## 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.

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

## When to use the Learning Computation Learning Tracks

Once your student has mastered the math facts (reached Level Z) in one of the four arithmetic operations, the Rocket Math Learning Computation worksheet Learning Track takes this student seamlessly all the way to the top of that operation’s ladder (at the top is the highest skill in that operation).
I recommend you start using the Learning Addition Computation track as soon as the student has mastered the Addition facts, and while the student continues learning the facts in the other operations. When the student masters the facts in another operation, start the Learning Computation track for that operation. And so on.

## What’s in the Learning Computation worksheets?

The four Learning Computation tracks are divided into “skills.” Each skill in each step of the ladder, in the natural order in which one is to learn them. Dr. Don has created five worksheets for each skill in each Learning Computation track.
For each skill in each operation, Dr. Don has prepared the following:
1… The most detailed and helpful and concise instructions for that particular skill, for the teacher/parent to learn how to teach it.

I think the four LC tracks are amazingly valuable because they help learn the different skills…
1… thoroughly because there are plenty of problems to practice specifically the new skill
2… seamlessly because the jump from one skill to the next is almost imperceptible, so it is an easy jump to take
2… A set of five numbered worksheets. The top half in each Learning Computation sheet has problems with new skill learned in that particular five-sheet step. The problems in the bottom half of the worksheet are a review of the immediately prior skills.

## How to use the Learning Computation (LC) Worksheets

How does one use it? Easy. We simply started with skill 1 sheet 1 and then follow onto sheets 2, 3,4, and 5. Then, you move on to skill 2 sheet 1, etc. If, by the time your student is in sheet 5 of a given skill, you think they have not mastered it, then you go back a few sheets or even to sheet 1 in that skill.
The teacher’s script tell you exactly how to teach the skill–it asks the student questions about each step in the process, so they learn how to think about what they are doing.  The script has sections where it reduces the amount of prompting you provide, until by the end of the five sheets the student is totally doing it on his own or her own.
There are placement tests for each operation which gives you a chance to see which skills are already mastered and where he or she begins to make errors.  The placement tests would allow you to skip some of the skills your student already knows, and begin where he or she has difficulty.  But it isn’t required.  We were happy to just go in order without using the placement test.

## Doing Learning Computation in several operations

When our student was doing Learning Computation (LC) in three operations (addition, subtraction and multiplication, and was still learning division facts), we would do all three LC tracks each school day, but only the left or the right half of the sheet in question. So he would do the left half of addition, the left half of subtraction, the left half of multiplication. That way he was not doing too much each day, while still using the recently learned facts and learning the skill at hand.

## Learning Computation makes it a painless process

At the time of this writing, we have completed the Addition and Multiplication LC tracks. LC tracks Subtraction and Division still ongoing (subtraction because it is by far the track with largest number of different skills; division because he started it not too long ago). For our student and for us this has been and still is a painless process. We like very much that there is plenty of practice of the new skill in each set of five sheets, so that he is most of the time ready to move to the next skill by the time he finishes the fifth sheet.
For us, working on learning computation for several operations at the same time has been a great way for our student to refresh and use the math facts he worked hard to master.

Here are the four Learning Computation Learning Tracks in the Rocket Math Worksheet Program.

## Why purchase these supplements to the Rocket Math Online Tutor?

Why supplement the Online Tutor?  The Online Tutor works best if your students are motivated and your teachers have all the support they need.  Purchasing these two key supplements will make the Online Tutor far more effective.  Make sure your purchase gets the job done.

## (1) Motivate your students to use the Online Tutor.

### The Wall Chart motivates within the classrooms.

Motivated students will use the Rocket Math Online Tutor more frequently and make more progress. The Wall Chart can motivate students on a daily basis.  It motivates by having students work together to reach a common goal.  Students receive stickers when they pass a level and get the honor of adding their sticker onto the class chart. The teacher sets goals for rows filled by a certain date.  If the class fills the rows before the date, the teacher rewards the class in some fashion.  (You can read the suggestions for use here.)

