Not meeting benchmarks: what should it mean?

When it comes to learning math facts, most students have had no opportunity to learn them in a systematic way.  Unless they have had an extraordinary school or an unusual teacher they have not received structured, systematic learning opportunities to memorize math facts. After three decades working in schools across the country, I know this to be the case.  Without systematic practice and effort, students will not meet math fact benchmarks. They won’t meet the Common Core expectation that students will “know [math facts] by memory.”   Whose fault is that?  It is not the student’s fault, nor the parent’s fault.  So “not meeting benchmark” should mean that here is an area where the school needs to provide some intervention to build fluency.

Are you certain your fluency intervention is effective?

The teacher and the school have an obligation to provide an intervention that is effective.  Some so-called “interventions” do not reliably produce increased fluency.  An essential part of using an intervention is to measure its effectiveness.  [That’s why IEP goals are supposed to have measurable short-term objectives!]  The best way to measure the effectiveness of a fluency intervention is with timed, curriculum-based fluency assessments.

If you measure the same way for the same amount of time, you can see if fluency is increasing. You can see that the student’s fluency is increasing if the student can complete more items during the timed test each time you measure. If the vast majority of all of the students improve in fluency, then you can be certain that the intervention is effective. The graph above shows that for Multiplication, 23,540 students have increased in fluency as they worked through the Rocket Math Online Game.  See evidence from all 16 Learning Tracks here.

Rocket Math Online Game is effective

As students work through the levels in each Learning Track in the Rocket Math Online Game, they are tested after completing the first level (A), then after completing 33% at level I, and then after completing 66% at level R, and then after they finish at level Z.  Each test is a 1-minute fluency test of a random selection of facts taught in that Learning Track.  Therefore, the scores are comparable. When the number goes up at each point in the curriculum, you can be sure that students are increasing in fluency.  The chart to the right shows site-wide data. You can see students improve on average as they work through the Learning Tracks in the Online Game.  You would not expect students to meet benchmarks until they have completed Set Z in the Learning Track.

Math fact fluency benchmarks in the Online Game: 16/minute in addition and subtraction.

The 1-minute RACEs in the Rocket Math Online Game are a good way to measure math fact fluency.  On average students exceed 16 per minute correct at Set Z and the average at the beginning is much less.  So a reasonable benchmark is 16 correct problems per minute.

The teacher can assign a 1-minute RACE at any time and the student will need to do it upon their next login.  The results will be available in the Review Progress screen as well as be exported from the button that gives “Results from Assigned races.”  However, the best measure of whether a student can meet the benchmark is after Set Z, when they have completed the Learning Track.  You can see the score by clicking on the pink button for exporting “Results from Scheduled Races.”

You can see the screenshot of an example of the results from scheduled races for all 16 Learning Tracks across our website.  You can see the Account Average shows improvement at each level.   Those scores after Set Z show that nearly all students are proficient by the end of the Learning Track.  So we know that the Online Game is an effective intervention.  But there’s a catch. At the Level Z test data there are no scores for students who had not completed Set Z in Multiplication.  Students have to actually play the game in order to learn.

Students must participate to learn: monitor and recognize effort

Assigning an effective intervention will not help unless students are engaged and participate.  Instead of reporting on benchmarks of academic achievement, why not report on benchmarks of effort?  Each time students login and complete a session (five, ten or fifteen minutes in length) on the Online Game their session is recorded towards their effort score for the last 14 days.  Students should complete a session every day in school and some at home for homework.  In the effort rating system every four sessions completed earns a star, so 15  completed sessions over the last 14 days earned the student to the left 3 and 1/2 stars.

If you monitor the effort scores and recognize students who are putting forth great effort, you’ll get more students participating.  Completing 12 sessions in the last two weeks is good effort and earns 3 stars.  16 sessions over the last two weeks would earn 4 stars!

You might consider giving out Star Effort Awards (available in the teacher section of the site) once a month for students who are putting forth super-star effort.  If you reward effort, we guarantee you’ll get achievement.   Soon after doing that, you’ll probably have to start awarding Learning Track certificates for students who are completing Learning Tracks. All awards are available on the admin page on Tab (K) in the main rainbow navigation bar.

Teaching Math Fact Fluency | 6 Signs Your Class Is Failing

High-stakes state tests do not directly test fluency on math facts, although they should.  Your students can become bogged down in deriving basic facts during state testing.  When that happens they will be unable to demonstrate the higher-level math skills they have been learning.  You may have a math fact fluency problem, depressing your math achievement scores, but not even know it.  Here are six things to look for–to evaluate for yourself.

