Tuesday, December 30, 2008

Purdue might require 4 years of HS math for new students

It makes sense for college admissions to require that some incoming students have a better math background, because this has been shown to correlate with how well the students will do, and their chances of actually graduating. You could argue that it seems unfair for a college to require students to complete more math than their high school does, but it's well known that completing the bare minimum at any high school in no way guarantees you admission into any good college. In fact, adding requirements at the college level gives students more flexibility - if they want to get a BA in something non-mathy, they might get away with less math - let that be their choice.

Side note: I find it interesting that articles like this often mention that more math background correlates with better college performance (anyone know of a primary reference for that fact?) Even if teachers find it difficult to articulate exactly why math is good for students, this is a big hint.

Here's the Purdue article:


Monday, December 22, 2008

MIT open courseware - very cool

Yesterday I was browsing MIT's open courseware pages:


The program offers a variety of very high-quality online course materials for undergraduate- and graduate-level classes. In many cases, they also have videos hosted on youtube.

I watched one class on practically solving large sparse linear equations with an introduction to partial differential equations, taught by Gilbert Strang - it was extremely well-taught! If you want to check out Prof Strang's Linear Algebra courses, search for "18.06" on youtube. Here's the first lecture in that series:


This stuff strongly suggests that online learning can very well work for more advanced materials. Personally, I'm guessing that a bottleneck for online learning (besides internet access of course) is the maturity of the students, so that online education resources actually become more effective as the intended audience gets older.

Saturday, December 20, 2008


A few days ago someone pointed me to teachertube, basically a version of youtube which is specific to educational videos. This has a lot of overlap with mathskool, although there are a few significant differences - in particular, mathskool will be much more focused in topic (only math stuff), and will supplement the videos with a rated question/answer system, along with other optional supporting materials.

I'm excited to see that teachertube has already gained a respectable library of videos in a variety of subject areas. This gives me hope that teachers are willing and able to contribute their time to a free online learning resource, and that there is strong potential to build an evolving math education community around mathskool.

Wednesday, December 17, 2008

Algebra video playlist

These six videos offer a quick introduction to the beginning ideas of algebra. I hope to use something like playlists, in the form of "previous" and "next" links, to tie together a string of videos that can be watched in order. The difference is that you can have multiple "next" videos, so that you can choose to elaborate on the parts of the video you care about the most. For example, imagine learning about Pascal's triangle for the first time. From there, you could learn more about similar types of sequences, about other things you can do with binomial coefficients, about proofs by induction, or about how it relates to fractals like the Sierpinski triangle.

Tuesday, December 16, 2008

Terence Tao on multiple choice tests

Just a quick link today to a blog post by Terry Tao (a pretty good mathematician). He recently posted some thoughts on the utility of multiple choice questions.

I remember, from my teaching days at NYU, that many undergrads think that "multiple choice" means "easy". I felt slightly guilty in showing them otherwise. I think Mr. Tao's example questions help illustrate some of the possibilities.

Monday, December 15, 2008

graphic novel / manga learning

When I was a kid, I learned a lot from a series of books by Larry Gonick called "The Cartoon Guide to X" where X could be anything from physics or genetics to computers or the history of the universe. The thing about these engaging, fun-to-read books is that they really conveyed the key ideas and unifying themes behind each subject - at least as much as any text could in a single book. These aren't comic books.

Reading the good math/bad math blog (also by a mathie who's been at google for a little bit), I saw this review on The Manga Guide to Statistics. Apparently it's good. A quick search on amazon reveals that there are even more of these manga guides around. If I had kids, I'd probably buy them these books. Very cool!

Sunday, December 14, 2008

Work in progress

Here's the state of the main video-watching page so far - this is a static image of a php page that's half-way done:

(You can compare this to the paper mock from six days ago, if you're curious :)

Saturday, December 13, 2008

pondering metaverse learning

Reading through a few blogs of others interested in math education, I came across the pioneering efforts of the cool cat teacher to promote online citizenship in a 3d web world (something like second life) among her students. In particular, this blog post outlines some of her key thoughts on the idea. I'll copy of her list of possible advantages teachers can promote for students who learn through an online 3d world:
  • You can go places that can't be visited today.
  • You can overcome stereotypes.
  • Student collaboration
  • Project-based learning possibilities
  • Role playing [think: trying out possible future careers]
  • Potential for group synergies
  • Storage, legacy, and global audience
  • Scenario simulation [think: virtually perform dangerous chemistry lab experiments]
  • Digital storytelling
I don't see mathskool starting out with a major role in the 3d web, but I think these are great ideas towards the evolution of technology and teaching. I expect that many of these possibilities can't come to full fruition until some aspects of the 3d web have improved, such as better bandwidth for the average student, better graphics processors in the average computer (that is moving along nicely, thanks partially to video games :), better user interfaces for online interaction (right now I feel that there's a too-huge gap between how natural it feels to "be" online vs reality), and better systems to enable safe yet open environments for young people.

