand.


[My notes about the last few minutes, and the questions, go cut off via brain-computer glitch. Sorry.]

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October 11, 2016

[liveblog] PAPIs: Cynthia Rudin on Regulating Greed

I’m at the PAPIs (Predictive Applications and APIS) [twitter: papistotio] conference at the NERD Center in Cambridge.

NOTE: Live-blogging. Getting things wrong. Missing points. Omitting key information. Introducing artificial choppiness. Over-emphasizing small matters. Paraphrasing badly. Not running a spellpchecker. Mangling other people’s ideas and words. You are warned, people.

The first speaker is Cynthia Rudin, Director of the Prediction Analysis Lab at MIT. Her topic is “Regulating Greed over Time: An Important Lesson for Practical Recommender Systems.” It’s about her Lab’s entry in a data mining competition. (The entry did not win.) The competition was to design a better algorithm for Yahoo’s recommendation of articles. To create an unbiased data set they showed people random articles for two weeks. Your algorithm had to choose to show one of the pool of articles to a user. To evaluate a recommender system, they’d check if your algorithm recommended the same thing that was shown to the user. If the user clicked on it, you could get an evaluation. [I don’t think I got this right.] If so, you sent your algorithm to Yahoo, and they evaluated its clickthrough rate; you never got access to Yahoo’s data.

This is, she says, a form of the multi-arm bandit problem: one arm is better (more likely to lead to a pay out) but you don’t know which one. So you spend your time figuring out which arm is the best, and then you only pull that one. Yahoo and Microsoft are among the companies using multi-arm bandit systems for recommendation systems. “They’re a great alternative to massive A-B testing

] [No, I don’t understand this. Not Cynthia’s fault!.].

Because the team didn’t have access to Yahoo’s data, they couldn’t tune their algorithms to it. Nevertheless, they achieved a 9% clickthrough rate … and still lost (albeit by a tiny margin). Cynthia explains how they increased the efficiency of their algorithms, but it’s math so I can only here play the sound of a muted trumpet. But it involves “decay exploration on the old articles,” and a “peak grabber”: If any articles gets more than 9 clicks out of the last 100 times they show the article, and they keep displaying it: if you have a good article, grab it. The dynamic version of a Peak Grabber had them continuing to showing a peak article if it had a clickthrough rate 14% above the global clickthrough rate.

“We were adjusting the exploration-exploitation tradeoff based on trends.” Is this a phenomenon worth exploring?The phenomenon: you shouldn’t always explore. There are times when you should just stop and exploit the flowers.

Some data supports this. E.g., in England, on Boxing Day you should be done exploring and just put your best prices on things — not too high, not too low. When the clicks on your site are low, you should be exploring. When high, maybe not. “Life has patterns.” The Multiarm Bandit techniques don’t know about these patterns.

Her group came up with a formal way of putting this. At each time there is a known reward multiplier: G(t). G is like the number of people in the store. When G is high, you want to exploit, not explore. In the lower zones you want to balance exploration and exploitation.

So they created two theorems, each leading to an algorithm. [She shows the algorithm. I can’t type in math notation that fast..]

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July 9, 2011

Conrad Wolfram on teaching math right

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December 9, 2010

How the Egyptians multiplied

The title refers to The Maths, people! Get your minds out of the gutter for once, will you? Jeez!

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