The Math Textbook I Would Buy

I have reams of notes at this point, compiled over a month, scattered across two legal pads, all of them attacking the same issue from a dozen different sides: what kind of textbook would a veteran teacher use?

My First Baldly Unsubstantiated Assertion

Veteran teachers lean on textbooks far less than new teachers do, choosing to build their curricula, instead, from a patchwork of problems and applications and sequences they’ve determined through years of trial and error. Like other teachers in the first thread, I use textbooks for longer practice sets, but little else.

The question hassles me, then, what kind of textbook or supplement would veteran teachers use? This seems like a potentially interesting, potentially profitable, discussion.

My Second Baldly Unsubstantiated Assertion

New teachers teach procedure better than concept. Procedure is important – you’ll never hear me suggest otherwise – but procedural knowledge is a lot easier to teach than conceptual knowledge, which demands of the teacher both a broad and narrow understanding of (eg.) Algebra, an understanding which can clearly explain (eg.) why the constraints of single-variable equations eventually demand two-variable equations which then demand upgraded solution procedures, etc.

I’m not very good at this, I admit, especially in the upcoming second semester of Algebra, but I know that teaching procedure, scaffolding those skills, and differentiating their assessments, doesn’t interest me like it used to. (And it used to interest me a lot.)

I’m very interested in better conceptual teaching and, especially, in teaching conceptual curiosity.

My Third Baldly Unsubstantiated Assertion

My students’ curiosity will make them better and smarter and more capable people in the long run. I suspect this, unburdened by anything sturdier than anecdote, but I know it can’t hurt and I know that I am rarely happier as a teacher than when my students and I discuss a scenario through a mathematical framework that they wouldn’t ordinarily have given a second thought. (The Golden Gate Bridge raised its toll from $5 to $6 in September, for example. What can’t you do with that?)

The fact is that dead-tree textbooks are at a disadvantage here. Like I said before, I am generally uninspired by my textbook’s perfunctory stabs at real-world relevance but even when the textbook stumbles over an interesting image (a ski lift, for instance) the nature of paper means they must apply the entire mathematical framework – the labeled points, the grid, the scaled axes, and the questions – before the student has even given the image a first glance.

They get the process exactly backward. They teach kids to support a math problem with a visual framework rather than teaching them to support visuals – the sort of images they’ll see long after they close their last math textbook – with a mathematical framework.

I can teach procedural fluency pretty well on my own but I need help teaching conceptual curiosity. I want to teach my students to ask questions for themselves and my textbook is no help. I need something else.

The Digital Archive Of Very Interesting Mathematical Media

I can’t put an exact price point on this hypothetical curriculum, but I promise I would pay a lot for a digital archive of very interesting mathematical media, high-resolution images and videos to propel long, rich, curious mathematical discussions and activities.

I want a DVD archive of (or online access to) innocent-seeming photos and videos, beneath each of which lurks meaty, curious mathematics. The publisher must include multiple versions of each digital artifact, each one identical to the last except for an increasingly rigid mathematical framework. (ie. the first clip is an unaltered long shot of a batter hitting a homerun in an empty stadium; the last clip is identical except the publisher has added measurements, labels, axes, a white line tracing the parabola, etc.)

The publisher would supplement the DVD with a small book of concise questions, the sort of visceral hooks we pursue in our What Can You Do With This? series.

What Would You Pay For This?

What would you pay for, let’s say, forty of these high-res digital artifacts and the relevant hooks, artifacts which students could download to their laptops or netbooks and play with, scaling a golden ratio rectangle all over a high-res image of the Parthenon, for example.

I would consider it a bargain at $80, but, I admit, this is my post.

A Postscript On Profit

The profit margin here should entice any publisher. You aren’t printing hundreds of student textbooks. Your printing costs are limited to a small run of color booklets. And some screen-printed DVDs, I guess, but we’re talking about pennies. This wouldn’t be a traditional standards-based textbook, though, so you can’t expect mass adoption. You’ll make your money on margin, not on volume.