Friday, December 12, 2008

The Khan Academy and other mathy youtubers

Yesterday the Associated Press published an article about students using youtube videos to help study up on classes on their own time. In particular, they mention a series of videos uploaded by Salman Khan, who has (at my latest check) well over 600 videos on youtube, many of which are math lessons.

The videos seem very friendly, and are easy to watch. I noticed that he uses a different method of recording his lessons - instead of a video of a chalkboard or a whiteboard, he simply uses a video capture of a paint-like program, with a voiceover to explain what he's writing. The result is pretty clear text (on youtube), although it is always harder to write neatly with a mouse than directly by hand.

I'm very happy to see that this idea already has some momentum, and that others are happy to contribute their lessons without any obvious reward (besides good karma and feeling good about what you're doing, of course :). I hope I can integrate work like this into the initial offerings of mathskool.

Thursday, December 11, 2008

a student perspective

I am extremely tempted to analyze this perspective of math education. But, really, this student speaks for herself.

Wednesday, December 10, 2008

math teacher supply and demand

The Center for the Future of Teaching & Learning released a report today about the status of California's teachers, comparing statistics of teacher credentials, experience, and student performance. The study makes several points; for mathskool, I found it most interesting that around one third of California's middle school algebra teachers are considered "underprepared", meaning that they either lack experience (<= 2 years) or that they do not possess full credentials to teach math (see appendix B of the full report - link below - for more details on what counts as "underprepared").

The downward trend in this graph is nice, but having 1/3rd of our students taught middle school math by underprepared teachers sounds a bit scary.

I hate to see hard-working teachers faced with labels that might be considered as demeaning their efforts. Every teacher has to start off as a newbie - this can't count against them. And I believe that every teacher genuinely wants to provide the best education possible for their students, regardless of their credential level.

There are some constructive lessons we can learn from this data. It seems clear that we need more teachers than are available. Relating this to the TIMMS report, it comes to mind that Asian cultures generally hold teachers in much higher regard than we do our American educators. As a graduate student in mathematics, I strongly felt pressure to avoid educational positions, as these are viewed as a "way out" of doing "real math" -- at least, that is the perception I had. And the percentage of our national budget which is allocated to education is a fraction of that we spend on defense. All of this adds up to a discouraging environment for potential future educators. If you're good at something, why teach it for less respect and less money, when you can have a better life working in industry, or at least in higher education (college or other research-friendly places) ?

I don't think there is a silver bullet toward improving the state of our education system, but I do believe that a general agreement in attitude among a strong community of educators can be the start of a better system - especially with a little political support. It is my hope that mathskool can play a role in empowering such a teacher community, by giving great, experienced teachers a stronger voice, new teachers a source of guidance, and our students an effective new resource for learning which is at once easy-to-use, non-intimidating, and responsive to their feedback and desire to understand.

Information on the report:

Tuesday, December 9, 2008

TIMMS: good work - now let's do better

The latest TIMMS (Trends in International Mathematics and Science Study) report came out today, with data from 4th and 8th grade science and math student scores from many countries throughout the world. TIMMS is directed by the International Study Center at Boston College. Every four years, they gather data about how well students perform, on average, in each of several different countries (and some individual US states) in some key areas within math and science.

I'm going to focus on 8th grade math performance results, since that's the most pertinent to mathskool. Based on this table, the average US student score (8th grade math) was 508. This ranks 9th in the world, and is pretty far behind several Asian countries lead by Taipei with 598. It's slightly above the international average of 500.

There are a few ways to look at this data. Some, such as Sam Dillon from the New York Times, are focusing on the fact that our scores have improved a bit since 2003 (cf. this table). Others, such as Maria Glod, Washington Post, point out that we're still way behind the Asian leaders in education.

I'd like to congratulate the hard work and improved results of our teachers and students. We're headed in the right direction. But at the same time, it would be great to see our students perform at a more competitive level. If we saw our average Olympic game performance was 9th in the world, we wouldn't say "hey, it's still top 10!" We would push for the gold, and if I can be any part of that, then I'd like to contribute.

Below is a chart comparing the 2007 TIMMS scores of the top 11 countries versus national GDP per capita, as a sort of measure of each country's wealth. I've circled South Korea and Taipei as doing particularly well, and the US and England as having room for improvement, especially considering our per capita GDP.

I got the GDP data from this wikipedia page, which credits the data to the CIA.