### The Wall Chart helps monitor engagement easily.

As a math coach or administrator, the Wall Chart helps you quickly assess if a class is using the Online Tutor.  Visit a classroom, look at the Wall Chart, praise the class for their efforts and give them a principal “Principal Free Space” by adding a different colored sticker of your own.  Then you can revisit the class in a week or two and easily see how much they have accomplished since your last visit.  Then you can praise the class and the teacher, or show a little disappointment if it is not happening.  This supplement to the Online Tutor is very helpful.

### The Super Hero Rocket Math cape helps motivate across the school.

When students complete a Learning Track (or other milestone of achievement), they get to wear one of the Rocket Math capes around school, at lunch or out to recess.  Everyone can see that they have accomplished something in Rocket Math.  It’s especially effective for students who haven’t been getting onto the Online Tutor and so haven’t had a chance to wear the Super Hero cape.  It’s also great for adults to notice and praise the student who has accomplished something in Rocket Math.  Healthier for students than candy prizes and it is re-usable.

## (2) Provide support and guidance to your teachers.

Teachers need support, help, and guidance to make the most of the Online Tutor.  This support package provides help in four ways.  This is in addition to the video series “Making the best use of the Online Tutor.”

### (First) Get a one-hour remote in-service training session with Dr. Don

Dr. Don will train your teachers.  Teachers can get either initial training or to get a refresher on the key points of how to implement the Online Tutor. Rocket Math will waive the normal \$250 charge for the one-hour session.  Schedule the training on the Rocket Math website here.  Training is flexible and can address any issues you have experienced as well as preparing you if you’re new.

### (Second) Receive a Weekly check-in/training Zoom call with Rocket Math staff

You will be able to schedule a weekly Zoom call with one of the helpful Rocket Math staff.  Usually you can set up a 15-minute call, but it can be longer if needed.  You can ask any questions or get trained on any aspect of how to use the Online Tutor.  You can rotate the calls among schools or staff for them to ask questions.  This will be a great way to get help on troubleshooting issues or a way to brush up on training.  We won’t require these calls every week–they are only offered as a resource.

### (Third) Get one of your teachers Certified as a Rocket Math expert through 20 Zoom sessions

We offer the Certified Teacher Program #3102  for \$600, but one teacher’s training is included here.  You choose the teacher on your staff to become Certified. In the first session we will explain how the Online Tutor works.  Then in each of the 20 sessions, together we will watch a student of the teacher’s choosing do an Online Tutor session.  The teacher will learn how the Rocket Math Online Tutor works and how it helps the teacher monitor what’s going on with the student.  The final wrap-up session we’ll answer all your questions and get you posted as a Certified Rocket Math Teacher on our website. A Rocket Math Certified teacher will be a great resource to your staff as they will have experienced all the issues that other teachers will be able to learn from.

### (Fourth) Receive direct White Glove access for IT help

We will give you a direct number to call to reach a member of the highly trained and exceptionally helpful Rocket Math staff to help you with IT problems.  We aren’t available 24/7, but we are available during school hours on school days.  Often we can explain or walk you through how to deal with IT issues that come up and fix it on the spot.  Sometimes we will have to research the problem or we will have to fix a glitch.  We will fix those glitches ASAP and get back to you with a solution.

## Student not progressing in Rocket Math Online Tutor? How to diagnose the problem. Part One

Progress in Rocket Math Online Tutor means passing levels in a Learning Track and then completing a Learning Track.  Students who are not progressing in Rocket Math will get discouraged.  The point of this educational app is for students to learn math facts by memory, by instant recall, instead of having to figure them out.  If students are not progressing, something is wrong.  Here’s the things to look for in order of how likely they are to be the problem.

## Problem 1: Not completing sessions

Students can start a session and work for only a couple of seconds and then quit.  If students are not completing sessions then they are not doing enough practice.  They will not make progress unless they complete sessions regularly.

