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I write a math textbook for which I want to make an overview chapter for each part of the textbook. In those overview chapters I want to motivate and introduce the new mathematical concepts. I also want to answer questions like: Why do we need those mathematical concepts? How did the concept evolve in history? What will be the content of the next chapters?

In this context, will the overview sections facilitate learning? How important are overview chapters in textbooks for the success of learning? Is there any research about it?

Note: I asked the same question on cogsci.stackexchange.com. Since I haven't got an answer there I want to reask this question here. I hope that's okay.

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  • $\begingroup$ What age level is the textbook for? $\endgroup$ – Amy B Mar 23 '16 at 10:48
  • $\begingroup$ It shall be a textbook for undergraduates. $\endgroup$ – Stephan Kulla Mar 24 '16 at 20:36
  • $\begingroup$ How could overviews possibly harm anything, except yet-again providing another opportunity for foolish people to be lazy? So the research would have to examine and weigh the benefits to sensible people against the opportunities for misunderstanding and self-destruction among misguided people... which is a more intense sociological/psychological issue than I'd think people would want to undertake... if their goal is publication in peer-reviewed journals to further an academic career, etc. $\endgroup$ – paul garrett Jun 7 '16 at 22:45
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Speaking from personal experience, I found such introductions extremely valuable, exactly for the reasons you give. You might even be able to set up larger problems which are then solved piece by piece during the following chapters; this would make a whole out of the parts.

You could also consider wrapping things up at the end of each part with a compact blurb as to what the results mean for the problems in the introduction.

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Are you familiar with the term "Dunning-Kruger effect"? To answer your question: yes there have been studies that show that many topics including mathematics can benefit from the Rule of the 3 T's: Tell 'em what your gonna tell them, Tell them, and the Tell them what you told them. Writing a good textbook actually is very difficult, and not necessarily related to having expert knowledge of the subject of the textbook. You may know this. Here is a question for you to ponder: which is more difficult mathematics or the teaching of mathematics? (for extra credit, prove your conclusion) It takes innate talent to be able to write a textbook without an enormous amount of trial, feedback, and error correction. Few do a great job without a lot of student input. There's no formula.

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    $\begingroup$ Actually I haven't found any study for the 3T's rule. I have found some blog articles proposing the 3T rule for presentations (1) (2) and some critics in other blog posts (3) (4). $\endgroup$ – Stephan Kulla Jun 12 '16 at 20:37
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    $\begingroup$ Can you provide a reference for such a study? $\endgroup$ – Stephan Kulla Jun 12 '16 at 20:43

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