Posts

Comments

Get Posts by E-mail

When we parted, I described the depressing character of the McGraw-Hill Algebra iBook. Since then, I’ve had a chance to review Pearson’s offering in the same category and, in every way that interests me today, it’s every bit McGraw-Hill’s equal. (In a blind taste test, the only way to tell Pearson from McGraw-Hill is that Pearson includes more embedded multiple-choice quizzes and fewer videos.)

My question, again: what could have been done here? Were the publishers’ ambitions stifled by Apple’s iBook Author tool, which couldn’t accommodate the vast scope of their designs? Or did the publishers lack ambition, and we’re still waiting for a band of enterprising math education bloggers to quit yapping about how awful everything is and release their own curricula with iBooks Author?

Unsatisfyingly, the answer is “a little bit of both.”

Let’s set aside some of our perennial complaints about math curricula. Yes, they are prone to all kinds of mathematical errors. They pander to kids with snowboarders and breakdancers and whatever else a middle-aged publishing executive thinks kids think are cool. They are written by committees who may never meet, who consequently lack any organizing principles to ensure that the goals of one chapter adhere to those of the next.

We could fix all of those problems in a print product. The problems that are most intriguing to me to me are the ones that are endemic to the print medium. Those are the problems that a digital platform like iBooks Author should help us solve. Here’s a monster:

Textbooks rush to the highest level of abstraction on a context as quickly as possible.

That isn’t a statement about the balance of pure math and applied math in our curricula. Both kinds of problems require abstraction. I’m saying that print products spend very little time letting students decide what features of a pure or applied context are fundamental and which are forgettable. I illustrated this process for applied math last week but the same is true of pure math:

Tell me two numbers that add up to five. Now find me three more pairs of numbers that add up to five. How could we draw a picture of those pairs of numbers? What would that graph look like? Would the points be scattered around randomly? Would there be a pattern?

Print products don’t let our students participate in that abstraction. They just do it. They define x + y = 5 and they describe its graph. They have to, really. The textbook serves a useful purpose as a reference text. At some point, it must define the vertex form of a parabola. It must describe the graphs of equations in standard form. It isn’t enough that the all of those formulas live online in different places. Internal coherence matters.

But textbooks also want to be instructional materials. They want to set up activities and ask questions that help students learn the vertex form of a parabola and learn how to graph equations in standard form.

Those two goals — the goals of a reference text and the goals of instructional materials — cut across each other. On one page you have the textbook asking you interesting questions about shadows and similar triangles. On the opposing page, it fully answers those questions and explains how to apply similar triangles to shadows. It’s like watching a suspenseful movie on one half of the screen while the ending loops over and over again on the other half.

It’s an enormous problem. It makes math too simple for some students by doing important work for them. It makes math too intimidating for others, by introducing math in its most abstract form. That enormous problem results of the limitations of the printed page. Paper is expensive and heavy so you have to make the most of it.

iBooks Author goes some distance to help us fix that problem, to resolve the tension between the textbook as a reference text and the textbook as instructional materials but the publishers either didn’t have the same sense that this was a problem or they sensed the problem and were uninterested in solving it. You can add a new page to your textbook in iBooks Author at the cost of zero dollars. Another page in iBooks Author adds zero pounds to your student’s backpack. The publishers could have afforded to let those problems unfold and breathe, but they didn’t want to or didn’t know how.

Watch how easy this is. Start with this problem from McGraw-Hill:

It’s abstracting the problem right in front of students, finding the first and second order differences. Put all of that on the next page. Start this problem with the sequence 32, 18, 8, 2, 0, and ask them:

What could be the next number in this sequence? Give a reason.

Students get the opportunity to look at the numbers and notice that they’re decreasing and then notice that the decreases are decreasing. You have the same high ceiling for exiting this problem. It’s on the next page. But you’ve lowered the barrier to entry for several more students and given everybody the chance to develop some number sense.

And that was pure math. Applied math is even easier:

Push all that abstraction onto the next page. Start here:

Suppose the average height of a man is about 1.7 meters, and the average height of an ant is 0.0008 meter. What are different ways we can compare their two heights?

Let me invent a few student solutions:

  • The man is a lot taller than the ant.
  • The man is 1.6992 meters taller than the ant.
  • The man is 2,125 times taller than the ant.
  • The man is three orders of magnitudes taller than the ant.

Part of the process of abstraction is to decide what makes some of those responses more useful than others? Students need to see that the first isn’t precise enough; the second doesn’t indicate the relative difference between the man and the ant (ie. the ant could be 10 meters tall, provided the man is 11.6992 meters tall); the third, under some circumstances, is more precise than you need (ie. the relative size of planets); and the fourth, under other circumstances, is just right.

Again, we’ll get to the reference material on the next page. But the only reason for including the reference material on the same page as the instructional material is to accommodate the cost and weight of paper and ink, all of which are totally irrelevant to the production of an iBook.

In that respect, iBooks Author solves a huge problem, but it doesn’t solve it well enough to be worth my while to develop for it. The best textbook I could design with iBooks Author is still one that I’d have to modify heavily for use in the classroom.

Here is the kind of page you can design in iBooks Author (jumping off our recent discussion):

But here’s the kind of page I need:

You see the difference? I’m not just asking the question to engage students. I need to know what they think. I need to know if they even have the first, most concrete clue about the height of lampposts. It’s curious that even though students own their iBooks forever (ie. they can’t resell them or give them away), they can’t write in them except in the most cursory ways.

Even curiouser, these iBooks could all be wired to the Internet and wired to a classroom through iTunes U, but they’d still be invisible to each other. Your work on your iPad cannot benefit me on mine.

Check out how awesome that could be:

Again: low barrier to entry. The student’s answers from the last screen prepopulate the table in the next.

The student might sense that one of those points was incorrectly chosen and check her work. Or maybe the student wasn’t expecting any kind of pattern to emerge so she’s nonplussed by the haphazard, non-linear arrangement of her points.

So then we pull in every point chosen by every student in the class and we finish the abstraction, examining points that deviate from the pattern, assigning variables to the pattern, giving the pattern a name, then creating and identifying other similar patterns.

Print textbooks are powerless to facilitate that moment right there. Teachers can’t facilitate it, not at anywhere near the speed and ease I’m suggesting. iBooks Author can’t facilitate it either, but if it could — if it had some kind of “Q&A” widget that lived alongside its other widgets and basically copied all the options from Google Forms — I’d find the platform difficult to resist.