Seriously: a good DSLR camera, a good HD camcorder, and a handful of travel vouchers. That’s your overhead.

A Postscript On Bundles

The shameful side to this proposal is that publishers have already budgeted money for this kind of supplement – the same bundled CD-ROMs which have driven textbook prices skyward.

Having just finished a textbook adoption process, sampling bundled materials from several publishers, I can report that in the rare case that these materials aren’t useless, they’re entirely cumbersome, locked down by web-access codes, DRM, proprietary Flash interfaces and constrained to printable textbook pages and videos of talking heads explaining rote procedural skills.

I’m pretty sure this kind of project would suffocate under the weight of any of the big four publishers (though I’d somehow convince myself to cash their checks). It would be great to see a smaller imprint take this on. Takers?

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. Why not do it yourself? You seem like you could easily arrange the material into a handy CD (/DVD) format with a book[let] to go along with it. Once you’ve got that done, you can burn and stamp CDs yourself (or enlist, say, CafePress – $5-$9/ea., depending on your packaging options) and get your “small book of concise questions” printed at Kinko’s (Okay, FedEx Office) if you’re willing to have it bound creatively. (Say, a spiral binding.)

    Sure, your costs would be a bit higher (at around $7-13ish plus shipping) per item than a publisher who did a big run of them ($3-5 each, max, most likely), but you would (1) have effectively total control over what you were giving out, and (2) none of the worry about having a few hundred extra copies sitting around.

    Or, if you felt like it, you could do most of the distribution over the Internet, and ship a CD/DVD as a backup/reference, which would probably not only halve your costs but get it into the hands of a lot more students a lot easier (most teachers would have no idea how to get your materials from your CD to students’ computers or homes, even if you let them). (I would actually be interested in seeing / making that happen.)

    Some options, anyway, if your preferred publisher doesn’t bite. (Or you decide you can get a better deal with one of those.)

  2. Hi Dan, I’ve been reading your blog for quite some time, not sure if I’ve commented before but just wanted to send a hearty “second the motion” to your interest in teaching the conceptual.. framework/curiosity/concepts and not just the procedural parts.

    I’m not a math teacher or anything close to it – in fact, I’ve been embarrassingly math challenged my entire life. But, in the last few years, my involvement with developing content in virtual worlds has suddenly led to more _conceptual_ understanding of mathematical topics than I ever learned in K-12 and college level math. I’ve even found myself feeling almost angry that my math teachers seemed to have skipped the “why it matters” and “what it means” pieces of the puzzle.

    I’m never sure how much of my math ineptitude is my own fault, and at times I’ve been convinced that there’s some biological basis for it because I have SUCH a hard time with things like simple arithmetic (today the Economist tempts me that I may be “dyscalculic” )..

    But whatever my personal challenges were/are, I’m pretty sure most of my teachers, at least at the grade school/high school level, focused primarily on the procedure. Being a “smart kid”, it wasn’t too hard to memorize steps and follow formulas, but despite getting all the way through the college prep math track with decent grades, I came away understanding very little, and remembering almost nothing.

    (I mean, it’s almost embarrassing to admit that as a pretty literate person, I didn’t _really_ understand degrees and rotation and angles until I started constructing things in a game-like virtual world! And I’m a gown up!)

    So, in response to your post, I think you’re on a very good track in recognizing that the personal curiosity that leads to good learning doesn’t come about by seeing graphics like the one pictured above in a text book, but that the _visual_ elements are really, really important. Seeing the effects of changes before I could even begin to grasp the math behind it helped me make the links between the the two.

    For me, a combination of visual + active learning – constructing things, making things, taking things apart, building moving things.. playing with pictures, media, and virtual objects, seeing representations of math concepts that looked like art ( these experiences have done more to ignite my personal curiosity than any class exercise I can recall. Whatever steps teachers can take to help students have THOSE kinds of experiences, instead of the excruciating feeling that you don’t quite get it and definitely don’t know why it matters or what it means, I say more power to you.

