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In my locality, many schools have this tendency to partially include this and that chapter in the syllabus (for almost every subject). For example, (most of the chapters are subdivided in two or more parts), they will take chapter 2, chapter 3.1, chapter 5.1, .2, chapter 14 and make this as a syllabus for a term/semester (out of 15 chapters, say). They complete the full textbook in a whole year, by the way.

Now, the textbook is actually well organised, and a student would understand the topics better if the syllabus followed the order the book is written. The concept of syllabus selection committee is to 'mix hard and easy chapters (parts)' and 'to give different tastes'. In my opinion, the hard parts do not need more work once the prerequisite chapters are done; I mean if you go step by step through the text book, it is always the same amount of difficulty. And for the 'taste', if we keep tasting this and that food frequently, we do not get any taste at all.

So my question is:

Is this normal in other places/countries too? If so, how does this practice benefit the students in learning (mathematics)?

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    $\begingroup$ if you go step by step through the text book, it is always the same amount of difficulty --- As someone who mostly self-learned all of school algebra, precalculus, single and multivariable calculus, some linear algebra, and some differential equations by going step by step, partially or fully (mostly partially, until I found a book that worked for me), roughly 12 to 15 textbooks during my high school years, not to mention all the self-study I've done since (recent example), I strongly disagree with your statement. $\endgroup$ – Dave L Renfro Aug 17 at 14:03
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    $\begingroup$ @Kawrno, are you sure of their motivations in how they split things? That sounds very odd. Many times textbooks are not organized the best way. I go out of order in Calculus, and in Precalculus, because I want the order to make sense, and the book's order doesn't. I'm sure it frustrates students sometimes. If I had the time to write a new calculus textbook, I think I would. $\endgroup$ – Sue VanHattum Aug 17 at 15:23
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    $\begingroup$ Personally, I am of the opinion that if you are going to use a book, then you should follow the topic outline of the book. If you don't like the order in which topics are laid out, find a different book (or write your own; or produce your own lecture notes; or, at the very least, regard the text as an "optional" resource and make it very clear that you aren't following it carefully). I suspect that this is an opinion shared by many, but I don't have the citations or experience to feel comfortable providing an answer. $\endgroup$ – Xander Henderson Aug 17 at 22:30
  • $\begingroup$ Now, the textbook is actually well organised, and a student would understand the topics better if the syllabus followed the order the book is written. Citation needed? Obviously not everyone agrees with this assertion, which is why they cover the syllabus in a different order. $\endgroup$ – mweiss Aug 19 at 1:09
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    $\begingroup$ In the ideal world — which happens to be the world that I was educated in — grade school textbooks are not 1000+ page bricks but sub-200 page books with large enough typeface, with well thought out sequencing of chapters, where each chapter has theoretical part, definitions, proofs, examples, and then a bunch of exercises. The complete book must be covered in a school year, first to last page, no omissions. Makes it easy for teachers, pupils and parents. College books are more of a mixed bag, and college profs tend to design their own courses, so selecting chapters is ok. $\endgroup$ – Rusty Core Aug 26 at 22:08
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My sense is that often authors are encouraged (required?) by publishers to make books very 'complete'. This means the book has all the topics that any instructor would be likely to want for a subject. However, it also means that books are often too big to entirely cover in a semester (or year). Thus an instructor must pick and choose chapters/sections based on the goals/objectives of their particular course. So depending on what is to be accomplished in the class, a certain amount of selection from the book is likely to occur, and may result in some topics in the book being skipped or being covered out of order.

To answer one of your specific questions, I don't think this particularly benefits students, except for perhaps giving them material for further self-study if the entire book didn't get covered during the course.

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I tend to see this in upper level college courses a lot. My impression is that the schools are trying to appear to have a solid course by using an iconic textbook (not often the best pedagogically). Often the course is too short to really cover the content properly.

I don't like the practice. Prefer to spend more time or more realistically, use a book tailored for the course length. But I understand the psychological basis in having shorter courses using iconic, much too long texts. It's the normal human desire to look fancier than one is.

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Yes they do so in many places, I think the point is that the students are forced to finish a certain curriculum (depends on the country ofcourse), for example when students finish the $9^{th}$ grade they must know this and this and that.

So in the years before the $9^{th}$ grade the teachers focus on what have to be finished and leave the other topics that are in the book either because they are not in the curriculum, or because they see that this topic is hard for students in this age so they explain it in the year after, and sadly there is another reason also, most teachers just ask the older teachers what they explain and in which order and do just the same just because the other teachers that used to teach before them do it.

But as a benefit for students, I think there isn't really any benfit, and that is why all around the world you see students and teachers, that wisely think about this issue, complaining about the curriculum and that it must be changed.

I am not so sure about this, but I think the ministries of education put the curriculum right? So the question is, are there really qualified people in these ministries to specify what the Mathematics curriculum should and should not include? I don't think so myself, and I see that this is the problem.

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Also, realize that many authors write "complete" (self-contained) texts, and by their own recommendations, may suggest various ways an instructor may want to approach the subject.

For example, an author of a text with 13 chapters, may suggest, in the event that an instructor is focusing on foo, to focus on chapters 1 - 3, chapter 4 (sections 1-3), and chapters 7, 9, 10. Occasionally, an instructor may designate two or three chapters and their sections to be addressed by students in presentations, or in a semester paper, based on the foundation of the text that's covered in class.

This is a common practice in classes, because some texts cannot be thoroughly covered in one or two semesters.

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