nhaliday + teaching   78

The Future of Mathematics? [video] | Hacker News
https://news.ycombinator.com/item?id=20909404
Kevin Buzzard (the Lean guy)

- general reflection on proof asssistants/theorem provers
- Kevin Hale's formal abstracts project, etc
- thinks of available theorem provers, Lean is "[the only one currently available that may be capable of formalizing all of mathematics eventually]" (goes into more detail right at the end, eg, quotient types)
hn  commentary  discussion  video  talks  presentation  math  formal-methods  expert-experience  msr  frontier  state-of-art  proofs  rigor  education  higher-ed  optimism  prediction  lens  search  meta:research  speculation  exocortex  skunkworks  automation  research  math.NT  big-surf  software  parsimony  cost-benefit  intricacy  correctness  programming  pls  python  functional  haskell  heavyweights  research-program  review  reflection  multi  pdf  slides  oly  experiment  span-cover  git  vcs  teaching  impetus  academia  composition-decomposition  coupling-cohesion  database  trust  types  plt  lifts-projections  induction  critique  beauty  truth  elegance  aesthetics 
8 weeks ago by nhaliday
Measuring actual learning versus feeling of learning in response to being actively engaged in the classroom | PNAS
This article addresses the long-standing question of why students and faculty remain resistant to active learning. Comparing passive lectures with active learning using a randomized experimental approach and identical course materials, we find that students in the active classroom learn more, but they feel like they learn less. We show that this negative correlation is caused in part by the increased cognitive effort required during active learning.

https://news.ycombinator.com/item?id=21164005
study  org:nat  psychology  cog-psych  education  learning  studying  teaching  productivity  higher-ed  cost-benefit  aversion  🦉  growth  stamina  multi  hn  commentary  sentiment  thinking  neurons  wire-guided  emotion  subjective-objective  self-report  objective-measure 
9 weeks ago by nhaliday
Foreign-Born Teaching Assistants and the Academic Performance of Undergraduates
The data suggest that foreign-born Teaching Assistants have an adverse impact on the class performance of undergraduate students.
study  economics  education  higher-ed  borjas  migration  labor  cost-benefit  tradeoffs  branches  language  foreign-lang  grad-school  teaching  attaq  wonkish  lol 
july 2019 by nhaliday
Teach debugging
A friend of mine and I couldn't understand why some people were having so much trouble; the material seemed like common sense. The Feynman Method was the only tool we needed.

1. Write down the problem
2. Think real hard
3. Write down the solution

The Feynman Method failed us on the last project: the design of a divider, a real-world-scale project an order of magnitude more complex than anything we'd been asked to tackle before. On the day he assigned the project, the professor exhorted us to begin early. Over the next few weeks, we heard rumors that some of our classmates worked day and night without making progress.

...

And then, just after midnight, a number of our newfound buddies from dinner reported successes. Half of those who started from scratch had working designs. Others were despondent, because their design was still broken in some subtle, non-obvious way. As I talked with one of those students, I began poring over his design. And after a few minutes, I realized that the Feynman method wasn't the only way forward: it should be possible to systematically apply a mechanical technique repeatedly to find the source of our problems. Beneath all the abstractions, our projects consisted purely of NAND gates (woe to those who dug around our toolbox enough to uncover dynamic logic), which outputs a 0 only when both inputs are 1. If the correct output is 0, both inputs should be 1. The input that isn't is in error, an error that is, itself, the output of a NAND gate where at least one input is 0 when it should be 1. We applied this method recursively, finding the source of all the problems in both our designs in under half an hour.

How To Debug Any Program: https://www.blinddata.com/blog/how-to-debug-any-program-9
May 8th 2019 by Saketh Are

Start by Questioning Everything

...

When a program is behaving unexpectedly, our attention tends to be drawn first to the most complex portions of the code. However, mistakes can come in all forms. I've personally been guilty of rushing to debug sophisticated portions of my code when the real bug was that I forgot to read in the input file. In the following section, we'll discuss how to reliably focus our attention on the portions of the program that need correction.

Then Question as Little as Possible

Suppose that we have a program and some input on which its behavior doesn’t match our expectations. The goal of debugging is to narrow our focus to as small a section of the program as possible. Once our area of interest is small enough, the value of the incorrect output that is being produced will typically tell us exactly what the bug is.

In order to catch the point at which our program diverges from expected behavior, we must inspect the intermediate state of the program. Suppose that we select some point during execution of the program and print out all values in memory. We can inspect the results manually and decide whether they match our expectations. If they don't, we know for a fact that we can focus on the first half of the program. It either contains a bug, or our expectations of what it should produce were misguided. If the intermediate state does match our expectations, we can focus on the second half of the program. It either contains a bug, or our understanding of what input it expects was incorrect.

