December EMT Institute Meeting - Developing Procedural Fluency from Conceptual Understanding

Our December EMT Institute was held on December 5, 2017. Our focus was on how to develop math procedural fluency from conceptual understanding.  We discussed how we "learned" our math facts as children and how and why that has changed today.

  

We read, discussed, and analyzed NCTM's position statement on Procedural Fluency in Mathematics, as well as the vertical progression of fluency standards.  We determined the difference between "memorization" versus "from memory".

 

  

We read the article, "Three Steps to Mastering Multiplication Facts" by Gina Kling and Jennifer M. Bay-Williams, and participated in an activity where we identified tasks in each of the three phases of fluency development.  We discussed the importance of the Strategy Development phase and reviewed the strategies we are emphasizing.  We learned about addition and subtraction strategies by reading the article, "The Road to Fluency and the License to Think" by Lisa Buchhotz. We determined that the three phases for achieving multiplication fluency also apply to addition and subtraction fluency development.

The Three Phases of Fluency Development

When we reflect on how we learned our facts as children, we jumped straight from Phase 1 to Phase 3 (and attempted to memorize them.)

Phase 2 is crucial for fluency development and is a major emphasis today. Strategies are developed through tasks, number talks, and games.  Strategy development leads to fluency!

 

We reviewed barriers to fluency for upper elementary and middle school students and what we could do to reduce those roadblocks.  Some of these barriers are formed from misconceptions developed in the earlier elementary grades, such as:  1) Thinking an equation always has the answer after the equal sign, saying "the most you can have is 100% of something", using "keywords" to solve problems to simplify the process, use of the term "reducing fractions" versus "simplify", saying the product is always "bigger" than the factors in a multiplication problem, saying you "move" the decimal point, etc.

We experienced the importance of strategic number talks and purposeful games in developing fluency. We were provided with numerous games and even played some of them! We also discussed the research on the negative effects of timed fluency tests, and explored alternatives to traditional timed assessments.


Sources: 
Articles from Teaching Children Mathematics & Mathematics Teaching in the Middle School, NCTM: Three Steps to Mastering Multiplication Facts by Gina Kling and Jennifer M. Bay-Williams, The Road to Fluency and the License to Think by Lisa Buchhotz, and 12 Math Rules that Expire in the Middle Grades by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty.
Principles to Actions: Ensuring Mathematical Success for All, NCTM