    Best of luck in your quest for finding/creating good materials, I look forward to seeing what you come up with!

  3. Dan,
    I find it amazing that in spite of the fact that I am a grade 4 generalist in another country that my frustrations with math programs are the same as yours. We recently transitioned programs from procedural (the same one I used when I was in 4th grade) to conceptual with little in between or curiosity. I think that our new program (Math Makes Sense) has potential but it seems to present the same frustrations as yours.

    I’m off to scan my new curriculum guide and Flickr CC. Wish me luck!

  4. Dan, I’ve been following your blog for a short time, but I love it. I especially love this post. I’m a new math teacher and I do tend to stick to the text book and the procedure, but at least I know it is insufficient and I hope I will do better when I have more experience.

    I suggest you visit Darren Kuropatwa’s classroom blogs (for example, if you want to see a veteran teacher doing exactly what you dream of here. I’ve had the honour of following Darren’s work for a while and all I can say is that when I grow up I want to be just like him.

    Keep up the good work!

  5. I’d certainly buy it for $80*.

    I know there are one or two commercially available CD ROMs out there. I’ve used some images from this one: It’s a simpler version of what you propose: mathematically interesting images with some thoughtful prompts to go along with them.

    * Cheap if it saves my relationship. I think my gf is getting a bit tired of me photographing anything with symmetry, pattern, or numbers in it.

  6. The content would have to be pretty compelling for me to pay for it. It would have to be difficult for an industrious individual with a digital camera and a laptop to create themselves. It would have to be usable and novel. Too often I get excited about something and then once I get into the weeds, it’s either irrelevant (“well I wish I taught spherical coordinates, oh well”) or redundant (“yet another linear regression thing. hoo-freaking-ray.”).

    I don’t want to be discouraging – this project could be the best thing to come around since the digital projector. I suspect a textbook company would just dumb it down, lock it down, and make it difficult to use. What about an existing content provider, like Explorelearning or The Futures Channel or United Streaming?

  7. Hey Dan,

    I’m late to the WCYDWT series. Just invested a couple of hours soaking it all up. Like Christian said on one of those posts: you had me at “hello”.

    Even before John Medina came around I’ve known, viscerally, that visuals trump every other sort of prompt; a strong image or short video like you’ve been writing about.

    You really nailed it when you talked about teaching curiosity while building students conceptual frameworks. Your three Baldly Unsubstantiated Assertions resonate because they align with the real lie experience of experienced classroom teachers. Your summary really crystallized my own thinking about this stuff as well. Thanks for that!

    I’ve been doing Technology Advisor stuff for a textbook company. I keep saying all the content has to be freely downloadable for teachers to use w. projectors or IWBs knowing all the while that’s not likely to happen for the reasons you mentioned at the end of your post.

    But the DIY idea resonates! It seems you’ve already assembled some of the content in the WCYDWT series. Why not do it collaboratively. Build a wiki and invite everyone in. Seed it with your WCYDWT content, include links to lesson plan ideas that came up in the comments, and open it up to further organic growth on the wiki. If the wiki had a tagging feature we could quickly find the content we needed or make custom designed virtual textbooks on the fly buy clicking on a tag.

    The Digital Archive Of Very Interesting Mathematical Media doesn’t need a textbook company to make it. They probably never will. But nothing stops us from doing it ourselves. The only thing you’d have to change is the No Derivatives clause of your cc license.

    What do you think?

  8. Just wanted to share a wiki that is being used with a math classroom. I think this is the direction you want to go in….take a good look at the direct variation experiments and the audio homework! I wish I could claim this as my own work, but it belongs to Mr. Vizza!

  9. I would advise against the “put up a wiki and invite everybody in” approach. It should be more like an open source software project where you control what goes in and other people can provide patches and you decide whether or not they make the main distribution. I think that’d be more satisfying and create better releases.