Question Things Efficiently

For practical purposes, inspecting intermediate state usually doesn't involve a complete memory dump. We'll typically print a small number of variables and check whether they have the properties we expect of them. Verifying the behavior of a section of code involves:

1. Before it runs, inspecting all values in memory that may influence its behavior.
2. Reasoning about the expected behavior of the code.
3. After it runs, inspecting all values in memory that may be modified by the code.

Reasoning about expected behavior is typically the easiest step to perform even in the case of highly complex programs. Practically speaking, it's time-consuming and mentally strenuous to write debug output into your program and to read and decipher the resulting values. It is therefore advantageous to structure your code into functions and sections that pass a relatively small amount of information between themselves, minimizing the number of values you need to inspect.

...

Finding the Right Question to Ask

We’ve assumed so far that we have available a test case on which our program behaves unexpectedly. Sometimes, getting to that point can be half the battle. There are a few different approaches to finding a test case on which our program fails. It is reasonable to attempt them in the following order:

1. Verify correctness on the sample inputs.
2. Test additional small cases generated by hand.
3. Adversarially construct corner cases by hand.
4. Re-read the problem to verify understanding of input constraints.
5. Design large cases by hand and write a program to construct them.
6. Write a generator to construct large random cases and a brute force oracle to verify outputs.
techtariat  dan-luu  engineering  programming  debugging  IEEE  reflection  stories  education  higher-ed  checklists  iteration-recursion  divide-and-conquer  thinking  ground-up  nitty-gritty  giants  feynman  error  input-output  structure  composition-decomposition  abstraction  systematic-ad-hoc  reduction  teaching  state  correctness  multi  oly  oly-programming  metabuch  neurons  problem-solving  wire-guided  marginal  strategy  tactics  methodology  simplification-normalization 
may 2019 by nhaliday
Harnessing Evolution - with Bret Weinstein | Virtual Futures Salon - YouTube
- ways to get out of Malthusian conditions: expansion to new frontiers, new technology, redistribution/theft
- some discussion of existential risk
- wants to change humanity's "purpose" to one that would be safe in the long run; important thing is it has to be ESS (maybe he wants a singleton?)
- not too impressed by transhumanism (wouldn't identify with a brain emulation)
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april 2018 by nhaliday
Information Processing: US Needs a National AI Strategy: A Sputnik Moment?
FT podcasts on US-China competition and AI: http://infoproc.blogspot.com/2018/05/ft-podcasts-on-us-china-competition-and.html

A new recommended career path for effective altruists: China specialist: https://80000hours.org/articles/china-careers/
Our rough guess is that it would be useful for there to be at least ten people in the community with good knowledge in this area within the next few years.

By “good knowledge” we mean they’ve spent at least 3 years studying these topics and/or living in China.

We chose ten because that would be enough for several people to cover each of the major areas listed (e.g. 4 within AI, 2 within biorisk, 2 within foreign relations, 1 in another area).

AI Policy and Governance Internship: https://www.fhi.ox.ac.uk/ai-policy-governance-internship/

https://www.fhi.ox.ac.uk/deciphering-chinas-ai-dream/
https://www.fhi.ox.ac.uk/wp-content/uploads/Deciphering_Chinas_AI-Dream.pdf
Deciphering China’s AI Dream
The context, components, capabilities, and consequences of
China’s strategy to lead the world in AI

Europe’s AI delusion: https://www.politico.eu/article/opinion-europes-ai-delusion/
Brussels is failing to grasp threats and opportunities of artificial intelligence.
By BRUNO MAÇÃES

When the computer program AlphaGo beat the Chinese professional Go player Ke Jie in a three-part match, it didn’t take long for Beijing to realize the implications.

If algorithms can already surpass the abilities of a master Go player, it can’t be long before they will be similarly supreme in the activity to which the classic board game has always been compared: war.

As I’ve written before, the great conflict of our time is about who can control the next wave of technological development: the widespread application of artificial intelligence in the economic and military spheres.

...

If China’s ambitions sound plausible, that’s because the country’s achievements in deep learning are so impressive already. After Microsoft announced that its speech recognition software surpassed human-level language recognition in October 2016, Andrew Ng, then head of research at Baidu, tweeted: “We had surpassed human-level Chinese recognition in 2015; happy to see Microsoft also get there for English less than a year later.”

...