If you open the Review Progress tab and scroll down to the listing of your students you will see a column titled Sessions in last 2 weeks.  For each student, for the last two weeks, you can see how many sessions they completed each day as well as how many they started.  The data showing here tells you the student is starting sessions, but not completing them.  They are only ten minutes long, so they can do it if you tell them they should.

## Solution 1: Require students to show Session Completed screen.

Rocket Math has a screen that proves students have completed their session each time they do Rocket Math. It comes up at the end of  the ten minute session.  This screen will stay up if they do not log out.  This is designed so you can require your students to show you they completed their session.  Because is will stay there, you can check them out (maybe use a clipboard?) and know they have completed their session.  Completing sessions is the first step in learning math facts and making progress.

## Problem 2: Not working during sessions

Most students seem to understand that going as fast as they can with Rocket Math is the road to learning their math facts.  Most students like going fast and when Rocket Math helps them learn these facts they are motivated to develop mastery.  They realize it will make their lives easier when they have to do any arithmetic for any reason.

However, some students focus their efforts on trying to avoid learning and working. These students may log into Rocket Math but then go on to do something other than work on learning their facts.  These students will not spend much time practicing even when they are logged in.  They won’t of course, make much progress and that will be discouraging for both them and the teacher.

On the Review Progress screen, you can see each day how many problems students have answered in their ten-minute session. Student should be able to complete over 100 problems in a full ten-minute session, if they are working steadily.  Students who complete less than half that many problems are spending a lot of time doing something other than practicing math facts.

## Solution 2A: Circulate and watch students while they are using the Online Tutor

If possible, monitor students closely while they are doing the Rocket Math Online Tutor.  Walk around, look over their shoulder and see them answer a couple of problems.  Pat them on the back, literally or figuratively, and move on. Praise people who are working hard, and do it aloud so other can here you.  Comment on anything you see, so they know you are watching and know you care how they are doing. Keep moving around the room so you can see everyone.  Keep circulating so that they know you will be coming by frequently.  If you do that you won’t have anyone off task.  If you did this for a month or two, you would build in good work habits and then you wouldn’t need to do it all the time.  If you never do this, you have no idea what is going on in the back corners of your room!

## Solution 2B: Post names of those answering the most problems

If you are teaching something else while students are working, you won’t be able to monitor them while they are working.  However, at the end of the day you can go to the Review Progress page.  Scroll down to the individual student rows and scroll over to the Problems Answered Today column.  At the top you can barely see a little gray arrow and a stack of tiles.  Click it once and it sorts from the lowest up to the highest.  Click it again and sort it from the highest down as you can see in this example here.  Then you can post the names of the students who answered the most problems.

Just before students begin working on Rocket Math the next day stand up and read aloud the names and praise those students who are really working hard.  “I know these students are working hard because of how many problems they were able to answer yesterday.  They are going to get really smart and know their facts.  Can you do better?  I’ll see tonight who can do more than 100 problems!  Maybe your name will go on the board tomorrow!”

And of course, you should have a talk with anyone who is doing very little.  They could always do an extra session of Rocket Math during recess or after school if they can’t get more done during the regular time.

## Still not progressing?  See Part 2

If your student is working hard and completing 5 to 10 sessions a week, they will most likely be making good progress and passing several levels each week.  If they are working hard and still not making progress go on to Part 2 of this blog.

## Student not progressing in Rocket Math Online Tutor? How to diagnose the problem. Part Two

If you have not, please read and implement Part One of this blog post.  You have seen that your student is completing 5 to 10 sessions a week and is working hard the whole time (answering a hundred or more problems each session).  But still the student isn’t making good progress passing several levels a week?  Let’s look deeper into the problems.