1) Finger counting during math testing shows a fact fluency problem

Students who are counting on their fingers (see above) during math testing are a definitive sign of a math fact fluency problem.  Finger counting is a bad sign in grades 3 and above, where they should have mastered math facts.  Students who don’t know the facts, need to use crutches to derive the answers to math facts.  Crutches make doing simple calculations take a long time to complete anything.  Your students may perform poorly on state tests just because they won’t complete the test for lack of time.

2) Students who lack math fact fluency need times tables available

When students in grades 3 or 4 and up have to do multiplication, they either have to know their facts or have a crutch.  If you see times tables on student desks that shows that the students need these crutches, and therefore do not know the basic multiplication facts.  Student folders sometimes come with these on the inside.  Some teachers put up a large poster of the multiplication facts–even though students find it nearly impossible to use from their seats.  Others provide laminated cards to the students which appear suddenly when students are set to do their “math work.”  When you see those times tables being used by more than a couple of students during math, you can tell you have a fluency problem.

3) Students who lack math fact fluency don’t participate in math lessons

Good teachers work to engage the class.  One good way, while working a problem for the class, is to ask the class for the answers to math facts.  Watching a lesson you may be able to spot a class that lacks fact fluency.  For example, imagine you watch the teacher demonstrating this problem.

Class, we begin this problem by multiplying nine times four.  What’s nine times four, everybody?”  [Only a couple of students answer.]  Yes, 36.  Now we write down the six and carry the 3 tens up to the tens place.  Next, we multiply nine times six.  What’s nine times six, everybody?”  [After a long silence, one student answers.] Yes, 54.  And we add the three to the 54, what do we get?  [Several students call out the answer.] Yes, 57.  That’s what we write down.

That interchange tells you there’s a math facts problem in this class.  When the problem is very easy, like 54+3 you get a good response.  When the fact is a “hard” one, you get silence and then one student answering.  Medium facts get minimal response.  This is a class that does not know their math facts.

4) Over-reliance on calculators signals a lack of math fact fluency

There are two kinds of over-reliance on calculators you may see in classrooms.  In the first kind, you see students who do not know facts using calculators to tell them the answer to single-digit facts they should have memorized.  Using calculators for single-digit facts is terribly slow and inefficient–and not what they are designed to do.  You can see this over-reliance on calculators when observing in a classroom.

The second kind of problem is harder to spot. Using calculators without knowing math facts instantly can be dangerous.  It is easy to make a data entry error, AKA a typo.  When a user does that, they’re assumed to know math facts well enough to know when the answer is wrong, as in the example pictured here.  A student who doesn’t know that 5 times 8 is 40 and therefore knows that 521 times 8 has to be more than 4,000 will accept the answer displayed on the calculator.  Accepting incorrect answers from the calculator is a sign that students do not have an adequate mastery of facts.

5) Avoidance behaviors in math signal a lack of math fact fluency

Having to count out facts or look each fact up in a table is very slow and onerous.  Students come to hate slogging through math computation that is so hard for them.  Conversely, students who know facts instantly, hop right into assignments to get them done.  Students like going fast doing math problems, just like they run for the joy of it on the playground.  How do you know there is a fluency problem in the classroom?  Students who lack fluency start avoiding getting started on computation work by getting water or sharpening pencils or just taking a break first.

6) Really slow computation during math lessons is due to a lack of math fact fluency

Good math teachers assign, within their lessons, a few math computation problems to do independently and then be checked as a group.  If students know math facts they can do a few problems in a minute or two.  Students who do not know math facts may take ten minutes or more to do the same mini-assignment.  Students who are done and waiting with nothing to do, begin talking and distracting the others.  When there’s that big of a discrepancy between the first and the last student to do a few problems, there is a fact fluency problem in the class.

To be sure–give school-wide 1-minute tests of math fact fluency

If you see hints that your school may have a math fact fluency problem, it isn’t hard to know for sure.  It only takes a couple of minutes.  You can have everyone in the school take written 1-minute tests of math facts pretty easily.  However, you’ll also need to evaluate how fast students can write.  Students can’t answer math fact problems any faster than they write.  You cannot expect a student who can write only 25 answers in a minute to answer 40 problems in a minute. Conversely, a student who can write 40 answers in a minute is not fluent with math facts if he answers only 30 problems in a minute.

