Math fact fluency

The first, and most important objective in elementary math is developing fluency with basic math facts. Practicing basic math facts should be a daily activity throughout the elementary years. All students need to develop fluency with basic single-digit math facts in the four operations. Students who do not develop fluency or ease of answering math facts are handicapped and overwhelmed by the rest of math, as is the girl above. Struggling to answer basic facts distracts students from focusing on higher-order math learning. While developing math fact fluency is not the only important objective, it is the prerequisite for all the rest.  

What is fluency practice in math?

Fluency is the ability to do a task quickly and accurately. Fluency in math facts is being able to answer quickly and correctly. The purpose of fluency practice is to develop improved fluency in answering math facts.

Some sources insist that developing strategies for figuring out math facts, such as doubles plus one (see above) is fluency practice. It is not. Such strategies consume time and attention. Students who are using them demonstrate that they are not fluent. To be fluent, students need to use direct recall without the use of any intervening strategy. To be fluent, students must move beyond figuring-it-out strategies to direct recall.  

Fluency practice means practice in direct recall of facts. To be effective, fluency practice requires a helper. You need either a person or a computer to give you the answer if you can’t quickly recall it. The helper should give you some extra practice on that specific fact to help you commit it to memory. The picture above illustrates effective fluency practice.

Math Fact Fluency vs. Math Fact Automaticity

Automaticity is the third stage of learning. When a learner first learns a skill, they work to develop accuracy. Accuracy is the ability to do a task correctly. After becoming accurate, the learner can, with still more practice, develop fluency. Fluency is the ability to do a task correctly and do it quickly. After developing fluency, with still more practice, a learner can develop automaticity. Automaticity is the ability to do a task accurately, quickly and without conscious attention or focus. 

Members of a marching band must be able to play each musical piece with automaticity, so they can focus on marching in step. Readers must be able to decode with automaticity, so they can focus on the meaning of the passage. Students doing complex math computations must be able to answer math facts with automaticity, so they can focus on the algorithm of solving the problem. After developing fluency, elementary students need to continue to get fluency practice so they can develop automaticity. 

Essential Components for Math Fact Fluency Practice to work

The focus of fluency practice should be on developing instant recall of math fact answers. Instant recall comes from committing the answers to memory. Math fact fluency practice must systematically help every student commit all the math facts to memory. If you want practice to help students do that, the practice must have four essential components: (1) bite-sized pieces, (2) corrective feedback, (3) measurement of mastery, (4) gradual, cumulative development, and (5) individual student placement.

(1) Bite-sized pieces 

Only a very small number of facts can be committed to memory at one time. Therefore, an essential component of effective fluency practice is to break it into bite-sized pieces. A bite-sized piece is between 3 and 6 facts at a time.  Students should only be working on one bite-sized piece at a time, although they should continue to practice pieces they have previously learned. When using flashcards, the term for the bite-sized piece is the working deck which should have only 3 new cards in it. 

(2) Corrective feedback

As noted earlier in this article, math fluency practice requires a helper, either a person or a computer. The helper is to provide corrective feedback for whenever the student can’t quickly and easily recall the correct answer. The helper is needed to give the correct answer and then provide some extra practice to help commit the fact to memory. Practice exercises without a helper to give corrective feedback are nearly useless. In flashcards, the helper gives the answer, has the student repeat it a couple of times, and then puts the card back only three spaces so it comes up again, soon before the student forgets. 

(3) Measurement of Mastery 

Before a student moves on to learn another bite-sized piece, they must have committed this set to memory. They should be able to answer these facts from direct recall, which is essentially instant, less than one second. Fluency practice must assess whether a student can answer the facts in this new bite-sized piece instantly, without hesitation. Practice with this set should continue until the student masters it with all the new facts. When using flashcards, students should be able to read the problem on the flashcard and be able to answer without any hesitation.

(4) Gradual Cumulative Development

These bite-sized pieces must be systematically learned and accumulated so that students come to know all the facts, eventually, in all four operations. Once mastery is achieved with one set, a new bite-sized set can be introduced. However, practice must continue on all the pieces mastered so far. Therefore practice needs to move gradually through all the facts in an operation. When using flashcards, the learned cards are kept in a separate deck and practiced once daily to keep them in memory. 