## Find out if it is too difficult for this student

When students make three errors or three hesitations in a part or a phase of Rocket Math, we have them start over and repeat those problems. In the Review Progress tab, in the individual student rows is a column titled “Difficulty.”  The Online Tutor calculates the difficulty score  by dividing the number of times the student had to “start over” or repeat a part by the number of parts passed.  We expect that students will usually have to start over once or twice in a part, earning them a difficulty score of “1 or 2”  However, if they have to start over an average of 3 times per part, (a difficulty score over 3.0) then it may be too difficult for this student.

In the Review Progress tab, you can look up the difficulty score for any student.  Or as was done in the picture here, you can sort the difficulty column to see the students with the highest difficulty scores at the top.  Then you should watch the students who are having high difficulty scores while they are working to see what the problem is.

## Problem 3: Problems using the keyboard quickly

Some students, especially those under 8 years old, are not as adept at using a computer keyboard as they need to be for the Online Tutor.  At the standard speed, answers must be entered within 3 seconds for a one-digit answer with only an additional second for subsequent digits. Some students cannot use two hands so they can quickly hit the answer and the enter key. Searching for and tapping separately with one hand both the numerical keys and the enter key will be too slow–they will have a lot of start-overs. If you watch such a student work, you will see that they know the right answer, but cannot get it input on the keyboard in time.  This will frustrate them and slow down progress.

## Solution 3A: Have the student use a touch screen

Using a touch screen is much easier than a computer keyboard.  For children under 8 years old, or students who are having difficulty entering the answers they know getting them a touch screen device should solve the problem.  To test if this will solve the problem, put the free Rocket Math app on your phone, log in for the student and let them do a session on your phone.  If they do better (have fewer start-overs) then you know how to solve the problem.  Touch screens are becoming more common, so we’re hoping you can locate one for the student who is having trouble.

## Solution 3B: Slow the Online Tutor answering speed

If a touch screen option doesn’t help–the student is still frustrated then you can adjust the speed required by the Online Tutor.  This will help an individual student who is having trouble keyboarding the answer quickly enough.  Here are the directions (and caveats) about changing the speed of answering. https://www.rocketmath.com/online-tutor-knowledge-base/b-too-hard-or-too-fast-check-the-difficulty-score/

## Problem 4: Student is not ready for the Learning Track

Students who are not ready for the Learning Tracks will have a lot of difficulty progressing through the Online Tutor.  Students won’t succeed who have not learned the basic prerequisites, such as understanding the operation they are trying to memorize.  For example kindergarten students who don’t know how to add two groups of objects (by counting) aren’t ready for LT 1-Addition.  Before students understand addition and subtraction they should not be memorizing the facts.  Generally we want first and second graders in Learning Track 1-Addition followed by LT 2-Subtraction.  The same thing goes for multiplication.  Students need to understand what multiplication means and be able to “figure it out” before being asked to do LT 7-Multiplication. After this concept is learned in third or fourth grade is a good time to begin LT 7-Multiplication followed by LT 8-Division.

## Solution 4: Stop Online Tutor and teach more basic math skills first

Students younger than these guidelines or who are cognitively delayed below these mental ages may not be successful with the Online Tutor learning tracks. If they aren’t successful, you’ll need for them to develop more basic math skills before using the Online Tutor.

## Can individualized computer-delivered instruction be effective and easy to manage?

When instruction is below the student’s level (sometimes called zone of proximal development) they don’t learn anything they didn’t already know.  When instruction is over the student’s level they lack the prerequisite information to understand the lesson, and so they don’t learn as well. If you have the luxury of a homogenous classroom, thank your administration for making it possible to teach whole group. Most teachers don’t have that luxury and need to deliver instruction to many different levels because instruction needs to be individualized for the student.  It’s relatively easy to have individualized assignments that students can successfully complete and practice what they already have learned. What’s difficult is to have effective individualized instruction, where they are learning something new they did not know.  Computer delivered instruction can be effective, if there are five keys components to the software.