One obvious advantage China enjoys is access to almost unlimited pools of data. The machine-learning technologies boosting the current wave of AI expansion are as good as the amount of data they can use. That could be the number of people driving cars, photos labeled on the internet or voice samples for translation apps. With 700 or 800 million Chinese internet users and fewer data protection rules, China is as rich in data as the Gulf States are in oil.

How can Europe and the United States compete? They will have to be commensurately better in developing algorithms and computer power. Sadly, Europe is falling behind in these areas as well.

...

Chinese commentators have embraced the idea of a coming singularity: the moment when AI surpasses human ability. At that point a number of interesting things happen. First, future AI development will be conducted by AI itself, creating exponential feedback loops. Second, humans will become useless for waging war. At that point, the human mind will be unable to keep pace with robotized warfare. With advanced image recognition, data analytics, prediction systems, military brain science and unmanned systems, devastating wars might be waged and won in a matter of minutes.

...

The argument in the new strategy is fully defensive. It first considers how AI raises new threats and then goes on to discuss the opportunities. The EU and Chinese strategies follow opposite logics. Already on its second page, the text frets about the legal and ethical problems raised by AI and discusses the “legitimate concerns” the technology generates.

The EU’s strategy is organized around three concerns: the need to boost Europe’s AI capacity, ethical issues and social challenges. Unfortunately, even the first dimension quickly turns out to be about “European values” and the need to place “the human” at the center of AI — forgetting that the first word in AI is not “human” but “artificial.”

https://twitter.com/mr_scientism/status/983057591298351104
https://archive.is/m3Njh
US military: "LOL, China thinks it's going to be a major player in AI, but we've got all the top AI researchers. You guys will help us develop weapons, right?"

US AI researchers: "No."

US military: "But... maybe just a computer vision app."

US AI researchers: "NO."

https://www.theverge.com/2018/4/4/17196818/ai-boycot-killer-robots-kaist-university-hanwha
https://www.nytimes.com/2018/04/04/technology/google-letter-ceo-pentagon-project.html
https://twitter.com/mr_scientism/status/981685030417326080
https://archive.is/3wbHm
AI-risk was a mistake.
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february 2018 by nhaliday
Deliberate Practice and Performance in Music, Games, Sports, Education, and Professions: A Meta-Analysis
We found that deliberate practice explained 26% of the variance in performance for games, 21% for music, 18% for sports, 4% for education, and less than 1% for professions. We conclude that deliberate practice is important, but not as important as has been argued.
pdf  study  psychology  cog-psych  social-psych  teaching  tutoring  learning  studying  stylized-facts  metabuch  career  long-term  music  games  sports  education  labor  data  list  expert-experience  ability-competence  roots  variance-components  top-n  meta-analysis  practice  quixotic 
december 2017 by nhaliday
Is traditional teaching really all that bad? A within-student between-subject approach
Results indicate that traditional lecture style teaching is associated with significantly higher student achievement.
pdf  study  learning  teaching  psychology  social-psych  academia  higher-ed  intervention  null-result  field-study  economics  sociology 
september 2017 by nhaliday
THE GROWING IMPORTANCE OF SOCIAL SKILLS IN THE LABOR MARKET*
key fact: cognitive ability is not growing in importance, but non-cognitive ability is

The labor market increasingly rewards social skills. Between 1980 and 2012, jobs requiring high levels of social interaction grew by nearly 12 percentage points as a share of the U.S. labor force. Math-intensive but less social jobs—including many STEM occupations—shrank by 3.3 percentage points over the same period. Employment and wage growth was particularly strong for jobs requiring high levels of both math skill and social skill. To understand these patterns, I develop a model of team production where workers “trade tasks” to exploit their comparative advantage. In the model, social skills reduce coordination costs, allowing workers to specialize and work together more efficiently. The model generates predictions about sorting and the relative returns to skill across occupations, which I investigate using data from the NLSY79 and the NLSY97. Using a comparable set of skill measures and covariates across survey waves, I find that the labor market return to social skills was much greater in the 2000s than in the mid 1980s and 1990s. JEL Codes: I20, I24, J01, J23, J24, J31

The Increasing Complementarity between Cognitive and Social Skills: http://econ.ucsb.edu/~weinberg/MathSocialWeinberger.pdf

The Changing Roles of Education and Ability in Wage Determination: http://business.uow.edu.au/content/groups/public/@web/@commerce/@research/documents/doc/uow130116.pdf

Intelligence and socioeconomic success: A meta-analytic review of longitudinal research: http://www.emilkirkegaard.dk/en/wp-content/uploads/Intelligence-and-socioeconomic-success-A-meta-analytic-review-of-longitudinal-research.pdf
Moderator analyses showed that the relationship between intelligence and success is dependent on the age of the sample but there is little evidence of any historical trend in the relationship.

