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How to Teach Mathematics
This third edition is a lively and provocative tract on how to teach mathematics in today's new world of online learning tools and innovative teaching devices. The author guides the reader through the joys and pitfalls of interacting with modern undergraduates--telling you very explicitly what to do and what not to do. This third edition has been streamlined from the second edition, but still includes the nuts and bolts of good teaching, discussing material related to new developments in teaching methodology and technique, as well as adding an entire new chapter on online teaching methods.
146 pages, Paperback
First published January 1, 1993
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Displaying 1 - 7 of 7 reviews
February 27, 2011
Straight-forward advice for college-level instruction. It's a good read.
my favorite quote: "All learning of significant knowledge requires considerable effort on the part of the learner."
my favorite quote: "All learning of significant knowledge requires considerable effort on the part of the learner."
July 11, 2017
Steven Krantz has produced here a serious reflection on a traditional approach to teaching and learning, specifically mathematics teaching. A mandatory reading for every math teacher concerned about the pedagogy of this subject.
The book is directed primarily for graduate students or novice instructors preparing to sumerge in the teaching world. It also may be of some interest to those who have been teaching for a few years. It's important to acknowledge that teaching will improve if it is subjected to periodic re-examination.
Krantz is a college professor, so the book is basically oriented to university level teaching. I am teaching myself in a high school, thus I had to adapt everything the author states to the level I am interested in. Besides the environment is clearly an american one, and I am european (from Spain), so here I had to adapt a lot, as well.
Krantz is a traditionalist, but one who sees many merits in the reform movement. In this book, he provide us with some tips, advice, and the benefit of his own experience. He does not tell us how to teach, we have to decide ourselves. He intends to sintetize to us certain issues attendant to teaching.
He states that nothing he says is essentially correct in any absolute sense, for there is no "correct" position in teaching topics. There is more than one way to get the job done. However, what I found of great interest in this book is that it is specific about issues that arise in the teaching of mathematics. Something not very usual in literature, where you can find much more bibliography about general pedagogy and education.
I quote him saying «the fact of having sat in a classroom for most of your life does not mean that you know how to teach». You really realize this fact whenever put in front of your own students for the first time. We, mathematicians, are not taught almost anything abot what constitutes teaching. I only took a six month course about teaching prior to my first job as a teacher. And it was of little use, for it was scarcely practical, too theoretical. Reading this book provided you with better information and a better outlook. I would have thanked it some years ago, when I was going to begin teaching. It would have been a fantastic reading during my teacher training, complementing the theoretical classes with more applied technics.
The book was written in 1993, and the second edition (the one I have read) in 1999. He has invited some professors who have different views of how to teach maths to write short pieces for this second edition. Something like the two fifths of the book are devoted to these pieces. They amplifiy and complement Krantz's opinion.
Having reading it almost twenty years later suposses that some issues are somewhat outdated, for instance the use of computers with educational goals. Nevertheless, I agree with Krantz when he says «use of computers should be based on a foundation of conceptual and technical understanding».
I also agree with him when he judges Mathematics as a hard subject, and every teacher must have as a goal not to make it harder for his students. «Do what works for you and for your students».
The book is directed primarily for graduate students or novice instructors preparing to sumerge in the teaching world. It also may be of some interest to those who have been teaching for a few years. It's important to acknowledge that teaching will improve if it is subjected to periodic re-examination.
Krantz is a college professor, so the book is basically oriented to university level teaching. I am teaching myself in a high school, thus I had to adapt everything the author states to the level I am interested in. Besides the environment is clearly an american one, and I am european (from Spain), so here I had to adapt a lot, as well.
Krantz is a traditionalist, but one who sees many merits in the reform movement. In this book, he provide us with some tips, advice, and the benefit of his own experience. He does not tell us how to teach, we have to decide ourselves. He intends to sintetize to us certain issues attendant to teaching.