## 1. Testing for placement or promotion

The software must place students in the correct starting point for their instruction. That requires some kind of testing.  Either some kind of placement test is needed or the software must allow students to “test up” through and out of material they already know. This testing should be the same as the testing for corrections and for mastery.  Any teaching program that doesn’t have a testing component is not focused enough to be effective. Without testing you cannot know what students have learned.  Without testing the software cannot know that it has taught anything.

## 2. Good Quality Instruction

The software must impart the information to be learned to the students. Even in practice-type programs, such as math facts or spelling programs, the software should tell students what they need to learn.  It may seem simple, but it is critical for students to learn.

For more complex topics, the instruction, the telling of the information, should be as clear and simple as possible, and to the point.  It should be given in small bits, followed quickly by testing to see if the students learned the information (see correction procedures).  Too much information and not enough testing or checking for understanding and a program will be ineffective.  Unfortunately, sometimes “educational” software does not do a good job of teaching, the exposition is not clear enough.  The testing and correction procedures must be in place, so that the exposition will be seen to be ineffective and can be corrected.  Hopefully, the software developers used the feedback of initial trials to improve the lesson delivery.  In any case, the school or parents need to check the testing to see if the software is effective in teaching what it claims to be teaching.

## 3. Testing and Correction procedures

The software must include some immediate checking-for-understanding type testing after each bit of instruction. If that testing shows that a student has not learned the objective, the program must have a correction procedure in place.  It needs to be robust enough to ensure that the student learns the bit of information that was missed.  An effective correction will re-give the initial instruction and then immediately check for understanding.  A good program will repeat this step as many times as needed for the student to be able to correctly answer and show their understanding.  Then the program should intersperse something else and then re-test the student a couple of times more.  Then the information can be assumed to have been learned until mastery testing, which comes next.

## 4. Mastery-based promotion

Before students go on to learn another part, chapter, concept or unit the software must test them for mastery of all the objectives in this segment.  Mastery-based promotion means the student doesn’t go on to the next thing until the student has demonstrated mastery of the current material.  Instruction should, of course, be broken down into manageable size pieces, but each piece should be mastered before teaching additional content to be learned.  That requires a test of some sort.  Lack of mastery means the part needs to be repeated until it is mastered.  Demonstrating mastery on the test will result in the student being promoted on to the next segment of instruction.

## 5. Logical instructional sequences

Instruction must proceed through carefully thought-out, logical sequences.  Students must learn the prerequisites and learn them to mastery before they can take on a new skill.  Instruction must proceed carefully and thoughtfully so that students are never expected to know something that has not been previously taught and taught well.  Many topics that teacher and students find difficult to learn are simply a result of having several prerequisite skills that have not been brought to mastery ahead of time.  For example, long division requires that students have mastered subtraction, multiplication and division facts, as well as estimating and place value.  When several of those skills are not properly developed, long division become quite difficult to teach.  If the instructional sequence is sound, then each new step will not happen before the prerequisite skills are mastered.  When they are in a logical sequence and they are mastered, the new step will be relatively easy and will be learned quickly.

With these five components in place, computer delivered instruction can indeed be effective.  Students will be learning and the purchasers can see that students are learning based on the mastery testing in place.

## Easy-to-manage requires that all the above are automatic

The above five components are necessary for instruction to be effective. They should be handled automatically by the software.  The testing and corrections, the re-teaching and the mastery testing, all should happen automatically and without fail.  When the instructional sequence is sound and students master each bit as they go along, then it will be easy-to-manage for the teacher.  For an example of an effective instructional program for math facts, see the Rocket Math Online Tutor.

## Online Tutor should be assigned as homework–here’s how

We call our app the Online Tutor for a reason.  It patiently teaches like a top-notch tutor would.  Why waste this resource when it can be assigned as a very valuable and easy-to-check-on homework assignment.  You don’t have papers for the dog to eat, or papers to correct, but students will greatly benefit from more time spent each day practicing math facts.  You have already paid for it, so make the most of this resource.