(5) Individual Student Placement

Math fact practice needs to be individualized for each student so they are working only on the facts they are currently trying to commit to memory. It must be structured so they move on to learning new facts only after successfully mastering the last set. They must accumulate the facts they have learned into daily practice. Students must move at their own pace and gradually work their way through all the facts in an operation. When using flashcards, each student needs to have their own deck so they have their own working deck, which includes the new bite-sized set, and their learned deck for review.    

Common Misconceptions about Math Fact Fluency Practice

Many activities that are commonly considered to be effective for math fact fluency practice are not, because they lack the essential characteristics needed. They don’t present facts in bite-sized pieces, they don’t give corrective feedback, they don’t accumulate gradually, and they aren’t individualized for each student.

Math games, although often recommended, are seldom effective fluency practice. Games often do not engage all the students at one time. Watching someone do math is not helpful. Games that do not require quick answering are not fluency practice. And of course, few games are structured to help students focus only on the facts they are currently trying to commit to memory. 

Math fluency practice that presents all the facts in an operation is unproductive because that’s too many facts to focus on committing a few to memory. Therefore any fluency practice activity that presents all the facts in an operation will not help students develop fluency. This is definitely the case with “mad minutes,” which tests students on all the facts in an operation weekly. Not only is this not helpful, it’s just a mean thing to do to kids.  

Practicing math facts without regard to how long it takes the student to come up with the answer is not fluency practice, it’s just practice doing math. Students need extra practice on facts they are trying to commit to memory, which should be few in number. Therefore, worksheet pages that students complete on their own, later to be graded by the teacher for accuracy, are not effective as fluency practice. 

Practicing math strategies, like the doubles plus one, are not focused on committing facts to memory and developing direct recall, so they are also not effective fluency practice. Math fluency practice needs to focus students on committing facts to memory so they can answer by recall. Anything other than that will not develop fluency.     

Why is Math Fact Fluency Practice Important?

Fluency practice that helps students commit math facts to memory is beneficial. When students can answer from recall, they can do math fast. They enjoy doing it and feel confident in themselves. Once they are fluent in math facts, students can develop automaticity. That is critical so they can concentrate on higher-order math concepts and procedures. Students who must count on their fingers or puzzle through a strategy just to answer 9 plus 7 are not going to do well in math. That struggle for facts distracts them from the lesson, interferes with their ability to follow a procedure, and makes the doing of math assignments a slow and onerous chore. Math fact fluency practice is essential to free students up to enjoy math because they can do it with ease. 

Ways to practice math fluency

Practicing math facts for fluency requires a helper to give corrective feedback. Whether using flashcards or orally practicing facts from a worksheet, the student practicing must have someone to give them the correct answer when they cannot recall it. After giving the student the answer, their partner needs to ask again for the answer.  In addition, they must get a little bit of extra practice on the fact they couldn’t recall before they forget the correction. Of course, a good computer program can do the same thing. 

Probably the best way to practice requires students to state aloud the complete fact and answer. This creates a verbal chain of the fact with the answer in the student’s memory. When using flashcards, it is important to have the student read the flashcard aloud and then answer it. Looking at and saying the answer is also acceptable. Students will look at a problem on computers and answer on a keyboard. Computer-assisted practice like this will also work.  

Most importantly, it’s important to carefully select the facts for each student to practice each session. They can’t be randomly selected, but must be sequential. They have to be individualized for each student. The practice set must include only the bite-sized set of new facts along with facts that were mastered previously. Math fact fluency practice must have a sequential structure so that students can gradually develop mastery of all the facts in an operation such as addition or multiplication. 

Online math fluency practice

There are lots of online resources that purport to provide math fluency practice. However, very few of them will be effective because very few have the five key components in place. Many provide practice on a large number of facts or randomly selected facts all at once. Without presenting facts in bite-sized pieces, students will have great difficulty in committing the facts to memory. Few provide effective corrective feedback that requires students to remember the answer or give extra practice. Most do not have individual student placement in a sequence to master the facts. Most do not have a method of keeping track of progress, so practice does not result in the gradual development of mastery. A very few programs do measure mastery of small bite-sized pieces and keep track of them, Extra Math and Rocket Math being notable examples. 

