HN Books @HNBooksMonth

I have been researching this for a couple of years and can recommend a couple of books that I thought were particularly good:

* Good questions for math teaching (http://amzn.com/0941355519)

* Young Mathematicians at Work (http://amzn.com/032500353X)

* Number Sense Routines (http://amzn.com/1571107908)

* Dr Wright's Kitchen Table Math book (there are three) - http://amzn.com/0982921128

I haven't finished these next two, but they look promising:

* Fostering Geometric Thinking (http://amzn.com/0325011486)

* Fostering Algebraic Thinking (http://amzn.com/0325001545)

I also like the approach of the Art of Problem Solving curriculum, though it doesn't currently have elementary school material. I haven't used it on my own kids yet because they're still too young, but I did buy the set and I think it looks good. If you read "Good Questions for Math Teaching" you will probably modify the way the problems are presented to make them more open-ended, but I like that topics are introduced with a problem that is later explained, instead of explaining then drilling.

http://www.artofproblemsolving.com/Store/curriculum.php

Finally, I thought that this online course was a nice introduction to the approach. It's a pretty short course, but I just put the audio on an mp3 player so I could listen while working on other things and there were only a couple of places where I couldn't tell what was happening in the video.

* https://class.stanford.edu/courses/Education/EDUC115N/How_to...

For a more general book about early childhood education, I really liked

* "Engaging Children's Minds - the Project Approach" (http://amzn.com/1567505015)

* Making Thinking Visible (http://amzn.com/047091551X)

* Learning Intelligence: Cognitive acceleration...(http://amzn.com/0335211364)

Sadly, most of these books are pretty pricey for the page count, but the material I thought was quite good. If you were to get only two, I'd say go with "Young Mathematicians at Work" and "Good Questions for Math Teaching" because they will probably give you the quickest jump start, especially if you can get the "How to Learn Math" course.

If you're interested in where my evidence for the approach outlined here comes from, my main sources are the following books:

* Effectiveness In Learning (cognitive load theory) http://amzn.com/0787977284

* Visible Learning (synthesis of 800 meta-analyses) - http://amzn.com/0415476186

Edited because I put some of them in the wrong spots and forgot links...

The blog post author is a provider of educational software sold to schools, writing to identify problems that he thinks arise from the Khan Academy approach to online education. I'll respond to what he said now that I've read the blog and the earlier thoughtful comments on his blog and here on HN.

1. It is hard to compete against free, especially in education.

Adam Smith pointed this out a long time ago: "In modern times [as contrasted with ancient times] the diligence of public teachers is more or less corrupted by the circumstances which render them more or less independent of their success and reputation in their particular professions. Their salaries, too, put the private teacher, who would pretend to come into competition with them, in the same state with a merchant who attempts to trade without a bounty in competition with those who trade with a considerable one. . . . The privileges of graduation, besides, are in many countries . . . obtained only by attending the lectures of the public teachers. . . . The endowment of schools and colleges have, in this manner, not only corrupted the diligence of public teachers, but have rendered it almost impossible to have any good private ones." -- The Wealth of Nations, Book V, Part 3, Article II (1776).

Thus the only way to compete effectualy against the current system is to offer something free-to-the-user as part of the mix. The current system of public schools in the United States gains revenues of more than $500 billion dollars per budget year for government-operated elementary and secondary schools.

http://www2.census.gov/govs/school/09f33pub.pdf

The blog author seeks to sell products for money to schools, and decries Khan Academy being provided directly to learners for free. Many other providers of educational products and services are doing what is REALLY hard: providing products and services to primary-age and secondary-age learners directly, on at least a cost-recovery basis, attempting to show a value proposition for products and services that families have to pay for after already paying their taxes.

Moreover, the monopoly or oligopoly the government-operated schools have on offering certain kinds of educational credentials ensures that Khan Academy and all competing providers of educational services have to rely on more than just price to win over users.

2. It takes guts to be an entrepreneur.

For anyone attempting to sell a product or service, the first challenge is competing against everyone else providing a product or service (including consumers who do it themselves). One of the entrepreneurs I most admire in the educational products space is a homeschooling materials supplier that has for more than a decade hosted a webpage called "27 Reasons NOT to Buy [Our Product]."

http://www.sonlight.com/not-to-buy.html

That takes courage and honesty. Rather than FUD, a stand-up entrepreneur lets prospective clients know what the competition offers. Clients are happier if they can shop and compare what's on offer from competing providers.

