Using LaTeX to generate dynamic mathematics worksheets for the Web
Arora, Pavneet
Mathematics worksheet generators abound on the web. Many use static content and focus on graphics and animation in order to package the material in an appealing manner. This approach comes across as a fight for \emph{eyeballs}\Dash all too common when trying to attract the target audience on the Internet. The emphasis on form often displaces the basis of learning at the primary education level, which is simple practise. Beginning with an exploration on effective learning strategies for grade school mathematics the use of \LaTeX{} to generate dynamic mathematics worksheets\Dash lots and lots of them\Dash is discussed.
 So I must say, I feel like a bit of a gatecrusher to a rather exclusive party, much like that couple in Washington. I consider myself a rank amateur technician, and I mean that in the typesetting sense. Boris yesterday said that he considered himself a wizard's apprentice. Well, if he's a wizard's apprentice, I'm in the stable cleaning up slot. So, Carl graciously or unwittingly left the door open when he invited talks about how tech is used out in the wild in the field. And I took the opportunity, I seized the opportunity, wedged myself in, and that's what this talk is about. I do use tech and late tech, which is how I grew up pronouncing it, in almost every aspect of my business. Here we are looking for the most. Okay, a mouthful of a title, using late tech to generate dynamic mathematics worksheets for the web. For the purpose of this project, that's my contact information. I, like the other speakers here, would really welcome your ideas, your input. The technical aspects of the discussion are rather rudimentary, so I'm going to spend a lot more time on the surrounding aspects of the project, and I ask your indulgence on that part. So, as an introduction, personal typesetting history. Bill Cheswick mentioned this program called Runoff. I think I'm probably one of the few people in the room that have not only heard of Runoff, but have used it. It was a deck standard runoff, and my personal history goes back even probably earlier than Bill's with UNIX. My uncle worked in Bell Labs in the early 70s, so as a kid I was wasting reams of thermal paper, dialing in with a TI Silent 700 with acoustic coupling onto a UNIX system and playing whatever was around in user games and getting kicked off in the middle of the night. So from there it progressed to EnRof and T-Rof. Softquad had a very elegant implementation of T-Rof, and then of course I saw the light and started to use late tech. I have a project management consultancy practice outside of Toronto, and it's related to the construction industry. We do renovations, commercial and residential. We do high-end automation, Lutron and shading controls. I also have the luxury, since it's a sole practice, that I can pick my own tool sets, so I did. We use late tech all throughout our business, or I do. That's the Royal Wii. But that gives you a sprinkling. I'll touch on those a little bit later. I also have props in the absence of the technical content. So there's another overarching theme to this talk, which is mathematics through practice. Sherry Turkle wrote this book, I think it was in the early 80s. It's a brilliant book. I'm talking generational now. If you haven't read it, just go out and buy it. It opens with the story of a feral child, Victor of Abiram, who when he came out of the forest in 1800, did so without an apparent ability to speak. It was later discovered that he could hear, but he could not speak. He was adopted by a scientist, Jean-Marc Gaspar-Nitard, who took it upon himself to educate Victor, which in the context of the times meant that he should learn language, the French language. Language marked a civilized person of the age. There are many controversies surrounding the story. I don't want to delve into it. I only wanted to mention it because the story was and remains compelling because it raises the question, is language innate or an acquired skill? And naturally, we're not going to have a control group of newborns shipped off into the forest and wait 11 years and check it out. The story resonates with me personally because I have two children, an elder daughter and a son, younger son. My daughter has struggled with maths from the get-go. The school system, at least in Canada, has tried many things and finally what ended up happening. It happened early in her student career is she was shunted off to what's known as a special stream that makes lots of accommodations. It uses assistive testing. I say assistive testing, not learning because it advocates open book tests, use of calculators at a very early age. I found that a bit disturbing. My daughter is precocious. She's eloquent. She's well-spoken. She has a remarkable memory. She has her memories far better than mine. And I was left struggling with the idea, much as Itard did in his time, is my daughter missing a mathematics gene? Is mathematics innate or an acquired skill? Well, according to Young, anything beyond concrete numbers is probably not amenable to human beings. But at least he gives an allowance that mere mortals can master concrete numbers. So the most frequent of such peculiarities is the incapacity to understand any form of mathematics that is not expressed in concrete numbers. My early education for just a brief couple of years was in India. And although it was brief, the memory of that experience remains quite vivid. In that educational system, there is no concept. There's no allowance made to this idea that there are two types of people in the world, especially children, those who get mathematics and those that don't. And at least with numeracy, it's an assume. If you go to school, you're going to learn mathematics. So unlike Itard's society, where language marked a civilized person, in the Indian educational system, both language and mathematics marks a civilized person. So mathematical ability is innate, but mathematical skill can only be acquired through practice. I've broken up my talk into three areas, three topics, motive, method, and metai. Metai is a word that's common to many South Asian languages, and it refers to sweets, sweet. So I'm going to refer to it in terms of iCandy. We're going to do a demo of the software at the end. And perhaps a vain hope that once you see the demo, you'll be letting out a resounding sweet idiomatically. Okay, we'll start with motive. I'm going to spend a lot of time with motive. As I said, the technical aspects from a typesetting perspective are rather rudimentary, so I hope I can entertain you with other things. Is numeracy desirable? Is it even necessary anymore? After all, we have computing power coming out of our pockets. I'm told that wristwatches are on their way out, which I don't buy. The founder of the Swatch Group passed away. The New York Times had an obituary, and I think the last year's revenues were $5 billion. So he did rather well on wristwatches. We can look at these questions in two ways. We can look at it in terms of basic fitness, like physical fitness. Mathematics or numeracy is mental fitness. It's good for you. It lowers healthcare costs. It leads to more productive and happier lives. It may even lead to mental equanimity. The second aspect is the one that I want to focus in on is that, and that's the thing that I think got skipped in my daughter's education, was that it is a necessary building block on which the edifice of mathematical literacy is built. Even though we have calculators and cell phones and everything else under the sun, if you miss that step, you're not only denying the student mastery over their environment at a very young age, but you're putting a big hole in their education that is very hard to recover from. And I'm going to lay out a bunch of these, well, let's go back to Aristotelian syllogism. I'm going to use proof by assertion. So I'm going to lay out a bunch of these propositions like Royal Fisben, the game of Royal Fisben, which I apologize to many of the international attendants. I tend to throw these cultural references in. Star Trek fans will remember that Royal Fisben was a game of arbitrary rules that Captain Kirk duped a few Chinese, sorry, Chicago gangsters out of a game. So the propositions would go something like this. So if it's Tuesday and if it's 11 o'clock and if we agree that numeracy is an essential step in the education towards mathematical literacy, then of course you have to use latex to achieve it. QED. Now, if we, I'm going to go back again, I skipped a point. If we divorce numeracy from symbolic algebra, I think what happens, and that's my own observations with my daughter, is that young children miss this step of gaining mathematical intuition. Numbers are really important in their daily lives. But in all, in very interesting ways, and I'm going to touch on that later. So by divorcing that and expecting that you can have assistive mathematics, what ends up happening is you end up with what I had in the next slide. So I think this was part of Hilbert's Top 10 in 1900 that you could go from the left-hand side to the right-hand side. So the other argument against that kind of numeracy is that, yes, it's a desirable goal, so is world peace, but it's too difficult, and it's only available to a select few. I'm going to throw out another prop. Dover used to put out these beautiful, elegant additions, both typesetting and content-wise. This one is the Divine Proportionist Study in Mathematical Beauty by H.E. Huntley. I'm not even sure when it was published, but a long time ago. So this is a quote from Professor Huntley, which I strongly object to. "'Teacher should be sympathetic to the mathematically ungifted for humane reasons,' sounds like euthanasia. "'Such should be dissuaded from any unaccountable ambition. They may have to take advanced mathematics.'" And I think the caveat he threw in is just advanced, but I think it means anyone who doesn't get it should be out of the system. So I don't agree. And unfortunately, I think that's an attitude that's prevalent in many schools these days as well. So how does one learn mathematics? And I went back to my own experience, not in maths, but in programming. So I think there's two ways. There are those that gain a kernel of comprehension, and they refine that kernel of comprehension using practice, and it leads to proficiencies. But there's the rest of us. I consider myself a slogger, although I have a long history in programming and in maths, where you don't gain the comprehension unless you scratch away at a problem or several problems. And then you get this aha moment and say, okay, now I know why everything I did before was wrong. So those are the two approaches. I think there's a wide band of students that fall into the second category that are getting missed in education, proof by assertion, remember? So Sherry Turkle's work in the 70s and 80s also hinted at this with the concepts of hard mastery and soft mastery. She I think it was mostly done in New England, Boston area, but she observed young students interacting with computers. Now at the time, if you wanted to interact with a computer, you had to know something about relatively low level language interaction. You didn't have the luxury of transition effects and lots of layers between you and the hardware. So it meant whether you were classified as a right brain or left brain child, you would be interacting with a computer at a low level. So some children would treat computers as transparent systems, whereas they'd like to know about the mechanical innards of it. They'd understand that and they'd need to know that before they could map input to output. That was the first approach. They gained the comprehension of the system and then they could interact with it. There were another class of students who treated this as a black box. And there was one very telling example where grade two class, this was with logo I think, not turtle, but logo was this graphical language several generations ago. I keep saying that because I'm really hard pressed to believe it so much has happened. So