Hello ICTM members! My name is Angie Shindelar and I serve on the ICTM Board as the Vice President for Elementary. I am currently a Math Consultant for Green Hills AEA in southwest Iowa. I taught elementary and middle school math at Nodaway Valley CSD for many years. While I am a huge Iowa State fan, I am a UNI alum with a BA in Elementary Education and a MA in Middle Grade Mathematics Teaching. On game day I just give in and cheer for both schools when they play one another. That always gets me some interesting looks.
Previously, in the spring newsletter, I wrote about basic fact fluency. You can read that article here if you missed it. In this article, I continue with the basic fact fluency theme by asking readers to consider the difference between memorization and automaticity and why the distinguishment is important.
The Iowa Core Math Standards specifically address basic fact fluency with one standard for each grade level, K-3. Examining these standards across K-3 reveals how the learning progression develops. It is important to note there is specific language indicating students should learn strategies for basic facts and work incrementally toward the fluency expectations.
In these standards, the language “know from memory” is used. Often the interpretation of this is the expectation to memorize. With this interpretation the instructional focus may emphasize time as a measure. In other words, the number of facts a student can retrieve in a short amount of time becomes a measure of fluency. Sadly, for many students, fluency is short-lived. The memorized facts are not retained over time and either have to be rememorized or fall back on less efficient strategies like counting.
“So, are you saying students don’t need to learn basic facts?”
Not at all. Anyone that has taught in the later elementary and middle school grades can describe what a nightmare it is for students that do not know their basic facts. My previous article and this one have been written to consider more effective basic fact instruction and practice. The end goal has not changed.
What might instruction look like if the expectation for learning basic facts were to develop solid mental strategies, reaching automaticity over time. Automaticity, in this case, meaning students have learned and practiced a mental strategy for a fact enough times that it is automatically known. A critical point here is if, over time, the basic fact cannot be recalled automatically, the student has a solid mental strategy that is quick and efficient. The tendency to guess or use a less efficient strategy like counting is rarely seen.
My work as a math consultant has provided opportunities to on basic fact instruction with many elementary teachers and students. These teachers have numerous annecdotals describing how students’ number sense has developed and grown by focusing basic fact instruction on building automaticity through mental strategies.
“So, I shouldn’t just expect a student to tell me 7 + 8 = 15?”
Yes, we want students to be able to do that! Of course!! However, it’s how we get them there that makes the difference in the long term. Consider three scenarios for a student that is solving
7 + 8:
1) Has it memorized now, but can’t recall consistently over time;
2) Not memorized, so counts on from either addend;
3) Knows automatically from lots of practice with a mental strategy;
a) 7 + 7 = 14, so 1 more = 15, or
b) 8 + 2 = 10, so 5 more = 15, or
c) 7 + 3 = 10, so 5 more = 15
4) Is getting close to automaticity and only hesitates briefly to think through one of the strategies listed above.
5) Has learned a couple different ways to solve mentally and is practicing regularly with games and activities to become more automatic.
There might not seem to be a big difference between memorization (#1) and automaticity (#3). After all, if you’ve reached automaticity isn’t that the same thing as memorized? In both cases, the student knows the fact. The difference is the process. Putting the emphasis on learning a strategy and practicing it until automaticity is reached is a process that will develop a strong neural pathway and move the fact into long-term memory. Memorization, for many students, does not provide enough experience and development of number sense to move the fact into long-term memory.
Basic fact fluency has always been important for elementary students to achieve. The Iowa Core Math Standards have given us, as teachers, a lot to think about. As I wrap up this article I am still thinking about another word that is used in the basic facts standards, “fluency.” It is often considered to be synonymous with memorization. I have a feeling there’s a third article on basic fact fluency brewing. Stay tuned.
I would love to hear any of your thoughts around basic fact fluency and any other topics of interest for elementary math. My email is firstname.lastname@example.org.