Math fluency practice online and RocketMath

The Rocket Math Online Tutor is demonstrably effective because it has all five key components in place. The A to Z sets in Rocket Math are bite-sized pieces of four facts each for students to learn. The program gives robust corrective feedback that ensures the student commits the fact to memory. There is a sequence, and each student progresses through it as they demonstrate mastery of each new set and cumulative mastery of the previous sets. In addition, Rocket Math has a strong motivational component because the Rocket Chart helps students see the progress they are making as they complete the A to Z sets. Students enjoy Rocket Math and find it gives them a sense of accomplishment. See for yourself that Rocket Math works on its unique Evidence of Effectiveness page, which shows that students develop increased fluency as they work through the levels of Rocket Math. 

Math Fact Fluency: What you need to know and avoid

Many common misconceptions float around in educational circles about math fact fluency. These misconceptions are mostly based on an incorrect reading of the research. Some common misconceptions are about:

• what math fact fluency is,
• if it is important,
• how to teach it,
• how to understand it,
• and finally, how to assess it.

These misconceptions lead to wasting time on incorrect strategies to teach math facts and math games that don’t work. More importantly, these misconceptions have led to an epidemic of students lacking fluency in math facts.  Teachers in the upper elementary grades still see students counting on their fingers or using multiplication fact charts.  Having math fact fluency is a key foundation for future success in mathematics. Wasting time on these misconceptions is the main impediment to developing this in all students.  Let’s look at the correct conceptions and contrast those with the misconceptions as we go.

Conceptual learning must precede committing math facts to memory

Students must be taught the conceptual meaning of operations and of course, know their numbers, before embarking on the task of committing facts to memory.  What do we mean by the conceptual meaning of an operation?  When you give a basic fact problem to a student, such as 9 + 6, the student can represent the problem and figure out the answer.  Whether they use manipulatives, or draw lines, is unimportant as long as they understand the process and can get the right answer.  The same goes for subtraction, multiplication and division.  Students must be able to show the problem and derive the correct answer to have a conceptual understanding of the operation. Students need to develop a conceptual understanding before committing facts to memory.

The misconception:  Continuing to require students to figure out math facts is all you need to do.  It will automatically lead to math fact fluency.  What is true is that students need structured teaching to develop fluency.

What is Math Fact Fluency?

Fluency is the second stage in learning.  In the first stage of learning, a learner develops accuracy, the ability to answer correctly given time.  Imagine not just math facts, but other learning, such as a musical piece or a dance step.  After some work you can do it, but slowly with a lot of concentration. You are accurate only. However, with a lot of practice you can do it correctly and quickly.  That is fluency or its synonym, mastery.  So fluency is accurate and quick, or efficient.

Math fact fluency is committing facts to memory and answering them by direct recall.  We want students to just remember the answer.

The misconception: Using “flexible strategies,” like the student in this picture, to figure out math facts is precisely NOT fluency.  It takes time to figure out math facts and so you are not quick.  You’re still at the accuracy stage. What is true is that to develop fluency students must use “recall” to get the answers, rather than “flexible strategies.” Time spent playing games or developing a variety of strategies is time that should be spent committing facts to memory.

Misreading the research

The research on students using strategies to figure out math facts came from following what students do when left to their own devices to learn math facts.  These students were not being taught correctly.  Their teachers did not help to commit a small number of facts to memory at a time.  Breaking this down into bite-sized pieces is necessary for memorization.  With no help memorizing facts, children were seen to get started by using various tricks to help themselves remember.

However, all evidence shows that such strategies for remembering are an intermediate stage in learning that is replaced with direct recall by proficient students and adults.

The misconception: Students must spend a lot of time developing various strategies for remembering math facts. There is no research showing this is a necessary stage.  We know that students who memorize facts directly have no problem if learning is structured correctly.  Common sense tells you that an intermediate strategy, that is later abandoned in favor of direct recall, cannot be necessary in the first place. In other words, if you aren’t going to keep using these flexible strategies, why learn them at all? Instead, students should be helped to memorize the facts by systematically giving them a small number of facts to commit to memory at a time.

However, being able to answer fluently is not enough.  Students need to keep practicing and learning so they can develop automaticity with math facts.