grade two students discovered that there was this mapping between numbers and the direction that the sprite would go. And I am certain there was no discussion of Togas, ancient Greeks, Euclid, but they got it. They treated it as a closed system and it was like breaking a code. So I would put them in the second category there. So we've arrived I think at a stop or at a point in education where the three Rs, which were never Rs, reading, writing and arithmetic are now classified to be reactionary, redundant and retrograde. And I think that's a shame. But I think there's a good reason for it and it has to do with language. I'm picky about language as well. I think it's the OAD that we all probably suffer from or our spouses accuse us of. The distinction is between rote versus practice and they're very different things. Every a lot of what was in the three Rs has not been the umbrella of rote and thrown away. But I think what's been lost in that is the value of practice. And if you go back to my overarching theme, it's mathematics through practice. So I'll take the easy way out. I'll begin with Miriam Webster. The details don't matter but I want you to pay particular attention to the second definition. I'll come back to it later. Mechanical or unthinking routine or repetition. Whereas for practice, we go back to the proficiency argument. You want to perform or work it repeatedly so as to become proficient. Okay, this is Camus and fortunately my literature teacher in high school forced us. He asked us to read this, read this out loud, write about it and that's practice. It's stuck in my head when I had to prepare for this talk. Isn't that what counts? This is from his essay, A Pause Between Yes and No. Surely not since doing homework and accepting manhood leads to nothing but old age. I suspect if you were asked, if you were to ask Camus if that applied to writing as well, he would say no. Writing was pure pleasure. Which means that practice leads to proficiency. My definition is synthesized here. Wrote implies tedium, simple repetition without improvement or acquisition of skill. It definitely indicates no purpose. It's done without purpose. Practice implies with purpose and it's gaining in capabilities. You do something because you're learning something about it. This is my second time in San Francisco. The first time was 21 years ago when I visited Redwood City and I committed to Next Step, which was a business blunder. I can't come into the Bay Area without hearing echoes of Mario Savio's speech at Sproul Hall. There's a time when the operation of the machine becomes so odious, makes you so sick at heart that you can't take part. Well, if you associate mathematics with tedium, tedious, wrote odious, I wouldn't want to do maths either. I think what we need is an open access movement for mathematics. A couple of examples, of course, MIT OpenCourseWare. Amazing program, but directed at secondary and higher education students. A couple of weeks ago, this came across on the BBC website. They have a maths busking program. So maths students are sent off into shopping malls to do maths tricks and attract students. Why do we hide mathematics? Why do we treat it as something that cannot be out in the open, regardless of your skill set? Okay. By now, I have no doubt convinced you that I am a loyal citizen in the land of King Lund. I hate machinery. I don't even have electricity. I walked 10 miles in blizzard conditions to school and even more on the way home, 16 kilometers, you know, 10 versus 16. Let me put that aside or suede your concerns a little bit. The next slide is not a very flattering slide, but I don't know whether you can tell what I am holding in my left hand. It's a calculator prototype. They are not allowed in the premises of Tash Mahal. The only electronic device allowed is a camera. I happen to have it in my pocket. How much of a calculator geek am I? I had a calculator in my pocket that went undetected through security. I fell in love with calculators with my first, which was a Texas Instruments SR50A for those who may remember back that far. And then came a fateful day, a Friday afternoon, when my high school electronics teacher, Mr. Keen, for whom I will remain forever indebted, said, you seem to be interested in calculators. Why don't you take this one home? It works a little bit differently. I don't have a manual, but I have an article. The article, as many of you probably can already ascertain, was Enter versus Equals. And the calculator was an HP35. Since then, I have been in love with anything with an Enter key. There have been some rocky periods in my relationship with HP. I remember buying one and phoning what I thought was Corvallis and asking how I switch an Omnigo 100 portable computer into RPN. And the voice at the other end said, I'm sorry, sir, I don't know what RPN is. This was a t-shirt prototype that I typeset for HP. I have written several critiques about the typesetting of their documentation, the demise in typesetting of their documentation, as well as the layouts on their keyboard. And I guess finally they said, you know what? You've got all of these criticisms. Why don't you come in on a design exercise? I don't work for HP. I'm not remunerated by them. This was a voluntary exercise. This was the result of the first one. I don't know whether you can see at all. This is a mask for a final pre-production mask of a business calculator. The earlier ones were really abysmal. The mathematical functions were done horribly, allegedly. And I'll give you an example of that. Font fanatics may notice that the math functions are typesetting gentium. My original proposal to them, I advocated Sumner Stones, beautiful stones, Sancero, Fuminist, and Serifons, HP's branding uses a variant of Futura. And it's called Lusense. We had to find something complementary. And it had to fit licensing issues. Boris has already talked about licensing legal. So gentium is what was selected. I'm going to pass around another, the second design exercise, the result of it. The second design exercise was to turn this, which is their entry level 10B, into this, which is a 10B2+. Rule number one was that no key label be shifted on the keypad. And rules number two and three were equally emphatic. Do not violate rule number one. So I'm going to pass these around. I want you to pay particular attention. This is a late-stage pre-production model. You can see it from the labeling in the back. There's some type setting that's off. The centering of the off label isn't quite there. But I want you to pay particular attention to the clear stat function, which was the clear sigma in the old one. Clear functions have been labeled, grouped on the left-hand side. And I'll just come back. So even when it makes ergonomic sense to shift the label, you're not allowed. And Hans illustrated this beautifully in his discussion about classifying Pluto not as a planet. One of the lines that you threw up, Hans, from the governor of this fine state, was that it would confuse the students because the textbooks are already written and they all say Pluto's a planet. So that's pretty much what the reasons for constraints one through three were, is that it would confuse the students. Too much of the use of calculators is done through exact key sequences. So if you wanted to operate a calculator, you are taught. Press key one, one, one, two, whatever, whatever. By the way, those who actually switch the prototype on and get to the enunciator, again, I have to let you know because we're in typography country, the enunciators we changed. I changed from Ariel to Jules Sainz. So that internationalized this a little bit. So we, going back to that example, they mandate that students are that fragile that they can't learn that a key, clear stat, has moved to the clear grouping but has to remain there. And there's another example, store and recall aren't on the same level. Recalls on the top level store is a shifted function. I just find that bizarre. I contrast that with Mr. Keen giving me an RPN calculator and saying go and play with it for a weekend and try to figure this out. And I want to try to go back, I hope I can do this, I asked you to recall the definition of rote, mechanical or unthinking routine or repetition. Isn't that what is being mandated in education? Forgive me. So keystroke consistency in calculator. Assisted iterations of models are required to maintain key label locations. We're encouraging rote with calculators and assistive device but we discourage practice with mathematics. So that really caught me by surprise. Boris mentioned that if you see computer modern, you know it's tech. Well, I have hunted long and hard. HP 95LX which was a DOS-based computer. I am convinced it's computer modern. I have gone to Corvallis. A lot of the old timers are gone, of course. No one seems to know whether it was done by tech. But it is my suspicion and if anyone in this crowd knows any different, I would really like to find out just for historical curiosity. Okay, method. Method is going to be like a 10 second presentation before we get to Matai. The history goes back a little bit. You already know I'm a UNIX user. I use UNIX and Linux interchangeably in terms. It began with Grenule which is a flash card system. I think it was done for KDE but at least I had it on Ubuntu. And I created a bunch of card boxes for my kids for multiplication, addition memory. So if you have two operands, let's say between 20 and 10, they're supposed to get the results by memory and it's simple practice. You sit and run a computer and you do flash drive. Open office spreadsheet, I graduated that for multiple operands. I was not very confident in my tech capabilities. I had never done anything like what I'm doing now. So it was, I had always intended to do it in tech or lay tech but I just didn't have the skill. But it got results. My daughter started to progress in mathematics which was really heartening. And one incident in particular stays with me. She was going, she was at her soccer practice which is in North America very highly participated sport especially among young girls. And she turned to her mother and she said, mama, that student, sorry, that player has number 12 on their back. Do you know that can be expressed as four by three and six by two? Now it may not rank up there with Hardy's discussion with Ramanujan about 1729. But for a parent of a daughter struggling with mathematics, I'll take it any day of the week. And I noticed that someone's reading The Indian Clerk which is an amazing book. I just happened to walk by. I'm not sure who has it. Okay, serendipitously around that time I was struggling with managing the complexity of my project management practice and project management. In my world doesn't mean scheduling. Scheduling is a very small part of it. It has to do with tasks, communications and whatnot. I came across Ron Dorfler and I don't know if anyone else has but I'd be quite happy if you ignored the rest of my talk and went to his website because what he's doing is just amazing. He's reviving the art of nomography and he uses tech to do it. But I came across him because he had produced this little utility which was a pocket sized organizer. You selected a bunch of template sheets. It would print them on a letter size paper, both A4 and letter, U.S. letter. And you could fold it and take it in your pocket for the day and it had all sorts of odd nomograms as well. And through Ron I discovered Tixie or as mandated in this state, Tixie. It does make it easier to remember the ditty that should you be required to draw sprites and pixies then you must surely use Tixie. The floodgates opened at that point. I was able to do a lot of things. Bill Cheswick talked about not knowing about geometry. I had stumbled across the geometry package but I didn't know about Tixie so I was late to the game. People who monitor Launchpad will have seen this example many, many times over. I think in the last two years every time CUPS gets upgraded or Ubuntu gets upgraded I use a very inexpensive HP printer, Rick Richardson's driver, ZJS. But I use this as my standard example