But iBooks Author doesn’t exist for the pleasure of math education publishers or even education publishers. “This is about Apple versus Amazon for who will sell digital literature in the future,” says Audrey Watters. “This isn’t really about textbooks.”

iBooks Author serves publishers, period. It’ll help you publish your Firefly fan fiction, your autobiography, or your Nana’s recipe collection. It’s extremely useful, broadly speaking, which inevitably means that, narrowly speaking to math education publishers, it’s much less useful.

64 Responses to “It’s Called iBooks Author, Not iMathTextbooks Author, And The Trouble That Results”

  1. on 20 Feb 2012 at 7:13 amEvan

    What role does the teacher play in this discussion? I’ve accepted the fact that the textbook I use for my 5th graders is mostly a source of practice problems, and that all instruction/discussion/construction will come from me. That seems a little dismal on the surface, but isn’t that the way things should be? My kids are learning in a group, not in a cave. Even in a very connected classroom, isn’t the best ‘app’ for differentiating, filtering, adapting, reacting, etc the meatbag in the front of the class?

    Also, so when are you going to make something better? I mean that sincerely, not snarkily. No attitude implied.

  2. on 20 Feb 2012 at 7:24 amClimeguy

    @Evan Dan can’t do it alone. We need to do it collectively. And that of course is the rub.

  3. on 20 Feb 2012 at 7:43 amEvan

    @Climeguy That’s essentially what I was getting at. What’s getting in the way of making it a reality? With the proliferation of devices like the iPad, and the low cost of entry to developing content, it seems like this is an area ripe for an OpenSource-like revolution. Let’s make this happen.

  4. on 20 Feb 2012 at 8:03 amChris

    This is a great post, but I don’t understand the last three paragraphs, and I don’t think they follow from the body of the post. I guess my confusion results from a couple things. First, of course, you can’t make a final judgment on iBooks Author based on version 1.0. Second, it’s not clear that the Q&A widget you mention can’t be created using Dashcode. (The merging of data from other students would probably be problematic, but I don’t use google docs, so I don’t know what features you’re thinking of.)

    I guess to me the interesting thing about iBooks Author is that it renders the big publishers irrelevant. Of course it has tons of limitations right now.

  5. on 20 Feb 2012 at 8:04 amClimeguy

    Evan says: “Let’s make this happen.” I love it.

  6. on 20 Feb 2012 at 9:04 amDavid Cox

    I’m not just asking the question to engage students. I need to know what they think.

    I think that makes all the difference and requires a tremendous amount of content/pedagogical understanding on the teacher’s part. This makes me wonder if the texts aren’t written the way they are for a couple of reasons:

    1. Misunderstanding of higher order thinking (as discussed in Scott McLeod’s recent post). You’re opening with higher level questions that have multiple entry/exit points that not only give you (the teacher) a ton of information but allow the students to construct meaning on their own terms.

    2. Fear that a teacher won’t really know what to do with the open ended questions you’re asking in the front end. This stuff can get away from a teacher quickly. I don’t like the “teacher-proof” phrase I’ve been reading lately, but it may kinda fit.

  7. on 20 Feb 2012 at 9:17 amRiley

    The interaction you envision at the end of this post sounds great, but like David says, a teacher would either need to a) be trained on this or b) invent this. I think so many of us end up reinventing our curriculum because we don’t understand or are otherwise unable to use the materials we have.

    The stacks of designs for a BetterLesson competitor are sitting around in my filing cabinet, and I imagine in a lot of teachers’ filing cabinets. It’s hard to envision a way to mass-distribute any materials in a way that the teachers receiving them could understand them to the necessary degree. I have been assuming for the last couple of years that we are headed towards much smaller levels of distribution or much higher levels of engaged training for teachers. We all acknowledge that students need to form knowledge in their own heads, but there’s a tendency to slip into the idea that teachers are somehow superior and can watch a video or use an iBook and just absorb training from external sources.

    I’ll cut the rambling off with this: I think the lesson you’ve imagined in software is beautiful, and making things like that possible is why I got into education software. We have a distribution problem that needs to be solved first, or at least in tandem. I think it’s coming soon, but I don’t know exactly what it looks like. I think everyone in a school building will need to know how to program a computer if we want this sort of thing to become a reality.

  8. on 20 Feb 2012 at 9:46 ammr bombastic

    Do you believe that the bigger problem is that teachers are not able to make lessons like your examples on their own, or that they actually view the current books as good instructional guides? It seems like you are basically proposing that the books incorporate “good” lesson plans.

    I like your work, and would greatly appreciate a book with usable lessons that a student might also have a chance of reading on their own. On the other hand, I am a little concerned that a book like that could end up being overly scripted and misused as an improved version of KA instead of addressing the problem of far too few competent math teachers.

  9. on 20 Feb 2012 at 9:47 amDavid Wees

    I don’t often point out posts I’ve written from my own blog, but in this case, I feel like we are getting at the same point. Here are the features that a digital textbook should have (or at least the authoring tool for textbooks should allow to be included.

    As David pointed out, Dashcode would allow for these types of issues to be resolved, but honestly, it’s not natural for ePub. The format we SHOULD be using for textbooks is HTML 5, and instead of textbook companies being people who deliver a copyrighted product, they should become consultants on designing products for school districts to own and deliver for their students. In the long run, I have a feeling that open licenses are inevitable for schools, and that textbook companies should be expecting much less profit for what they do.

    I suspect that most (if not all) of the major textbook publishers have read my post, and they almost certainly follow your blog. They KNOW that what they are doing isn’t either the best pedagogy, or the most sustainable model for schools. The problem for them is, any significant change/solution to either problem is going to result in gigantic “losses” in profit for them.

  10. on 20 Feb 2012 at 10:01 amblaw0013

    They are written by committees who may never meet, who consequently lack any organizing principles to ensure that the goals of one chapter adhere to those of the next.

    An insight gained from experience, no?

    [No. — dm]

  11. on 20 Feb 2012 at 10:10 amKarim

    (Forgot to include this):

    The examples in the post start open-ended, but eventually converge to a “right” answer: a linear equation; the height of a light pole. For these, perhaps iBook + extra pages + crowd-sourcing is sufficient to scaffolding the problem-solving process, and in this way is a huge advancement over traditional books.

