A Squiggle-Line Dilemma: How Creating Bends Gives us Freedom in Planning

Have you read one of my all-time favourite books The Dot and the Line: A Romance in Lower Mathematics by Norton Juster? It’s not a new book it was originally written in 1963.  I not only read it to my classes on Saint Valentine’s Day but I gave it to my wife as a present way back on our first valentine’s day together.

I love that every time I read it it makes me reflect on who I want to be as a human and also as a math teacher!

If you haven’t read it you can watch the Academy Award winning Short Animation by Chuck Jones right here, now! Watch it before reading the rest.

Lately I’ve been thinking about this story as it relates to how we math teachers feel the need pursue the “perfect” math lesson or that shiny new tool/technique we hear we should try.

We seem to be after the perfectly engaged class (behaviourally and cognitively) learning the chosen standard at just the right pace for all students. And why shouldn’t we? It sounds great. But, what is the likelihood that we’ll ever achieve this “perfectness”. The reality is that teaching is messy; all classrooms are different.

We see so much positivity on the internet and from our peers. Looking at twitter or blog posts suggests that so many teachers are having these perfect classes or that the shiny new tool/technique solves all our problems. And it leaves us sometimes feeling inferior and overwhelmed.

I think some of us feel that we need to be using that iPad, or new tech tool, or shine new learning model everyday to create this perfect happy class.

Let’s relate this situation to The Dot and the Line story.

Imagine for a moment that you are the main character from the book; the line. The dot is ….. well, the dot is that “perfect” class lesson where all students are using that new shiny tool or technique that we’re not quite sure about.

When the line first meets the Dot and sees that “she” only has eyes for the whimsical squiggle, the line feels that “he” needs be more like the squiggle.

Many of us teachers also feel or have felt that we have to become the whimsical squiggle to win the dot to our side. We feel that we have to become not just entertainers, but we have to become someone we are not. Many teachers also feel that we have to give up core beliefs on what creates good a good learning moment so we can have this other, supposedly great learning tool or technique. 

But that’s not true.  We don’t need to change our core beliefs of what creates great learners. We don’t need to give up on teaching students dedication, determination, and rigour to bring in curiosity, creativity and openness into our lessons.

For example, some math teachers believe that by teaching through problem solving with tasks like Popcorn Pandemonium, or Kyle Pearce’s Candle Burning problem you HAVE to sacrifice procedural fluency.  They believe that you can’t have both mathematical rigour and learning through problem solving. You either have to be a squiggle or a straight line. They believe it’s one way or the other.

What I believe is that we may have to BEND, just like our pal the Line to truly create math moments that matter for our students.

Like the line, Bending gives us permission that it’s not an all or nothing transformation. We don’t just have to choose between a squiggle and a perfect line.

Like the line, bending means though that we may have to work harder and smarter.

Like the line, bending means that we can teach through problem solving as well as getting students the practice they need to become fluent without sacrificing time.

Like the line, bending means that we can recreate ourselves — in a stronger way that supports learning.

Bending means that we need to actively think about how we can incorporate our core beliefs of good learning in our lessons while meeting the needs of ALL our students.

To address one common Line vs. Squiggle comparison:

How do we incorporate practice and procedural fluency in lessons while building resiliency in problem solving — without sacrificing time?

I use purposeful practice routines that encourages student discourse, self assessment, peer assessment, movement, and error checking that bring my students closer to procedural fluency after we’ve used productive struggle to learn a topic.

Download and learn more about 5 practice structures I highly recommend you add to your practice routines. 

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5 Practice Structures in Math Class

Learn about 5 of my go-to practice structures for self assessment, peer assessment, movement, and error checking!
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