You need a test of writing speed as well as a chart to evaluate their performance and the tests for the four main operations of addition, subtraction, multiplication, and division.  Print these out for free at this link.  But basically, a student who cannot answer math facts at 75% of the rate at which they can write, needs intervention.

Learn more about teaching math fact fluency

Teaching math fact fluency is necessary, of course, for fluent computation. Math fact fluency is also required for understanding and manipulating fractions. Find out more ways of successfully teaching math fact fluency to your students and why this skill is essential.

If you would like the free use of use the Rocket Math Online Game to assess for fluency, please contact Dr. Don at [email protected]

How to set math fact fluency goals and objectives for IEPs

Setting IEP goals and short term objectives is a snap when you measure growth in fluency.  Not only are fluency growth goals easy to write and set, they are easy to measure and monitor.  You can adjust the intensity of the intervention ensuring the student can achieve the goals and objectives.   Finally, you’ll be able to demonstrate growth and improve student achievement.

Fluency with math facts ensures success in math

Math facts are a “tool skill” of mathematics.  Students need to be able to call math facts to mind instantly.  Students should not have to hesitate or stop to “figure out” single digit math facts.  This is a tool they need in order to do math assignments quickly and easily. Knowing math facts instantly enables students to concentrate better and learn math more easily than students who are distracted by figuring out facts.  Once students are fluent in math facts they can keep up successfully in regular math classes.

Test the student’s present level of performance (PLOP) on facts

It only takes a minute to have students take a timed test in an operation to see how well they know their facts. You want to know how many facts in that operation the student can answer in one minute.  Test first-grade students in addition and second-graders on subtraction. Starting in 3rd grade and up, multiplication has priority, so test and focus on multiplication facts for your IEP.  You can move on to other operations once multiplication facts are fluent.  Here is a link to a page with Rocket Math’s one-minute pre-tests in all four basic operations.  However, you can’t evaluate whether a given student is fluent until you know how fast they can write. Students who are fluent with facts can answer them about as fast as they can write.  But they cannot answer them any faster than they can write.

You must also test the student’s writing speed

You cannot set achievable goals of how many facts a student should answer in a minute without first knowing how fast they can write.  That sets the upper limit.  So test their writing speed by having them write a mix of one and two digit numbers for one minute.  See to the left, Rocket Math’s one-minute Writing Speed Test From the link you can print it out for free.  Once you know how fast your student can write you can evaluate their performance on the one-minute fluency tests.

Is math fact fluency an area of need?

Now that you know the student’s writing speed you can evaluate their present level of performance.  Rocket Math has a handy evaluation sheet you can use to determine if there’s a need.  Or you can do the math yourself.  If students answer math facts at a rate less than 75% of their writing speed, they are weak and math facts is an area of need. Putting math fact fluency on the IEP and working on it as a goal would be very helpful.  If the student can answer math facts at a rate that is 90% of their writing speed, they are strong and this is not an area of need.  Between 75 and 90% of their writing speed they are good, but could benefit from some more work.

Get a starting point on the progress monitoring measure

If you’re going to test every week with 1-minute timings and you have a bunch of those available, you already have a 1-minute timing starting point.  If you’re using the Rocket Math Worksheet Program as your intervention, it uses 2-minute timings to measure progress weekly, so you’ll want to use one of those for your starting point.  (You can’t just double the 1-minute score because students don’t usually keep up at the same rate for two minutes.)  So give one of the 2-minute timings, in the operation you’re going to focus on, to set a starting point.

Set the math fact fluency goal based on writing speed

Students who have successfully developed math fact fluency in an operation can write answers to math facts almost as fast as they can write. As fast as their fingers can carry them is the most you could expect.  You could set a goal at 80% of their writing speed. It would still be rigorous enough.  If they met that goal the student would be fluent in math facts.

You can do the math yourself from their writing speed test. The Rocket Math Worksheet Program has weekly progress monitoring 2-minute timings.  In that case, your student’s goal for the 2-minute timing is on the handy goal sheet ** that you put into each student’s folder.  You can see the student shown here filled in 24 boxes on the Writing Speed Test, so his or her goal for 2-minute timings would be 38 for the annual goal for the IEP.

