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Wednesday, June 22, 2016

Memorizing Facts Versus Knowing Facts From Memory

I used to think one of the most important things I did with my fourth graders was to make sure they were fluent with their multiplication and division facts.  My definition of fluency was synonymous with fast.  To me fast = fluent.  To ensure my students all had "fluency" with their multiplication and division facts, we had daily timed tests which some kids loved and others dreaded.  We used a boxed program that was on my self when I started teaching.  

As much as I thought I was doing the right thing, there were a few things that bothered me about this process.  There were a few kids who were very proficient mathematicians who just were not doing well with these timed tests.  I also had some kids who were doing really well with the timed tests yet they were really struggling to multiply larger numbers.  

After more and more of these concerns popped up over several years, I started doing some more research into what exactly fluency meant.  I stumbled upon the work of Catherine Fosont and read her Young Mathematicians at Work series.  I learned about models for multiplication, using equal groups, arrays and the open area model.  I learned about helping kids develop strategies for multiplication facts.  Strategies based in understanding and the properties of multiplication. Strategies that will help kids develop number sense.  

I still focus on fluency with multiplication facts in fourth grade but fluency has a completely different meaning to me now.  The way I work on fluency now does not involve timed tests.  It does not involve kids being anxious or feeling unsuccessful at math.  Instead I focus on developing number sense which helps kids learn and remember strategies that make them fluent with their multiplication facts.  To the untrained eye, it often appears as if my fourth graders have memorized their facts when they actually know their facts from memory. 

This short video does a great job of explaining the difference I am talking about:

How do you think about or teach fact fluency? Please share your ideas in the comments below!

Looking for more?! A reader asked some great questions about this post and I answered her question and followed up with more thoughts on fact fluency in this post! 


  1. I entirely agree, Tara! I think teaching math facts using strategies is the key to providing the foundation of conceptual understanding of the operations which will then be applied later on in their math journey. The idea of teaching 8 + 5 by taking 2 from the 5 to make 10 with the 8 and then adding the remaining 3 to get 13 is applied when we add fractions like 4/5 + 3/5. Rather than having to remember to add numerators but not denominators and then have a fraction that has more on top than the bottom, we can just take 1/5 from the 3/5 to make a whole and add the additional 2/5. It just makes so much more sense! Have you heard of Dr. Nicki Newton and her new book (coming out today) Math Running Records? I've been implementing them in both my K-2 and 3-5 schools for all operations and it is changing everything! I'm able to educate teachers and assistants on what to look for with early numeracy strategies like counting all vs counting on and so on. I has allowed me to zoom in for each student exactly what I need to do to further them on their math journey. Magical!!

    1. Math running records is on my to read list! I have 12 books awaiting my attention that I hope to read before summer is over!

  2. The video was too helpful for me to understand the facts for teaching. Thank you for sharing it.