that I send out to the Ubuntu mailing list when custom page sizes break. What I ended up doing was creating an agenda application using TixZ. And as if my life wasn't complicated enough I found that our friends in Allentown, Pennsylvania, Daytime or Corporation didn't have a template that worked for me. So I created a four pages per day if you can imagine. That's quite a bit of note taking. Around the time I was suffering with that complexity issue there was a buzz in productivity circles about something known as GTD, getting things done. And the primary tenet of that approach is known as ubiquitous capture. You get everything down that you possibly can. The time that it happens. I use Richard Skoll's Remind. I use all the other cool tools. But when you're out in the field and I'm out in the field a fair bit, there's just no time. Even for instant on. I used Scion Revo way back with the Epoch operating system. But nothing beats pen and paper to capture. So what that ends up looking like and people are welcome to look at that. The website's not up but I will offer it and put it up. So it's custom page sizes, very illegible, but there's all kinds of templates. Great. So my short feature list was it should be whatever software was going to use tech and late tech would have an easily extensible list of worksheets, parameterized worksheet generation which would allow a graduated level of difficulty that would lead a student, a parent or an educator through the process. I think the footnote is lost in that but it's the ability to create beautiful documents. I think what I intended to say was this is strictly dependent on the skill set of the technician which I don't have. So you'll have to pardon some of that. Okay. Very, very simply, there's a bash script associated with each group of worksheets. There's a bash script which uses BC at the back end to generate operands. There's a late tech template and they're married together with set to create a spool tech file which is then converted to a PDF and delivered to your browser. In many cases the generator does nothing more than marry operands to the tech file but in other cases as the complexity grows in the worksheet it does spew out code snippets and fragments. I tried to resist the temptation to generate the tech code from scratch. I found it unwieldy. It's difficult to debug. It's easier to get a template and then intercede with that. Okay. Mithai. I hope this demo goes smoothly. I'll do my best. I'm not sure if I can anyhow. Bear with me. There we are. Okay. I'm running this locally but the website is active and I will just get rid of all the ancillary stuff so we get most of it on. The grouping of the worksheets is done based on the Ontario curriculum for mathematics. This is a Rails application which meant I had to learn Rails as it goes on. You end up having to learn a lot more than you think in delivering. Within each category it's table driven, easy to augment with new worksheets. There's graduated difficulty which was one of the prime directives and it's operand driven. So in my case I've, for instance, multiplication I grouped it one through six and seven through twelve it could be one through four, five through eight, it doesn't really matter. So geometry measurement which is I focused on analog time. Ask Nicholas Hayek, the former chairman of Swatch Group whether analog time has any significance in this day. Five billion dollars should say otherwise. Algebra which in Canada really means algebra and patterns. So I've done sequences here. Study some event trees. This area I haven't had a chance to work on, it's applications. I would like to do things of interest. Aviation arithmetic, vector arithmetic, codes and ciphers. So let's, we're running short of time. I'll just focus on measurements. So here you can see it goes from hourly intervals with labeled markers all the way down to one minute intervals without markers and with a MPM all done with the same generator. So I'm just going to invoke this. What's happening right now is it's doing all the things that I mentioned. It's generating this PDF on the fly. Had fun with this because I have, watches are one of my interests. So I hope you will agree that this one isn't bad. It is of course inaccurate. Watch nuts will know that the hour hand has to be below the minute hand but it would obscure in certain instances. So I took an executive decision and put the hour hand above the minute hand. The standards are labeled. Many watches have the minute hand, sorry, the minutes labeled on the inside but anyway, that's what that looks like. Contrast that going all the way down. So a student would begin with that where the operands would be whole hours versus something like this. And this one raised another subtle type setting issue is that with the MPM, pardon me, it would, there was no way of not obstructing the MPM indicator. So you can see here, for AM, the hour hand is lighter shade for PM, it's a darker shade so the shading changes in that. And each worksheet is generated on the fly. So if you did this 30 seconds later, you'd get your own different custom variation. So I'm really running short of time but I wanted to show you a lot more of this. I'll just throw up an event tree. So these questions relate to this event tree, in this case, fair dice. Again generated on the fly. There are sentence snippets and based on the operand results, the sentence are collated together. Chomsky would be happy. Every, you start with angles, acute and obtuse and you can run right the way through to reflex. Rotation is done dynamically, so not to confuse students. There are hints at the bottom. Anyway, so in there, as the number of worksheets grows, there's of course a search function. So if I was to search for scaling, right, you've got the one worksheet that has scaling in there. In closing, I wanted to just talk about a couple of refinements and acknowledgments. Refinements, I'm going to be working through the summer augmenting these worksheets and hope that I can speak to some school boards, at least in Canada. My hope is that if you find it useful, you could spread the word. Mostly the first question when I give a talk like this is what the heck is a Buncie and why does it have its own world? Well, Professor Buncie Law was my maternal grandfather and he was a mathematician and a math teacher. He prided himself not in his research, but in his teaching. And so Buncie's world, these are some of the textbooks that he wrote. There was a time in Punjab if you went through and did engineering, science or math, you could not escape either having used his textbooks or having been taught directly by him. I still meet his students, believe it or not. So that's what Buncie's world is. It's for me, it's a synonym for open access of mathematical learning. So thank you very much for your time. I'm not sure whether there are any questions, but I'm happy to take them or speak in the break. I'll let... Okay, very quick question. I understand that you use Tixie for all pictures, right? Yes, I did. Oh, thank you. By the way, it's great. Oh, thank you. Really great thing for you doing. So, can we have a last question? Okay, can we get those books that they are available? They are not available. Yeah, I did a few, three documentation lessons. I suppose I could scan them. The books that I have up there are only the books that were published after 1968, I believe. They just happened to be given to me when I visited him in India. I don't think he made any great effort at archiving. So there were many... If you go to the website, you'll see he was the head of the Department of Mathematics of DAV College from 29 to 65. And so he wrote lots and lots of books. What would the third name? Buncie, which means flute. But do you have some names or...? Well, it's Buncie Law. But the names in that time, I mean, it was a very different era. He was... I spoke with Mirko. He's a graduate of Lahore University, pre-partition, and came to Punjab in the 20s. And it was not uncommon to simplify those names at the time. So we are all accidents of history, if not geography. Thank you. Okay. Thank you. Thank you. Thank you. Thank you.
 So I must say, I feel like a bit of a gatecrusher to a rather exclusive party,  much like that couple in Washington.  I consider myself a rank amateur technician, and I mean that in the typesetting sense.  Boris yesterday said that he considered himself a wizard's apprentice.  Well, if he's a wizard's apprentice, I'm in the stable cleaning up slot.  So, Carl graciously or unwittingly left the door open when he invited talks about how tech is used  out in the wild in the field.  And I took the opportunity, I seized the opportunity, wedged myself in,  and that's what this talk is about.  I do use tech and late tech, which is how I grew up pronouncing it,  in almost every aspect of my business.  Here we are looking for the most.  Okay, a mouthful of a title, using late tech to generate dynamic mathematics worksheets for the web.  For the purpose of this project, that's my contact information.  I, like the other speakers here, would really welcome your ideas, your input.  The technical aspects of the discussion are rather rudimentary,  so I'm going to spend a lot more time on the surrounding aspects of the project,  and I ask your indulgence on that part.  So, as an introduction, personal typesetting history.  Bill Cheswick mentioned this program called Runoff.  I think I'm probably one of the few people in the room that have not only heard of Runoff,  but have used it.  It was a deck standard runoff, and my personal history goes back even probably earlier than Bill's  with UNIX.  My uncle worked in Bell Labs in the early 70s, so as a kid I was wasting reams of thermal paper,  dialing in with a TI Silent 700 with acoustic coupling onto a UNIX system and playing whatever  was around in user games and getting kicked off in the middle of the night.  So from there it progressed to EnRof and T-Rof.  Softquad had a very elegant implementation of T-Rof, and then of course I saw the light  and started to use late tech.  I have a project management consultancy practice outside of Toronto, and it's related to the  construction industry.  We do renovations, commercial and residential.  We do high-end automation, Lutron and shading controls.  I also have the luxury, since it's a sole practice, that I can pick my own tool sets,  so I did.  We use late tech all throughout our business, or I do.  That's the Royal Wii.  But that gives you a sprinkling.  I'll touch on those a little bit later.  I also have props in the absence of the technical content.  So there's another overarching theme to this talk, which is mathematics through practice.  Sherry Turkle wrote this book, I think it was in the early 80s.  It's a brilliant book.  I'm talking generational now.  If you haven't read it, just go out and buy it.  It opens with the story of a feral child, Victor of Abiram, who when he came out of the forest  in 1800, did so without an apparent ability to speak.  It was later discovered that he could hear, but he could not speak.  He was adopted by a scientist, Jean-Marc Gaspar-Nitard, who took it upon himself to educate Victor,  which in the context of the times meant that he should learn language, the French language.  Language marked a civilized person of the age.  There are many controversies surrounding the story.  I don't want to delve into it.  I only wanted to mention it because the story was and remains compelling because it raises  the question, is language innate or an acquired skill?  And naturally, we're not going to have a control group of newborns shipped off into  the forest and wait 11 years and check it out.  The story resonates with me personally because I have two children, an elder daughter and  a son, younger son.  My daughter has struggled with maths from the get-go.  The school system, at least in Canada, has tried many things and finally what ended up  happening.  It happened early in her student career is she was shunted off to what's known as a special  stream that makes lots of accommodations.  It uses assistive testing.  