3. You can lead a horse to water, but you can't make it drink.

Khan Academy is provided over the Internet, entirely for free, but not everyone who has an Internet connection makes use of it. (Some readers who have commented here have suggested that the blog author should watch more Khan Academy videos before making a global evaluation of the quality of Khan Academy instruction.)

The public school system is free (that is, tax-subsidized) for all pupils, and the pupils are compelled to attend in default of government-approved, parent-funded alternatives besides. Even at that, teachers can't count on pupils being engaged in their lessons. It's not clear that providing this or that new lesson material will bring about more learning in a compulsory attendance environment, as another reader here pointed out while mentioning the interesting writings of the late John Holt.

4. Khan Academy leaves a lot of room for a better service.

I have watched SOME Khan Academy videos, including some of the most recently revised videos. My children have watched others. We have also done various Khan Academy online exercises. My homeschooled children's main online mathematics course is NOT Khan Academy, but ALEKS,

http://www.aleks.com/

which to date offers much superior exercises (which are more like open-ended problems than mere exercises), much more relentless focus on steady skill development of learners, and a more complete and articulated curriculum for precalculus mathematics. I have urged the Khan Academy collaborators in past replies here on HN basically to reinvent the research ALEKS has done on knowledge spaces in K-12 mathematics

http://www.aleks.com/about_aleks/Science_Behind_ALEKS.pdf

and eventually to build a comparable framework to integrate all the Khan Academy exercises into a coherent curriculum.

Anyone can try out ALEKS for an unlimited number of free, time-limited trials. (I'm not paid to endorse ALEKS; I learned this from a local friend who telephoned the company and asked about this.) So you and the blog author and any member of the Khan Academy staff and any other person with an Internet connection can try out ALEKS and see what is like. What ALEKS conspicuously lacks compared to Khan Academy is audio explanations, and what differs from Khan Academy most conspicuously about ALEKS is that ALEKS costs money, but I'm happy to spend money on ALEKS for four learners in my family.

An even better source of videos on prealgebra topics than the Khan Academy videos are the Art of Problem Solving videos by Richard Rusczyk,

http://www.artofproblemsolving.com/Videos/index.php?type=pre...

also free and worthwhile for mathematical accuracy and engaging presentation, with very challenging problems. Art of Problem Solving links to other videos, some produced in-house and some from other providers,

http://www.artofproblemsolving.com/Videos/index.php?&;

that are also very good.

Competition is good. I like the public school system, the lessons I teach locally as supplemental classes for advanced elementary-age learners, and Khan Academy and Art of Problem Solving and ALEKS all to be subject to competition, the better to have incentive to improve and to do better.

5. There will continue to be an important role for in-person teachers.

Khan Academy will not make in-person teachers become obsolete. I tell all my prospective clients for my own local in-person math classes about Khan Academy before the first day of each new term. A good classroom teacher, who knows the latest research on educational effectiveness,

http://www.amazon.com/Visible-Learning-Synthesis-Meta-Analys...

will take care to form a community of shared curiosity and reality checks on one another's thinking while teaching. There is an abundance of research on effective mathematics teaching,

http://math.berkeley.edu/~wu/Lisbon2010_4.pdf

http://math.berkeley.edu/~wu/Lisbon2010_2.pdf

http://math.berkeley.edu/~wu/NCTM2010.pdf

http://math.berkeley.edu/~wu/NoticesAMS2011.pdf

http://math.berkeley.edu/~wu/CommonCoreIV.pdf

http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf

http://www.math.wisc.edu/~askey/ask-gian.pdf

http://www.ams.org/notices/199908/rev-howe.pdf

http://www.ams.org/notices/200502/fea-kenschaft.pdf

ftp://math.stanford.edu/pub/papers/milgram/milgram-msri.pdf

ftp://math.stanford.edu/pub/papers/milgram/report-on-cmp.html

and much of that research has yet to be implemented in most classrooms in the United States. It's even possible to compete with wholly free services and provide supplemental classes in mathematics that families pay for willingly and without compulsion. The key thing for a teacher to do is build a class that is engaging and that welcomes curious learners who are willing to challenge themselves.

