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Why are math textbooks so often boring? It requires some mental discipline to do math; cartoons can help make the principles easier to digest.

The Mathematical Association of America has many FUN artistic Advanced Math books. Maybe more Math textbooks could be written with an emphasis on interesting summaries first $BEFORE$ filling in the precise details? I think learning a lot of details first that you have to memorize tend to obscure a general appreciation of the whole 'layout' of the subject. Look at the success of the 'For Dummies' series like Algebra For Dummies..

So in summery, why are math books uninspiring? Could Math Books be written with an emphasis on fun informal summaries of various concepts before the precise details are 'filled in'?

Sue VanHattum
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user128932
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    I voted to close for now, as I believe your question as it currently stands is too vague. You'll need to provide additional information to support your claims. You claim that "most Math Textbooks [are] VERY VERY DRY." What educational level are you talking about (pre-school, elementary, high school, undergraduate, graduate)? From what country are the textbooks you are referring to? From my experience, high school and undergraduate textbooks from the USA have color and numerous illustrations. – JRN May 03 '14 at 07:26
  • The question is not off-topic, but it did mix two separate issues together. I have edited to pull them apart. I think the issue of dry textbooks is worth discussing. I would also like to know the OP's answers to @JoelReyesNoche's questions - what level is being referred to, and what country's textbooks? – Sue VanHattum May 04 '14 at 14:39
  • The question got closed, edited, reopened. In the process various comments accumulated, most now obsolete or tangential. I deleted all in one sweep and only undeleted very few that seemed essential to me. Please @ notify me if you consider your delted comment as still important. – quid May 04 '14 at 17:31
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    I don't see how this question can be asked when the context ("textbooks") is so broad, and there is no evidence provided for the underlying assumption (my understanding mirrors that of @JoelReyesNoche, namely, that US textbooks have a lot of illustrations, artwork, and even cartoons). I would additionally challenge the assumption that excluding pictures makes something dry (and is somehow related to rote learning? I don't understand). I am quite sure that many great works of literature have fewer illustrations (i.e., none) than even the "drier" of textbooks. I hope this will be re-closed. – Benjamin Dickman May 04 '14 at 18:57
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    There might be a good question in here, but it would have to be re-written by the author, because too much is unclear.

    First, a solid definition of "dry" is needed. I suggest an illustrative example and comparison with non-dry content.

    Once we know for sure what "dry" means: possible, coherent questions: 1) Why do some schools choose the more dry textbook? 2) Given that it is not "fun" what are the advantages of the dry approach? 3) What is the evidence of the impact of these approaches on student motivation/test scores/learning/identity/etc.

    I'd like to see the question return, edited.

     – JPBurke May 04 '14 at 19:26
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    A Dry textbook is boring , soporific , too many uninspiring or non-creative explanations ; something used in a classroom that students have to read to do the required lists of exercises and pass exams. DRY could also mean not fun , not inspiring to one's creativity . I love Mathematics but to find a Math Textbook or just a book on Math (not used in a school) that is EXPLAINED well and in a way that is FUN and CREATIVE and INSPIRING is difficult. – user128932 May 04 '14 at 21:57
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    often with boring black and white print This is pure economics. In traditional printing (as opposed to print on demand), a color text is produced using four colors of ink, which makes it cost about four times as much to set up the presses for one run. That makes economic sense only for a book that's going to sell a very large number of copies. This dry approach makes me think there is nothing exciting there, and that I'll just have to memorize. I don't see any logical connection between memorization and dryness. –  May 05 '14 at 02:04
  • @user128932, don't look farther than Sturgeon's law – vonbrand May 05 '14 at 04:14
  • These aren't textbooks, but you might be interested in looking at books by Lillian Rosanoff Lieber that were illustrated (on nearly every page) by her husband. See my answer to the Math StackExchange question Dr Seuss style prose advanced mathematics text. – Dave L Renfro May 05 '14 at 14:08
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    This question is a troll, whether intentional or unintentional I don't know. – Jim Hefferon May 05 '14 at 21:14
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    Soggy textbooks just make a mess. – vonbrand May 07 '14 at 22:24
  • Dry textbooks stick in your throat like old breadcrumbs . I have seen alot of TV and Movies and it SEEMS like popular opinion is that most people don't like Math. All the jokes about nerds who love Math; most students find Math just something to endure. I've looked at ALOT of math books myself and to find one that explains hard concepts well and is ( dare I say it) FUN is a challenge. If anybody really wants to teach Math effectively , to people who are NOT initially receptive why not add humor and art ( that has some active role in a lesson)? – user128932 May 08 '14 at 06:25
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    I don't think the popular opinion of math is greatly improved since we started making highschool math texts that have color and more pictures etc. Of course, I also like texts with humor and some conversational aspect. But, numbered definitions and superior organization are welcome features when you're actually doing some work with a text. – James S. Cook Sep 07 '14 at 02:21
  • Maybe one can say there are two types of learners (possibly more), Creative ( and visual) learners and very disciplined rote or detail-aquiring learners. Both are respect-worthy yet I think alot of academics and teachers and writers ( of math books ) are the detail-aquiring type of learner. So there might be a bias against creative and visual learners. Certainly MANY mathbooks tend to ignore the creative approach. – user128932 Sep 07 '14 at 05:43
  • I think this is a great question - a similar one was asked on Mathoverflow a while ago with interesting answers http://mathoverflow.net/questions/13089/why-do-so-many-textbooks-have-so-much-technical-detail-and-so-little-enlightenme – Marius Kempe Jul 28 '15 at 11:59