I say assistive testing, not learning because it advocates open book tests, use of calculators  at a very early age.  I found that a bit disturbing.  My daughter is precocious.  She's eloquent.  She's well-spoken.  She has a remarkable memory.  She has her memories far better than mine.  And I was left struggling with the idea, much as Itard did in his time, is my daughter missing  a mathematics gene?  Is mathematics innate or an acquired skill?  Well, according to Young, anything beyond concrete numbers is probably not amenable  to human beings.  But at least he gives an allowance that mere mortals can master concrete numbers.  So the most frequent of such peculiarities is the incapacity to understand any form of  mathematics that is not expressed in concrete numbers.  My early education for just a brief couple of years was in India.  And although it was brief, the memory of that experience remains quite vivid.  In that educational system, there is no concept.  There's no allowance made to this idea that there are two types of people in the world,  especially children, those who get mathematics and those that don't.  And at least with numeracy, it's an assume.  If you go to school, you're going to learn mathematics.  So unlike Itard's society, where language marked a civilized person, in the Indian educational  system, both language and mathematics marks a civilized person.  So mathematical ability is innate, but mathematical skill can only be acquired through practice.  I've broken up my talk into three areas, three topics, motive, method, and metai.  Metai is a word that's common to many South Asian languages, and it refers to sweets,  sweet.  So I'm going to refer to it in terms of iCandy.  We're going to do a demo of the software at the end.  And perhaps a vain hope that once you see the demo, you'll be letting out a resounding  sweet idiomatically.  Okay, we'll start with motive.  I'm going to spend a lot of time with motive.  As I said, the technical aspects from a typesetting perspective are rather rudimentary, so I hope  I can entertain you with other things.  Is numeracy desirable?  Is it even necessary anymore?  After all, we have computing power coming out of our pockets.  I'm told that wristwatches are on their way out, which I don't buy.  The founder of the Swatch Group passed away.  The New York Times had an obituary, and I think the last year's revenues were $5 billion.  So he did rather well on wristwatches.  We can look at these questions in two ways.  We can look at it in terms of basic fitness, like physical fitness.  Mathematics or numeracy is mental fitness.  It's good for you.  It lowers healthcare costs.  It leads to more productive and happier lives.  It may even lead to mental equanimity.  The second aspect is the one that I want to focus in on is that, and that's the thing  that I think got skipped in my daughter's education, was that it is a necessary building  block on which the edifice of mathematical literacy is built.  Even though we have calculators and cell phones and everything else under the sun, if  you miss that step, you're not only denying the student mastery over their environment  at a very young age, but you're putting a big hole in their education that is very hard  to recover from.  And I'm going to lay out a bunch of these, well, let's go back to Aristotelian syllogism.  I'm going to use proof by assertion.  So I'm going to lay out a bunch of these propositions like Royal Fisben, the game of Royal Fisben,  which I apologize to many of the international attendants.  I tend to throw these cultural references in.  Star Trek fans will remember that Royal Fisben was a game of arbitrary rules that Captain  Kirk duped a few Chinese, sorry, Chicago gangsters out of a game.  So the propositions would go something like this.  So if it's Tuesday and if it's 11 o'clock and if we agree that numeracy is an essential  step in the education towards mathematical literacy, then of course you have to use latex  to achieve it.  QED.  Now, if we, I'm going to go back again, I skipped a point.  If we divorce numeracy from symbolic algebra, I think what happens, and that's my own observations  with my daughter, is that young children miss this step of gaining mathematical intuition.  Numbers are really important in their daily lives.  But in all, in very interesting ways, and I'm going to touch on that later.  So by divorcing that and expecting that you can have assistive mathematics, what ends  up happening is you end up with what I had in the next slide.  So I think this was part of Hilbert's Top 10 in 1900 that you could go from the left-hand  side to the right-hand side.  So the other argument against that kind of numeracy is that, yes, it's a desirable goal,  so is world peace, but it's too difficult, and it's only available to a select few.  I'm going to throw out another prop.  Dover used to put out these beautiful, elegant additions, both typesetting and content-wise.  This one is the Divine Proportionist Study in Mathematical Beauty by H.E. Huntley.  I'm not even sure when it was published, but a long time ago.  So this is a quote from Professor Huntley, which I strongly object to.  "'Teacher should be sympathetic to the mathematically ungifted for humane reasons,'  sounds like euthanasia.  "'Such should be dissuaded from any unaccountable ambition.  They may have to take advanced mathematics.'"  And I think the caveat he threw in is just advanced, but I think it means anyone who  doesn't get it should be out of the system.  So I don't agree.  And unfortunately, I think that's an attitude that's prevalent in many schools these days  as well.  So how does one learn mathematics?  And I went back to my own experience, not in maths, but in programming.  So I think there's two ways.  There are those that gain a kernel of comprehension, and they refine that kernel of comprehension  using practice, and it leads to proficiencies.  But there's the rest of us.  I consider myself a slogger, although I have a long history in programming and in maths,  where you don't gain the comprehension unless you scratch away at a problem or several  problems.  And then you get this aha moment and say, okay, now I know why everything I did before  was wrong.  So those are the two approaches.  I think there's a wide band of students that fall into the second category that are getting  missed in education, proof by assertion, remember?  So Sherry Turkle's work in the 70s and 80s also hinted at this with the concepts of hard  mastery and soft mastery.  She I think it was mostly done in New England, Boston area, but she observed young students  interacting with computers.  Now at the time, if you wanted to interact with a computer, you had to know something  about relatively low level language interaction.  You didn't have the luxury of transition effects and lots of layers between you and the hardware.  So it meant whether you were classified as a right brain or left brain child, you would  be interacting with a computer at a low level.  So some children would treat computers as transparent systems, whereas they'd like to  know about the mechanical innards of it.  They'd understand that and they'd need to know that before they could map input to output.  That was the first approach.  They gained the comprehension of the system and then they could interact with it.  There were another class of students who treated this as a black box.  And there was one very telling example where grade two class, this was with logo I think,  not turtle, but logo was this graphical language several generations ago.  I keep saying that because I'm really hard pressed to believe it so much has happened.  So grade two students discovered that there was this mapping between numbers and the direction  that the sprite would go.  And I am certain there was no discussion of Togas, ancient Greeks, Euclid, but they got  it.  They treated it as a closed system and it was like breaking a code.  So I would put them in the second category there.  So we've arrived I think at a stop or at a point in education where the three Rs, which  were never Rs, reading, writing and arithmetic are now classified to be reactionary, redundant  and retrograde.  And I think that's a shame.  But I think there's a good reason for it and it has to do with language.  I'm picky about language as well.  I think it's the OAD that we all probably suffer from or our spouses accuse us of.  The distinction is between rote versus practice and they're very different things.  Every a lot of what was in the three Rs has not been the umbrella of rote and thrown away.  But I think what's been lost in that is the value of practice.  And if you go back to my overarching theme, it's mathematics through practice.  So I'll take the easy way out.  I'll begin with Miriam Webster.  The details don't matter but I want you to pay particular attention to the second definition.  I'll come back to it later.  Mechanical or unthinking routine or repetition.  Whereas for practice, we go back to the proficiency argument.  You want to perform or work it repeatedly so as to become proficient.  Okay, this is Camus and fortunately my literature teacher in high school forced us.  He asked us to read this, read this out loud, write about it and that's practice.  It's stuck in my head when I had to prepare for this talk.  Isn't that what counts?  This is from his essay, A Pause Between Yes and No.  Surely not since doing homework and accepting manhood leads to nothing but old age.  I suspect if you were asked, if you were to ask Camus if that applied to writing as well,  he would say no.  Writing was pure pleasure.  Which means that practice leads to proficiency.  My definition is synthesized here.  Wrote implies tedium, simple repetition without improvement or acquisition of skill.  It definitely indicates no purpose.  It's done without purpose.  Practice implies with purpose and it's gaining in capabilities.  You do something because you're learning something about it.  This is my second time in San Francisco.  The first time was 21 years ago when I visited Redwood City and I committed to Next Step,  which was a business blunder.  I can't come into the Bay Area without hearing echoes of Mario Savio's speech at Sproul Hall.  There's a time when the operation of the machine becomes so odious, makes you so sick at heart  that you can't take part.  Well, if you associate mathematics with tedium, tedious, wrote odious, I wouldn't want to do  maths either.  I think what we need is an open access movement for mathematics.  A couple of examples, of course, MIT OpenCourseWare.  Amazing program, but directed at secondary and higher education students.  A couple of weeks ago, this came across on the BBC website.  They have a maths busking program.  So maths students are sent off into shopping malls to do maths tricks and attract students.  Why do we hide mathematics?  Why do we treat it as something that cannot be out in the open, regardless of your skill  set?  Okay.  By now, I have no doubt convinced you that I am a loyal citizen in the land of King Lund.  I hate machinery.  I don't even have electricity.  I walked 10 miles in blizzard conditions to school and even more on the way home, 16 kilometers,  you know, 10 versus 16.  Let me put that aside or suede your concerns a little bit.  The next slide is not a very flattering slide, but I don't know whether you can tell what  I am holding in my left hand.  It's a calculator prototype.  They are not allowed in the premises of Tash Mahal.  The only electronic device allowed is a camera.  I happen to have it in my pocket.  How much of a calculator geek am I?  I had a calculator in my pocket that went undetected through security.  I fell in love with calculators with my first, which was a Texas Instruments SR50A for those  who may remember back that far.  And then came a fateful day, a Friday afternoon, when my high school electronics teacher, Mr.  Keen, for whom I will remain forever indebted, said, you seem to be interested in calculators.  Why don't you take this one home?  It works a little bit differently.  I don't have a manual, but I have an article.  