    But what about questions that don’t have a “right” answer, e.g. ones that begin with “Is it fair that…” or “Should…” or “How would this influence your decision to…?” Has anyone seen effective examples of these in an [asynchronous] online/iPad environment, or are blog comments the best mechanism we’ve come up with?

  12. on 20 Feb 2012 at 10:38 amblaw0013

    Dan, we had some brief back & forth on instructional text vs. reference text. I understand better now your meanings for both terms.
    And so now I argue even more strongly for the instructional text to be (almost) all that should make up a textbook.
    The reference text, as you allude to it, seems to assume a particular way of interpreting a problem, to demonstrate a particular way of analyzing/solving a problem, and to silently indicate this was the only correct/good/smart way to have done so.
    I prefer to work toward enacting an approach to mathematics education that works very hard to build (mathematical) autonomy and (mathematical) authority in children.
    Many mathematics educators who see themselves first as epistemologists question the possibility for a textbook written in advance of the child (or the children assigned to any one classroom). This would include Constance Kamii, Les Steffe, and — from my understanding — the CGI crew of Carpenter, Fennema, Franke, Levi, etc. I believe the same argument would be made by those who promote a Culturally Relevant Pedagogy, as would John Dewey himself (see The Child and the Curriculum).
    So, as a curriculum author myself, rather than sound as though I am refuting the whole idea of or potential for a curriculum, I am fascinated by the potential of the dynamic rather than static nature of what an electronic curriculum might offer.
    Putting the rich problem in front of the “how to do it” is already a well-known curricular practice (not necessarily one that sells well, however).
    Your final example, of a space in which students could play and interact and collaborate, and the teacher could draw upon, and the students could modify themselves, is very intriguing.
    Wolfram’s CDF seems to have great potential, as do most graphing tools and dynamic geometry tools. My concern about embedding things like this is when do they become too much “explore until you discover what I want you to see”; rather than true mathematical microworlds–my extension of Seymour Papert’s notion of how children become mathematical through generating their own relationships and rules governing these relationships by programming/building within the dynamic space a computer can help to simulate. When they can act as a micro world, they can function for the learner as my paper and pencil (and sometimes only my mind) can be used to represent a rich mathematical, and then act on these representations to enhance my ability to explore.

  13. on 20 Feb 2012 at 11:27 amBryan

    Like blaw0013, I love your examples of how technology can offer a dynamic, interactive, exploratory environment that paper certainly limits. To me, these technological components should always be a supplement to investigation and not a sole means of curriculum organization. In this way, I wonder if it would be better to focus more on technological tools that aid experimentation and less on transferring/recreating curriculum?

    I was also interested by the distinction between the textbook as reference vs instructional material. As has been already mentioned, the idea of a reference text seems to ensure that students will be learning about someone else’s mathematics and never engaging in creating or doing their own mathematics. It may be naive, but I would argue for taking any such reference material out of the hands of students. I guess that leaves us with deciding what, exactly, instructional material should look like (which, it seems, you are pursuing). I’m not sure we can create one(s) that can be distributed across different learning communities. Perhaps instead, as mr bombastic seemed to be alluding to, teachers need to be trained/educated/trusted/whatever in creating explorations that are suited to their specific learning community?

  14. on 20 Feb 2012 at 11:31 amDavidC

    For all your criticism of the Khan Academy, it seems like they might be the people most ready to think about the technology required to realize the sort of textbook you’re talking about.

    I’d love to see people like you involved with them (helping to address the criticisms you’ve leveled), if they aren’t already.

  15. on 20 Feb 2012 at 11:41 amBowen Kerins

    I’ve used transparencies and an overhead projector to achieve the effect you have for the graph of x+y=5, but obviously it’s much more efficient and cool with technology as the aggregator.

    Woo, a shout out for our cover graphics! Quick story about the Algebra 1 cover of CME Project: we didn’t care about the snowboarders. Sure it’s dumb, but what SHOULD be on the cover? All I care about is that it’s easily distinguished from other books by color and by sight. No kid that I know of will go “Holy crap a snowboarder, NOW I love math”. That kid will probably enjoy the next shiny object too.

    But the graphics designers at Pearson also put the equation “y = mx + b” on the cover, and our book actively tries to work on multiple forms of linear equations, with the slope formula as the basis. We don’t use y = mx + b much. So we told Pearson to change the cover, and they did. I’ll bet if we told them to change the snowboarder to… um, what exactly?… they would probably do that too. What SHOULD be on the cover? Nothing? You must not have a copy of our Precalculus book, because its wakeboarder is totally badass.

    There is a lot more to say, so I’ll write a post on my own blog sometime soon about these general comments about textbooks: “They are written by committees who may never meet, who consequently lack any organizing principles to ensure that the goals of one chapter adhere to those of the next” and “Textbooks rush to the highest level of abstraction on a context as quickly as possible.” I don’t feel these are true about our work. I’m guessing they were meant as general “ills of the textbook”.

    The mathematics in CME Project was written by a small core team who met nearly every week for five years. Its organizing principles are quite clear and specific, and one thing I feel very proud about is that the chapters’ goals are quite closely aligned and carefully sequenced. We keep hearing from teachers amazed at how well students handle challenging content in the back half of our books because they’ve been set up with the right mindset and skills from earlier activities.

    I also think this is a HUGE issue with crowd-sourced curriculum. Coherence across the grades is important and helps kids see the big picture of math. How could a crowd-sourced curriculum have a set of organizing principles that everyone agrees to work under, or write an Algebra 2 lesson that piggybacks on the big ideas learned in Algebra 1?

    That’s for another time though. For CME it is true that the math design team and graphics design team had relatively little contact. I agree that most textbooks transition to the abstract far too quickly, and some of that is forced by the goal of being a reference. Most decisions you make to spend more time on “open” problems increase the page count because you must still bring things to a conclusion. With interactive texts, page count is no longer a cost issue. (Sort of: it still costs money to design each page.) Hopefully we will see this sort of transition.

    Also, just out of curiosity: what stops a kid from “flipping forward” in an interactive textbook like they might in a paper textbook? Often while teaching I mirror a book’s lesson without telling kids that we’re doing so, in order to stop them from reading the upshot instead of learning it themselves.