Math Fact Fluency should be developed into Math Fact Automaticity

Automaticity is the third stage of learning.  It only comes after fluency is developed and only with additional practice.  Not only can the learner do the task fluently (correctly and quickly), but does so without much, if any, conscious thought.  Imagine a member of a marching band who has to play a piece of music quickly enough to keep time, but also has to think about marching in step with the rest of the band.  That musical piece must be learned to automaticity so the band member doesn’t have to put much attention into playing the right notes.

Decoding in reading and math facts in math are both tool skills. These skills are but a tool to do a more complex task.  Tool skills need to be learned to the level of automaticity so the learner can focus on the bigger task.  Automaticity in decoding (reading words) is essential so that students can focus on the author’s meaning rather than figuring out the words.  Students who read slowly, puzzling out words one at a time, lose the gist of the passage.  Students use math facts to do higher order computation.  Therefore math facts need to become automatic so that the student has cognitive capacity left to focus on the larger problem or procedure.

The misconception: Playing games and knowing a variety of strategies for deriving math facts are essential for developing fluency.  The truth is that math fact fluency and automaticity are related to simple recall of facts and are developed through practice recalling facts.  On the other hand, after facts can be recalled instantly, lots of games and “number sense” type activities are easy and fun for students.

Why is Math Fact Automaticity Important?

Automaticity in recall of math facts is important because it enables students to…

1. focus on the processes in which they are using math facts rather than on deriving the facts as they go.
2. better follow instruction in the classroom without being distracted by trying to figure out math facts during the lesson.
3. solve difficult problems and to complete math assignments quickly and easily.
4. have more confidence in their math abilities.
5. have more success in their future math classes and careers.

How to assess Math Fact Fluency and Automaticity

I know a piano player who can play “The Flight of the Bumblebee” almost faster than I can hear it.  He has clearly learned this piece to the level of automaticity.  That being said, he doesn’t have to play it fast and it’s better when he slows it down some.

Unfortunately, there’s no better way to measure the development of fluency and automaticity than by measuring the rate at which the person can perform the task.  There is a limit after which more speed makes no difference.  But there is also a lower limit below which you know the person does not have automaticity.  Research shows that direct recall of math facts happens in a little less than a second.  So if a student is reading a fact off a flashcard or on the screen, once they have finished reading more than a second has passed and their answer should be instantaneous.  If it takes two or three seconds after someone reads aloud the equation for the answer to come to mind, then that fact is not yet fluent or automatic.

The misconception: It shows fluency if, after reading a fact off the card or a screen, a student has to think for 2 seconds to come up with the answer.  The truth is, we want direct recall which, after reading the fact, is instantaneous, less than 1 second.  Having to stop and think about facts is not automaticity and it means that students need more practice recalling facts, not figuring them out.

Best ways to assess math fact fluency

Interestingly, the fact that an individual may automatically recall the answer to one math fact does not tell you about their recall of other math facts.  Students memorize math facts better in small handfuls, not all at once. As they are learning we would expect students to be able to answer some facts instantly, but need more time to learn the rest. The ideal way to assess math fact fluency is with flashcards or a computer display. These tools help keep track of the ones that are answered instantly and which are not. So, it is not an all-or-nothing result, but determining which facts students know at a fluent level and which ones they still need to learn.

Giving students a sheet of 100 math facts to answer, some of which they know and some which they don’t, gives you a mixed result.  On top of that issue, there is the issue of how fast a student can write.  Most elementary students cannot write as fast as they should be able to answer math fact problems.  Expectations for fluency would be for students to answer math facts at between 66% and 80% of their writing speed.

The misconception: Students are either fluent or not. We know that learning math facts is not an all or nothing proposition.  Students learn facts individually by committing each fact to memory individually.  Students can have memorized some of the facts but still need to learn others.

How to Memorize Math Facts to the level of Automaticity

Students must first learn the concept of  the operation, such as addition or multiplication, before they begin memorization.  Once students can represent and figure out any fact in the operation, then they understand the concept.  Then they are ready to begin memorization.

A few at a time

Also as mentioned above, the only way to memorize the many facts in an operation is a few at a time.  One memorizes the words to a song one stanza at a time, or your lines in a play one response at a time.  This requires organization and a system to work through all the facts in some sequence so that gradually the students learn all of them.