The article, as many of you probably can already ascertain, was Enter versus Equals.  And the calculator was an HP35.  Since then, I have been in love with anything with an Enter key.  There have been some rocky periods in my relationship with HP.  I remember buying one and phoning what I thought was Corvallis and asking how I switch an Omnigo  100 portable computer into RPN.  And the voice at the other end said, I'm sorry, sir, I don't know what RPN is.  This was a t-shirt prototype that I typeset for HP.  I have written several critiques about the typesetting of their documentation, the demise  in typesetting of their documentation, as well as the layouts on their keyboard.  And I guess finally they said, you know what?  You've got all of these criticisms.  Why don't you come in on a design exercise?  I don't work for HP.  I'm not remunerated by them.  This was a voluntary exercise.  This was the result of the first one.  I don't know whether you can see at all.  This is a mask for a final pre-production mask of a business calculator.  The earlier ones were really abysmal.  The mathematical functions were done horribly, allegedly.  And I'll give you an example of that.  Font fanatics may notice that the math functions are typesetting gentium.  My original proposal to them, I advocated Sumner Stones, beautiful stones, Sancero,  Fuminist, and Serifons, HP's branding uses a variant of Futura.  And it's called Lusense.  We had to find something complementary.  And it had to fit licensing issues.  Boris has already talked about licensing legal.  So gentium is what was selected.  I'm going to pass around another, the second design exercise, the result of it.  The second design exercise was to turn this, which is their entry level 10B, into this,  which is a 10B2+.  Rule number one was that no key label be shifted on the keypad.  And rules number two and three were equally emphatic.  Do not violate rule number one.  So I'm going to pass these around.  I want you to pay particular attention.  This is a late-stage pre-production model.  You can see it from the labeling in the back.  There's some type setting that's off.  The centering of the off label isn't quite there.  But I want you to pay particular attention to the clear stat function, which was the  clear sigma in the old one.  Clear functions have been labeled, grouped on the left-hand side.  And I'll just come back.  So even when it makes ergonomic sense to shift the label, you're not allowed.  And Hans illustrated this beautifully in his discussion about classifying Pluto not as  a planet.  One of the lines that you threw up, Hans, from the governor of this fine state, was  that it would confuse the students because the textbooks are already written and they  all say Pluto's a planet.  So that's pretty much what the reasons for constraints one through three were, is that  it would confuse the students.  Too much of the use of calculators is done through exact key sequences.  So if you wanted to operate a calculator, you are taught.  Press key one, one, one, two, whatever, whatever.  By the way, those who actually switch the prototype on and get to the enunciator, again,  I have to let you know because we're in typography country, the enunciators we changed.  I changed from Ariel to Jules Sainz.  So that internationalized this a little bit.  So we, going back to that example, they mandate that students are that fragile that they can't  learn that a key, clear stat, has moved to the clear grouping but has to remain there.  And there's another example, store and recall aren't on the same level.  Recalls on the top level store is a shifted function.  I just find that bizarre.  I contrast that with Mr. Keen giving me an RPN calculator and saying go and play with  it for a weekend and try to figure this out.  And I want to try to go back, I hope I can do this, I asked you to recall the definition  of rote, mechanical or unthinking routine or repetition.  Isn't that what is being mandated in education?  Forgive me.  So keystroke consistency in calculator.  Assisted iterations of models are required to maintain key label locations.  We're encouraging rote with calculators and assistive device but we discourage practice  with mathematics.  So that really caught me by surprise.  Boris mentioned that if you see computer modern, you know it's tech.  Well, I have hunted long and hard.  HP 95LX which was a DOS-based computer.  I am convinced it's computer modern.  I have gone to Corvallis.  A lot of the old timers are gone, of course.  No one seems to know whether it was done by tech.  But it is my suspicion and if anyone in this crowd knows any different, I would really like  to find out just for historical curiosity.  Okay, method.  Method is going to be like a 10 second presentation before we get to Matai.  The history goes back a little bit.  You already know I'm a UNIX user.  I use UNIX and Linux interchangeably in terms.  It began with Grenule which is a flash card system.  I think it was done for KDE but at least I had it on Ubuntu.  And I created a bunch of card boxes for my kids for multiplication, addition memory.  So if you have two operands, let's say between 20 and 10, they're supposed to get the results  by memory and it's simple practice.  You sit and run a computer and you do flash drive.  Open office spreadsheet, I graduated that for multiple operands.  I was not very confident in my tech capabilities.  I had never done anything like what I'm doing now.  So it was, I had always intended to do it in tech or lay tech but I just didn't have  the skill.  But it got results.  My daughter started to progress in mathematics which was really heartening.  And one incident in particular stays with me.  She was going, she was at her soccer practice which is in North America very highly participated  sport especially among young girls.  And she turned to her mother and she said, mama, that student, sorry, that player has  number 12 on their back.  Do you know that can be expressed as four by three and six by two?  Now it may not rank up there with Hardy's discussion with Ramanujan about 1729.  But for a parent of a daughter struggling with mathematics, I'll take it any day of  the week.  And I noticed that someone's reading The Indian Clerk which is an amazing book.  I just happened to walk by.  I'm not sure who has it.  Okay, serendipitously around that time I was struggling with managing the complexity of  my project management practice and project management.  In my world doesn't mean scheduling.  Scheduling is a very small part of it.  It has to do with tasks, communications and whatnot.  I came across Ron Dorfler and I don't know if anyone else has but I'd be quite happy  if you ignored the rest of my talk and went to his website because what he's doing is  just amazing.  He's reviving the art of nomography and he uses tech to do it.  But I came across him because he had produced this little utility which was a pocket sized  organizer.  You selected a bunch of template sheets.  It would print them on a letter size paper, both A4 and letter, U.S. letter.  And you could fold it and take it in your pocket for the day and it had all sorts of odd nomograms  as well.  And through Ron I discovered Tixie or as mandated in this state, Tixie.  It does make it easier to remember the ditty that should you be required to draw sprites  and pixies then you must surely use Tixie.  The floodgates opened at that point.  I was able to do a lot of things.  Bill Cheswick talked about not knowing about geometry.  I had stumbled across the geometry package but I didn't know about Tixie so I was late  to the game.  People who monitor Launchpad will have seen this example many, many times over.  I think in the last two years every time CUPS gets upgraded or Ubuntu gets upgraded I use  a very inexpensive HP printer, Rick Richardson's driver, ZJS.  But I use this as my standard example that I send out to the Ubuntu mailing list when  custom page sizes break.  What I ended up doing was creating an agenda application using TixZ.  And as if my life wasn't complicated enough I found that our friends in Allentown, Pennsylvania,  Daytime or Corporation didn't have a template that worked for me.  So I created a four pages per day if you can imagine.  That's quite a bit of note taking.  Around the time I was suffering with that complexity issue there was a buzz in productivity  circles about something known as GTD, getting things done.  And the primary tenet of that approach is known as ubiquitous capture.  You get everything down that you possibly can.  The time that it happens.  I use Richard Skoll's Remind.  I use all the other cool tools.  But when you're out in the field and I'm out in the field a fair bit, there's just no time.  Even for instant on.  I used Scion Revo way back with the Epoch operating system.  But nothing beats pen and paper to capture.  So what that ends up looking like and people are welcome to look at that.  The website's not up but I will offer it and put it up.  So it's custom page sizes, very illegible, but there's all kinds of templates.  Great.  So my short feature list was it should be whatever software was going to use tech and  late tech would have an easily extensible list of worksheets, parameterized worksheet  generation which would allow a graduated level of difficulty that would lead a student, a  parent or an educator through the process.  I think the footnote is lost in that but it's the ability to create beautiful documents.  I think what I intended to say was this is strictly dependent on the skill set of the  technician which I don't have.  So you'll have to pardon some of that.  Okay.  Very, very simply, there's a bash script associated with each group of worksheets.  There's a bash script which uses BC at the back end to generate operands.  There's a late tech template and they're married together with set to create a spool  tech file which is then converted to a PDF and delivered to your browser.  In many cases the generator does nothing more than marry operands to the tech file but in  other cases as the complexity grows in the worksheet it does spew out code snippets and  fragments.  I tried to resist the temptation to generate the tech code from scratch.  I found it unwieldy.  It's difficult to debug.  It's easier to get a template and then intercede with that.  Okay.  Mithai.  I hope this demo goes smoothly.  I'll do my best.  I'm not sure if I can anyhow.  Bear with me.  There we are.  Okay.  I'm running this locally but the website is active and I will just get rid of all the  ancillary stuff so we get most of it on.  The grouping of the worksheets is done based on the Ontario curriculum for mathematics.  This is a Rails application which meant I had to learn Rails as it goes on.  You end up having to learn a lot more than you think in delivering.  Within each category it's table driven, easy to augment with new worksheets.  There's graduated difficulty which was one of the prime directives and it's operand driven.  So in my case I've, for instance, multiplication I grouped it one through six and seven through  twelve it could be one through four, five through eight, it doesn't really matter.  So geometry measurement which is I focused on analog time.  Ask Nicholas Hayek, the former chairman of Swatch Group whether analog time has any significance  in this day.  Five billion dollars should say otherwise.  Algebra which in Canada really means algebra and patterns.  So I've done sequences here.  Study some event trees.  This area I haven't had a chance to work on, it's applications.  I would like to do things of interest.  Aviation arithmetic, vector arithmetic, codes and ciphers.  So let's, we're running short of time.  I'll just focus on measurements.  So here you can see it goes from hourly intervals with labeled markers all the way down to one  minute intervals without markers and with a MPM all done with the same generator.  So I'm just going to invoke this.  What's happening right now is it's doing all the things that I mentioned.  It's generating this PDF on the fly.  Had fun with this because I have, watches are one of my interests.  So I hope you will agree that this one isn't bad.  