  16. on 20 Feb 2012 at 12:55 pmTyson Spraul

    I happened to be reading an article today as I try to integrate Scratch (a programming environment for kids) into my 4th grade classroom, and I came across a quote that I think is relevant to the recent conversation on this blog about iBook Author and the problems of with print media.

    “In Mindstorms (Papert, 1980), I asked (choosing one out of a vast number of possible examples) why the quadratic equation of the parabola is included in the mathematical knowledge every educated citizen is expected to know. Saying that it is “good math” is not enough reason: The curriculum includes only a minute sliver of the total body of good mathematics. The real reason is that it matches the technology of pencil and paper: It is easy for a student to draw the curve on squared paper and for a teacher to verify that the assignment has been done correctly.”

    Lots more good stuff in the article:
    http://papert.org/articles/school_reform.html

  17. on 20 Feb 2012 at 1:48 pmScott Powell

    I know exactly what you are talking about. I really think that wolfram has a much better solution check out education.wolfram.com and you will see a textbook with a combination of their widgets and wolfram alpha. An added bonus is it is free. I think that Texas instruments Nspire navigator system would solve the other problem.

    You could send out a quick poll with the question about numbers adding to five then aggregate the data and send it back ou to graph. You would have it separate from the text but still a nice combination of text with embedded stuff and a handheld to do further exploration

  18. on 20 Feb 2012 at 3:20 pmDavid Petro

    I have to say that I found iBooks Author severely underwhelming. Out of the gate it looked so promising (and I am still not completely giving up) but when I tried to use it to actually create an “iBook” I found it totally clunky and not very intuitive.
    But there was one particular part that really bugged me. You have the ability to create a table of value, graph them and even give you the line of best fit. I was so excited when I saw this feature until I “published” the book. Once published, the table and graph become static. What the heck is the point of that? A totally missed opportunity for something dynamic.
    Personally I have been experimenting with Sketchpad Explorer (http://www.dynamicgeometry.com/General_Resources/Sketchpad_Explorer_for_iPad.html) and to be honest, I think that is the closest we have to interactive math right now.

  19. on 20 Feb 2012 at 3:33 pmDavid Petro

    Tyson, I think that one great reason to include quadratics is that quadratics show up so many places in real life. It is truly the funnest concept to teach. I mean come on, projectile motion. If there is a funner branch of mathematics, I don’t know what it is.
    Especially when the vast majority of what we teach has very little to do with real life. Or at least, everyday life. And no, people don’t need to know about quadratics to survive in everyday life but it is important for students to know that things around us can be described by mathematics.

  20. on 20 Feb 2012 at 3:33 pmAndrew Price

    we’re still waiting for a band of enterprising math education bloggers to quit yapping about how awful everything is and release their own curricula with iBooks Author?

    Have you considered…

    http://www.kickstarter.com/

    You might get enough funding to create your own iBook/app/ website…

    It may be worth a try.

  21. on 20 Feb 2012 at 4:22 pmCorey

    >As David pointed out, Dashcode would allow for these types
    >of issues to be resolved, but honestly, it’s not natural for
    >ePub. The format we SHOULD be using for textbooks is HTML
    >5, . . .

    ePub standard version three will be HTML5 based. People should really stop thinking of these as ‘text’ books. Imagine having a tinkerplot embedded in the book. Or what if you had interactives like phet.colorado.edu in a science version? Or having a space for students to write and show their work instead of fill in the blank or multiple choice? There is huge potential here for those thinking outside of the ‘text’.

    You can crate your own widgets with things like Scracth HTML5 (http://scratch.mit.edu/) or adobe Edge (currently a free preview version). Now if only that ePub3 will get finalized soon . . .

  22. on 20 Feb 2012 at 6:35 pmblaw0013

    So, I just ran across an example of student-initiated mathematics that she or he derived to compute the area of a fractal . Can the potential of an iPad-like hardware and connectivity device, paired with a textbook like software, enhance possibilities for student reasoning like this.

    Note: read the blog entry prior to the one I linked to see that this teacher’s students struggled to determine the area of a figure drawn on grid paper the day before.

  23. on 20 Feb 2012 at 6:40 pmblaw0013

    Sorry, I meant to include the link to the blog posting I mentioned. Here it is http://bit.ly/zjGqxl

  24. on 20 Feb 2012 at 10:05 pmLisa Nuss

    Hi Dan,
    I have been enjoying your posts, and I have to say I agree:
    1) Creating an ebook can be just as dull as a regular textbook. I have a school iPad and ended up downloading HMH fuse Alg I and was so disappointed
    2) The iPad could make the coolest textbook ever

    Agree with @David: maybe some teachers won’t be able to be flexible enough with open-ended questions in textbooks.
    Response to @Evan: that is great if you are my son’s teacher, but we have to allow all students to experience marvelous teaching and curriculum and not just the lucky few that have teachers that will can reimagine dull textbooks into mathematical discourse.

    Finally, my own experience, staying up to one am writing my own powerpoints for students to make the best learning opportunities (imho) for them…and then stopping after a while because I didn’t have the stamina. (and I strongly believe in feeding my family food that doesn’t come out of a window)

    When I looked at your screenshots, I thought, “Wow! exactly!!”

    Keep agitating!
    Lisa
    @nussder

  25. on 21 Feb 2012 at 7:00 amjosh g.

    Just to clear out the obvious… from Bowen:

    Also, just out of curiosity: what stops a kid from “flipping forward” in an interactive textbook like they might in a paper textbook? Often while teaching I mirror a book’s lesson without telling kids that we’re doing so, in order to stop them from reading the upshot instead of learning it themselves.

    The “book” itself could require student input before moving on to the next part of the activity. (And ideally, it ought to.) iBooks may be lousy at this – maybe it’d be possible once you can embed an activity as an applet in an HTML5 page – but that doesn’t change the fact that an interactive textbook format SHOULD enable these kinds of possibilities.

    More generally, if we’re still holding expectations that these eBooks will have the same limitations as paper textbooks, we’re really not getting the potential of the medium. At minimum, we should be expecting the same capacity for interaction that the web has. (After all, the web has evolved out of the same basic transition – taking text and images from paper to digital.)