With corrective feedback

When learning facts it is essential that there is corrective feedback, either from a partner or from a computer.  Someone or something needs to give the learner the correct answer when the learner is uncertain.  And someone needs to give the learner additional practice when there is a hesitation.  Computers can reliably do this. Student partners can, too, but they need some training, which takes little effort to learn.

Bring facts to mastery before teaching more

Next, there has to be a way to ensure that each small batch of facts has to be learned to mastery before the next batch is introduced to be learned. This is the principle of feeding mush to the baby.  One spoonful at a time, making sure the baby swallows the last one before giving them more. It is important to base the decision on when a student goes on to learn the next set when they’ve mastered the last set and not some pre-set schedule.

The misconception:  You can push a class of students through the facts at the same pace.  Truthfully, if you place learners in a position to try to memorize more before they have digested the previous sets you will cause proactive and retroactive inhibition.  The student will begin getting more confused and lose ground.

After memorizing math facts, use them daily.

After students have learned math facts to automaticity, they enjoy using them in computation, which they can do very easily now. Students who are automatic in math facts are happy to race through math computation.   They can also do mental math, which they now find fun.  Math games can be used to practice using math, not as a method to learn, but as a method to practice what has already been learned.

All of the interesting relationships among numbers (that are incorrectly touted as a method to learn math facts), can be engaged in after committing these facts to memory.  Second grade students who were in the process of learning subtraction facts, volunteered to their teacher, “These are easy because they are just the opposite of adding.”  Because they had previously memorized their addition facts, this aspect of number sense was perfectly obvious to them, without any instruction.  Memorizing math facts does not hinder number sense, it just makes it easy.

Find out more about the Rocket Math Worksheet Program for peer partner math facts learning

or the Rocket Math Online Tutor for computer-assisted math facts learning.

Students should be automatic with facts. How fast is automatic? Well, it depends on which research you read and timing methods. In general, students should be able to answer 40 math fact problems per minute. Read on to learn why and see timed math fluency expectations by grade level.

Why Is Math Fact Fluency Important?

Being able to recall math facts quickly and accurately is a critical skill for students as they progress through school. In the early grades, knowing the answers to math facts from memory serves as a foundation for more complex problem-solving. As students move on to higher grades, they will be expected to complete more difficult, multi-part math tasks. If students cannot quickly remember the answers to basic math facts by the time they reach these higher grades, it will interfere with their ability to concentrate on more advanced tasks. Students who must stop and think about, or count out, simple math facts get lost in the steps of multi-part, complex mathematic procedures. Not to mention the fact, that math work becomes a slow and onerous process when you have to look up or figure out most facts.

What Is Math Fact Fluency?

Knowing math facts from memory means being able to automatically recall the answers to these facts without hesitation. Most psychological studies have looked at automatic response time as measured in milliseconds and found that automatic (direct retrieval) response times usually range from 400 to 900 milliseconds (less than one second) from presentation of a visual stimulus to a keyboard or oral response.

In most school situations, students take tests on one-minute timings. 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 ability and writing speed.  

How To Account For Writing Speed

One way to take a student’s writing speed into account is to set math fact fluency expectations at a rate in digits per minute that is about 2/3 of the rate at which the student can write digits. For example, a student who writes 100 digits per minute should be able to write 67 math fact digits per minute. This translates to between 30 and 40 problems per minute.

Teachers should modify this expectation if a student writes less than 100 digits per minute. To modify expectations, treat the student’s digits per minute rate as a percentage of 100, and then 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.  Here is a blog that helps set math fact expectations based on student’s writing speed.  

Timed Math Fluency Expectations by Grade Level

If measured verbally, a response delay of about 1 second would be automatic. When writing, students should be able to complete 40 math facts per minute. However, expectations vary by grade level and writing speed. 

In general, students should be able to complete 100 problems correctly in five minutes by the end of second grade, 150 problems correctly in five minutes by the end of third grade, 200 problems correctly in five minutes by the end of fourth grade, and so on. However, it is important to note that these are just general guidelines and only apply to students who can write at those speeds.

There is noted research that indicates 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.

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 as well as identifying fractions, learning equivalent fractions and fraction and decimal equivalents.