It is of course inaccurate.  Watch nuts will know that the hour hand has to be below the minute hand but it would obscure  in certain instances.  So I took an executive decision and put the hour hand above the minute hand.  The standards are labeled.  Many watches have the minute hand, sorry, the minutes labeled on the inside but anyway,  that's what that looks like.  Contrast that going all the way down.  So a student would begin with that where the operands would be whole hours versus something  like this.  And this one raised another subtle type setting issue is that with the MPM, pardon me, it  would, there was no way of not obstructing the MPM indicator.  So you can see here, for AM, the hour hand is lighter shade for PM, it's a darker shade  so the shading changes in that.  And each worksheet is generated on the fly.  So if you did this 30 seconds later, you'd get your own different custom variation.  So I'm really running short of time but I wanted to show you a lot more of this.  I'll just throw up an event tree.  So these questions relate to this event tree, in this case, fair dice.  Again generated on the fly.  There are sentence snippets and based on the operand results, the sentence are collated  together.  Chomsky would be happy.  Every, you start with angles, acute and obtuse and you can run right the way through to reflex.  Rotation is done dynamically, so not to confuse students.  There are hints at the bottom.  Anyway, so in there, as the number of worksheets grows, there's of course a search function.  So if I was to search for scaling, right, you've got the one worksheet that has scaling  in there.  In closing, I wanted to just talk about a couple of refinements and acknowledgments.  Refinements, I'm going to be working through the summer augmenting these worksheets and  hope that I can speak to some school boards, at least in Canada.  My hope is that if you find it useful, you could spread the word.  Mostly the first question when I give a talk like this is what the heck is a Buncie and  why does it have its own world?  Well, Professor Buncie Law was my maternal grandfather and he was a mathematician and  a math teacher.  He prided himself not in his research, but in his teaching.  And so Buncie's world, these are some of the textbooks that he wrote.  There was a time in Punjab if you went through and did engineering, science or math, you  could not escape either having used his textbooks or having been taught directly by him.  I still meet his students, believe it or not.  So that's what Buncie's world is.  It's for me, it's a synonym for open access of mathematical learning.  So thank you very much for your time.  I'm not sure whether there are any questions, but I'm happy to take them or speak in the  break.  I'll let...  Okay, very quick question.  I understand that you use Tixie for all pictures, right?  Yes, I did.  Oh, thank you.  By the way, it's great.  Oh, thank you.  Really great thing for you doing.  So, can we have a last question?  Okay, can we get those books that they are available?  They are not available.  Yeah, I did a few, three documentation lessons.  I suppose I could scan them.  The books that I have up there are only the books that were published after 1968, I believe.  They just happened to be given to me when I visited him in India.  I don't think he made any great effort at archiving.  So there were many...  If you go to the website, you'll see he was the head of the Department of Mathematics  of DAV College from 29 to 65.  And so he wrote lots and lots of books.  What would the third name?  Buncie, which means flute.  But do you have some names or...?  Well, it's Buncie Law.  But the names in that time, I mean, it was a very different era.  He was...  I spoke with Mirko.  He's a graduate of Lahore University, pre-partition, and came to Punjab in the 20s.  And it was not uncommon to simplify those names at the time.  So we are all accidents of history, if not geography.  Thank you.  Okay.  Thank you.  Thank you.  Thank you.  Thank you.
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So I must say, I feel like a bit of a gatecrusher to a rather exclusive party, much like that couple in Washington. I consider myself a rank amateur technician, and I mean that in the typesetting sense. Boris yesterday said that he considered himself a wizard's apprentice. Well, if he's a wizard's apprentice, I'm in the stable cleaning up slot. So, Carl graciously or unwittingly left the door open when he invited talks about how tech is used out in the wild in the field. And I took the opportunity, I seized the opportunity, wedged myself in, and that's what this talk is about. I do use tech and late tech, which is how I grew up pronouncing it, in almost every aspect of my business. Here we are looking for the most. Okay, a mouthful of a title, using late tech to generate dynamic mathematics worksheets for the web. For the purpose of this project, that's my contact information. I, like the other speakers here, would really welcome your ideas, your input. The technical aspects of the discussion are rather rudimentary, so I'm going to spend a lot more time on the surrounding aspects of the project, and I ask your indulgence on that part. So, as an introduction, personal typesetting history. Bill Cheswick mentioned this program called Runoff. I think I'm probably one of the few people in the room that have not only heard of Runoff, but have used it. It was a deck standard runoff, and my personal history goes back even probably earlier than Bill's with UNIX. My uncle worked in Bell Labs in the early 70s, so as a kid I was wasting reams of thermal paper, dialing in with a TI Silent 700 with acoustic coupling onto a UNIX system and playing whatever was around in user games and getting kicked off in the middle of the night. So from there it progressed to EnRof and T-Rof. Softquad had a very elegant implementation of T-Rof, and then of course I saw the light and started to use late tech. I have a project management consultancy practice outside of Toronto, and it's related to the construction industry. We do renovations, commercial and residential. We do high-end automation, Lutron and shading controls. I also have the luxury, since it's a sole practice, that I can pick my own tool sets, so I did. We use late tech all throughout our business, or I do. That's the Royal Wii. But that gives you a sprinkling. I'll touch on those a little bit later. I also have props in the absence of the technical content. So there's another overarching theme to this talk, which is mathematics through practice. Sherry Turkle wrote this book, I think it was in the early 80s. It's a brilliant book. I'm talking generational now. If you haven't read it, just go out and buy it. It opens with the story of a feral child, Victor of Abiram, who when he came out of the forest in 1800, did so without an apparent ability to speak. It was later discovered that he could hear, but he could not speak. He was adopted by a scientist, Jean-Marc Gaspar-Nitard, who took it upon himself to educate Victor, which in the context of the times meant that he should learn language, the French language. Language marked a civilized person of the age. There are many controversies surrounding the story. I don't want to delve into it. I only wanted to mention it because the story was and remains compelling because it raises the question, is language innate or an acquired skill? And naturally, we're not going to have a control group of newborns shipped off into the forest and wait 11 years and check it out. The story resonates with me personally because I have two children, an elder daughter and a son, younger son. My daughter has struggled with maths from the get-go. The school system, at least in Canada, has tried many things and finally what ended up happening. It happened early in her student career is she was shunted off to what's known as a special stream that makes lots of accommodations. It uses assistive testing. I say assistive testing, not learning because it advocates open book tests, use of calculators at a very early age. I found that a bit disturbing. My daughter is precocious. She's eloquent. She's well-spoken. She has a remarkable memory. She has her memories far better than mine. And I was left struggling with the idea, much as Itard did in his time, is my daughter missing a mathematics gene? Is mathematics innate or an acquired skill? Well, according to Young, anything beyond concrete numbers is probably not amenable to human beings. But at least he gives an allowance that mere mortals can master concrete numbers. So the most frequent of such peculiarities is the incapacity to understand any form of mathematics that is not expressed in concrete numbers. My early education for just a brief couple of years was in India. And although it was brief, the memory of that experience remains quite vivid. In that educational system, there is no concept. There's no allowance made to this idea that there are two types of people in the world, especially children, those who get mathematics and those that don't. And at least with numeracy, it's an assume. If you go to school, you're going to learn mathematics. So unlike Itard's society, where language marked a civilized person, in the Indian educational system, both language and mathematics marks a civilized person. So mathematical ability is innate, but mathematical skill can only be acquired through practice. I've broken up my talk into three areas, three topics, motive, method, and metai. Metai is a word that's common to many South Asian languages, and it refers to sweets, sweet. So I'm going to refer to it in terms of iCandy. We're going to do a demo of the software at the end. And perhaps a vain hope that once you see the demo, you'll be letting out a resounding sweet idiomatically. Okay, we'll start with motive. I'm going to spend a lot of time with motive. As I said, the technical aspects from a typesetting perspective are rather rudimentary, so I hope I can entertain you with other things. Is numeracy desirable? Is it even necessary anymore? After all, we have computing power coming out of our pockets. I'm told that wristwatches are on their way out, which I don't buy. The founder of the Swatch Group passed away. The New York Times had an obituary, and I think the last year's revenues were $5 billion. So he did rather well on wristwatches. We can look at these questions in two ways. We can look at it in terms of basic fitness, like physical fitness. Mathematics or numeracy is mental fitness. It's good for you. It lowers healthcare costs. It leads to more productive and happier lives. It may even lead to mental equanimity. The second aspect is the one that I want to focus in on is that, and that's the thing that I think got skipped in my daughter's education, was that it is a necessary building block on which the edifice of mathematical literacy is built. Even though we have calculators and cell phones and everything else under the sun, if you miss that step, you're not only denying the student mastery over their environment at a very young age, but you're putting a big hole in their education that is very hard to recover from. And I'm going to lay out a bunch of these, well, let's go back to Aristotelian syllogism. I'm going to use proof by assertion. So I'm going to lay out a bunch of these propositions like Royal Fisben, the game of Royal Fisben, which I apologize to many of the international attendants. I tend to throw these cultural references in. Star Trek fans will remember that Royal Fisben was a game of arbitrary rules that Captain Kirk duped a few Chinese, sorry, Chicago gangsters out of a game. So the propositions would go something like this. So if it's Tuesday and if it's 11 o'clock and if we agree that numeracy is an essential step in the education towards mathematical literacy, then of course you have to use latex to achieve it. QED. Now, if we, I'm going to go back again, I skipped a point. If we divorce numeracy from symbolic algebra, I think what happens, and that's my own observations with my daughter, is that young children miss this step of gaining