  26. on 21 Feb 2012 at 8:26 amBelinda Thompson

    This post and discussion are destined to become classic. Thanks Dan and others for the clear examples.

    I’m reminded of a quote by the prolific Ice-T: “Don’t hate the playa. Hate the game.” The fact is that the big textbook playas sell books because people buy those books. It should be no surprise that what they offer through a screen is no different from what they sell in print. Unless there’s broad demand for something different, there won’t be anything different offered broadly.

    I’ve been using “the sum of two numbers is 6″ as an anchor problem to help students understand that there are infinitely many pairs of numbers that add up to six, and if we plot those on a coordinate plane they fall in a straight line. Also, we can communicate this with mathematical notation. Others mention that approach, as well. I started doing it because I was dissatisfied with the Algebra 1 textbook treatment of linear equations. I developed several problems and units of my own based on this dissatisfaction, and the belief that students could come to understand math concepts through messing around themselves. However, in my work with many teachers in many middle schools, I found that often I was confronted with the fear that students would not be able to solve problems they hadn’t been taught to solve yet. This disposition is born out of teachers’ own experiences in math class for sure, but deadly to what we discuss here. It is more aligned with many of the textbooks we fuss about here.

    My conclusion is that we should expect evolution rather than revolution even though the tools for revolution are now available. Evolution is hard work. It takes a particular knowledge ofmathematics and disposition toward teaching andlearning mathematics to take up and implement these types of materials, and the demand is not there yet. I’m really not as hopeless as this may sound, and honestly, blogs and comments like those shared here keep me energized. Viva la evolution!

  27. on 21 Feb 2012 at 8:36 amRiley

    @Belinda – Evolution is great, but let’s not rule out intelligent design altogether ;)

    Seriously, though, I think you’re right that small changes can, in this case, add up to a totally different paradigm. It doesn’t have to be all at once. My company is trying to contribute to this evolution by making assessment data as fluid and personal as the textbook dan describes here. I think many aspects of education are going that way – PD is being replaced by small chunks of conversations that add up to different things for each participant. Textbooks can head the same way – as soon as a math teacher can make a little note in his textbook that is transferred to all of his students’ books, someone else will think “what if he could write a little program here?” and make it happen. I’m very optimistic about this happening, as long as we can keep the internet as free and open as it is now.

  28. on 22 Feb 2012 at 8:33 amFrancis

    Hi,

    Your graph example is totally doable, I made a quick proof of concept widget, you can see a demo on Vimeo : http://vimeo.com/37252854

    The classroom graph is not done but could be. Student could be invited to enter a class id, submit their results, and the classroom graph tab could connect on a server to retrieve every results for that particular class id.

  29. on 23 Feb 2012 at 6:02 amTim

    Interesting that you use only the Mcgraw-Hill iBook to make your point; where’s the critism for Pearson now that you are working with them?

  30. on 23 Feb 2012 at 7:29 amDan Meyer

    First paragraph:

    Since then, I’ve had a chance to review Pearson’s offering in the same category and, in every way that interests me today, it’s every bit McGraw-Hill’s equal. (In a blind taste test, the only way to tell Pearson from McGraw-Hill is that Pearson includes more embedded multiple-choice quizzes and fewer videos.)

  31. on 23 Feb 2012 at 10:26 amjosh g.

    Ok, now I’m interested. Francis, what is that widget built on? Something proprietary to iBooks, or something semi-standard (Javascript / Java / etc)?

  32. on 23 Feb 2012 at 10:34 amFrancis

    Only html and javascript, plus php for sending results but could be anything

  33. on 23 Feb 2012 at 10:54 amDan Meyer

    I admit I found these comments difficult to dig into with their relentless big picturism on what was a very detail-oriented post. My gratitude, then, to folks like Francis and Josh and others who engaged the post on that level. Extra credit to Francis for donating time to mocking up an interface.

    I want to point out one way in which my vision and Francis’ implementation differ. Francis presents an optional widget. Something to be tapped in the margin or ignored. My mockup suggested a required form in the body of the text. I’ve tried to make a case that the difference matters.

  34. on 23 Feb 2012 at 1:04 pmBentham

    Dan, is THIS what you’re looking for?

    http://www.mindresearch.net/cont/programs/demo/tours/SolvingLinearEquations/progTour.php

    Admittedly, it’s at the K-6 level. But the idea is similar. Plus, it passed random controlled trials with a 0.37 effect size.

  35. on 23 Feb 2012 at 1:11 pmBud Hunt

    English teacher – so please excuse the intrusion – but the interactive interface you’re pointing towards here would also be wicked handy on the reading side of any book that might get made. Building a view in the text for “Stuff your classmates highlighted” or “Teacher view of all highlights” or “Class notes” or any overlay/transparency of how others marked up the text would be useful for a teacher in a classroom, as well as for the students. Heck – an administrator able to dig into that annotation/problem set/whatever data could have an interesting time, too. And might see that the folks in Mr. Meyer’s math class were really good at annotating the text. And that the students in Mr. Hunt’s class never do the homework. Although, when “the homework” lives in “the book,” maybe more of it would get done – especially if it were worth doing.

    Of course, you get into some really interesting data problems – who is “the class?” How do you assign the teacher/student relationships? Why is “the principal” able to see into “my book?”(These are solvable problems, but they add a new level to the activity formerly known as “passing out the books on the first day of class.”)

    There are tools that exist around the Web for making these sorts of collaborative annotations/highlights – but it’d be neat if someone were pulling them together to make these kinds of texts.

  36. on 23 Feb 2012 at 6:52 pmMarielle Lange

    @DanMeyer
    I admit I found these comments difficult to dig into with their relentless big picturism on what was a very detail-oriented post.

    Technically, there is no real obstacle if you want to implement these details in activities that you design for your own students.

    (in both examples, click on the big |> arrow on the big division on the right side of the screen, enter some values in the input boxes, then click on the ‘graph data’ button)

    http://jsdo.it/widged/activity-graphdata – version that requires no server setup of any kind. If you were to change the files slightly so that they run from your file system, they can run offline. Strictly javascript. The easiest way to proceed is to simply create an account on jsdo.it Simply ‘fork’ the activity, change the code to suit your needs, then click the embed button to embed in any website, or even on your blog.

    http://jsdo.it/widged/graph_data_gsheet – version that saves data to a google spreadsheet, for teacher review. You don’t need access to a server, but you need to create a google spreadsheet. Then create a form that let you enter data remotely.

