By Joe Caruso

(You can find the original post on Joe’s awesome blog here.)


I am going to be writing a series of posts as part of my #NotABookStudy learning around Cathy Fosnot’s book, “Young Mathematicians at Work – Constructing Multiplication and Division“.  It’s the second book in a 3-part series and I was turned onto it through the Mathematics Leadership Network composed of math leaders throughout North Eastern Ontario.  Chapter 1 is titled, “Mathematics” or “Mathematizing”?

I really love how the chapter starts out with explicitly stating the purpose of teaching – “…to help students learn.”  Teaching and learning is often seen as two separate entities.  In fact, when I look up the word “learn” on, “teach” appears as an antonym.  Learning and teaching should look like an interwoven, seamless process in a classroom.  Teaching should be like mood stones – only instead of the colour changing when it touches a student, the teaching changes.

The chapter goes on to describe the traditional approach to mathematics as “school mathematics” and how “big ideas”, in “school mathematics“, are explained using procedures and process.  Some teachers may use manipulatives to demonstrate but it is still a process whereby teachers do all the work and students absorb facts, concepts, formulae, and algorithms.

In Terry Anderson’s second-grade classroom, depicted in this chapter, a very different process is evident.  In her class, students are constructing the big ideas through the use of real-life mathematical tasks and showing and talking about their thinking.  The focus is not on answers – it’s on their thinking.  Terry asks questions to move students’ thinking forward based on what she hears and sees from them.  Through this process, students must construct their own strategies and defend them.  In this way, students are just like mathematicians.  They experience what it’s like “… to organize and interpret their world through a mathematical lens.”  In his framework, teaching and learning are connected.

In summing up, Cathy gives us the key to making math more meaningful for our students.


When mathematics is understood as mathematizing one’s world – interpreting, organizing, inquiring about, and constructing meaning through a mathematical lens – it becomes creative and alive.”

Featured image by Ian Schneider on Unsplash