#NotABookStudy Chapter 1


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 thesaurus.com, “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.


2 thoughts on “#NotABookStudy Chapter 1

  1. Congratulations, Joe, on making your own thinking about Chapter 1 visible and available openly to others. It’s by working openly that we mobilize learning for all.

    I am working on my own reflection, but this is SO complex for me. I can’t seem to read a sentence of this book without going down a rabbit-hole of thought.

    What I do love, though, about your post is “Teaching should be like mood stones – only instead of the colour changing when it touches a student, the teaching changes.” It reminds us that, as Dr. Fosnot outlines so well, learning is NOT linear, and the path is different for every child.

    Spray and pray is NOT effective if our goal is for ALL children to learn mathematics (it is most effective for those with outside support, so this teaching method is also inequitable).

    Responsive, reflective, effective pedagogy is essential and this is difficult work. Elementary teachers have intensely complex work to do, though this is rarely reflected in society’s understanding of teacher work.

    Our math strategy can’t be just about more teachers and more time for math. It has to be a full societal understanding of the gateway that math understanding is to the possibilities of a fulfilling life, and the complexity of the work needed to ensure ALL of our kids have this opportunity.

    Liked by 1 person

    • Thanks Donna. I know what you mean about the “rabbit hole.” I wanted to include thoughts on unitizing and how important Terry’s approach is to unitizing 10’s and place value. (I guess I have now.) And that sent me down the rabbit hole of the math processes and how important they are to name and troubleshoot. There is so much here to uncover…I’m looking forward to the rest of the book.


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