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It seems to me that the question rests on a false dichotomy: either (1) the book has cartoons or artwork, or (2) the book consists of non-exciting material which the author expects the reader to memorize by rote. However, in mathematical writing I think that (1) and (2) are almost orthogonal. (Diagrams are certainly useful in some fields of math, such as geometry, but I wouldn't call them cartoons or artwork and I'm not sure if that's what the OP meant.)

It is possible that some readers are only excited by cartoons and artwork. However, these readers cannot be expected to learn any math. So naturally, mathematical writing is geared to other readers, ones for whom it is at least possible to be excited by the mathematical ideas themselves.

Certainly some authors are more successful than others in writing mathematics in an exciting and engaging way. However, including pictures is neither necessary nor sufficient for this, except with very young readers for whom pictures may be necessary. (Even so, I would call the useful pictures "diagrams" and maintain that cartoons and artwork would mostly serve to distract the reader from the mathematical ideas being presented.)

If, due to deficiencies of the author or the teacher, a mathematical idea is presented so poorly that rote memorization is the only way for the student to "learn" it (and I wouldn't even call this learning) I don't think that adding cartoons and artwork to the text would be likely to make in improvement.

Trevor Wilson
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  • What if the cartoons and artwork were used as 'active' participants in some story plot that teaches Math , and not just basic Math as in many children's shows on T.V. ( that proceed at a snail's pace) , but also a story plot that teach something advanced. I partly remember some cartoon on TVO I think ,(at 3:00 am) that was explaining the Mole principle in Chemistry ; it was a better expanation than any I read in any Textbook. – user128932 May 04 '14 at 21:31
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    @user128932 It would help me understand your point of view if I saw the cartoon (and knew what you meant by the mole principle.) I can certainly believe that there was an explanation in a cartoon that was better than the one in your textbook (some textbooks are pretty bad) but I'm also sure that it would be possible to write a good explanation of a chemistry principle without cartoons or a story to go along with them. Also, I think that if too many things were accompanied by this kind of fluff then it would lose any value it might have had... – Trevor Wilson May 04 '14 at 22:17
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    .... I can't imagine learning any significant proportion of what I learned as an undergrad through cartoons. Some of the cartoons would have to be very complex, and at some point I would start wishing that everything would just be written down simply and clearly, without fluff. – Trevor Wilson May 04 '14 at 22:18
  • I don't think there could be too many books using this kind of fluff because there are HARDLY ANY. Also I don't think many acedemics respect the possibility of using humour to enhance learning. – user128932 May 04 '14 at 22:22
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    @user128932 Regarding humor, I think it is better to use it in the classroom than to put it into books. A lot of jokes don't work as well on the printed page. Also, in my experience, there is a lot of fluff in textbooks (although maybe not the exact kind that this thread is about.) For example, freshman calculus books tend to have random pictures (e.g. a guy on a surfboard) that are only there to make the book look "cool" (no applications of calculus to surfing were given, if I recall correctly.) Some students might rightly be insulted by this pandering. – Trevor Wilson May 04 '14 at 23:09
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    I'm not talking about random art or art and cartoons just used as a kind of 'decoration' , I mean art and/or cartoons that specifically add interesting ideas and interpretations to something being taught. I think a book on Integration , for example , could be written about using ONLY cartoons. – user128932 May 04 '14 at 23:17
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    @user128932 I think that some authors may be able to pull that off, and other authors should stick to mostly text. People have different writing styles just like they have different learning styles. I think it would be terrible if a publisher defaulted to saying "you need to stick some cartoons in here to make it appeal to students." A lot of really bad textbooks would result (worse than the current crop, even.) – Trevor Wilson May 04 '14 at 23:25
  • I think most acedemic authors and publishers are biased against the use of cartoons and other humor. A publisher is more LIKELY to default if an author has alot of cartoons and humor in his or her acedemic book. I don't think humor is considered an instructive or effective way to teach even though a Teacher could probably teach a classroom of NON- math enthusiasts many important math concepts with humor. – user128932 May 08 '14 at 06:38
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I know that for many people, illustrations (not necessarily cartoons/comics) can help them visualize what is being described, and can make the task of reading a mathematical exposition easier. But illustrations need to be well-matched to the content to be useful.

