# A Book: Thinking Mathematically

I’m re-reading Thinking Mathematically, an assigned book from a math course I took years ago in Portland. I was teaching science at the time but signed up anyway because I’ve always loved math.

Thinking is still so good and resonates much more now that I’ve been teaching mathematics.

In the Introduction, under “How to use this book effectively!”:

Recalcitrant questions which resist resolution should not be permitted to produce disappointment. A great deal more can be learned from an unsuccessful attempt than from a question which is quickly resolved, provided you think about it earnestly, make use of techniques suggested in the book, and reflect on what you have done. Answers are irrelevant to the main purpose of this book. The important thing is to experience the process being discussed.

… our approach rests on five important assumptions:

1. You can think mathematically
2. Mathematical thinking can be improved by practice and reflection
3. Mathematical thinking is provoked by contradiction, tension and surprise
4. Mathematical thinking is supported by an atmosphere of questioning, challenging and reflecting
5. Mathematical thinking helps in understanding yourself and the world

These assumptions need to live in our classrooms.

The problems in Thinking are mostly brief and simply stated — yet each one has the potential to make you linger a bit longer because you want to savor your own thinking. Not even productive struggle, this is sweet struggle.

How many rectangles are there on a chessboard? [Page 43]

I have just run out of envelopes. How should I make myself one? [Page 35]

A certain village in Jacobean times had all the valuables locked in a chest in the church. The chest had a number of locks on it, each with its own individual and distinct key. The aim of the village was to ensure that any three people in the village would amongst them have enough keys to open the chest, but no two people would be able to. How many locks are required, and how many keys? [Page 176]

I’m finding out that the 2nd Edition came out in 2010. Amazon does not have it in stock currently, but when it does become available, we can rent it for \$54.77 or buy it new for \$91.29. What??

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### 8 Comments

1. Posted July 10, 2015 at 3:38 am | Permalink

You can get a second hand first edition for \$8.64 via Amazon

• Posted July 10, 2015 at 2:37 pm | Permalink

Thinking Mathematically is expensive!

Maybe Bill Gates can buy us all a copy!

2. Sandy Robins
Posted July 10, 2015 at 10:31 pm | Permalink

I like shopping at Abe Books – good price for used books that you can find in good condition. It’s still \$40, but better than Amazon:
http://www.abebooks.com/servlet/SearchResults?an=burton&bi=0&bx=off&ds=30&isbn=9780273728917&recentlyadded=all&sortby=17&sts=t&tn=thinking+mathematically

• Fawn
Posted July 12, 2015 at 10:46 am | Permalink

Thanks, Sandy. I should really check into other sources other than Amazon. It’s such a one-stop shopping for me there that I forget others exist.

3. Jenni Fuller
Posted July 11, 2015 at 6:50 am | Permalink

Looks like a great book! I see (on Amazon) that the newest edition is sixth Ed and is over \$200! However, the fifth Ed is only 20 something, so maybe I can get a copy of that one.

WhIch course in Portland did you take that used this text?

• Fawn
Posted July 12, 2015 at 10:44 am | Permalink

Hi Jenni. Do you have the link for the book as I don’t think we’re talking about the same one?

The course was Visual Math for Middle School Teachers. Dr. Michael Shaughnessy was the instructor — he later served as NCTM President.

4. Posted July 12, 2015 at 1:45 am | Permalink

That envelope-making one looks interesting, and one that primary kids could do. What does it say on page 35 about it? (The book is expensive!)

• Fawn
Posted July 12, 2015 at 10:41 am | Permalink

Hi Simon. I’m having trouble inserting image of that page on here. Will tweet it out to you.

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