Create a graph and draw an aimline from starting point to goal

Now the coolest thing about progress-monitoring a fluency goal is that it is easy to graphically see on a weekly basis if the student is on track to meet the goal.  You simply create a graph, with enough spots at the bottom for all the weeks in the year.  Next you put in the starting point performance in the first week of the graph (or whenever you tested).  Then put in your goal performance at the end of the year.  Then draw a line between those two points.  That line is called the aimline and is shown in the example at the top of this article.

The pictured student began at 29 problems in 2-minutes.  Their PLOP was 29 problems correct in 2 minutes.  The student had a writing speed of 40 problems in a minute.  Therefore 80% of that is 32 problems in a minute or 64 problems in two minutes by the end of the year.  The aimline is simply a straight line between those two.  You can see that the first couple of two-minute tests did not meet the aimline, but by the third test the student was right on track for meeting the goal by the end of the year.

Short term objectives (STOs) are set by the aimline

Once the aimline is drawn, the STOs are found by reading up from the date of the quarterly STO reporting date.  Wherever the aimline is on that date, that’s the STO.  In the example above the quarter 1 objective looks to be about 38 problems in two minutes.  The second quarter looks to be 45 problems in two minutes with the 3rd quarter at 53.  Very simple and easy to set and to read and report.  Since every student in Rocket Math should have a graph like this reporting to parents on a quarterly basis would be more more than showing them this graph.

What if they aren’t meeting the aimline?

In all the struggle with writing and evaluating IEPs many times we forget the purpose.  IEPs are designed to evaluate whether our intervention is adequate to meet the student’s needs.  So if the student is falling below the aimline or doesn’t make the STOs what are we supposed to do?  Wringing our hands or shaking our heads sadly at the IEP meeting at the end of the year is not what is supposed to happen.  Instead we are supposed to be using these goals as a way to determine if we need to intensify our intervention.

How do you intensify your intervention?

So if a student is not meeting the aimline when we monitor their progress we should re-double our efforts.  With Rocket Math that’s quite doable.  If the student is falling below the aimline for three weeks in a row, add another practice session each day.  The standard ten minutes a day for Rocket Math may not be enough for this student. So you need to arrange for them to get in another practice session each day.  Often a short trip to the Special Education room for a second quick session with the teacher or an aide will do the trick.  If two a day at school aren’t enough, maybe you can add one each evening at home.  Some students do need more practice to meet these goals.  The good news is that you can find out quickly with your graph and get going soon.

**The Goal Sheet was updated in 2021 to reflect the 80% expectation for IEP goals.  The update shows that students who can fill in 15 boxes in a minute can go ahead and do Rocket Math, while those who can only fill in 14 boxes are candidates for help with writing numerals in the Rocket Writing for Numerals Learning Track.

Instant assessment for basic math fact fluency: Ask ’em!

Teachers and parents often ask, “How do I know if my children need to study math facts?” Here’s an instant math assessment you can do to test them for math fact fluency. Ask a student a “hard one” such as, “What’s 9 times 7?” or if they are in first or second grade, “What’s 8 plus 9?” If they start counting on their fingers or hesitate while puzzling it out, they do not have “math fact fluency.” They need a program of systematic math facts practice until they know them all “by memory,” as the Common Core State Standards (CCSS) say.

Math fact fluency means instant recall

Some teachers and schools teach “tricks” for remembering facts that are supposed to help children. However, they should at most be a temporary crutch. Such techniques need to be replaced with instant recall. The student shown here is using the commonly-taught “doubles plus one” trick for figuring out the answer to, “What’s 8 plus 9?” This is not fluency. He needs practice in math facts so they become “automatic” in recall. If he is still having to do this in fourth or fifth grade, he’ll find math work slow-going and drudgery. He’ll also find it hard to follow a math lesson when he has to stop and puzzle out simple facts like this.

Math fact fluency makes math easy

Students who know the math facts instantly can fly through their math assignments. They enjoy the exercise and feel good about their math abilities. On the other hand, students who have to count on their fingers, or use a number line or a times tables chart to do their math assignments come to hate math. It is so-o-o-o-o slow. I’m sad to say that when I taught elementary and middle school remedial students I knew they hated math because they had to puzzle out most of the facts. What else could I do but assign lots of math fact practice that they hated?

In graduate school, I learned how to design a math facts practice program in a way that every student can succeed in memorizing the facts. I put a paper-and-pencil program together back in the ‘90s and have been sharing it with people ever since. I called it Mastering Math facts, but everyone else just called it Rocket Math. That became its official name in 2007.

