My V

Five Books That Have Shaped My Mathematical Worldview

Thanks to Matt Oldridge (@MatthewOldridge) for providing the impetus for this post. Thanks Matt for including me in the tweet and for nudging me to give this some thought. It was enjoyable to look at the book shelf and identify those personal seminal works but also a little depressing as I saw all of those that remain untapped.

I haven't looked at Matt's post at the time of writing as I didn't want to be influenced in any way by seeing his top five. I will as soon as this post is complete...I promise Matt.

A Concise History of Mathematics (Dirk J. Struik)
There are many other history of math tomes and there are probably many that are better written than Struik's history but timing is everything. This is the text that accompanied Israel Kleiner's third year History of Mathematics course at York University and that is the course that sealed my passion for the subject. I still have my notes for that course and that short 256 page book crammed in all of the wonder and joy of mathematics.

Good Questions: Great Ways to Differentiate Mathematics Instruction (Marian Small) and More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction (Marian Small and Amy Lin)
Hard to think of a list without Marian Small (@marian_small) on it at least once! Cheating a bit here as I am thinking of these as one when they are in fact two separate books. It is also a good way to give a shout out to notorious cat-lover Amy Lin (@amylin1962). I tell the story frequently to those who haven't tired of hearing it that these two books remain the most popular resources in my department. Everyone in the department asked for their own personal copies of these books when they were published. These books changed the way we teach and assess. Thank you Marian!!!

Elementary and Middle School Mathematics Teaching Developmentally (John A. Van de Walle)
A truly seminal work in the teaching of mathematics and one that I would argue belongs on all math teacher book shelves regardless of division. I really delved into this work during my time as a resource teacher and it cemented in me my belief that the foundation of learning mathematics must first come from a visual approach and then proceed to the abstract. Some call it concreteness fading. I used it to introduce concepts such as integers and fractions when my own kids were going through the intermediate grades and have incorporated many of its lessons in workshops to parents and my own teaching.

Damned Lies and Statistics (Joel Best)
This is a super short book (about 200 pages) but I was so happy after reading it that I made it required reading one year when I taught data management. I have read many books about the importance of being data literate and a few of them contain more recent examples but this was the first and as I read it, I kept thinking that students could easily digest the message of the book. The book hits many of the historical blunders of statistical incompetence but also introduces some subtle concepts that aren't covered in any data management texts!

Dataclysm (Christian Rudder)
A book recommended to me by Judy Mendaglio (@judy11235813) knowing my enjoyment of books that explore our relationship to data. Rudder is the co-founder of OkCupid and his book is by far my favourite (especially since it was more recent) book about data. Not a day or week would pass without me sharing a nugget I read with my (exasperated) department and classes. This book is jammed with content that will amaze, amuse and anger.

Two Honourable Mentions...

The Incident of the Dog in the Night-time (Mark Haddon)
A work of fiction. A soon as I saw that the chapters were numbered using primes, I was hooked. Lots of math is embedded in a story that will keep you turning the pages.

Proofiness (Charles Seife)
Another book with data and statistics at its heart but this one serves as a cautionary tale. It harkens to that old saying: with great power comes great responsibility...and some are not being very responsible with numbers.

Well that's it but there are plenty that I left off that deserve mention (e.g. Boaler, Humphries, Burns and on and on and on) but only so much time to write and read. And this doesn't include the articles and shorter pieces that I return to from time to time to inspire and revive that passion like Apostolos Doxiadis's Embedding mathematics in the soul: narrative as a force inmathematics education. I could go on but I need to get to the stack left to read.