I hope you know that students are automatically scheduled by the Online Tutor to take a fluency test (1-minute Race) when they finish Set A, Set i, Set R, and Set Z. This tracks whether they are improving in fluency as they work through a Learning Track.  In addition to these four scheduled races, you can also assign additional fluency tests on your own schedule.  These assigned fluency tests are kept in a separate spreadsheet from the scheduled race results.  If you want to see if improvements in fluency are occurring across time, this is the tool to do it.

You can assign fluency tests in the Rocket Math Online Tutor.

Assigning fluency tests is a good way to see if students are progressing.  We recommend doing that.  We just call them 1-minute races, so the students don’t worry about having to take tests!

I would recommend assigning a 1-minute RACE to assess what is going on.  I would also recommend doing 1-minute RACEs class wide once a week. You have the ability to set these up on a recurring basis in the Online Tutor.

At any time, you can Assign a Fluency Test 1-Minute RACE for all your students.

1) Select the students to whom you want to assign the test 1-min Race, or Select All.

2) Click on the orange Bulk Action button.

3) Pull down to “Assigning Fluency Testing (1-min Races).”

You can assign fluency tests on a recurring basis or just once.

After doing that, in your dashboard you will see options for how to schedule fluency testing. Below is a video covering the options.  You can assign a one-time 1-minute Race, or you can schedule it weekly or bi-weekly or monthly and assign it a certain day of the week.  You can assign the Learning Track the students are currently studying, or assign a different Learning Track.  Please note: the results from these Assigned 1-minute Races will be in a different file than the automatically Scheduled 1-minute races after the four milestones in each Learning Track (after Set A, Set i, Set R, and Set Z).

When the students login on the assigned day, they will be given the mission of doing a 1-minute race with ALL the facts in the Learning Track you assigned. They can skip facts they don’t know, by hitting the checkmark.  You can see notification of whatever you’ve assigned in the dashboard. These 1-minute Races will be comparable from one test administration to the next because the problems are randomly chosen from the Learning Track.  Therefore, you can gauge whether or not students are improving in fluency from these tests.

Assign a fluency test individually–at any time you wish–once or recurring regularly.

You can assign a 1-minute RACE at any time for specific individuals as well, using the green Individual Action button at the end of their row.

You will see similar options, for whether it’s a one-time or a recurring assignment.  However, on the Individual Action button you will see the option of choosing the “current Learning Track” displayed, and on the pull-down menu.  Obviously, most of the time you’ll want to be measuring improvement in the Learning Track in which the student is working, so that’s the default.  But you can choose differently.

Fluency tests are called 1-minute races

Starting in the fall of 2020, the Rocket Math Online Game began scheduling 1-minute races for students as they worked through the 16 different Learning Tracks taught in the game. The 1-minute races present a random selection of all the facts in each Learning Track.  Students are allowed to skip facts they haven’t learned yet, but the scores shown here are the correctly answered problems. The races (really fluency test) are scheduled after sets A, i, R, and Z.  They are scheduled after students complete Set A, so we know they know how to use the interface and answer questions.  So that score is really a starting score.  Then intermediate in their learning after finishing Set i and Set R.  Finally, after Set Z. So the score after Set Z represents the fluency they have achieved by playing through the 26 A to Z levels in that Learning Track.

Data show improved fluency as students work through every Learning Track

It is clearly obvious that there is a steady rise in fluency as students work through each Learning Track.  Note that fluency test scores go up steadily at each measuring point in every Learning Track.  Remember, the tests are exactly the same every time, a random selection of problems taught in the Learning Track.  The fact that students can answer more correctly on each test, shows clearly that they are learning and the data prove it.  That is very important, as you don’t purchase this game simply to entertain children.  The goal is improved fluency and it is being achieved.  Individual results will of course vary.

Fluency Test: An excellent tool for research

These 1-minute races can also be assigned by the teacher at any time, or even on a weekly basis.  However, the scheduled tests demonstrate best the effect of the Online Game as the amount of work done to reach the tests is equal among students.   Both scheduled and teacher-assigned results are kept, and the results of these tests can be exported in excel files, so they are available for research purposes.  There are many options of things to be studied.  For my purposes, I love that we can so definitively prove that the Rocket Math Online Game works.