Teachers have been successfully using my nearly secret curriculum with wild success for decades. Oddly enough, students actually enjoy the Rocket Math Worksheet program. They enjoy the paired practice with a partner, and can actually see themselves learning and getting better.

How to assess students in math

Before you start Rocket Math’s Online Game or Worksheet Program, it’s a good idea to find out which operations your student needs to practice most. Rocket Math offers a few tests to identify where your student should start their Rocket Math journey.

Writing Speed Test

Many students aren’t able to write the answers to 40 problems in one minute, which is normal and doesn’t affect their math fact knowledge. Before administering the Operation Pretests, evaluate your student’s writing speed to make sure the results reflect your student’s true proficiency, and that they are not held back by their writing speed.

Operation Pretests

Once your student has completed the Writing Speed Test, give them a pretest in one or more of the four basic operations.

Evaluate Results

For students in 3rd grade and above, test multiplication first and then division. If students struggle with either of those two operations, they should start learning those operations. For 3rd graders and above who don’t struggle with multiplication and division, test addition and subtraction to assess any weakness. For students in 1st and 2nd grade, test addition first and then subtraction.

Evaluate your student’s results based on their individual writing speed with the Evaluation Chart for Pretests. Use their writing speed to determine if their performance on the Pretest is weak and shows a real need for work on math facts, or is good but could use some help, or strong and no practice is needed.

Free Online Game subscription as long as you need to decide

There is no reason for students to be bogged down and discouraged by math, especially by lack of math fact fluency. This doesn’t need to happen to children. Every student is capable of memorizing basic math facts with a little effort and a carefully sequenced curriculum, like the Rocket Math Worksheet Program.

Or if a paper-and-pencil curriculum like the Rocket Math Worksheet Program involves standing at the copy machine, is not what you are looking for, Rocket Math is now online. The Online Game app starts with a complimentary initial subscription of 14 days. You can learn more about it at that link. Or you can just go ahead and register an account and start it on this link

Send an email to me at don at rocketmath.com and I’ll extend the complimentary subscription as long as you need to decide.** If you need one to ten seats it is a whopping \$4.50 a seat for a year. Twenty or more seats are \$2.50 each for the year and per-seat prices go down from there. Really there’s no reason to leave kids counting on their fingers.

Math Fluency Programs should be part of on-going elementary school routines

Most elementary teachers do some activities to promote math fluency.  Yet many elementary children are not fluent with math facts by the time they hit upper elementary or middle school.  A hit-or-miss approach allows too many students, especially the most vulnerable, to slip through the cracks.   Math fluency programs, like Rocket Math’s Worksheet Program, need to be part of your elementary school’s routine.  Effective math fluency programs should be properly structured and every math teacher should be on board, every year.

Math fact fluency enables students to develop number sense

Many teachers learn in their training programs about the importance of “number sense.”  Students who have “number sense” can easily and flexibly understand relations between numbers.  They can recombine numbers in various ways and see the components of numbers.  Students with number sense can intuit the fact that addition and subtraction are different ways of looking at the same relations.

What is not taught in most schools of education is that developing fluency with the basic math facts ENABLES the development of number sense much better than anything else.  Once students memorize facts, they are available for students to call upon to understand alternate configurations of numbers. Students find it much easier to see the various combinations when they when they can easily recall math facts.  Once students master the basic facts, math games that give flexibility to thinking about numbers become much easier.

It may be hard for new teachers, straight from indoctrination in the schools of education, to imagine this is true.  However, if they land in an elementary school with a strong math fact fluency program they will see the beneficial effect of memorization.

Why is math fact fluency important

In the primary grades, students who have not developed fluency in math facts will have a harder time learning basic computation.

Students who are not fluent with math facts find the worksheets in the primary grades to be laborious work.  They finish fewer of them and may begin to dislike math for this reason.

By the time students reach upper elementary, if they have not memorized the math facts, they find it very difficult to complete math assignments at their grade level.  They find themselves unable to estimate or do mental math for problem-solving.  The need to figure out math facts will continue to distract non-fluent students while they are learning new math procedures like algorithms.

In the upper grades, their inability to figure out multiplication facts becomes a huge stumbling block.  Manipulations of fractions, decimals, and percentages will not make intuitive sense to students because they haven’t memorized those facts.  Without math fact fluency, students rarely succeed in pre-algebra and may be prevented from learning algebra and college-level math entirely.