    If, as @AndrewRice suggested, you want to create your own book, or just a single chapter, to give for free to your student or to sell for a modicum price on any store, it is not very difficult. Relatively simple programming (manageable by a 15 year old as they tend to have more time for personal projects than teachers). It doesn’t cost a penny. Bundle your html and javascript in a phonegap project and you get a native application for most of the devices.

    But there is little point discussing these “details” unless you are prepared to write a textbook yourself or find somebody who can do it for you.

    In terms of business, there is no incentive for publishers to allow iBooks readers to save their data. What sells the book is the lobbying. Not the ‘nice-to-have’ details.

    To start with, iBooks only support a subset of html5. No interactivity. No javascript. You have to write your own native app for that (which is not very difficult). Once it comes to saving data, that’s a lot more complex for a publisher than for a class teacher. A teacher has to guarantee that the data are accessible (read/write) to a known number of students, for the duration of the school year, at most. A publisher has to guarantee that it is accessible forever ever, for whatever country in the world, whatever the network setup (many people are still on modems, here, in the countryside).

    What could happen is that some other company will provide some “for schools ibook data cloud storage” service that they will charge schools for (by the month or the year) and that schools could enter their subscription id in the ibook to get access to the data save functionality. But I wouldn’t count on it too much.

  37. on 23 Feb 2012 at 8:52 pmMarielle Lange

    If you after examples of interactive activities, done by mathematicians – similar philosophy as the Andes system.

    http://wims.unice.fr/wims/en_home.html

    This has been possible for at least 10 years (WIMS was built in 1998). However, this is not something you can hope to embed in the content you are gonna write with iBook author.

  38. on 24 Feb 2012 at 9:31 amjosh g.

    Marielle:

    To start with, iBooks only support a subset of html5. No interactivity. No javascript. You have to write your own native app for that (which is not very difficult). Once it comes to saving data, that’s a lot more complex for a publisher than for a class teacher.

    Okay, now I’m confused again. So was Francis’ demo above a mockup in a browser, and not something running in iBooks? Or is the deal that iBooks lets you link to widgets that run in iOS Safari with full Javascript, but the iBooks pages themselves can’t run JS?

    Just trying to figure out here if anyone’s actually giving a counter-example to Dan’s claim or not.

    Also, Marielle, I can get from the technical side why sharing data with the class is a trickier ballgame to implement than a standalone javascript graphing activity. However, you’re envisioning something running on a persistent database that the publisher has to maintain; I think it’d be just as useful for the teacher if the student book knew an ID for the teacher’s book, and simply sent data to that device directly. It’d only work when students and teacher are all looking at the same activity at the same time, but in a classroom setting that would be just fine.

  39. on 24 Feb 2012 at 2:11 pmMarielle Lange

    My understanding was based on reviews like this:
    http://www.techradar.com/reviews/pc-mac/software/graphics-and-media-software/desktop-publishing-dtp-software/apple-ibooks-author-1062792/review

    “Apple provides you with 7 widgets that you can use to add interactivity to your book: Gallery, Media, Review, Keynote, Interactive Images, 3D and HTML.”

    “The Review widget is obviously aimed at textbooks and allows you to create multiple-choice quizzes. There doesn’t seem to be a way to save the results of these, though, and hence there is no way to tally them up at the end.”

    But checking further, the HTML option let you use custom javascript. Tutorial:
    http://vallandingham.me/ibooks_and_d3.html and ibook widget boilerplate: https://github.com/TrevorBurnham/iBooks-HTML-Widget-Boilerplate

    The official apple page on iBooks widgets:
    http://support.apple.com/kb/HT5068
    Apparently, it supports primarily Dashboard widgets, which is just a Apple’s way to bundle html and javascript. http://www.dashboardwidgets.com/

    On saving data, they add:
    HTML widgets can only post to external web services if those web services have implemented the appropriate CORS (Cross-Origin Resource Sharing) headers.

    No apparent option other than that. On that page, they state that there is no access to system or to the filesystem outside the widget, so it’s not clear how you could communicate with other devices.

    Obviously, I haven’t tried out iBookAuthor yet. The iPad at home belongs to my husband. I develop primarily for Android. Based on the info I have come across.

    The only way to send data to another device without having them go by a server is by sending data “over the air”, by wi-fi or bluetooth. For instance by bumping the student device against the teacher one, the way the bump application does it. http://bu.mp/. Due to the limited access a widget has to the system, that “over the air” data transmission would need to be managed by a native application, which would require the widget to be able to save data locally.

    That could be arranged if a html5 feature called local dataStorage is enabled (http://www.jstorage.info/) or if it is possible for the widget to save data to a sqlite database held in the widget folder.

    The outlook may well be a lot better than I thought. According to this thread on the Apple support forum, local storage is supported: https://discussions.apple.com/thread/3686472?start=0&tstart=0.

    An extra difficulty to consider is that the device could be offline at the time the student attempts the activity (for instance while on the bus). You then need a system to save the data temporarily on the device (local storage would do) and some way to send the data to a server once the device gets back online. The simplest way would be to have somewhere in your iBook a page with a separate widget doing nothing but letting you “save all iBook data” or “save data from all completed activities” or “save data from chapter one” somewhere in your ebook.

    It may well be that the type of very low-tech Google sheet export that I demonstrated work from within a iBook widget. Then it may be possible to streamline the solution a bit so that it is more easily “usable” by anybody. All you would have is to specify a spreadsheet, a form id, and the student id.

    Still publishers may prefer to wait for a company emerges that proposes iBook data management as a service. Once the other service emerges, then they can provide an easy to use API for publishers and individual authors to use in their iBook widgets. But with both custom and local datastorage available, it is a lot more likely to see startups give it a shot.

  40. on 24 Feb 2012 at 5:44 pmMarielle Lange

    “iBooks Author can’t facilitate it either, but if it could — if it had some kind of “Q&A” widget that lived alongside its other widgets and basically copied all the options from Google Forms — I’d find the platform difficult to resist.”

    Quickly borrowed my husband computer (iBookAuthor requires OSX10.7) and iPad. Happy to report that saving widget data to a google spreadsheet works (saving data without any PHP code).