## Three ways to access the Rocket Math Online Tutor at home

Of course, the first way is to log into a web browser such as Google Chrome, Firefox, Microsoft Edge (anything other than Apple’s Safari which is not compatible with our app) and go to https://play.rocketmath.com .   You can play from there, but if the student is using a mobile device the apps work better and are free.

Rocket Math has a mobile app that parents can download for free.  The apps can run on a phone as well as other mobile devices, so it is not necessary that children have a computer available at home.  On the Enter page there are two buttons to access the mobile apps.  We have two versions:

one on the Apple App store https://apps.apple.com/us/app/rocket-math-online-tutor/id1538196379  and

You can send these links home so that students can work with the Online Tutor on any mobile device.

## Use the Parent Letter to send home login credentials.

You can find the Parent letter on tab (i) Parent Letter on the rainbow navigation bar of the admin account or herePrint enough copies for your whole class.  Enter the student’s name at the top and the Username, Passcode, and your Account number on the lines provided. (If it were me, I’d then copy them all to have another set for lost copies).  Then you can send these home with students so parents know how students can logon and do a 10-minute session.  The letter explains about the “Session Completed” screen so that students can be encouraged to show that to their parents each evening to prove they have “done their homework.”

## Promote homework during Back-to-school night.

It will take a little effort to build in this expectation, but it will be well worth it.  Working with the Online Tutor, students can’t help but develop math fact fluency and they never practice errors.  You don’t have papers to grade, so this will be the best homework ever.  There is nothing other than reading fluency that is more important to future academic success than math fact fluency.  Why not add some additional practice as homework?

On Back-to-school night, bring in a couple of students to demonstrate a session for parents, so they can see how it works to correct errors.  You can have parents access the links to download the app right onto their phones and give them the Parent Letter.  (See why I would make copies?)  If during conferences, you can download the app onto their phone and have their child login and use the app right then and there.  Seeing is believing, and parents will see that their children can learn their math facts by using this app.

## How do you know which students do Rocket Math as homework?

We’ve got that handled for you.  Simply go to the blue “Enable Daily Progress Report” button on the Review Progress tab on your admin site.   Click on that button and you’ll get a pop-up asking you to verify the email to which the reports should be sent and expecting you to hit the green “Enable” button to get these started.

The Daily Progress Report tells you how many sessions students started and how many they completed yesterday.  So if you had students do a session in school (And you made sure they completed it, right?) they would have a “1” by sessions completed.  If they went home and completed another session they would have a “2” by their name.  So you can tell who did homework and who didn’t, right on this report.  It also tells you who passed which levels. (And therefore earned the right to color those levels in on their Rocket chart.)

## How can you motivate your students to do the Online Tutor as homework?

First, you should assign it.  Put it on the board.  Send home notes.  Send home the parent letters–again. (Aren’t you glad you made copies?)  You need to convince your students that this is important and that you expect them to do it.  That’s the start.

But then you need to show them you are impressed by the students who do it as homework.  You may have to read from the daily progress report with disappointment, that nobody did it as homework yet.  But then one day, you’ll have someone who does it as homework.  Have them stand up and give a cheer and get a round of applause.  The next day, do it again. And the day after that.  Eventually you’ll have a few doing it.  Put their names on the board as math superstars.  Keep praising them.  Make up a note to send home with the reminder to do Rocket Math as homework, praising the ones who have been doing it.  Keep acting like you care and are impressed by the ones who are “doing their homework” and eventually almost all of your students will be doing it at home regularly.  Their progress will take off and they will become math success stories.  It’s a lot of work, but it is your mission, right?

## Pre-algebra Learning Tracks for advanced students

Teachers can assign Rocket Math for all their students whether they are behind or advanced. Rocket Math has four pre-algebra topics for those students who already know their multiplication facts. Each of these topics will help them do pre-algebra processes more fluently and to quickly recognize relationships that they have memorized.

## Learning Track 13: Identifying Fractions

When students initially learn about fractions they are often only shown proper fractions. As a result, they have a limited understanding of fractions and can be confused by improper fractions or mixed numbers. Rocket Math prevents this problem.

