An Aggravating And Energizing Hypothetical

Andrew Leonard:

All we need is one superb remedial algebra course that can be effectively delivered online and, theoretically, the demand for a zillion remedial algebra courses taught at a zillion community colleges suddenly drops off a cliff.

This hypothetical drives me up the wall, oblivious as it is to all the very interesting things that can happen in a brick-and-mortar classroom that can’t yet happen on the Internet.

The Internet is like a round pipe. Lecture videos and machine-scored exercises are like round pegs. They pass easily from one end of the pipe to the other.

But there are square and triangular pegs: student-student and teacher-student relationships, arguments, open problems, performance tasks, projects, modeling, and rich assessments. These pegs, right now, do not flow through that round pipe well at all.

So I’m aggravated by the hypothetical and, especially, its seductive allure to money-men and policy-makers.

But it also energizes me. It makes our job rather clear, doesn’t it?

Promote the hell out of the square and triangular pegs.

Push them into the plain view of anybody who’d love to believe math education isn’t anything more than a set of round pegs ready for a trip down the round pipe.


I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. I have a couple of trapezoid pegs in my class right now too. She started out triangular in September but has since added another dimension onto herself. Kinda cool to see. Thanks for calling these out, Dan.

  2. I was a terrible teacher the first few years of my career. I was/am a round peg. Therefore, everyone else is a round peg. If they don’t get it, that means they are lazy.

    Were my eyes opened when all these different sized pegs started coming into my vision (I was metaphorically blind when I started teaching). All those pegs and one round tube. I ate my words quickly.

  3. I teach at a small school. There are two members in our 7-12 math department (me plus one). We teach so many different courses each year that it borders on insanity (though I wouldn’t trade my current position for anything from a job-satisfaction point of view). This requires some serious efficiency in our out-of-the-classroom planning and reflecting if we’re going to pull off the in-the-classroom teaching bit with any degree of success. You can imagine the temptation to go all round pipe in my courses simply from the demands on my time.

    With that as context, I offer this: Thank you to everyone (Dan, other bloggers, Twitter users, and thoughtful commenters) who through their vision casting, content creation, and continual critiquing of the less-than-ideal inspire me to improve my own classroom, one small step at a time. My students (and I) are blessed by your insights and arguments. I only wish I could participate more in this vibrant online community. Maybe one day soon I will. In the meantime, know that there is one more thankful lurker out there.


  4. I very much agree. I have put zero energy into putting “my best explanations” online since I know it is not more explanations we need, but have instead focus on creating better activities for students to do.

  5. “All we need is one superb online course.”
    “All we need is one superb classroom course.”
    “All we need is one superb dishwasher.”
    “All we need is one superb novel.”
    “All we need is one superb song.”
    “All we need is one superb medication.”

    It’s clear that one good novel wouldn’t satisfy everyone. A novelist has an audience and writes for that audience. It’s also clear that a really good dishwasher would attract pretty much all of the market, if it were good enough.

    So is a course like a dishwasher or a novel? Can one good course replace all its competitors?

    I’ll offer that, no, it can’t, and the reason is because so much of the quality of a course is tailored for the individuals in the room with the kid. Even in a lousy classroom the direction of the course is being guided in a million ways by the actual inhabitants of the desks. Pace, interest, motivation, questions, tone, etc.

    Here’s a heuristic: the more human X is, the less likely it is that one X can work for everyone.

    Or does everyone just reach for The Dark Knight when they want to watch a movie?

  6. Thoughts about a singular fix-it-all online service seems to suppose that remediation is in order because students weren’t given enough resources or enough time. Those are the principal arguments for stand-alone, online services. The students are allowed to pace themselves and they have the internet’s worth of resources at their disposal.

    However, these don’t seem to be the problems from my vantage point. Students aren’t falling behind because we are moving too fast with limited resources. They are falling behind because we aren’t engaging them. They don’t need more time. They need live-action activities that draw them in and give them something interesting to do.

  7. I’m a bit baffled by the hue and cry. My local library has for years had completely free books for people to borrow and learn things from. I taught myself Java to make applets, I installed a bathroom, I demolished and reconstructed an inside wall.
    As far as I know, none of these lead to the demise of any colleges. As usual, anyone who wants to learn things will: the rest will sit in a class and pretend to do what they’re told until released. I can only hope they are secretly fomenting insurrection.

  8. I, too, get frustrated with the ONLINE DRILL AND KILL approach to Math. I have used them and I even think they have a place. HOWEVER, they do not lead to critical thinking or application of the drill and kill concepts we have all taught.

    I have been fortunate to have a High School that is letting me EXPERIMENT with a Math Applications course. It is definitely in the DEVELOPMENT STAGE. But, I love teaching this class. Frankly, my own colleagues are skeptical because it is very unique. I was asked to do this course ONLINE. I tried explaining YOU CAN”T TEACH THIS COURSE WITHOUT STUDENT-TEACHER INTERACTION. I am starting to realize you can’t teach ANY math course without this interaction.

    I love technology but it can NEVER replace that personal interaction between teachers and students.

  9. The real problem with the round pegs, and maybe the roundest of all, is the idea that math instruction is linear and should be conducted at a constant speed so to “finish”by “June”. The second roundest peg is that math is taught, divorced from the real world. Do not teach algebra, explore the ideas that need algebra to understand.

  10. Your point is valid and of course, it It’s true for all courses, not just remedial algebra. But just as it makes sense for teachers to leverage professionally written curriculum and other learning materials, teachers should be orchestrating resources available, not reinventing the wheel. By taking away the busy admin of education ( thanks to say, VocabularySpellingCity) and of lecturing and reinforcement ( thanks to khan), they can add value as teachers. Right?