    What it does is send data to the spreadsheet via a Google form. So yes, anything the form can do, you can do from within the widget.

    A word of caution. I have only tried in Preview mode so far. A real ibook needs to be approved by Apple and it is not always a straightforward process.

    I will put together a video demo, tutorial, and demo code by the end of the week-end.

  41. on 26 Feb 2012 at 5:35 amSteve Dickie

    I’ve been playing with iBooks Author and I like it. But I think I approached it differently than many people. Much of what I read on the net seems to imply the textbook should be able to replace classroom teaching. I simply saw iBooks Author as a way to create good content for my own students.

    I’m not waiting for textbook companies to do my work for me. I’m working to create resources for my own students that will directly supplement classroom instruction. The dichotomy that Dan points out between guides for teaching and reference was exactly what I’d needed. Thanks! With that in mind it is much easier to build what I’m trying to build.

    I’m in the process of creating interactive widgets so students can do virtual mini-labs. Reading your post made me realize I can put in Google Forms to collect data/answers from my students so I can see what they’re getting out of it. With google forms I think I should be able to create graphs that will self populate with data as my students collect and enter it.

    If you’re interested you can see a sample of what I’m working on over on my blog. (linked from my name on this post).

  42. on 26 Feb 2012 at 4:16 pmDan Meyer

    @Marielle and @Steve, I’m looking forward to the demos, of course. I don’t know how demanding to be of strangers, but let me be clear about what I’m envisioning in this post.

    I need persistence. When a student shuts down the iPad and turns it back on, all her additions to the book should exist the next time she opens it.

    I need peer visibility. What I enter in my textbook (say, a pair of numbers that add to five) should show up on yours and vice versa, depending on the task. (Sometimes the data won’t be visible to others. Sometimes they will.) All of these data should be persistent also.

    This needs to happen with as little friction as possible. Opening a browser and heading to Wikispaces may work for me and a handful of other geeky math teachers but it’ll be a hassle for students and a hassle for 90% of math teachers and it’ll create a separate record of our learning. So this all needs to happen within the iBooks app. My sketch above describes it all happening inline. That’s important but if all we can manage for now is a margin widget (living in the margin, requiring another tap) that’ll be interesting anyway.

  43. on 27 Feb 2012 at 2:43 amSteve Dickie

    OK, I think I’m getting a better idea of what you’re looking for. It sounds like in part you’re looking for a workbook combined with a textbook.

    Which makes a lot of sense when we consider that students will keep their book forever and every student from year to year will get a new clean copy. Hmm… I’ll have to ponder this. I’m not sure there’s a good easy way to get persistence right now. Unless the html content in iBooks can set cookies, but then if the cookie were cleared…

    I think it would also be tough to implement peer visibility in a way that would not violate school network policies, unless individual teachers were setting this up for their own individual schools. But then you’re into that 90% of teachers who’d be unable/unwilling to do the work to make that happen.

    The more I think about it the more I want my students to have the pages of their lab notebooks embedded permanently in their books. I like this idea. It would be even cooler if we could easily aggregate the class data when building our models.

    Thanks for the blog post one the follow-up comments. You’ve given me a lot to ponder…

  44. on 27 Feb 2012 at 6:56 amMarielle Lange

    @Dan

    persistence, you can have it. If you use localStorage (which is HTML5 improvement on cookies), the data persists even if the student shuts down the device altogether. I put it to the test, works on the iPad, in preview mode.

    visibility, you can have it. There is no friction on the side of the users. Possible (very likely) friction with the technical staff at your school, either not happy with the pressure put on the school bandwidth or a bit reluctant to help implementing a solution that he may not be able to support school-wide.

    There is a simple, low-tech solution that pretty much anybody can implement without the assistance of a technical staff of the use of school resources, but it could easily overtax the school network (not recommended). There is a live demo of that there – http://jsdo.it/widged/graph_data_gsheet/. Click on the right frame to play, type some data, click “Send Data to Teacher” and after a very short delay, you will see the new data appear under “Saved Data”. The data are not stored locally but on a google spreadsheet. You can use the link to the spreadsheet in the readme tab to check that your data really were posted there.

    There is a much more advanced solution that requires access to a (closed) network. It relies on some variant of a remote debugging approach (http://phonegap.github.com/weinre/, http://jsconsole.com/).

    I have started writing stuff as an iBook. The first draft is available at, as a PDF export (obviously, the interactivity doesn’t get to be exported):
    https://github.com/widged/iwidgets-for-learning/blob/master/Interactive%20iBooks.pdf

    Got a bit delayed. Ended up installing Lion on an external disk to avoid bothering my husband too much. Which meant full backup beforehand. My first attempt at a video capture of the iPad didn’t give good enough results to be shared (I need to figure out a good angle). I will give it another try later on.

    Still, I am committed to giving it a chance. I will add code and demos at: https://github.com/widged/iwidgets-for-learning, ASAP. That will include the iba (ibook author) file. If you have iBookAuthor on your computer and an iPad to connect to by USB, you will be able to run the iBook on your ipad and try the different widgets.

  45. on 27 Feb 2012 at 7:48 amMarielle Lange

    @Steve Another scenario to consider.

    The fact that any (iBook) HTML Widget from can also play on your local file system gives you the opportunity to replay a given activity to the class, on the computer connected to the whiteboard or projector (yours), using the data of a specific student.

    Not so interesting for a simple input box activity, but potentially much more so for interactive simulations.

  46. on 27 Feb 2012 at 7:52 amFrancis

    I have updated my demo widget to include localStorage for saving student answers, and a “Save Results” that sends the results to a server for class sharing.

    The student enters his email (could be anything, as long as it is unique to each student) and a class id (given by the teacher, in order to display only results for a particular class).

    You can see a demo here : http://vimeo.com/37528436

  47. on 27 Feb 2012 at 8:38 amMarielle Lange

    “I don’t know how demanding to be of strangers”.

    I can turn this into a speech for the next meet-up of the local javascript community or some other conference. The iBrand also means established marketplace and opportunities to turn a few bucks if it started to take too much of my time. All in all, the more demanding you are, the better the opportunities. So, no worries, fire ahead.

