Thinking Mathematically

by John Mason

Thinking Mathematically unfolds the processes which lie at the heart of mathematics. It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians.

Genres: Mathematics, Science, Education, Logic, Nonfiction, Textbooks

224 pages, Paperback

First published January 11, 1982

About the author

Librarian Note: There is more than one author by this name in the Goodreads database.

John Mason, Professor, The Open University, is well known for many books including Thinking Mathematically with Leone Burton and Kaye Stacey and Learning and Doing Mathematics. More recently he has published Practitioner Research Using the Discipline of Noticing. He has a wealth of experience of helping practitioners to develop their own practice, and to turn that into research.

Reviews

[Enzo Altamiranda · Rating 5 out of 5]

This book tries to teach you mathematical thinking by making you aware of the optimal mental process (according to the author) that should occur when solving problems which are mathematical in nature. To do this, he introduces a methodology called the RUBRIC, which basically consists in documenting your train of thought as you resolve a problem. In documenting, you force yourself to either slow down and ponder about what you're doing more carefully, or you get inspired (using past experience) if you're stuck.

By the end of the book the author makes a confession; this book is not actually about mathematical thinking, it's about thinking in general. According to him the key of thinking is awareness of several aspects that occur when investigating an issue, abstract or concrete.

Another theme that is present in most of the book is the identification of one's own feelings when solving problems. A feeling that was particularly relevant to me is the emergence of the ego when having a tough time with a problem.

[Maricruz · Rating 4 out of 5]

Pensé que había leído este libro cuando era bien joven, pero ya no estoy tan segura. Quizás es que entonces lo cogí con más ganas (es lo que tiene la juventud, supongo). Estaba predispuesta a decir que en aquel entonces hizo más por mis habilidades matemáticas de lo que había conseguido toda la educación reglada que me condujo hasta el bachillerato de letras puras, a excepción de mi profe de ciencias en EGB, Sagrario, con su elegancia no sólo matemática y sus acertijos de los viernes. De cualquier modo, incluso si no se trataba del mismo libro, ha de ser tratarse de uno muy parecido, y sus autoras y autor han dedicado buena parte de sus carreras a la didáctica de la Matemática (Leone Burton se ha aplicado incluso a la relación entre su aprendizaje y el género o la desigualdad social, ¡interesante!), así que lo recomiendo sin duda a quienes piensen que los números no son lo suyo.

Recuerdo que también leí por esa época un libro que mostraba la belleza de las demostraciones matemáticas. ¿No sería el que yo creía que era este? ¿Tenía la cubierta azul? Desde luego, yo, pensamiento matemático no sé, pero memoria, una mierda.

[Katia N · Rating 4 out of 5]

It is wonderful book if you want to refresh your math or simply train stretch your grey matter a bit. But it would benefit if it would contain the answers. I know they were not there on purpose. But still you can google the majority and it seems it would be easier to trust the readers not to use them unless they cannot progress without them. Some of the stuff there increased my self esteem and some has returned it back where it was:-)

It would not be interesting for anyone who is not into mathematics.

[Saman · Rating 1 out of 5]

This book can't help you to be a better mathematician or a better teacher.
But in the last chapter in the last lines suddenly it seems the book has nothing to do with mathematics. It seems it wants to understand how human thinks and how awareness works and math was just a tool to see how we think. It's very nice idea but I guess the book is not very successful in that goal too.
But it has an important aim even if it's not accomplished. Plus in the last chapter there are a lot of nice questions to think about.

[Arghavan · Rating 5 out of 5]

موردعلاقه‌ترین کتاب درسی‌م تا به این‌جا. روون و خوش‌خوان و صریح و دوست‌داشتنی و منطقی.

[mono · Rating 5 out of 5]

This book is best read with a notebook and a two month time frame. It is true that most of the problems are superficial at best, but that isn't the point. Y0u need the courage to forge your own way in this peculiar universe and to do that you need practice. This is about the journey not the goal. You're own goal is more important that what anyone else could possibly impose.

[Kareem]

بيحسسني بغبائي شوية بس في أمل :)

[Malek · Rating 5 out of 5]

Quite possibly the best book I've read.


The book is so good that even the authors don't seem to realize how good it is.

This may sound like an exaggeration, but it isn't.

With mild tweaking, the lessons in this book are applicable to virtually all domains of thinking, not just mathematics.

[Beth · Rating 2 out of 5]

Subject knowledge not theory link - 2*