Math fact fluency must be assured through regular monitoring

Some students will need up to ten times more practice to develop math fluency than other students.  Therefore, monitoring student success in memorizing the facts is critical. Teachers can assume that what is “enough practice” for some students is NOT going to be enough practice for all students.  Effective math fluency programs must have a progress monitoring component built in.  Progress monitoring gives comparable timed tests of all the facts at intervals during the year.  Teachers look at the results of these timed tests to check on two things:

1. Are students gradually improving their fluency with all the facts gradually over the year?

In other words, are students able to answer more facts in the same amount of time?  If they aren’t improving, then the instructional procedures aren’t working and need to be modified or replaced.  Math fluency programs like Rocket Math’s Worksheet Program have two minute timings of all the facts in each operation that can be given and the results graphed to see if there is steady improvement.

2. Are all students reaching expected levels of performance at each grade level each year?

Proper math fluency programs identify students who are not meeting expectations and give them more intensive interventions.  Ultimately, by the end of fourth grade all students should be able to fluently answer basic 1s – 9s fact problems from memory in the four operations of add, subtract, multiply and divide. Fluent performance is generally assumed to be 40 problems per minute, unless students cannot write that quickly.

Expectations vary by grade level and the sequence with which schools teach facts can vary.  While it is great to achieve all that the Common Core suggests, it is critical only to assure that students master and gain fluency in 1s through 9s facts.  Some schools in some neighborhoods may find that waiting until second grade to begin math facts may not provide enough time for all students to achieve fluency.  When to begin fact fluency and how much to expect each year should be based on experience rather than some outside dictates.

Successful math fluency programs must have these 3 features

1. Sequences of small sets

No one can memorize ten similar things, like the 2s facts, all at once. Students easily master math facts when they can learn and memorize small amounts of facts at one time. Effective math fluency programs define math fact sequences, which students memorize at their pace before moving onto new math facts. Rocket Math’s fluency program uses only two facts and their reverses in each set from A through Z.

2. Self-paced progress

Even if you only introduce small sets of math facts, some students need more time to memorize than others.  If you introduce the facts too fast, students will begin to jumble them together and progress will be lost. The pace of introducing facts must be based on mastery—not some pre-defined pace.  This is why doing all the multiplication facts as a class in the first six weeks of third grade does not work.  It is just too fast for some students.  Once they fall behind it all becomes a blur.

3. Effective practice and corrections

When students are practicing facts, they will come to ones they have forgotten or can’t recall immediately.  Those are the facts on which they need more practice.  Allowing students to stop and figure out the facts they don’t know while practicing, does not help the student commit them to memory.  Instead, students need to IMMEDIATELY receive the fact and the answer, repeat it and try to remember it.  Then they need to attempt that fact again in a few seconds, after doing another couple of problems.  If they have remembered the fact and can recall it, then they are on their way to fluency.  But students must practice the next day to cement in that learning.

Math fluency programs like Rocket Math’s Worksheet Program teach students math facts in small sets, allow students to progress at their own pace, and support effective practice and error correction. Each Rocket Math Worksheet program has 26 (A to Z) worksheets specially designed to help kids gradually (and successfully) master math skills. Gain access to all of them with a Universal Subscription or just the four basics (add, subtract, multiply, divide–1s to 9s) with a Basic Subscription.

Just playing a math facts game won’t build math fact fluency

There are a lot of apps out there that look like they would help your child learn math fact fluency.  If they have to answer math facts, won’t that work?  Not really.  Just playing a game that asks you to answer facts won’t help you learn new facts.  In fact, most apps for practicing facts are discouraging to students who don’t know their facts well.  Why?  Because most of the people designing the app don’t have any experience teaching.  A teacher, like the creator of the Rocket Math App, is trained to effectively teach new math facts (or any facts) to a student and knows an effective math app from an ineffective one.

3 essential features of an effective math fact app

There are plenty of ineffective math apps.  Some apps don’t give the answers when a student doesn’t know them.  Some apps just fill in the answer for the student and then move on.  When the student doesn’t know the answer, the app has to teach it.  To teach math fact fluency, the app has to do these three things:

3. It has to ask the problem again after a short delay to see if the student can remember the answer.

Without doing these three things there’s no way the app is going to be able to teach a new fact to the student.

