Criminal offences in maths textbooks

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Discussion Overview

The discussion revolves around perceived shortcomings and problematic practices in mathematics textbooks and educational approaches. Participants express frustrations regarding the clarity, accuracy, and pedagogical choices made in these texts, touching on both theoretical and practical aspects of mathematics education.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation
  • Meta-discussion

Main Points Raised

  • Some participants criticize textbooks for asserting incorrect mathematical facts, such as the treatment of square roots of negative numbers, which can lead to confusion for students transitioning to higher education.
  • Concerns are raised about the use of equals signs inappropriately, as illustrated by an example where the square root of 2 is claimed to equal 1.41.
  • There is a critique of teaching methods that prioritize reasoning over established algorithms for basic arithmetic operations, which some believe hinders students' understanding of mathematical concepts.
  • Participants express frustration with textbooks that present formulas without adequate derivation, leading to confusion about their applicability and feasibility.
  • Some argue that proofs and arguments in textbooks are often designed for the author's convenience rather than the student's understanding, which can detract from the learning experience.
  • There is a shared sentiment that providing answers to exercises can undermine the learning process, as it may discourage students from engaging deeply with the material.
  • Participants note the persistence of serious errors in well-known textbooks, with some authors failing to correct these mistakes across multiple editions, which can mislead students.
  • Concerns are voiced about instructors who do not adequately engage with student work or who impose inconsistent expectations regarding mathematical writing.

Areas of Agreement / Disagreement

Participants generally express dissatisfaction with various practices in mathematics textbooks and education, but there is no consensus on the best approaches or solutions to these issues. Multiple competing views on the effectiveness of certain teaching methods and textbook practices remain evident.

Contextual Notes

Participants highlight limitations in textbook content, such as the omission of derivations for formulas and the presence of unresolved errors. The discussion reflects a variety of personal experiences and opinions regarding educational practices, which may not apply universally.

  • #31
The Boubaki syndrome really means the writing of mathematics in its 'purest' form, i.e. statements with minimal hypotheses and a very dry style without motivation and in principle from the ground up. The lay reader at this point should not think that by motivation I mean solving a problem in the real world. I mean explaining the reasons why one might wish to prove such a theorem.

The style has its benefits, and its drawbacks, naturally. The reader can decide for themselves if they want articles with lots of statements like 'let M be a monoid, now...'
 
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  • #32
Theorem n.m

Blablabla (insert an arbitrary theorem here) blabla.

Proof: See exercise p.q \square

...
...
...

Exercise p.q.

Prove theorem n.m.Okey I understand that sometimes it is reasonable to leave proofs as exercises, but on the other hand sometimes it is not even reasonable. It can be impossible for a student to do it without asking somebody how knows it. When I saw this for some couple first times, I actually eagerly searched the exercise in hope of finding hints for the proof. But there's no hints ever, just the dry "Prove theorem n.m." Besides, if there's no hints given in the exercise, then why should the reader see it for the proof?
 
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  • #33
this exercise should be followed by the words "gotcha!"
 
  • #34
It would be reasonable if they provided you with enough information to do the proof yourself but in some cases I've known they use something that isn't even covered in the text.
 
  • #35
Criminal offenses in math textbooks:

#2 Useless diagrams.
Refer to fig 1.a on page#<somepagefaraway>,
fig 1.a (a right triangle with the right angle <ABC labeled 90 degrees)
what is the sin of angle <ABC?
Just say what is sin(90) !

When they make you do problems according to the diagram *they* assign, using the variables *they* pick, so you have to flip back and forth to their stupid pictures and premises. Just so you have to use *their* book! I know what sin90 is but what the hell is sin (<ABC) is unless I buy their textbook?!
 
  • #36
matt grime said:
The Boubaki syndrome really means the writing of mathematics in its 'purest' form, i.e. statements with minimal hypotheses and a very dry style without motivation and in principle from the ground up. The lay reader at this point should not think that by motivation I mean solving a problem in the real world. I mean explaining the reasons why one might wish to prove such a theorem.

The style has its benefits, and its drawbacks, naturally. The reader can decide for themselves if they want articles with lots of statements like 'let M be a monoid, now...'

I did a google on "Boubaki syndrome", and it yielded one single hit - which was this very page. Though I think I'm pretty sure from the discussion provided here what is meant by the term, I'm curious as to whether it is the actual name of the phenomenon?

I do not doubt, though, that there are several authors to whom one could argue that the phenomenon was attributable to the extent that eponymocity is justified.
 
  • #37
It helps to spell Bourbaki right. :smile:
 
  • #38
Nesk said:
I did a google on "Boubaki syndrome", and it yielded one single hit


woo-hoo, we're a googlewhack. That means I've now been a googlewhackee twice.
 
  • #39
jhat21 said:
Criminal offenses in math textbooks:

#2 Useless diagrams.
Refer to fig 1.a on page#<somepagefaraway>,
fig 1.a (a right triangle with the right angle <ABC labeled 90 degrees)
what is the sin of angle <ABC?
Just say what is sin(90) !

When they make you do problems according to the diagram *they* assign, using the variables *they* pick, so you have to flip back and forth to their stupid pictures and premises. Just so you have to use *their* book! I know what sin90 is but what the hell is sin (<ABC) is unless I buy their textbook?!

I have something similar to this. My calculus booked had a theorem and stated (proof in section 14.3) We were in Chapter 7. I look ahead to find the proof and turned out...the proof wasn't there.
 

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