mathematical intuition. Numbers are really important in their daily lives. But in all, in very interesting ways, and I'm going to touch on that later. So by divorcing that and expecting that you can have assistive mathematics, what ends up happening is you end up with what I had in the next slide. So I think this was part of Hilbert's Top 10 in 1900 that you could go from the left-hand side to the right-hand side. So the other argument against that kind of numeracy is that, yes, it's a desirable goal, so is world peace, but it's too difficult, and it's only available to a select few. I'm going to throw out another prop. Dover used to put out these beautiful, elegant additions, both typesetting and content-wise. This one is the Divine Proportionist Study in Mathematical Beauty by H.E. Huntley. I'm not even sure when it was published, but a long time ago. So this is a quote from Professor Huntley, which I strongly object to. "'Teacher should be sympathetic to the mathematically ungifted for humane reasons,' sounds like euthanasia. "'Such should be dissuaded from any unaccountable ambition. They may have to take advanced mathematics.'" And I think the caveat he threw in is just advanced, but I think it means anyone who doesn't get it should be out of the system. So I don't agree. And unfortunately, I think that's an attitude that's prevalent in many schools these days as well. So how does one learn mathematics? And I went back to my own experience, not in maths, but in programming. So I think there's two ways. There are those that gain a kernel of comprehension, and they refine that kernel of comprehension using practice, and it leads to proficiencies. But there's the rest of us. I consider myself a slogger, although I have a long history in programming and in maths, where you don't gain the comprehension unless you scratch away at a problem or several problems. And then you get this aha moment and say, okay, now I know why everything I did before was wrong. So those are the two approaches. I think there's a wide band of students that fall into the second category that are getting missed in education, proof by assertion, remember? So Sherry Turkle's work in the 70s and 80s also hinted at this with the concepts of hard mastery and soft mastery. She I think it was mostly done in New England, Boston area, but she observed young students interacting with computers. Now at the time, if you wanted to interact with a computer, you had to know something about relatively low level language interaction. You didn't have the luxury of transition effects and lots of layers between you and the hardware. So it meant whether you were classified as a right brain or left brain child, you would be interacting with a computer at a low level. So some children would treat computers as transparent systems, whereas they'd like to know about the mechanical innards of it. They'd understand that and they'd need to know that before they could map input to output. That was the first approach. They gained the comprehension of the system and then they could interact with it. There were another class of students who treated this as a black box. And there was one very telling example where grade two class, this was with logo I think, not turtle, but logo was this graphical language several generations ago. I keep saying that because I'm really hard pressed to believe it so much has happened. So grade two students discovered that there was this mapping between numbers and the direction that the sprite would go. And I am certain there was no discussion of Togas, ancient Greeks, Euclid, but they got it. They treated it as a closed system and it was like breaking a code. So I would put them in the second category there. So we've arrived I think at a stop or at a point in education where the three Rs, which were never Rs, reading, writing and arithmetic are now classified to be reactionary, redundant and retrograde. And I think that's a shame. But I think there's a good reason for it and it has to do with language. I'm picky about language as well. I think it's the OAD that we all probably suffer from or our spouses accuse us of. The distinction is between rote versus practice and they're very different things. Every a lot of what was in the three Rs has not been the umbrella of rote and thrown away. But I think what's been lost in that is the value of practice. And if you go back to my overarching theme, it's mathematics through practice. So I'll take the easy way out. I'll begin with Miriam Webster. The details don't matter but I want you to pay particular attention to the second definition. I'll come back to it later. Mechanical or unthinking routine or repetition. Whereas for practice, we go back to the proficiency argument. You want to perform or work it repeatedly so as to become proficient. Okay, this is Camus and fortunately my literature teacher in high school forced us. He asked us to read this, read this out loud, write about it and that's practice. It's stuck in my head when I had to prepare for this talk. Isn't that what counts? This is from his essay, A Pause Between Yes and No. Surely not since doing homework and accepting manhood leads to nothing but old age. I suspect if you were asked, if you were to ask Camus if that applied to writing as well, he would say no. Writing was pure pleasure. Which means that practice leads to proficiency. My definition is synthesized here. Wrote implies tedium, simple repetition without improvement or acquisition of skill. It definitely indicates no purpose. It's done without purpose. Practice implies with purpose and it's gaining in capabilities. You do something because you're learning something about it. This is my second time in San Francisco. The first time was 21 years ago when I visited Redwood City and I committed to Next Step, which was a business blunder. I can't come into the Bay Area without hearing echoes of Mario Savio's speech at Sproul Hall. There's a time when the operation of the machine becomes so odious, makes you so sick at heart that you can't take part. Well, if you associate mathematics with tedium, tedious, wrote odious, I wouldn't want to do maths either. I think what we need is an open access movement for mathematics. A couple of examples, of course, MIT OpenCourseWare. Amazing program, but directed at secondary and higher education students. A couple of weeks ago, this came across on the BBC website. They have a maths busking program. So maths students are sent off into shopping malls to do maths tricks and attract students. Why do we hide mathematics? Why do we treat it as something that cannot be out in the open, regardless of your skill set? Okay. By now, I have no doubt convinced you that I am a loyal citizen in the land of King Lund. I hate machinery. I don't even have electricity. I walked 10 miles in blizzard conditions to school and even more on the way home, 16 kilometers, you know, 10 versus 16. Let me put that aside or suede your concerns a little bit. The next slide is not a very flattering slide, but I don't know whether you can tell what I am holding in my left hand. It's a calculator prototype. They are not allowed in the premises of Tash Mahal. The only electronic device allowed is a camera. I happen to have it in my pocket. How much of a calculator geek am I? I had a calculator in my pocket that went undetected through security. I fell in love with calculators with my first, which was a Texas Instruments SR50A for those who may remember back that far. And then came a fateful day, a Friday afternoon, when my high school electronics teacher, Mr. Keen, for whom I will remain forever indebted, said, you seem to be interested in calculators. Why don't you take this one home? It works a little bit differently. I don't have a manual, but I have an article. The article, as many of you probably can already ascertain, was Enter versus Equals. And the calculator was an HP35. Since then, I have been in love with anything with an Enter key. There have been some rocky periods in my relationship with HP. I remember buying one and phoning what I thought was Corvallis and asking how I switch an Omnigo 100 portable computer into RPN. And the voice at the other end said, I'm sorry, sir, I don't know what RPN is. This was a t-shirt prototype that I typeset for HP. I have written several critiques about the typesetting of their documentation, the demise in typesetting of their documentation, as well as the layouts on their keyboard. And I guess finally they said, you know what? You've got all of these criticisms. Why don't you come in on a design exercise? I don't work for HP. I'm not remunerated by them. This was a voluntary exercise. This was the result of the first one. I don't know whether you can see at all. This is a mask for a final pre-production mask of a business calculator. The earlier ones were really abysmal. The mathematical functions were done horribly, allegedly. And I'll give you an example of that. Font fanatics may notice that the math functions are typesetting gentium. My original proposal to them, I advocated Sumner Stones, beautiful stones, Sancero, Fuminist, and Serifons, HP's branding uses a variant of Futura. And it's called Lusense. We had to find something complementary. And it had to fit licensing issues. Boris has already talked about licensing legal. So gentium is what was selected. I'm going to pass around another, the second design exercise, the result of it. The second design exercise was to turn this, which is their entry level 10B, into this, which is a 10B2+. Rule number one was that no key label be shifted on the keypad. And rules number two and three were equally emphatic. Do not violate rule number one. So I'm going to pass these around. I want you to pay particular attention. This is a late-stage pre-production model. You can see it from the labeling in the back. There's some type setting that's off. The centering of the off label isn't quite there. But I want you to pay particular attention to the clear stat function, which was the clear sigma in the old one. Clear functions have been labeled, grouped on the left-hand side. And I'll just come back. So even when it makes ergonomic sense to shift the label, you're not allowed. And Hans illustrated this beautifully in his discussion about classifying Pluto not as a planet. One of the lines that you threw up, Hans, from the governor of this fine state, was that it would confuse the students because the textbooks are already written and they all say Pluto's a planet. So that's pretty much what the reasons for constraints one through three were, is that it would confuse the students. Too much of the use of calculators is done through exact key sequences. So if you wanted to operate a calculator, you are taught. Press key one, one, one, two, whatever, whatever. By the way, those who actually switch the prototype on and get to the enunciator, again, I have to let you know because we're in typography country, the enunciators we changed. I changed from Ariel to Jules Sainz. So that internationalized this a little bit. So we, going back to that example, they mandate that students are that fragile that they can't learn that a key, clear stat, has moved to the clear grouping but has to remain there. And there's another example, store and recall aren't on the same level. Recalls on the top level store is a shifted function. I just find that bizarre. I contrast that with Mr. Keen giving me an RPN calculator and saying go and play with it for a weekend and try to figure this out. And I want to try to go back, I hope I can do this, I asked you to recall the definition of rote, mechanical or unthinking routine or repetition. Isn't that what is being mandated in education? Forgive me. So keystroke consistency in calculator. Assisted iterations of models are required to maintain key label locations. We're encouraging rote with calculators and assistive device but we discourage practice with mathematics. So that really caught me by surprise. Boris mentioned that if you see computer modern, you know it's tech. Well, I have hunted long and hard. HP 95LX which was a DOS-based computer. I am convinced it's computer