Monday, December 8, 2008

lessons from video #2

There will probably be a few improvements over time as I figure out how to produce better math lesson videos for the site. Some tips:
  • Write big! I'm aiming for a letter height that would allow me to have about 7 lines from top to bottom of the video view. Some quick testing seems to show that trying to fit 8 or more lines in results in text that is too small.
  • Don't use fine point markers - use the big ones - also because readability on youtube videos is challenging.
  • Record in short takes, say 1 minute or so each. This allows for easier re-do's when something goes skewampus. I also step out of the frame at the end of each take, and back in at the start, to preserve continuity.
  • Before you start recording, check that the video frame includes the entire area (such as a whiteboard or chalk board) that you want to include.
  • Check for distracting lighting elements, such as reflections, glare, or shadows.
  • Be aware of any branding or slogans on your clothes. I'm wearing a google jacket here, which is ok, but in the future I plan to wear plain colors to avoid any mistaken associations.
The second video (shorter, more readable than the quadratic formula one):

paper mocks

Don't you love the amazing top quality design work of aesthetically-pleasing companies like Apple? Don't you wish all websites could implement easy-to-use, nice-looking interfaces that worked on basically every web browser? Me too.

Unfortunately, the nice round figure that is the mathskool budget does not allow for fancy design tools. Hence I present the first slightly-low-tech mock for a video-watching page on mathskool (click to bigify):

The idea is that users can search or browse for videos they'd like to see from the frontpage, and from there arrive at a video-watching page which clearly associates the given math video with supplementary materials, such as links to subsequent videos to watch, other sites exploring the topic, or a PDF of worked example problems. From the same page, users can also view questions and answers based on the topic of the video (there might be more than one video per topic), rate the video or the related questions, or bookmark it as a favorite for easy reference.

Sunday, December 7, 2008

first video: the quadratic formula

The first video is up on youtube! It's a two-parter on the quadratic formula:


I learned a few things putting this together:
  • youtube currently supports higher quality video than google video, but with a 10 minute limit
  • google video allows longer videos, but the quality is not good enough for typical slides or board writing
  • it takes a while to compress and upload videos!
Despite the 10 minute limit being cumbersome, I think we might be able to use this as a constructive constraint, in that it enforces short videos which students are more likely to actually watch. I've seen first-hand how challenging it can be to compress a certain amount of material into a short time-limit -- my first video is about 20 minutes! I'll have to work on this for my own video contributions.

Saturday, December 6, 2008

tips for teachers creating videos

Here are a few tips for teachers who are interested in contributing videos to the initial offering of mathskool:

The idea is to create a brief (say, 10 min or less) presentation about a single, focused topic. Some students are self-motivated, but anyone is more likely to watch a <10 min video that covers the one part they want to learn or review instead of a comprehensive 40 min video, part of which may be redundant to the student.

Once mathskool is set up, it will support sections for various types of supplementary materials for each video. The design will prominently show links to "next" videos that the student may want to explore immediately after watching the current video; you may also indicate "prerequisite" videos in case you assume some knowledge in your lesson. This is meant to encourage teachers to break down longer lessons into smaller pieces, and then string those pieces together with links so that students can easily follow.

What's a good outline for a single video? I don't want to constrain the creativity of the teachers - I can imagine many different types of information being expressed in many different ways. But, in case it helps, here are some possible outlines for short lessons, based on the type of lesson at hand.
  • Introducing a new method of solution (e.g. solving quadratic equations)
    • Define terms and clearly state the general question to answer
    • Give a concrete example of the question
    • Explicitly state the general solution, and how to apply it
    • Solve one or more concrete examples

  • Introducing a new definition or concept (e.g. the idea of a function)
    • You could frame the concept in terms of how it is useful - what problem is made easier using this idea?
    • Clearly and explicitly define the new concept
    • Give several examples and non-examples
    • If appropriate, solve a problem using the new concept

  • Working out examples
    • Very briefly review the idea being illustrated by these examples
    • For each example, start by clearly stating the problem to solve
    • Work through each step carefully, writing down and saying aloud the process
    • Write out the final solution
    • If appropriate, explain how this demonstrates the idea being illustrated

Friday, December 5, 2008

mathskool headquarters

As of today, mathskool now has an official headquarters. With a little help from Ikea, Target, Wal-mart and Fry's, the office is now fully equipped with all the essential tools of any productivity center:
  • bookshelf with some math books
  • pen/pencil holder and notepads
  • whiteboards
  • docking station for the macbook
  • mini-fridge
  • ramen noodles

the stuff:


Kepler (the dog) offers moral support:


Thursday, December 4, 2008

Introducing the mathskool blog

Welcome to the mathskool blog! Here you'll find updates as we build the site, and - eventually - news about the site once it's up and running.

mathskool is about connecting motivated students and great teachers. Imagine a version of youtube where every video is short and focused on a single math topic, such as the Pythagorean theorem, the quadratic formula, or the fundamental theorem of calculus. Now imagine we replace the (often inane) comments with an interactive forum of questions and answers, sorted by user votes for quality and usefulness.

Any teacher is free to upload any video for a topic, along with tags for related topics, their teaching notes, sample questions, sample answers, graphics, data files for applications, embedded interactive applets, or links to related sites. When there are multiple videos for a single topic, students can vote up the ones they like the best. It's my hope that the videos and community can enable students to use mathskool as a complement to their regular classes, as a way to review material, or to explore and learn independently.

That's the idea!

And the (ever-so-slightly-ambitious) goal is to launch a working beta by January 1st. Go mathskool!