  10. Elaborating on Tom’s comment…then once it reached a critical mass of awesomeness, you could start charging for access. (If the revenue-generating is important, which, why wouldn’t you want to be compensated for all that work?) Maybe with contributors getting free access or a reduced rate.

  11. I’ve been happy with our new physics “text” this year. It is actually a book on CD. No, it’s not just a PDF of a traditional text but a platform that provides text, interactions, simulations and practice problems that guide students through problems based on need.

    It’s not my dream text but it is a good start. Check it out:
    Looks like they do math too.

    Now for my dream book… students log in from the web and fill out a questionnaire which determines there interests and learning styles. From this point their “text” is tailor-made just for them. If a student has an interest in soccer, they get problems themed around soccer.

    The dream “text” would also crawl a delicious/digg-like site that teachers are feeding with bits from the web and tagging them to fit the concepts taught in class. Teacher’s could be rated by the quality and quantity of their tagging and given a discount on future “textbooks” or supplementary equipment based on their work.

  12. I do think this would work better as a freely developed online resource than as a textbook. Is there grant money for this? Wouldn’t it make sense for school districts to pitch in to create resources like this to replace textbooks long term?

    I hear what Tom is saying about the problem with the wiki framework. I think the dream version of this would need a gatekeeper (or gatekeepers), but it would also support “forking” and “user comments”. For example, a given sequence of images might have a variety of lesson plans, some edited carefully, others posted by users, and all with comments from teachers who had tried them and had suggestions/tweaks/etc. You might also have variant images brought in by different teachers working with different populations etc. (thinking of your ball in motion, I could imaging you’d get different levels of engagement with a basketball / baseball / hockey puck / etc. depending on your group of students).

    As a language teacher, I’ve often wished for a similar resource. In language, there are two things I’d like:

    1. Interesting illustrations/situations to use for conversations/skits (a set of comics with no speech bubbles would be ideal).

    2. Compelling images to array vocabulary, etc. around.

    In all cases, a free license seems vital, because it would allow teachers to add value by altering the image to suit their purpose, and then, ideally, to give the best of those modifications back to the community.

  13. I think Tom Hoffman’s right. An Open Source rather than an Open approach is probably best. But I think the steering committee should probably be small. Then again, Jimmy Wales manages to make Wikipedia work nicely. There are lessons there to be learned from.

  14. Dan–My advice is the same as others, do it yourself. If you sold 1000 copies, you’d have $80,000 to fund your next endeavor.
    Tom– regarding vocabulary pictures–have you seen this contest? Students make short videos to enhance the learning of the vocabulary words on the SAT. I certainly got the meaning of “vacillate” from watching the video? pudding or fruit?

  15. I’m obliged for the feedback and for keeping the commentary running while I spent the last few days trying not to act my age. I’m looking forward to running down the links y’all left me, looking to see if anyone has already made the curriculum I’m after. That would be the happiest outcome here, I suppose, though not the most interesting.

    Anyway, taking the “can’t kids make this?” suggestion (per George) and the “can’t we wiki this?” suggestion (per Darren, initially, and others) one by one, I think the answers are (1) no, and (2) no. And as long as I’m being pessimistic, I think the answer to the question “can’t any teacher make this?” is also (3) no.

    Kids can’t make what I’m after for the same reason that a lot of teachers can’t make what I’m after for the same reason that I would have a lot of difficulty making what I’m after: we lack the necessary broad conceptual understanding of mathematics.

    But I’m hesitant, also, to recruit a bunch of top-notch teachers with a great conceptual grasp of K-12 math and let ’em loose on a wiki. This kind of project, bound up entirely in visuals, really requires a consistent, heavily prescribed aesthetic. (ie., “when we take the pictures, we take them like this; when we shoot the videos, we shoot them like this.”)

    As fun and useful as the first day wiki is, the fact that everyone’s worksheets and activities are, aesthetically, all over the map, helps nobody.