One of the best series of textbooks available to people who are learning on their own are those produced by Art of Problem Solving. Almost no illustration, but definitely based on understanding. I would like to know if the original poster would consider those dry, or not.

I have definitely seen an author's attempt at humor get in the way, making their explanations less helpful.

One author who uses illustrations (including comic strips) well is Harold Jacobs, whose textbooks are a joy to work from.

The textbooks I had to face in my college math work (back in the 70's and 80's) were so dense, and lacked not only illustrations, but any sense of the author's voice, any connection to anything outside the math topic at hand. I like making connections, and if I needed to read much (as opposed to just doing the exercises), I might have described them as dry.

You asked why this happens. I think mathematicians are very interested in making logical arguments. They aren't always aware of the psychology related to learning from a text. If you tell us more, especially the level you're interested in, I can recommend delightful books.

Sue VanHattum
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  • There must be more people like me who love both Math and clever art or cartoons at the same time. The Demystified books and ' ..for Dummies' books are very good , yet they should have a 'Topology for Dummies' or a Category Theory Demystified . I think it's best to start off any hard subject with a FUN yet well written summary of the subject. Many Math books are either too hard , where you need a degree just to understand the introduction ; OR too easy. Good explainers are hard to find. I think W.W. Sawyer and Dan Pedoe are two of them. – user128932 May 04 '14 at 21:20
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    I'll have to look up Dan Pedoe. I love W.W. Sawyer. Now that I see your level, I can recommend Math Girls and Math Girls2. They are both fabulous. I'm trying to learn more about generating functions after getting a taste from Math Girls. – Sue VanHattum May 05 '14 at 21:55
  • Actually I like very advanced math also , I just like very clear , fascinating explanations of important math concepts that aren't too hard. It's hard to find this in Topology of Category theory books. – user128932 May 06 '14 at 03:24
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I see two factors:

  1. Most good math authors tend to not be good entertainers and vice versa. I feel that the two talents are not correlated. But, to me, Colin Adams and his Knot Book (which I just used as a textbook) are a great example of how math can be informative and fun.
  2. Fun can get in the way of understanding. I've read papers or explanations of math that had a very joke-y attitude and it was very hard to keep track of what is fun and what matters.
Brian Rushton
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  • I really like Colin Adams Knot Book, it is fun and helped to get me interesed in Knot Theory. His style of writing should be the norm. I know FUN can be distracting but if it is handled well it can GREATLY enhance learning. Edward de Bono has written Humour and creativity are related ( I think).If a Math writer is uninspiring he could hire a 'ghost humorist' to add comic interpretations of a lesson. A great way to remember something is if it's FASCINATING and/or FUNNY – user128932 May 04 '14 at 21:45
  • I partly rewrote the question if anybody notices.. – user128932 Sep 07 '14 at 03:16