See an earlier HN comment

http://news.ycombinator.com/item?id=2760663

for a bit more on the distinction between problems and exercises.

I wish the blog author, the Khan Academy developers, and everyone teaching mathematics well in spurring the development of better materials and teaching practices so that more mathematics learners learn more mathematics better.

http://educationnext.org/teaching-math-to-the-talented/

⬐ zargon

ALEKS is awesome, I used it 10 years ago to refresh on some math topics. I should try it again just to see how much has improved since then.

⬐ jeffreymcmanus

It's great that you're contrasting Khan to ALEKS. I'm not drinking the Khan kool-aid; my kid just started using ALEKS in the last month and I agree it's terrific. It's really puzzled me why Khan is getting all this attention when ALEKS has been around so much longer (and seems to be better in many respects -- just lacking instructional video). It would actually be terrific to have some kind of integration between ALEKS and Khan -- to be able to see a video lecture on a particular topic would be quite useful for the student.

⬐ ig1

Because KA has had a much bigger impact, millions of people are using it.

⬐ jeffreymcmanus

You have the tail wagging the dog there.

⬐ ig1

KA had a much bigger impact when it was growing word of mouth, long before it got publicity.

This is not time-series data. The study design here (a cross-sectional survey of varying countries, showing a bare correlation between two variables) is not adequate to show causation.

http://norvig.com/experiment-design.html

(By the way, the scatter of data points around the regression line in their plot suggests that the model is subject to large degrees of error in prediction.) It would take an experimental design (randomly assigning one group of teachers in the same country to receive pay raises while another group does not, with before-and-after comparisons of pupil performance) to show that paying teachers more results in higher pupil performance.

http://escholarship.org/uc/item/6hb3k0nz

There have been hundreds of studies of educational interventions over the years,

http://www.amazon.com/Visible-Learning-Synthesis-Meta-Analys...

and many thoughtful international comparisons of teaching practice,

http://www.amazon.com/Teaching-Gap-Improving-Education-Class...

http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...

http://www.amazon.com/Making-Learning-Whole-Principles-Trans...

but none of those conclude that simply raising teacher pay, without changing teaching practices and perhaps also the composition of the teaching workforce, will have much to do with raising pupil performance in any place. Raising teacher pay systematically has been tried in the United States (notably in the state of Connecticut) and has not been shown to markedly raise pupil performance.

An economist who closely studies education policy has suggested that pay and other incentives be used to encourage the least effective teachers to seek other occupations while rewarding the most effective teachers with increased compensation and more professional support.

http://edpro.stanford.edu/hanushek/admin/pages/files/uploads...

Such a policy, he estimates (showing his work in his article) would raise United States educational achievement to the level of the highest-performing countries. This is something worth verifying by experiment, although that will be politically difficult in any state of the United States

http://www.cato.org/pubs/journal/cj30n1/cj30n1-8.pdf

and perhaps in Britain as well.

http://www.economist.com/node/17849199

P.S. I'm curious about why the United States underperforms so much compared to salaries paid to teachers in the chart shown in the submitted blog post.

⬐ qdog

Everyone in the US has the opportunity (or close to everyone) to attend a near-standard public school in the US. Not all countries subscribe to this model, I believe. Although the US average is low, I strongly suspect that the top 10% of US students perform at or above the levels of all other countries.

As for paying more, this increases competition as stated, but you'd need all other factors to remain equal. The class size in US public schools is now ridiculous, 30+ kids per teacher at the local elementary here. Education funding should basically be doubled imho, and the number of teachers per student dropped to 17 or 18 maximum.

⬐ petervandijck

Agree. Triple it, 10 students per teacher, and see performance shoot up.

⬐ d0mine

Monetary reward could destroy intrinsic motivation http://www.youtube.com/watch?v=u6XAPnuFjJc

⬐ quanticle

I'm not sure about that. Doctors get paid a lot, but if you talk to them very few cite money as the reason they continue to practice medicine. I think increasing the compensation granted teachers could pull in talented folks who would make good teachers but also have other things that they like to do and are good at.

⬐ electromagnetic

I know in my highschool all our science teachers had previous 'job' training. The chemistry teacher worked down in mines in (IIRC) Australia. The physics teacher had worked at a lab doing radiological work. The biology teacher actually went from field work, to university professor to highschool vice principal.