    I know what kind of aesthetic I’m looking for, what kind of aesthetic (I think) would do kids the most good. By chance, I have done a lot of work editing video and designing graphics so I don’t fear the technical challenges too much. This is what I do and do not bring to the table.

    Open source always interests me (in the same way that hip charity work and vogue volunteerism always interests me – personality defect) but I don’t really know how that model fits here or, especially, how I profit off it. I’m not particularly interested in going into hock for a DSLR and a three-chip hi-def video camera only to turn the product over for free. I can’t embed a Google search field into any toolbars here, so what’s the incentive, again, to go open source?

  16. What did you expect from this crowd? :-)

    I certainly think there is a market for what you are selling. And with this blog you already have a healthy portfolio that shows your vision and capabilities. Shop it around! Good luck!

  17. I second the open source idea, not just open. But you haven’t said anything about partnering with a university. This might be just the thing that our multimedia/math departments would think an excellent student research project. I will see if some folks at my institution are interested.

  18. I agree this is one of those things that needs a unified aesthetic. There are plenty of lesson plan compilation sites, but they tend to be frustratingly uneven and difficult to use because of the variety-of-approach problem. Someone up top who nudged both quality and format with an iron fist could probably get things in order, but that’d be just an electronic version of one of those books that has an “editor” — nearly just as much work for them as if they wrote it themselves.

  19. I’m really curious, Jason, about your work on Hot Chalk’s Off-Road Algebra series. To what extent were you involved in the video production? How much could you influence the visuals? That series has fascinated me ever since a link first crossed my desk. It mirrors my intent exact but contradicts my chosen aesthetic completely. But, then, I just talk about stuff that Hot Chalk has actually done.

  20. Something better than videos and graphics for teaching math: programming! I taught an after-school tech club for a couple of years, teaching kids to use the Scratch programming language to make animations and games. Since the goal was fun, rather than any specific content, I did not worry about how much they learned, but many of them learned a lot of geometry, in order to get the effects they wanted. Scratch is a particularly accessible language for beginning programmers. (free from

  21. For people looking for math texts suitable for brighter students (less drill, more problem solving, nicely written) I recommend the Art of Problem Solving series. I’ve only looked at the Algebra and Geometry books, but was impressed by both of them.

  22. I’m glad I came across this blog. My son is a math teacher too. Although his expertise is to teach high school students, the school where he is working like him to teach in college instead. I will let him read your blog to gain insights for his teaching skills. He graduated cum laude recently.

  23. re: Off-Road Algebra.

    I wrote the questions, and I supervised the shooting of the script. A professional (who shoots motorsports for a living) shot the visuals and did the editing.

    There were some pragmatic considerations in shooting — some shots that I had planned in the questions were simply unfeasable to do with real motorcycles rumbling around.

    There are plans to do more videos relating different subjects to math.

  24. Teaching for conceptual understanding requires teachers to understand how children develop mathematical concepts from an early age right up to the teen years.

    We all know high school students who are years behind conceptually even though they can “monkey-do” the procedures.

    Until recently, there hasn’t been a developmental continuum for conceptual understanding in math but fortunately there is one now. The First Steps in Mathematics project from Western Australia is based on their own research and a meta-analysis of research worldwide. There are resources and PD related to First Steps and (for me anyway) it has been the most important and transformative learning of my teaching and mathematics life.

    Full disclosure–I have no financial interest in First Steps in Math. I work for a school district that uses the program extensively.

    Once you ‘grok’ the way students construct concepts, it will change you forever as a teacher.

    I suggest you check it out, let me know if you want any more info. on it.

    By the way, I don’t think you don’t have to *teach* conceptual curiosity as the human brain is naturally curious if we let it make connections between ideas to build concepts (constructivism) naturally. We only *think* we have to teach curiosity because student brains have been so dulled by procedures that they merely memorize without stimulating existing neural pathways.

  25. We only *think* we have to teach curiosity because student brains have been so dulled by procedures that they merely memorize without stimulating existing neural pathways.