modern. I have gone to Corvallis. A lot of the old timers are gone, of course. No one seems to know whether it was done by tech. But it is my suspicion and if anyone in this crowd knows any different, I would really like to find out just for historical curiosity. Okay, method. Method is going to be like a 10 second presentation before we get to Matai. The history goes back a little bit. You already know I'm a UNIX user. I use UNIX and Linux interchangeably in terms. It began with Grenule which is a flash card system. I think it was done for KDE but at least I had it on Ubuntu. And I created a bunch of card boxes for my kids for multiplication, addition memory. So if you have two operands, let's say between 20 and 10, they're supposed to get the results by memory and it's simple practice. You sit and run a computer and you do flash drive. Open office spreadsheet, I graduated that for multiple operands. I was not very confident in my tech capabilities. I had never done anything like what I'm doing now. So it was, I had always intended to do it in tech or lay tech but I just didn't have the skill. But it got results. My daughter started to progress in mathematics which was really heartening. And one incident in particular stays with me. She was going, she was at her soccer practice which is in North America very highly participated sport especially among young girls. And she turned to her mother and she said, mama, that student, sorry, that player has number 12 on their back. Do you know that can be expressed as four by three and six by two? Now it may not rank up there with Hardy's discussion with Ramanujan about 1729. But for a parent of a daughter struggling with mathematics, I'll take it any day of the week. And I noticed that someone's reading The Indian Clerk which is an amazing book. I just happened to walk by. I'm not sure who has it. Okay, serendipitously around that time I was struggling with managing the complexity of my project management practice and project management. In my world doesn't mean scheduling. Scheduling is a very small part of it. It has to do with tasks, communications and whatnot. I came across Ron Dorfler and I don't know if anyone else has but I'd be quite happy if you ignored the rest of my talk and went to his website because what he's doing is just amazing. He's reviving the art of nomography and he uses tech to do it. But I came across him because he had produced this little utility which was a pocket sized organizer. You selected a bunch of template sheets. It would print them on a letter size paper, both A4 and letter, U.S. letter. And you could fold it and take it in your pocket for the day and it had all sorts of odd nomograms as well. And through Ron I discovered Tixie or as mandated in this state, Tixie. It does make it easier to remember the ditty that should you be required to draw sprites and pixies then you must surely use Tixie. The floodgates opened at that point. I was able to do a lot of things. Bill Cheswick talked about not knowing about geometry. I had stumbled across the geometry package but I didn't know about Tixie so I was late to the game. People who monitor Launchpad will have seen this example many, many times over. I think in the last two years every time CUPS gets upgraded or Ubuntu gets upgraded I use a very inexpensive HP printer, Rick Richardson's driver, ZJS. But I use this as my standard example that I send out to the Ubuntu mailing list when custom page sizes break. What I ended up doing was creating an agenda application using TixZ. And as if my life wasn't complicated enough I found that our friends in Allentown, Pennsylvania, Daytime or Corporation didn't have a template that worked for me. So I created a four pages per day if you can imagine. That's quite a bit of note taking. Around the time I was suffering with that complexity issue there was a buzz in productivity circles about something known as GTD, getting things done. And the primary tenet of that approach is known as ubiquitous capture. You get everything down that you possibly can. The time that it happens. I use Richard Skoll's Remind. I use all the other cool tools. But when you're out in the field and I'm out in the field a fair bit, there's just no time. Even for instant on. I used Scion Revo way back with the Epoch operating system. But nothing beats pen and paper to capture. So what that ends up looking like and people are welcome to look at that. The website's not up but I will offer it and put it up. So it's custom page sizes, very illegible, but there's all kinds of templates. Great. So my short feature list was it should be whatever software was going to use tech and late tech would have an easily extensible list of worksheets, parameterized worksheet generation which would allow a graduated level of difficulty that would lead a student, a parent or an educator through the process. I think the footnote is lost in that but it's the ability to create beautiful documents. I think what I intended to say was this is strictly dependent on the skill set of the technician which I don't have. So you'll have to pardon some of that. Okay. Very, very simply, there's a bash script associated with each group of worksheets. There's a bash script which uses BC at the back end to generate operands. There's a late tech template and they're married together with set to create a spool tech file which is then converted to a PDF and delivered to your browser. In many cases the generator does nothing more than marry operands to the tech file but in other cases as the complexity grows in the worksheet it does spew out code snippets and fragments. I tried to resist the temptation to generate the tech code from scratch. I found it unwieldy. It's difficult to debug. It's easier to get a template and then intercede with that. Okay. Mithai. I hope this demo goes smoothly. I'll do my best. I'm not sure if I can anyhow. Bear with me. There we are. Okay. I'm running this locally but the website is active and I will just get rid of all the ancillary stuff so we get most of it on. The grouping of the worksheets is done based on the Ontario curriculum for mathematics. This is a Rails application which meant I had to learn Rails as it goes on. You end up having to learn a lot more than you think in delivering. Within each category it's table driven, easy to augment with new worksheets. There's graduated difficulty which was one of the prime directives and it's operand driven. So in my case I've, for instance, multiplication I grouped it one through six and seven through twelve it could be one through four, five through eight, it doesn't really matter. So geometry measurement which is I focused on analog time. Ask Nicholas Hayek, the former chairman of Swatch Group whether analog time has any significance in this day. Five billion dollars should say otherwise. Algebra which in Canada really means algebra and patterns. So I've done sequences here. Study some event trees. This area I haven't had a chance to work on, it's applications. I would like to do things of interest. Aviation arithmetic, vector arithmetic, codes and ciphers. So let's, we're running short of time. I'll just focus on measurements. So here you can see it goes from hourly intervals with labeled markers all the way down to one minute intervals without markers and with a MPM all done with the same generator. So I'm just going to invoke this. What's happening right now is it's doing all the things that I mentioned. It's generating this PDF on the fly. Had fun with this because I have, watches are one of my interests. So I hope you will agree that this one isn't bad. It is of course inaccurate. Watch nuts will know that the hour hand has to be below the minute hand but it would obscure in certain instances. So I took an executive decision and put the hour hand above the minute hand. The standards are labeled. Many watches have the minute hand, sorry, the minutes labeled on the inside but anyway, that's what that looks like. Contrast that going all the way down. So a student would begin with that where the operands would be whole hours versus something like this. And this one raised another subtle type setting issue is that with the MPM, pardon me, it would, there was no way of not obstructing the MPM indicator. So you can see here, for AM, the hour hand is lighter shade for PM, it's a darker shade so the shading changes in that. And each worksheet is generated on the fly. So if you did this 30 seconds later, you'd get your own different custom variation. So I'm really running short of time but I wanted to show you a lot more of this. I'll just throw up an event tree. So these questions relate to this event tree, in this case, fair dice. Again generated on the fly. There are sentence snippets and based on the operand results, the sentence are collated together. Chomsky would be happy. Every, you start with angles, acute and obtuse and you can run right the way through to reflex. Rotation is done dynamically, so not to confuse students. There are hints at the bottom. Anyway, so in there, as the number of worksheets grows, there's of course a search function. So if I was to search for scaling, right, you've got the one worksheet that has scaling in there. In closing, I wanted to just talk about a couple of refinements and acknowledgments. Refinements, I'm going to be working through the summer augmenting these worksheets and hope that I can speak to some school boards, at least in Canada. My hope is that if you find it useful, you could spread the word. Mostly the first question when I give a talk like this is what the heck is a Buncie and why does it have its own world? Well, Professor Buncie Law was my maternal grandfather and he was a mathematician and a math teacher. He prided himself not in his research, but in his teaching. And so Buncie's world, these are some of the textbooks that he wrote. There was a time in Punjab if you went through and did engineering, science or math, you could not escape either having used his textbooks or having been taught directly by him. I still meet his students, believe it or not. So that's what Buncie's world is. It's for me, it's a synonym for open access of mathematical learning. So thank you very much for your time. I'm not sure whether there are any questions, but I'm happy to take them or speak in the break. I'll let... Okay, very quick question. I understand that you use Tixie for all pictures, right? Yes, I did. Oh, thank you. By the way, it's great. Oh, thank you. Really great thing for you doing. So, can we have a last question? Okay, can we get those books that they are available? They are not available. Yeah, I did a few, three documentation lessons. I suppose I could scan them. The books that I have up there are only the books that were published after 1968, I believe. They just happened to be given to me when I visited him in India. I don't think he made any great effort at archiving. So there were many... If you go to the website, you'll see he was the head of the Department of Mathematics of DAV College from 29 to 65. And so he wrote lots and lots of books. What would the third name? Buncie, which means flute. But do you have some names or...? Well, it's Buncie Law. But the names in that time, I mean, it was a very different era. He was... I spoke with Mirko. He's a graduate of Lahore University, pre-partition, and came to Punjab in the 20s. And it was not uncommon to simplify those names at the time. So we are all accidents of history, if not geography. Thank you. Okay. Thank you. Thank you. Thank you. Thank you.
title, using late tech to generate dynamic mathematics worksheets for the web. For the known as a special stream that makes lots of advocates open book tests, use of calculators at that I want to focus in on is that, and that's afternoon, when my high school electronics recall aren't on the same level. Recalls on the The Indian Clerk which is an amazing book. I just I had stumbled across the geometry package but I things done. And the primary tenet of that parameterized worksheet generation which would mathematics. This is a Rails application which markers and with a MPM all done with the same