  48. on 27 Feb 2012 at 3:11 pmRobert Hansen

    I reviewed the Pearson book and it is one of the first honors level books that have shown up in this electronic form. Last year I looked at HMH’s Algebra but it was obviously bent towards a slower and less filling approach. I gave the Pearson book high marks for plenty of worked examples, exercises and a modest number of problems (I was spoiled by the large number of problems in Dolciani texts). I gave it low marks for text content, it didn’t talk to the math enough.

    This is what honors algebra texts look like. This is how a student truly ready for algebra takes on the subject. Imagine students of music of this age. I don’t think the music teachers have to spend a lot of time explaining what music is to those students. Of course, those students chose to pursue music.

    Btw, the secret to doing your (Dan) work in iBooks Author is obviously video but also HTML 5. There are several widgets that can be inserted into an iBooks 2.0 book, one of them being the HTML widget which supports HTML 5 and thus animation.

    iBooks Author isn’t the end all, but it was a big leap forward and finally a textbook format can be published electronically. The only other acceptable format before this was PDF.

  49. on 27 Feb 2012 at 9:01 pmDan Meyer

    @Francis, thanks for updating the demo. Where are those login credentials going?

    @Marielle, the PDF was extremely useful. Do let us know as you update it. I’ll be giving the Google Forms hack a try in the meantime.

  50. on 28 Feb 2012 at 12:33 amFrancis

    @Dan, this is just a very basic demo. For the moment, results are sent to a server and saved in a simple file. You can see the output of this file, in json, that is used to populate the classmates graphic here : http://www.francisthomas.fr/jsonp3.php?load=1

    It could stay as simple as that (a simple php script saving to a file and outputting json), or evolve to a more sophisticated setup (storing results in a database).

  51. on 28 Feb 2012 at 3:51 pmMarielle Lange

    @Dan regarding friction, some cloud service like PubNub – http://www.pubnub.com/ – could just do the trick.

    I just bumped into it and didn’t get a chance to experiment yet. In their documentation (http://www.pubnub.com/how-it-works), they say that you can communicate “client to client” so you may not even need a server setup. Free for 5 million messages per month. You can run tests and pilots without any upfront investment.

    What this would allow is to have the data entered by one student on one tablet immediately visible to all other students, without them having to press a button to request a widget refresh.

    If having to press a refresh button is acceptable, then nothing more is needed than google spreadsheets to develop widgets enabling group participation / collaboration.

  52. on 29 Feb 2012 at 2:42 amMarielle Lange

    @Dan I updated the project at https://github.com/widged/iwidgets-for-learning. I

    Now with:
    - widgets demonstrating the locally persistent and remote (google-based) functionalities, with full source code,
    - iBook Author file (iba) made available to enable those who have both iBookAuthor and an iPad to connect, to run the widgets in an iBook context, on the device. (See the README on github for details)
    - pdf exported again.

    This is the second draft. Not the final version. I need further proof-reading and ask a native speaker to double check (I am not one).

    I also intend to add more examples to showcase interesting libraries like jsxgraph (http://jsxgraph.uni-bayreuth.de/wp/examples/) and I will seriously consider covering more ground (principles of multimedia learning, for instance). But that will be slow progress over the next weeks. I need to finish some other work before I can spend more time on this.

    I won’t be mentioning future updates here. Best is to check the project page on github. The “age” column will let you know if anything changed recently.

    People with issues or suggestions should use the “issues” section in the github project (you will have to create a github account for this). It is perfectly okay to use the issues functionality to suggest new templates (use the enhancement label).

  53. on 29 Feb 2012 at 12:15 pmDan Meyer

    Thanks for the update, Marielle. I signed for a github account and have you on my watch list.

  54. [...] Meyer, and Keith Devlin have been critical of Silicon Valley, edtech startups, and iPad textbooks which hope to “disrupt” education. In my opinion, the real stumbling block to [...]

  55. [...] om, i stora drag? Pekar på det sociala som något viktigt för gamification. (kolla detta inlägg, främst sista exemplet, det här är bra. Man kan inte förmedla känsla på samma sätt en [...]

  56. on 06 Mar 2012 at 1:33 pmandy

    2.5+3.5 does not add up to 5, it makes 6

    but maybe that was an obvious mistake to get students thinking.

    Great blog

    keep it coming

  57. on 06 Mar 2012 at 1:36 pmandy

    next time I will read whole post before posting

  58. on 09 Mar 2012 at 10:59 pmLinktipps 10.3.2012 | Lehrzeit

    [...] mal eine Algebra iBook genauer an und kam zu dem Schluss, dass es in der aktuellen Version noch keinen wirklichen Mehrwert [...]

  59. on 14 Mar 2012 at 2:55 amStuart McNaughton

    Hi, I’m a first year teacher at a small country school in NZ. I’ve hit on a way to do the graphing part in the class. I have access to netbooks and PCs in the class, and with small class numbers, it’s often possible to have 1 computer per one or two students. I use Google docs Spreadsheet, share it with my students and get them to edit one of the cells according to the rule. Google docs can graph this in real time, updating the cells as the students enter their data.

  60. on 16 Mar 2012 at 12:40 pmThe 2012 CSMC Sessions | Plenary

    [...] LinkIt’s Called iBooks Author, Not iMathTextbooks Author [...]

  61. [...] inputs be privileged in the texts that we make, use and create at school? # Dan sketches out, here, how a math text might look when spaces for inputs are considered thoughtfully.  I wonder about [...]

  62. [...] important is that reference sources make poor pedagogy tools and vice versa, as pointed out by Dan Meyer. A reference text is meant to give simple right answers, but pedagogy involves [...]

  63. [...] It’s Called iBooks Author, Not iMathTextbooks Author, And The Trouble That Results: se revisan las dificultades para crear libros de matemáticas con iBooks Author en su versión 1.0 Algunos de los problemas han sido corregidos en la versión 2.0 con la opción de insertar fórmulas escritas en Latex o MathML. [...]

  64. on 29 Mar 2013 at 11:41 amKyle Pearce

    Just stumbled back upon this thread as I was searching for ways I could create an iBook in iBooks Author, but also give the reader an opportunity to do some math practice using their finger like in GoodNotes or iAnnotate, etc.

    I’m thinking the only possibility would be to add a “link” to a handout/worksheet or have the user take a screenshot and bring into their own favourite iPad annotation app.

    I love the interactivity of an iBook, but I’d still like to offer opportunities for the student to “try it” themselves.

    Ideas? Suggestions?