  26. Finding my way back to this thread… the question is do you want to create a product for someone to sell or do you want to be a total effing rock star? It isn’t about being altruistic, it is about making something awesome, retaining control over it, and getting help (a handful of) from other cool likeminded people around the world in making it even awesomer. You can do that, or you can sell some videos to a textbook company.

  27. Look, I’d prefer a free model but, as you’ve pointed out before, I kind of fake my way through that definition. There are overhead costs I’d need to recover. How would that work? Off your comment, above, I think you get that this thing can’t be some free-for-all wiki with any kind of loose-limbed aesthetic. Do I find my crowd of collaborators through forums like this one and, once I find that crowd, how do I limit the creation to that group alone? (eg. are we talking some ass-ugly pbwiki set-up with limited admin privileges?) I’m not asking you to hold my hand through every step here, just admitting that I can’t get within two zipcodes of answering any of these questions, while I can, to some hazy extent, answer the question, “How do I convincingly pitch this to O’Reilly?”

  28. After I had read this post tonight, I was a bit behind on my reading, I was spreading top soil in the back yard.

    Then I realised the maths teacher inside me had made a fundamental mistake. I hadn’t taken a picture of the 3 cubic metres of top soil after it was dumped by the truck!

  29. I’m willing to try to do some hand-holding. As you might expect, I have some pretty specific ideas about how this ought to be done, and I think they’re right. ;-)

    We’ll have to have a voice chat if we can pull this within a couple zip codes. One step in that direction: would well designed S5 presentations with embedded video potentially be a sufficient wrapper for these resources?

  30. There are a lot of websites with bits and pieces of what you’re looking for, but even all of those together isn’t enough. There are two parts here, I think.

    (1) Skills and Drills. You want to make sure certain skills, procedural stuff, is covered and mastered. Ideally this should be done on a computer with software that automatically differentiates and provides instant feedback. ALEKS is a good example of this, though it would be nice if it were free and designed to run on clunkier machines.

    (2) A warehouse of topics and ideas. Not necessarily lesson plans, but ideas, problems, examples and techniques. I’ll give you an example: ever taught linear programming? Its cute in the usual way its offered. Two dimensions which tie in the solving systems of equalities and inequalites. However, its still very limited. I’ve recently learnt that Excel has a tool called Solver that will allow you to do much more realistic linear programming problems. Who knew?

    There’s also a part 3. I think the problem of part 2 is bound up in the fact that we teach mathematics in isolation. I have an extremely broad knowledge of mathematics. I have taught everything from prealgebra to calc 2 and have taken such courses as Measure Theory and Homological Algebra. However, its ridiculous for us to expect math teachers to also have a broad knowledge all of science, economics, construction etc.

    Instead we need to integrate math and science together. Science is just overflowing with useful mathematics. Such an integration (not two classes in one, but two classes coordinate) would allow a double helping of math and science and then you’ve got the modeling aspect and the critical reasoning skills that come from discussing data, errors, modeling, etc.

    I’ve been frustrated by the fact that half of my students might have taken physics, or maybe most are in biology but some aren’t, etc.

    I think its a good idea and practical. I don’t think it takes any money, just time. Done over four years (freshmen, then sophomores, etc) you could create a curriculum map and then execute it jointly. Teachers could take turns developing the content (worksheets etc).

    my two cents.

  31. I know, I just posted.

    About text books: we should get rid of them.

    I’ve got plans on creating a website that will have lots and lots of problems. My hope is that over a couple years I’ll have a large resource that I can just give away. Of all the things schools spend money on, cheesy word problems and ridiculously irrevelant color images is not one of them.

    Besides, as you say, we only use them as problem banks. Very heavy problem banks.

    Actually I don’t even use them for that. I just use the supplements and photocopy a worksheet for homework and then create problems for in class work.

  32. I just noticed that there is another kevin posting comments (and who has probably been here longer than me). Should I choose a different handle?