Figuring out a word problem. Calculating area and perimeter. Finding the measure of an unknown angle.
All these tasks, and more, draw on an essential foundation of math knowledge, said Brian Bushart, a 4th grade teacher in West Irondequoit 69传媒 in New York: fluency with math facts.
鈥淓verything else we do in math relies on your ability to use that knowledge pretty quickly,鈥� he said.
Bushart was speaking on an Education Week panel on May 25, focused on two important pieces of early math instruction: fact fluency and beginning word problem-solving.
Having a strong grasp on fact fluency鈥攕uch as single-digit arithmetic, and multiplication tables鈥攆rees up mental space for students to solve more advanced, multistep problems, said Nicole McNeil, a professor of psychology at the University of Notre Dame, and another speaker in the panel.
鈥淚f we are spending all of our time 鈥榗ounting on鈥� to solve a pretty basic arithmetic fact, we鈥檙e not going to have resources available to do those higher-order problem-solving tasks,鈥� she said.
Here are three takeaways from the panel about how teachers can help students develop fact fluency. To read more about this topic, or others in early math education, see Education Week鈥檚 new report, Math Foundations for All.
Learning math facts is a 鈥榤ulti-year progression鈥�
The end goal of math fact practice is for students to be able to recall them 鈥渁utomatically,鈥� or calculate them 鈥渨ithin a second or two,鈥� said McNeil.
But students work up to that goal, said Bushart: 鈥淭here鈥檚 a multi-year progression of learning.鈥�
In kindergarten, students learn how to do basic work with numbers鈥攈ow to count, for instance. Then, teachers introduce the idea that it鈥檚 possible to join and separate numbers.
From there, students learn strategies for joining and separating numbers in a more efficient way. For instance, Bushart said, students can use their knowledge of adding by 10 to make adding by 9 easier鈥攑ulling 1 from the other number to transform the problem into one where students are adding by 10, so that 9 + 6 is transformed into 10 + 5.
Then, quickly recalling these facts becomes the goal. Bushart tells his students: 鈥淭he reason we鈥檙e doing it is that practice of remembering is actually what鈥檚 going to strengthen your memory over time.鈥�
Math facts should be taught as part of an 鈥榠nterconnected network鈥�
Automaticity with math facts is important, but students should understand the why behind them too, Bushart said.
He talked about teaching students who could solve 8 x 5 quickly, but didn鈥檛 know what 8 x 6 was. Part of his goal is to help students see these two equations as related.
鈥淚 want kids to start to notice that 鈥� 8 x 5 is almost 8 x 6, which is almost 8 x 7. That鈥檚 the kind of space I want them to be in,鈥� he said.
This is one reason why calculators can鈥檛 replace prowess with math facts, said McNeil鈥攊f kids are relying on calculators, they鈥檙e not developing this relational knowledge. 鈥淲hen students are fluent in math facts, it becomes part of an interconnected network,鈥� she said.
Avoid 鈥榖ombarding鈥� children with failure when they practice
Bushart only assesses his students on math fact recall once a week or once every other week. He also intersperses facts that students already can recall easily with ones that they鈥檙e trying to memorize.
鈥淵ou don鈥檛 want to bombard them with, I don鈥檛 know, I don鈥檛 know, I don鈥檛 know,鈥� he said. 鈥淵ou want a lot of success in there.鈥�
McNeil endorsed this strategy. 鈥淐hildren are only developing automaticity with a few facts at a time,鈥� she said. 鈥淒o not practice all of the facts at one time.鈥�
She offered another suggestion: It鈥檚 important that students have strategies, like making 10, to compute the facts that they can use if they can鈥檛 recall the answer automatically. These strategies can act as a back-up, she said, so that kids can still solve for the answer.
Watch the entire panel below.