  11. Michelle Stewart

    February 15, 2013 - 6:13 am -

    Amen for the Square and Triangle Pegs…as difficult as they can be at times! Thank you SO MUCH for sticking up for them/us!

  12. @JohnEdelson:

    Agreed that teachers shouldn’t reinvent the wheel, and it’s a shame for a teacher to spend all of his/her instructional time on skills reinforcement. It would be great if we did a better job leveraging technology to help students practice skills.

    To Dan’s point, though, this isn’t what DC and Silicon Valley are advocating. Instead, they’re advocating using technologies like Khan Academy for both rote practice and teaching, in part because they don’t see a difference, and in part because what is really needed — professional development, human capital, better curriculum, etc. — isn’tscalable.

  13. @Karim. The techies are just techies, I think you are misreading what they are saying about their technology. The techies are producing amazing tools that free almost all professions, teachers too, from drudgery and low value-added work. This is why productivity rises in most industries every year. Only teaching has not shown much productivity increase over the last half century. Its time for that to change!

    The opportunity for teachers is to embrace the technology and start really adding value, not drowning in busy-work which is easily automated. BTW, the remote lectures liberate them from having to spend time covering the material in class. When Khan talks about the miracle of “creating” educational opportunities, it’s more about third world situations where kids, with no decent schooling, have used a cell phone and Khan academy to educate themselves. This is far from the US situation where we have competent teachers at all levels.

  14. Good thought’s dan, but I have to jump in and make a case for “widening the round pipe”. I am a distance educator, and thus am forced into the internet medium, however my passion is square pegs, triangular pegs and especially pentagonal pegs…

    And the pipe is getting wider. When you are forced to work through the pipe…. then you find ways to get build relationships, and build technologies that drive towards open problems and rich assessments.

    So by finding myself in a round pipe… yet a “square” guy, being a software and curriculum developer (curricula ware) I am trying to widen the pipe, and push the interaction envelope!

  15. Dan, this is so true and as a middle school teacher, I find that the students who struggle need a positive connection to their teachers and that is something you do not get from learning on a computer.

    I teach a remediation class for all math students at my school which is smaller and allows me to provided interesting/meaningful math activities (thanks to your 3-Act Math site). I work hard to connect to the students and their needs.

    Yesterday in class, some of the students asked if they could be moved into my pre-algebra class because they were understanding math better than they had before. I attribute that to the fact that I have worked to build a relationship with each of them.

    The students who struggle in Algebra 1 need a person who is going to connect with their struggles and facilitate their learning using different tools including technology. They need a cheerleader to provide encouragement and patience as they change their mindset about mathematics.

  16. a different Dave

    February 15, 2013 - 8:48 am -

    Is it forward of me to suggest that we start talking about action steps? To get a discussion rolling:

    Share positive stories with your friends and family. Talk about the kid who had a breakthrough. Talk about the student who needed someone to listen and found you. Take out the details and mention them on Facebook.

    Be willing to politely stand up for education in a political discussion. It’s not about instantly convincing an opponent of education to abandon their beliefs, it’s about finding a middle ground that moves them one little step toward understanding reality. It’s about repeatedly sanding down the points on their pitchfork.

  17. @Kristen

    I love what you said! We talked a lot about differentiation in my teaching liscensure program, in the sense of having varying levels of rigor through out a lesson. For the last couple of years during my evalulations with administrators most all have noticed that I talk to each student differently. Some I support and encourage, others I start a “math fight” with, some I ask how their day is going (and listen to them) before talking about math, others are uncomfortable asking me for help so I start a discussion with thier neighbor and wait for them to join in. I don’t think about it, it just happens as a by-product of my effort to reach each individual student. Its a different sort of differentiation, but its the one that gets the students to come in with a smile, engage in problems with me and their peers, and leave with a smile. (Sometimes they even come after school for more math!)

    I wonder if anyone has ever counted the smiles on kids faces before, during, and after a session of learning math from software…

  18. > All we need is one superb remedial algebra course that > can
    > be effectively delivered online and, theoretically, the > demand for a zillion remedial algebra courses taught at a > zillion community colleges suddenly drops off a cliff.

    Such a course does not seem to exist at the moment. Where I teach, we have many remedial math courses, with high failure rates. We would notice the advent of such a course, as we would no longer need to run these courses.

    I think it would be great if something like this appeared, but I’m not optimistic that anything like this is about to appear in the near future.

    Consider the huge increase in computing power available to individuals over the past 50 years. What proportion of the population understands fractions now, as opposed to 50 years ago? It is not clear that this proportion has increased.

    I’m wary of people who discuss online education in terms of transmitting information. Its now easy to transmit information to me, but suppose I don’t understand it?

    Is teaching easier than grading homework? Think how far we are from a computer program that can read a written solution and grade it, as opposed to just checking whether the final answer is correct…

  19. John Edelson:

    The techies are just techies, I think you are misreading what they are saying about their technology. The techies are producing amazing tools that free almost all professions, teachers too, from drudgery and low value-added work.

    Karim is reading Leonard’s quote literally, in fact. Leonard doesn’t argue that digital technology will increase the efficiency of existing algebra courses. (Which is your point, and true.) He’s saying digital technology will eliminate those existing algebra courses entirely. Which is true only if we accept a really impoverished definition of “algebra.”

  20. Are you aggravated by someone wanting to make the best remedial online course possible (which can include rich tasks as well, granted, less so than IRL) or are you aggravated by policymakers seeing this is a quick fix and a way to cut costs. I’m aggravated by the latter, not so by the former, as certainly in maths education there is place for both and both serve a purpose. The key word to me is variety, I’m not sure if always having rich discussions all of the time when you’re practicing Integration skills is a good thing.