He states that nothing he says is essentially correct in any absolute sense, for there is no "correct" position in teaching topics. There is more than one way to get the job done. However, what I found of great interest in this book is that it is specific about issues that arise in the teaching of mathematics. Something not very usual in literature, where you can find much more bibliography about general pedagogy and education.
I quote him saying «the fact of having sat in a classroom for most of your life does not mean that you know how to teach». You really realize this fact whenever put in front of your own students for the first time. We, mathematicians, are not taught almost anything abot what constitutes teaching. I only took a six month course about teaching prior to my first job as a teacher. And it was of little use, for it was scarcely practical, too theoretical. Reading this book provided you with better information and a better outlook. I would have thanked it some years ago, when I was going to begin teaching. It would have been a fantastic reading during my teacher training, complementing the theoretical classes with more applied technics.
The book was written in 1993, and the second edition (the one I have read) in 1999. He has invited some professors who have different views of how to teach maths to write short pieces for this second edition. Something like the two fifths of the book are devoted to these pieces. They amplifiy and complement Krantz's opinion.
Having reading it almost twenty years later suposses that some issues are somewhat outdated, for instance the use of computers with educational goals. Nevertheless, I agree with Krantz when he says «use of computers should be based on a foundation of conceptual and technical understanding».
I also agree with him when he judges Mathematics as a hard subject, and every teacher must have as a goal not to make it harder for his students. «Do what works for you and for your students».
September 10, 2012
Essential reading for math profs.
December 22, 2017
Excellent book, lots of food for thought. I must read this again and again ...
January 27, 2025
Even though the most recent version of this book is fairly recent, it already feels quite dated. The author often comes across as a dinosaur whose target audience is other experienced teachers rather than young people who are entering academia in the 2020's.
Despite this, it's still worth the read. It's quite helpful for people who have upcoming classes and need to sit down to have a thorough think about what policies they are going to enforce during these classes. Even if the advice given is sometimes a bit wishy-washy, the author does a good job of making the reader think about the many possible dilemmas that may arise during a semester of teaching and what strategies might be available for dealing with them.
Despite this, it's still worth the read. It's quite helpful for people who have upcoming classes and need to sit down to have a thorough think about what policies they are going to enforce during these classes. Even if the advice given is sometimes a bit wishy-washy, the author does a good job of making the reader think about the many possible dilemmas that may arise during a semester of teaching and what strategies might be available for dealing with them.
August 7, 2025
I found a lot of information helpful, but was disappointed at the passages about sexual harassment and math anxiety, which to me seemed to lack the context and experience one would have as a woman/minority in the field.
September 5, 2016
Um livro pequeno e sentido, por um professor universitário de matemática que partilha a sua experiência (De sucesso) e revisita muitas das questões do que é ser professor e ensinar na universidade.
Uma leitura sempre interessante para quem é professor na universidade e com bastantes pontos curiosos. Para quem tem anos de experiência é algo redutor e menos útil do que pensaria, embora tenha o bom senso e a bondade de proporcionar conselhos que se espera, em grande parte, constituam a norma de quem ensina (nesse contexto é útil até para os alunos universitários lerem).
O livro de 2000 é no entanto, de uma época que estava ainda centrada na transmissão de conhecimento e não na criação de experiências de aprendizagem como parece ser o tempo presente. Não obstante, uma leitura interessante, enquanto se carrega baterias para mais um ano letivo.
Uma leitura sempre interessante para quem é professor na universidade e com bastantes pontos curiosos. Para quem tem anos de experiência é algo redutor e menos útil do que pensaria, embora tenha o bom senso e a bondade de proporcionar conselhos que se espera, em grande parte, constituam a norma de quem ensina (nesse contexto é útil até para os alunos universitários lerem).
O livro de 2000 é no entanto, de uma época que estava ainda centrada na transmissão de conhecimento e não na criação de experiências de aprendizagem como parece ser o tempo presente. Não obstante, uma leitura interessante, enquanto se carrega baterias para mais um ano letivo.
Displaying 1 - 7 of 7 reviews