An effective math app will only teach a few math facts at a time

Nobody can learn a bunch of new and similar things all at the same time.  A person can only learn two, three, or four facts at a time. You cannot expect to learn more.*  That’s enough for one session.  The student has to practice those facts a lot of times to commit them to memory.  Once or twice is not enough. It also won’t help to practice the same fact over and over.  Proper math fact fluency practice intermingles new math facts along with facts the learner has already memorized.  However, no more than two to four facts should be introduced at a time.  If a student has to answer a lot of random untaught math facts, you will have a very frustrated learner.

Practice must focus on building math fact fluency

Some students learn to solve addition problems by counting on their fingers.  That’s a good beginner strategy, but students need to get past that stage. They need to be able to simply and quickly recall the answers to math facts. An app is good for developing recall.  But the app has to ask students to answer the facts quickly, faster than they can count on their fingers.  The app has to distinguish when a student is recalling the fact (which is quick) from figuring out the fact (which is slow).  Second, the app must repeatedly ask the learned facts in a random order, so students are recalling.  But the app should not throw in new facts until all the facts are mastered and can be answered quickly.

Introduce new facts only when old facts are mastered

The trick to effectively teaching math facts is to introduce new math facts at an appropriate pace.  If you wait too long to introduce math facts, it gets boring and wastes time.  If you go too fast, students become confused.  Before introducing new facts, students need to master everything you’ve given them.  An effective app will test whether students have mastered the current batch of math facts before introducing more facts.  And it will also introduce math facts at a pace based on student mastery.  That’s the final piece of the puzzle to ensure students learn math facts from an app.

*Rocket Math App focuses on two facts and their reverses at a time, such as 3+4=7, 4+3=7, 3+5=8 and 5+3=8.

How to Grade 1-Minute Math Fluency Practice Tests

Katy L from Wilson Elementary asks: How can I keep up with everyday Rocket Math grading? Do you teach students to grade their own 1-minute math fluency practice tests?

Dr. Don answers:

Only grade 1-minute math fluency practice tests if students pass

An integral part of the Rocket Math Worksheet Program is the 1-minute math fluency practice test. One-minute fluency practice tests are administered every day, to the whole class, and only after students practice in pairs for two to three minutes each. Check out the FAQs page to learn more about conducting 1-minute math fluency practice tests in class.

Teachers do NOT need to grade, score, or check daily Rocket Math 1-minute math fluency practice tests unless the student has met their goal. Students do NOT need to grade their own daily Rocket Math fact fluency tests either.

Why grading each math test is not important

The important part of math fluency practice is the oral practice with the partner before the test–what’s going on in this picture. Because the students are orally practicing every day and getting corrections from their partners, there should be VERY FEW errors on the 1-minute math fluency written tests.

Correcting written tests doesn’t help students learn anyway. Corrections are only helpful if they are immediate, the student has to acknowledge the correct answer, and remember it for a few seconds–all of which is part of the oral correction procedure. “Correcting” what’s on the paper takes a lot of time and does not help students learn more, so it shouldn’t be done. But you have to check them before declaring that the student has passed a level.

How do you know if a student passes?

Students should have a packet of 6 sheets math fact fluency sheets at their level. Each Rocket Math student has an individual goal. For example, if a student has a goal of 32 (based on their Writing Speed Test) and they only do 31, they know they did not pass. If the student does 32 or more, they pass!

What to do when a student beats their goal (passes)

If a student meets or beats their goal, then have them stand up, take a bow, and then turn their folder into a place where you check to see that all problems were answered correctly. When YOU check (after school?), make sure all of the completed problems were correct and the student met their goal. If so, then you put the unused sheets in that packet back into the filing crate and re-fill the student’s folder with a packet of 6 worksheets at the next level and hand the folder back the next day.

When students receive the new packet of worksheets, they know to color in another letter on the Rocket Chart (and maybe put a star on the Wall Chart).

What to do if a student doesn’t pass?

Students who don’t meet their goals, don’t pass. These students should put the non-passing sheet into their backpacks and take the sheet home for more practice.

The next day they will use the next sheet in their packet of 6. If you want to give them points, do that the next day after they bring back their worksheet where they did a session at home (signature of helper should be there) and all items on the test are completed. If that’s done, they get full points.

Sometimes you’ll catch errors on sheets that students turn in as “passes.” If you see an error, the student doesn’t pass. As a result, the student keeps the old packet and has to continue with that same level worksheet.

For more information about conducting 1-minute math fluency practice tests in class and how to implement the Rocket Math worksheet program, visit the FAQs page.