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Procedural Fluency Versus Memorization


  • What is Procedural Fluency?

  • Do Students Need to have a Strong Number Sense?

  • Does Memorization Work?

My principal passed me a book called Visible Learning For Mathematics written by John Hattie, Douglas Fisher and Nancy Frey.

Apparently, John Hattie is coming to the forefront in mathematics learning. Is he the one mathematical guru to focus on?

Through my Masters studies and ongoing reading of various books and articles over the past few years, there are a few gurus who make reference to each other regularly. Presently, I have read approximately half of this book and it is very interesting and so true. If you are looking for professional learning I most definitely recommend this as an educational read.

His thoughts are similar to that of Cathy Fosnot's, in that we are putting students at a detriment by teaching algorithms without understanding. He refers to this understanding, the ability to explain the how and why when doing the work, as procedural fluency.

If you had the opportunity to view the video, Deep Understanding Versus Memorization (below), my colleague, Mary Schatz and I spoke of the importance of students developing a strong number sense before introducing the traditional algorithms. The Clarifications of the Alberta Curriculum that came out last spring indicated that teachers are to teach a variety of strategies and then each student chooses the strategy (or strategies) in which their understanding lies.


The question I pose is:

Are educators aware of the different strategies to teach and do they know the ways in which to teach these strategies for understanding?

Why I ask this is because of two recent scenarios: One that I experienced and another I heard from my colleague, Mary Schatz. As I said in the video, I was having a conversation with a grade two teacher back in October and she was already introducing the algorithm for adding to her grade 2 students. I teach grade 3, and I have not yet introduced the algorithm. I won’t until they have had the opportunity to learn other strategies that will help further develop their number sense.

The day after I interviewed Mary, she emailed me about a teacher expressing her frustration in helping her students learn the traditional algorithm. Her comment was that she was repeatedly showing them the steps again and again but they just couldn’t get it! They kept forgetting to carry the regrouping from the ones to the tens place value.  In conversing over email about this, Mary asked how I would provide this teacher help. My reply was that those students need further work to enhance their number sense (understanding that a digit in a given place value has a specific meaning or value, eg. 85 is 8 tens and 5 ones or 80+5, NOT 8+5 ) and until they do the steps of the algorithm can be demonstrated hundreds of times and they still won’t get it. Well,  perhaps they may memorize the steps eventually, but there won’t be any procedural fluency in which they can explain the how and why. Mary’s final response was that sometimes we need to go back before we can go forward. So very true!

Here are pictures of two strategies in which my grade 3 students have learned up to the present time in the school year. I also have included 2 short video clips.  It will allow you to hear a student explain their thinking using these two strategies.

Your Turn!

Try it with your students

I am unsure as to what grade you are teaching and where you are at, but take a moment to reflect and carefully observe as well as listen to your students. It doesn’t matter if you are simply working on the single digit basic facts or with multi-digit numbers.

Do your students have procedural fluency? Can they explain the how and the why? Take this back to your classroom and please share with us the outcome and/or ask questions for clarification. 

I look forward to hearing how it is going! Leave a comment or question below. 



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