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Suppose a math textbook contains an overview chapter for each part of the textbook. The intent of those overview chapters is to motivate and introduce the new mathematical concepts which will be discussed in the respective part of the textbook. For example, why do we need the mathematical concept? 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?

Note: I reasked this question on matheducators.stackexchange.com.

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  • $\begingroup$ Some math books only have this chapter at the beginning, in the form of an introduction motivating and outlining the book. I guess whether individual introductions for each part of the book are warranted or not depends on a few other factors, how much material is covered, how related are the parts etc. $\endgroup$
    – got trolled too much this week
    Commented Jan 5, 2018 at 9:15

2 Answers 2

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There is something called "advance organizer", that traces back to Ausubel (1960). It is some kind of overview, in which a short summary is given and (more important), in which the following topic is connected to prior knowledge (= Associations are being activated). In that sense it activates schemes, in order to assimiliate the new knoweldge to the old one or to accomodate/correct the prior knowledge. So, to be useful, advance organizers should have certain features:

  • Connections between the following topic and prior knowlege

  • Catch the attention of the student

  • Be concret, insted of abstract

F.e. Before teaching equations the teacher could give the analogy of a scale.

From a scientific perspective it is known, that advance organizers can have supportive effects on learning and retention (see f.e. Luiten, Ames & Ackerson, 1980)

Luiten, J., Ames, W., & Ackerson, G. (1980). A meta-analysis of the effects of advance organizers on learning and retention. American Educational Research Journal, 17(2), 211-218.

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Yes, an overview chapter helps for most people.

An overview chapters allows the reader to develop a stronger associative network, for instance this read:

Sowa, J. F. (2006). Semantic networks. Encyclopedia of Cognitive Science.

Considering the importance that one is able to connect the dots while learning math, facilitating the development of the associative network is beneficial for learning. This effect is further elevated by visual learners.

I can suggest you these:

Presmeg, N. C. (2006). Research on visualization in learning and teaching mathematics. Handbook of research on the psychology of mathematics education, 205-235.

Gilbert, J. (2005). Visualization: A metacognitive skill in science and science education. Visualization in science education, 9-27.

For less visual learners, or those too lazy to appreciate the overview pages, I personally believe it will not reduce learning or provide any other harm for that matter.

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