Fluency is much more than automaticity. That is part of the eventual goal, but it is not necessarily the most important goal. In fact, while fluency is a part of every grade level's standards, 2nd and 3rd grades are the only grades where "instant recall" or "knowing from memory" (automaticity) is mentioned. Both of these grade levels ask for this piece to be mastered by the end of the school year. In grades K-1, students are focusing on the fluency piece which builds students' number sense.
We need to seek out ways to measure this "knowing from memory" other than timed tests. Jo Baeler, a professor at Stanford and a leading researcher in mathematics instruction wrote this interesting article for the NCTM in April 2014.
So...how can we measure instant recall without giving timed tests? I know they are easy to administer--I gave them, too, for many years, but I eventually found that the students who excelled on timed tests were the same kids who picked up on their facts easily no matter what practice we used.
There are a number of ideas that I think we could try.
*Observation in the classroom is an easy example. Watch your students as you work in small group, during minilessons, or when they are playing games. Do they know their facts in these situations?
*The use of games and student data from games can help demonstrate instant recall. *Consider using a fact exit slip before leaving for a special....you could present a fact and students would write the answer on the slip or on a dry erase board before leaving the room. You could use this data over time to help show instant recall of facts.
*Have your students self-assess: provide them with a list of 10 facts and have them complete them and mark the ones that they knew automatically.
*Take a few minutes of transition and have the students roll two dice or draw two cards, write down the numbers, and perform the operation they are currently working on. They just keep rolling and computing until you tell them to stop. (In this scenario, you could differentiate the problems by giving specific dice or cards to the child) When they are done, they turn in a list of facts that they completed.
There are many alternatives, and you are all so creative. Besides, you know what works best for your kids.
The thing is... this goal of instant recall is for the end of the year. We don't need to begin measuring the instant recall until later in the year in 2nd and 3rd grade. We should be working to immerse our students in the facts that best fit their needs. Our books lay out a plan for fact acquisition. Many of your students will move according to this rate. Games and activities would build off of only the facts that have been instructed. If doubles haven't been taught yet, the students would only be working on facts which have been covered in the classroom. If we begin measuring the automaticity of these facts too early, we just beat kids into believing that they aren't good at math. We need to work to show them different ways to build their fluency throughout the year, and saving our worries about instant recall until the end of the year. This will allow our students to interact with the numbers and patterns in a more meaningful way, and hopefully, lead to the acquisition of these facts.
Many teachers use Xtramath to help build this automaticity; while this program does have a timed piece to it, I don't believe that the time factor is as negative as it is in a timed test or another program like RocketMath. As mentioned above, many children just gain anxiety about their facts from these timed situations.
Most importantly, we want our students to feel good about math and their skills. I was doing a math running record the other day on a student, and I asked him if he liked math. His response was, "No, I'm not good at it." Yet, when we completed his running record, he had used very high-level strategies to determine all of his answers. He was not automatic about all of the answers, but it was impressive the ways he had learned to acquire the answers. That, to me, is more important than the instant recall. I told him how good he was with math, and he was surprised to hear that. :(
I have read multiple articles comparing math fluency to reading fluency. We would not expect students to read or work beyond their level in reading. Why do we do that in math--pushing them into facts before they have mastered others? Would we rather have a student who can comprehend or one who can read all the words but has no idea what they mean? I believe we need to revisit our beliefs about math fact fluency and look to make our instruction match what the research shows.
So--as we work to build our students' fluency in facts--here is another activity you can use this month for individual practice. By using different dice and menus, you can differentiate it for each student. I shared this with a friend a couple of years ago, and her students liked it so much that she created one for many different times of the year.
What do you think about this? Do you have other ways to informally assess this standard?