Students learn to name fractions shown in a picture as parts shaded.  Fractions are always shown with two or more whole units with a number of parts shaded. From the start, we teach students using examples of both proper and improper fractions as well as whole numbers and mixed numbers. Students learn from examples of proper fractions, improper fractions such as 5/3 that are equal to more than 1, and mixed numbers such as 2 and 1/2.

Students learn to identify over 90 different fractions quickly and easily by getting lots of practice. Their understanding of fractions will deepen and become more flexible as they learn to recognize many examples of fractions. Here’s half of the examples students learn from.

## Learning Track 14: Equivalent Fractions

Students will memorize the most common equivalent fractions (by reducing them to lowest terms) with this Rocket Math Learning Track. They will also learn to identify a number of fractions, such as 2/9,  that do not “reduce” or for which there are no equivalent fractions in lower terms. Students also learn to recognize a fraction equal to 1 whole in its various forms. When students don’t instantly know the answer they are told the equivalent fraction and given practice on it. The computer gives help in the Online Game.  Their partner gives that help in the Worksheet Program. By the end of the program, students will learn over 90 equivalent fractions. This gives students an excellent start on being able to manipulate fractions quickly and easily.

## Learning Track 15: Factors & Primes

Students are required to “find the factors” when dealing with unlike fractions and reducing fractions. Rocket Math Worksheet and Online Game teach students how to find factor pairs. Students learn how to find all the factor pairs and what they all are for many common numbers. They also learn to identify prime numbers and their characteristic of having only one and themselves as factors.

Students learn Dr. Don’s foolproof method for finding the factor pairs in order. https://www.rocketmath.com/2020/12/29/foolproof-method-finding-factor-pairs/ By this method they know the “last” factor pair when they see it. When the game asks “What’s next?” students can provide the next pair of factors or click the checkmark to indicate there are no more factors. When students go through this Learning Track they will no longer hesitate when asked for the factors of common numbers.

## Learning Track 16: Fraction & Decimal Equivalents

Learning common fractions and their decimal equivalents, learning fractions and their fraction equivalents in 10ths or 100ths.

Common fraction and decimal equivalents should not require a laborious process to “figure out.” Students should just know these, so this Learning Track in the Online Game allows them to memorize a bunch of common decimal and fraction equivalents.

Having a facility with a lot of fraction and decimal equivalents means faster computation as well as a way to check their process when manipulating fractions and decimals. Students also learn another essential pre-algebra skill that often confuses them.  They learn to correctly and fluently translate a fraction into a division problem and vice-versa.

“Test Drive” any of the 16 Learning Tracks in our Online Game demo accounts.

## Assign re-take when results of a 1-minute race go down

As students take the scheduled 1-minute races we display the results of the last two races on the Tab (A) Review progress screen.  As they learn more, they should be improving, their fluency should be going up.  These “races” are really fluency tests of a random selection of problems from throughout the Learning Track they are practicing.  The student shown above answered 8 of those problems in a minute the day they finished the first set (A).  After working a while and getting up to set (i) they are then scheduled for another fluency test. Then, the day the student finished set (i) the student was able to answer 10 in a minute. That’s what we expect to see.

Their score really should not go down (unless they happened to get more problems they didn’t know).  If their score does go down significantly, as this student did, we offer the teacher the opportunity to assign a re-take of that test.  Perhaps the student was distracted during the 1-minute race, or they weren’t really giving it their best effort.  We leave this up to the teacher or parent to decide, because they know the student.  If the student may not have made their best effort, a re-take can give them another opportunity.

Once that is scheduled, the student will do the re-take the next time they login.  In the meantime, the assignment will show on that student’s row on the Review Progress screen.  If on the re-take, the student’s score improves, the improved score will replace the lower score.  If it does not improve, then the current score stands.

