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Timed Math Fact Fluency Expectations by Grade Level

Posted on by Dr. Don

Students should be automatic with the facts. How fast is fast enough to be automatic?

Editor’s Note: “Direct retrieval” is when you automatically remember something without having to stop and think about it.

Some educational researchers consider facts automatic when a response comes in two or three seconds (Isaacs & Carroll, 1999; Rightsel & Thorton, 1985; Thorton & Smith, 1988). However, performance is not automatic; direct retrieval when it occurs at rates that purposely “allow enough time for students to use efficient strategies or rules for some facts (Isaacs & Carroll, 1999, p. 513).”

Timed Math Fact Fluency Expectations by Grade Level

Most of the psychological studies have looked at automatic response time as measured in milliseconds and found that automatic (direct retrieval) response times are usually in the ranges of 400 to 900 milliseconds (less than one second) from presentation of a visual stimulus to a keyboard or oral response (Ashcraft, 1982; Ashcraft, Fierman & Bartolotta, 1984; Campbell, 1987a; Campbell, 1987b; Geary & Brown, 1991; Logan, 1988). Similarly, Hasselbring and colleagues felt students had automatized math facts when response times were “down to around 1 second” from the presentation of a stimulus until a response was made (Hasselbring et al. 1987).” If, however, students are shown the fact and asked to read it aloud, then a second has already passed. In which case you expect a timely response after reading the fact. “We consider mastery of a basic fact as the ability of students to respond immediately to the fact question. (Stein et al., 1997, p. 87).”

In most school situations, students take tests on one-minute timings. Expectations of automaticity vary somewhat. Translating a one-second-response time directly into writing answers for one minute would produce 60 answers per minute. However, Some children, especially in the primary grades, cannot write that quickly. “In establishing mastery rate levels for individuals, it is important to consider the learner’s characteristics (e.g., age, academic skill, motor ability). For most students, a rate of 40 to 60 correct digits per minute [25 to 35 problems per minute] with two or few errors is appropriate (Mercer & Miller, 1992, p.23).” This 35 problems per minute rate seem to be the lowest noted in the literature.

The Correct Math Fact Rates

Other authors noted research that indicated that “students who can compute basic math facts at a rate of 30 to 40 problems correct per minute (or about 70 to 80 digits correct per minute) continue to accelerate their rates as tasks in the math curriculum become more complex…[however],…students whose correct rates were lower than 30 per minute showed progressively decelerating trends when more complex skills were introduced. The minimum correct rate for basic facts should be set at 30 to 40 problems per minute, since this rate has been shown to be an indicator of success with more complex tasks (Miller & Heward, 1992, p. 100).” Rates of 40 problems per minute seems more likely to continue to accelerate than the lower end at 30.

What is the recommended time to finish problems?

Another recommendation was that “the criterion be set at a rate [in digits per minute] that is about 2/3 of the rate at which the student can write digits (Stein et al., 1997, p. 87).” For example, a student who writes 100 digits per minute expects to write 67 digits per minute. This translates to between 30 and 40 problems per minute. Howell and Nolet (2000) recommend an expectation of 40 correct facts per minute, with a modification for students who write at less than 100 digits per minute. The number of digits per minute is a percentage of 100, and you multiply that percentage  by 40 problems to give the expected number of problems per minute. For example, a child who writes 75 digits per minute would expect 75% of 40 or 30 facts per minute.

If measured individually, a response delay of about 1 second would be automatic. In writing, 40 is the minimum, up to about 60 per minute for students who can write that quickly. Teachers themselves range from 40 to 80 problems per minute. Sadly, many school districts have expectations as low as 50 problems in 3 minutes or 100 problems in five minutes. These translate to rates of 16 to 20 problems per minute. At this rate, students can count answers on their fingers. So, this “passes” children who have only developed procedural knowledge of how to figure out the facts rather than the direct recall of automaticity.

Conclusion

With the right tools, any student can develop math fact fluency and have fun while doing it! Students use Rocket Math’s Subscription Worksheet Program to practice with partners, then take timed tests. Rocket Math also offers math facts practice online through the Rocket Math Online Game. Students can log in and play from any device, anywhere, any time of day! Start a free trial today.

Both the worksheet program and the online game help students master addition, subtraction, multiplication, and division math facts.

 

 

Don’t I need to teach doubles and other combinations first?

Posted on by Dr. Don

There is a lot of advice out there that teachers need to introduce different tricks to remembering math facts to help students learn the facts. Things like doubles, or doubles plus ones, or special combinations that add to ten are recommended to be taught to students. Teachers are exhorted to use many different kinds of exercises to teach these different ways of remembering facts. Is that necessary to do before memorizing facts as we do in Rocket Math? The simple answer is, “No, that’s not necessary.”
DoublesPlusOne
How do we know? What’s the evidence? There are two basic sources of evidence, one from experience and another from logic.
Let’s look at the logical reasons these are not necessary. The goal of Rocket Math, and any good math fact memorization program, is to develop automaticity in answering math facts. Automaticity means the student can instantly answer the fact, without any intervening thought process. So even if students first learn those memory tricks they have to be abandoned in favor of simply recalling the fact from memory.

An intervening thought process would go like this, “Four plus five is like four plus four but one more. Four plus four is eight , so one more is nine. So four plus five is nine.” But the goal of Rocket Math is to simply come to the point where the student reads, “Four plus five is,” and the answer, nine, pops into mind without another thought. Logic tells us that if the learner ultimately has to abandon the strategy, the only reason for learning the strategy is if it is needed as a transition. In other words, if students have to learn the facts to the point where they don’t use the strategy, then the only reason to learn the strategy is if they need it to get to the point of memorizing the facts.
This brings us to the second piece of evidence, experience. I know from experience tha students don’t need these strategies to learn the facts.  When I started using my original hand-written version of Rocket Math with my students with learning disabilities–it worked without them knowing other strategies!  In the past fifteen years thousands of children have learned math facts to automaticity using Rocket Math without learning those different tricks. If it were necessary, then they wouldn’t be able to do it. The reason it is not necessary is that students only have to memorize two facts at a time and that’s just not difficult to do. Give them plenty of practice with those two (enough so that they come to be able to answers as fast as they can write) and they will know the facts without some other (intervening) strategy.
So you don’t have to teach all those different tricks to students to remember facts. Just use Rocket Math, and make sure they are practicing the right way with corrective feedback from their partner. Their results will speak for themselves.