Memorizing Facts

All of us who are in the job of teaching mathematics get put in the position by principals, parents, or people we meet socially to defend our profession.  I spent 5 years as head of K-12 Mathematics for Minneapolis Public Schools and am currently the President of the Minnesota Council of Teachers of Mathematics.  In these roles I have been put in the position many times to give QUICK & meaningful messages about what I believe about teaching mathematics.  Over the last 10 years I’ve created several Elevator Messages on common questions about mathematics.

This is a first in a series of blog posts I am calling ‘Elevator Messages‘. An ‘Elevator Message or Pitch’ is a short summary used to quickly and simply define a process, product, service, organization, or event and its value. The name ‘elevator pitch’ reflects the idea that it should be possible to deliver the summary in the time span of an elevator ride, or approximately thirty seconds to two minutes.  My goal in these blog posts is to give you a 2 minute ‘pitch’ you can use with parents at a school family night or with principal/leaders or those you meet socially when asked about mathematics.  (though it may take me more than 2 minutes to explain each message to you).

One of the most common comments I hear from parents, teachers and principals goes something like this “If only the kids knew their math facts like we did when we were in school.  I just saw a student grab a calculator to type in 4 x 6.  We need to do something about this.”.  There is a lot in this statement, but I want to spend this post talking about one of the underlying beliefs in this message that the reason students struggle with math is they have not MEMORIZED their math facts and if we could change this, student’s success in math would increase.

This message comes from a session Justin Lanier did at the November, 2015 NCTM Regional conference in a session I attended entitled ‘Chains and Webs’. (If you don’t know Justin, check out his blog and a really cool website he hosts called Math Munch.  He is great)  Most of the message below comes from a minute or two of his session when he convinced me (not that I needed convincing) that Memorizing Math Facts is different than other things we memorize.

Think back to Elementary School.  BuzzFeed has a funny take on useless things we learned in Elementary school.  The Atlantic had an article titled ‘When Memorization gets in the way of Learning‘.  In the article the author defined ‘Memorization’ as learning an isolated fact through deliberate effort.  What things were you asked to memorize?  For me, I remember several:

The Preamble to the Constitution

The  Presidents (in order)

Periodic Elements Table

Math Facts – Multiplication chart up to at least 10

State Capitals

30+ years later I have forgotten lots of what I once had memorized.  Because I have traveled a lot and have always had a fascination with maps, I still remember a lot of the state capitals.  Because I teach math, I am pretty good with my multiplication facts.  That said I totally can’t remember the capital of Kentucky and I always blank on the product of 7 and 6. There is a difference though in me forgetting these 2 things.

THERE IS A DIFFERENCE IN WHAT WE MEMORIZE.

If you look at a grid of the State Capitals, there is no pattern in the grid that helps me figure out what the capital of Kentucky is.  Kentucky is not like Oklahoma and the state capital is not Kentucky City.  Kentucky is not like Minnesota and does not have a capital named after a Saint.  There is no nearby fact that I have memorized that can help me figure out the capital of Kentucky.  Unless I have the capital memorized, I need help.  Thank goodness I live in age of cell phones and google.

Let’s contrast the memorization of state capitals with knowing your math facts.  I believe we all have a few math facts we blank on from time to time.  My nemesis is 7 times 6.  Unlike state capitals, I know a lot of things that can help me quickly recreate this missing fact in my brain.  I have strategies to recreate this missing information.  I don’t have to reach for my cell phone or a calculator.  I was lucky enough to learn a lot of strategies that have given me a fluency with the base 10 number system. I can figure out that 6 times 7 is 42.

I don’t need to have memorized every math fact as an isolated fact.  Math facts are connected to the facts surrounding it.  For me, I can figure out 6×7 by adding 7 to 5×7=35.  There are lots of other strategies that I can use to help me too.  I know 3×7 is 21.  So I know I can double this solution to get the solution to 6×7…and there are more things I can do.  Fluency in mathematics is someone who has developed strategies to make sense of the patterns that exist in our number system.

My Elevator Message to those who say ‘kids need to memorize their facts’ is that (using the stuff above) our students don’t need to memorize facts, they need to see these facts as connected facts and have developed strategies to create any facts they don’t know.  As a teacher I need to teach and model these strategies.  I don’t need to create flash cards.

In recent years, I’ve de-emphasized memorization of most things in mathematics, especially with things I can reconstruct from knowing other things.  For example, I don’t have to memorize the formula for finding the distance tetween 2 points.  I can reconstruct this from the Pythagorean Theorem.

For further study: NCTM has a position statement on Fact Fluency.  Read it.  Linda Gojak, past NCTM President wrote a blog post titled ‘Fluency: Simply Fast and Accurate? I think not!’

My biggest learning around fact fluency as a secondary mathematics teacher has come from reading the following 3 books in the last few years.  I highly recommend you read one or all of them.

Making Number Talks Matter by Cathy Humphrey (my current favorite)

Building Powerful Numeracy by Pamela Weber Harris

Number Talks by Sherry Parrish (Elementary, but helped me a lot).  She has a new book coming out soon on Number Talks and Rational Numbers.  I’ll be for sure buying that one.

Again, thank you to Justin Lanier for giving me a visual (state capitals an a multiplication) to support my elevator message.

I wrote this post quickly.  I’d love to hear from you on how I can better craft this elevator message.  Tweet me @saravdwerf or email me at sarav@mpls.k12.mn.us or comment below.

p.s.  The capital of Kentucky is Frankfort.  Just in case you were wondering.