## Students can also choose to re-take a poor showing.

Sometimes during the 1-minute race, students get distracted, upset, or confused and they are pretty sure they can do better.  We give them a chance to prove it.  At the end of the race, it displays their score and gives them the choice to re-take the race to try for a better score.  If they click on the green “I want to re-take it.” button they get another chance to take the 1-minute race. If their score is better, it will replace the score they had earned previously.  If it isn’t any better, they get to keep the original score.  On the other hand, if the student thinks they did their best, they can click the top red button and they don’t have to do a re-take.

Tens of thousands of students have taken these 1-minute races and demonstrated improved fluency as a result of doing Rocket Math.  See this link to see the real-time data as more students improve their fluency with Rocket Math.

## The Effort Rating screen–a tool for motivating students

The effort rating screens, shown above, pop up every time a student logs into Rocket Math Online Tutor.  It shows the number of sessions the student has started and completed in the last 14 days. It’s a rolling mini-calendar.  Students see a letter for any day (SMTWTFS) when there was no session.   On days when they start sessions, students instead see the number of sessions they started.  On days when they complete sessions, students instead see the number of sessions they completed. For every two sessions completed in the last 14 days, they earn one-half a star and four sessions a full star.  The more stars they have, the more effort they are making.

## It’s powerful to recognize students based on their effort.

Every student can put in effort regardless of their academic prowess.  The really bright students, who learn easily, get a lot of recognition, sometimes with little effort.  If you want to be fair and if you want to help and motivate all of your students focus on their effort rather than their level of success.  Some students have to work harder than others to achieve, but you want to recognize and reward students based on their effort when you can.  This will help them later in life as well. Rocket Math Online Tutor makes that easy with the effort rating screen shown above that pops up after they log in.

Our goal should be for students to complete a session each school day and one more at home for homework.  Over the previous 14 days that would normally amount to 20 sessions which would earn them five stars.  If they only complete a session per day at school that would be ten sessions or 2 1/2 stars.  You’ll want to aim at getting students to do Rocket Math as homework as well.

## Your enthusiasm signals what is important.

When students log in, the effort screen comes up first before they start working. You need to show interest in how much effort your students have been exerting.  You and the student can view this when students log into Rocket Math.  If you publicly praise students with stars for  effort, then students will know that effort is important.  Just walking around and exclaiming something like, “Wow, Julie, you got one and a half stars for effort!  I’m impressed!” will cause other students to look at their star effort screens.  Soon, students will show you if their effort rates more stars, so you can see it and praise them.  Looking at a few students’ effort rating screens should become a daily routine when Rocket Math begins. But wait, there’s more you can do.

## How to find out who has done the most sessions?

On the Review Progress tab, in the part with individual student data, you can sort by the “Total” column.  Click twice until the arrow is pointing down.  You will then have sorted to the top the students who have done the most number of sessions in the last 14 days.  By doing this you can find the 10-20% of your students who are doing the most sessions.  Recognize them, put their name on the board, call their parents, point out how you are impressed by their hard work and how smart they are going to become by working so hard. You can see in the pictured example that the four hardest working students completed 12 or more sessions in the last 14 days. When you see that in your class, there’s even more you can do for them.

## Star effort awards available to give out to hard-working students.

If any of your hardest-working students have done 8 or more sessions in the last 14 days, you can give them the “2 Star” effort award.  Give these out with a lot of fanfare, as soon as anyone has completed enough sessions to earn them.  Everyone can put out the effort, so all of your students should be able to earn these!

Completing sessions every day at school and then doing some as homework will earn more stars.  Doing twelve sessions in 14 days will earn three stars. Doing 16 will earn four stars and doing 20 will earn five stars.  These awards are available under tab (K) Award Certificates.

Of course, it would be better to earn the “4 Star” award, so you’ll want your students to strive to earn one of those.  Award that with even more fanfare, once someone earns the “4 Star” award.  And eventually, you may be able to reward some students with the “5 star” award, which is the best of all.

When most of your class is earning these awards you’ll be on your way to really helping them become fluent in math.  Way to go!