⬐ Symmetry

That sort of thing is strongly discouraged in the US by teacher pay structures.

⬐ wisty

My mum is a doctor and a teacher. As in, part time practicing MD (mostly women's health). She gets a decent salary teaching in the private sector, but only really does it because she likes teaching and hates working with sick people. In the public sector, they offered her a very low salary, and told her to get her paperwork together to prove she was senior enough (after over a decade of teaching, but she hadn't kept every pay stubb).

⬐ d0mine

From tokenadult' comment:

Raising teacher pay systematically has been tried in the United States (notably in the state of Connecticut) and has not been shown to markedly raise pupil performance. </quote>

See the video from my comment above to understand why the following obvious suggestion might not work in practice:

An economist who closely studies education policy has suggested that pay and other incentives be used to encourage the least effective teachers to seek other occupations while rewarding the most effective teachers with increased compensation and more professional support. </quote>

⬐ LilValleyBigEgo

> P.S. I'm curious about why the United States underperforms so much compared to salaries paid to teachers in the chart shown in the submitted blog post.

Because in the US if you flunk out of high school you can still get a job at a gas station and supplement it with welfare and food programs.

In other countries if you flunk out of school you starve to death.

⬐ archgoon

Yep, no welfare state in Finland or the Netherlands. I hear over there if you break a leg they just shoot you.

⬐ lutorm

Yeah, my immediate reaction was that it looked like a practically uncorrelated scatter plot with most of the correlation signal coming from a few outliers on the high/low pay ends. At $35k, the outcomes scatter from 100% to 35%, which would be the same magnitude as raising pay from $15k to $55k according to their fit.

There are so many systemic differences between those countries that could correlate with pay that interpreting it is pointless without controls. Not to mention that there's a difference between test performance and learning, there could be "optimization by proxy" effects in play.

Visible Learning, by John Hattie

http://www.amazon.com/Visible-Learning-Synthesis-Meta-Analys...

Teaching as Leadership, by Teach for America

http://www.teachingasleadership.org/

http://www.amazon.com/Teaching-As-Leadership-Effective-Achie...

Understanding Numbers in Elementary School Mathematics by Hung-hsi Wu

http://www.amazon.com/Understanding-Numbers-Elementary-Schoo...

Most of the achievement gap actually comes from parenting, not schools.

John Hattie in his book Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement

http://www.amazon.com/Visible-Learning-Synthesis-Meta-Analys...

reviews a lot of research studies from a lot of countries and suggests that that view, although it is conventional wisdom, grossly underestimates the importance of schools. I agree with you, because the data agree with you, that the most stark differences in school performance are among different teachers in the same school rather than between one school and another, but throughout the Western world, students with tough home conditions tend to get the lousiest teachers and the most underperforming curricula.

Other writers who have important points to make about how to help learners with the worst home environments by improving schools include the collaborators from Teach for America who have put together the book and website Teaching as Leadership

http://www.teachingasleadership.org/

and Eric Hanushek at Stanford with his research on the effects of variance in teacher quality.

http://edpro.stanford.edu/hanushek/content.asp?contentId=60

There is a lot yet to be done that is very feasible (well, except for politically feasible in most states of the United States) to improve the education of the most disadvantaged learners and to help them reach significantly higher levels of academic achievement.

⬐ Alex3917

Good points, all of which I agree with, and I'll check out those sources. The book I snapped the pic from was Equality and Achievement, which is similar to the book you're linking to.

"reviews a lot of research studies from a lot of countries and suggests that that view, although it is conventional wisdom, grossly underestimates the importance of schools. "

I do think it's important to note though that you can believe that the achievement gap is mostly coming from home factors, while also not underestimating the importance of school. That is, you can believe that all kids are basically receiving an equally crappy education. You're certainly right though about the kids from the worst home conditions getting stuck with the worst teachers within schools.

⬐ shasta

And just as importantly, stuck in classes with each other. There's an amplifier effect as a result.

The evidence suggests that . . .

Citation, please? I'm reading a very good book about evidence for best practice in education,

http://www.amazon.com/Visible-Learning-Synthesis-Meta-Analys...

recommended to me by a candidate in the current school board race in my school district, and I'd like to check what the research says with any source you recommend.

Do you have any evidence for any of other assertions in your comment? I will look it up if you would kindly provide citations.