https://twitter.com/khazar_milkers/status/898996206973603840
https://archive.is/7gLXv
that feelio when america has crossed an inflection point and EQ is obviously more important for success in todays society than IQ
I think this is how to understand a lot of "corporate commitment to diversity" stuff.Not the only reason ofc, but reason it's so impregnable
compare: https://pinboard.in/u:nhaliday/b:e9ac3d38e7a1
and: https://pinboard.in/u:nhaliday/b:a38f5756170d

g-reliant skills seem most susceptible to automation: https://fredrikdeboer.com/2017/06/14/g-reliant-skills-seem-most-susceptible-to-automation/

THE ERROR TERM: https://spottedtoad.wordpress.com/2018/02/19/the-error-term/
Imagine an objective function- something you want to maximize or minimize- with both a deterministic and a random component.

...

Part of y is rules-based and rational, part is random and outside rational control. Obviously, the ascent of civilization has, to the extent it has taken place, been based on focusing energies on those parts of the world that are responsive to rational interpretation and control.

But an interesting thing happens once automated processes are able to take over the mapping of patterns onto rules. The portion of the world that is responsive to algorithmic interpretation is also the rational, rules-based portion, almost tautologically. But in terms of our actual objective functions- the real portions of the world that we are trying to affect or influence- subtracting out the portion susceptible to algorithms does not eliminate the variation or make it unimportant. It simply makes it much more purely random rather than only partially so.

The interesting thing, to me, is that economic returns accumulate to the random portion of variation just as to the deterministic portion. In fact, if everybody has access to the same algorithms, the returns may well be largely to the random portion. The efficient market hypothesis in action, more or less.

...

But more generally, as more and more of the society comes under algorithmic control, as various forms of automated intelligence become ubiquitous, the remaining portion, and the portion for which individual workers are rewarded, might well become more irrational, more random, less satisfying, less intelligent.

Golden age for team players: https://news.harvard.edu/gazette/story/2017/10/social-skills-increasingly-valuable-to-employers-harvard-economist-finds/
Strong social skills increasingly valuable to employers, study finds

Number of available jobs by skill set (over time)

Changes in hourly wages by skill set (over time)

https://twitter.com/GarettJones/status/947904725294260224
https://archive.is/EEQA9
A resolution for the new year: Remember that intelligence is a predictor of social intelligence!
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august 2017 by nhaliday
soft question - Thinking and Explaining - MathOverflow
- good question from Bill Thurston
- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:
- symmetry as blurring/vibrating/wobbling, scale invariance
- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy
comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic
comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy
I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.
To remind myself later:
- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally
- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)
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january 2017 by nhaliday
Learn Difficult Concepts with the ADEPT Method – BetterExplained
Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description.
thinking  education  learning  teaching  tutoring  better-explained  analogy  visual-understanding  examples 
july 2016 by nhaliday
PHYS771 Lecture 9: Quantum
There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Next you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex.

The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs. Once you know what the theory is actually about, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want. This second approach is the one I'll be following here.
exposition  teaching  physics  quantum  tcs  rhetoric  aaronson  tcstariat  lecture-notes  positivity  nibble  thinking  hi-order-bits  big-picture  quantum-info  signum 
may 2016 by nhaliday
Teachers: Much More Than You Wanted To Know | Slate Star Codex
Random Thoughts on the Idiocy of VAM: https://educationrealist.wordpress.com/2016/05/20/random-thoughts-on-the-idiocy-of-vam/
Scott Alexander reviews the research on value-added measurement of teacher quality. While Scott’s overview is perfectly fine, any such effort is akin to a circa 1692 overview of the research literature on alchemy. Quantifying teacher quality will, I believe, be understood in those terms soon enough.

Value-Added and Social Desirability Bias, Bryan Caplan: http://econlog.econlib.org/archives/2016/09/value-added_and.html
The policy that dramatically passes the cost-benefit test is "deselection," better known as firing bad teachers.

What's up? I once again point my accusatory finger at Social Desirability Bias. Rewarding good teachers sounds a lot nicer than firing bad teachers. So when research comes along that potentially recommends both, pundits and politicians don't coolly crunch the numbers. They leap to the recommendation that's pleasing to the ear. So what if the original researchers find that firing bad teachers wins with flying colors? Move along folks, nothing to see here...
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may 2016 by nhaliday
Gradescope
edtech startup cofounded by an ML prof at Berkeley
education  tools  software  saas  webapp  startups  teaching  higher-ed  organization 
april 2016 by nhaliday

bundles : ed

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