elementary

Help your kid get fast at math facts

Posted on by Dr. Don

Your kid wants to go fast at math.

Having to count out all your math facts is simply painful.  There is no need for it.  Every child is capable of memorizing math facts so that they can be recalled within less than a second.  Like any other facts we know and use daily, math facts, once learned, can be brought to mind instantly.  This makes math assignments easy and fast.  It enables students to easily recognize many things about numbers that teachers call “number sense.”  It gives them confidence.  And frankly, they like going fast much better!

The usual kind of practice will not make them fast.

I used to think, as a teacher, that just giving students practice with math facts would help them to get faster.  Years of teaching proved me wrong.  Students will count and count and count and fill out worksheet after worksheet and never get faster.  They hated it and I was discouraged.  This is why veteran teachers are most interested in Rocket Math.  They’ve learned the hard way that just any old practice sheet won’t work.   Then in grad school I learned a simple fact about memorizing.

You can only memorize a handful of math facts at a time.

If a task presents any more than a handful of facts, your brain gives up.  Your brain won’t even try to remember, it will just focus on a strategy for figuring it out.  However, if you have a small handful of thing to remember, and you get asked right away, you can remember.  “Oh, I can remember this. I’m having to come up with this fact again.  I should try to remember it.”  Rocket Math only presents two facts and their reverse to remember at a time.  And that makes all the difference.  Well, most of it.

Calling math facts to mind again, before they are forgotten, is key.

Many teachers and parents think that struggling to remember is valuable.  Not so much.  Instead, just calling to mind the answer, quickly and easily, before it is hard, is all that is necessary.  Correctly recalling a fact is what strengthens the neural connections.  Forgetting it and having to figure it out again does not help.  In fact, it teaches students that the job is figuring it out, rather than remembering it.  That’s why the correction in Rocket Math is to simply tell the student the answer.  The message is to “just remember it” rather than having to figure it out over and over.

Practicing math facts fast requires recalling them.

Once your brain is focused on calling to mind a small handful of facts, you can recall them quickly.  Now, you can go fast and you should be required to go fast.  First, requiring you to go fast ensures that you are recalling.  Second, it’s more fun.  Third, you can get a lot of practice done in a short amount of time.  This is why Rocket Math only has students practice for a few minutes at a time.  That’s all that’s needed if you are going fast.

Cumulatively adding more facts needs to be done carefully

To get beyond that initial handful of facts, you have to learn more.  But we have to be careful not to add too many, too soon.  First, make sure everything introduced so far is well mastered without any hesitations.  Then and only then are you ready to get another handful.  A small handful, lots of practice, so they can be recalled, and then add them into the mix of mastered facts.  As the saying goes, “How do you eat an elephant? One bite at a time.”

Practicing fast math facts needs to be daily

There are a lot of math facts to learn.   A lot students take four years to learn all four operations.  The task should begin early and continue until all are learned, so daily practice is a must.   Also, spreading the learning out over time means it is learned more fully.  Learning something in a day, it’s forgotten in a week.  Learning something over a year, it’s remembered as long as it is still being used.  A few minutes a day is all we ask, but it is very important to make math facts practice a daily regimen throughout elementary school.

Sign up for a 30-day free trial of the Rocket Math Online Tutor.  It works in ten minute sessions. And kids like it!

Things-to-look-for (any time of day) for Rocket Math implementation

Posted on by Dr. Don

Evaluating a Rocket Math implementation when you aren’t observing Rocket Math in action.

Most of the time when you go into classrooms, something other than Rocket Math® will be going on. These are the things you can check on even when there are no students in the room. There are eight indicators you can see by looking at student folders.  There are four indicators while looking at the Rocket Math filing crate.  There are additional indicators to look for if there is a Wall Chart being used or if there are Race for the Stars games in the room.  Here’s a link to the checklist.

Look at several Student Folders

(1). Students all have folders that appear to be used daily. The folders are the heart of the organizational system. Students should keep their materials in the folders and keep track of their progress on the folders. Whether the students keep folders in their desks, cubbies, or are collected each day, there should be some signs of wear and tear.

(2). Rocket Charts on student folders show dates of each attempt to pass a level. Each day when students take a 1-minute timing test to try to pass a set of facts, they should write the date of the “try” on the Rocket Chart on the front of their folder. Without this record you cannot tell if a student is stuck because he or she has missed two weeks of school, or if students are only doing Rocket Math® twice a week (not recommended!), or if a student has exceeded six tries without intervention.

(3). Rocket Charts on student folders are colored in when passed. Coloring in the row on the Rocket Chart for the fact set that was just passed is the primary reinforcer of all that hard work. It is essential that students are given the time (and the colored pens, pencils, or crayons) to celebrate their success. Don’t get fooled by the older students or the students who are “too cool” to color in the chart. Even if they only want to color in the row with their regular pencil, students need to be told that they have accomplished something important, and giving them the time to color in their chart is a critical component of the program. This is way more important than you might think. You can also praise students who have accomplished a lot or who have just passed a level. Hearing from an administrator or coach about progress in math facts sends a huge message regarding the importance of the task.

(4). Student folders include packets of answer keys on colored paper. In order to practice correctly, each student’s partner needs to have an answer key in front of them when practicing. Each student needs their own answer key packet (so they can practice with someone who doesn’t have that answer key or with a volunteer who has no answer key). All the answer sheets for their operation should be copied and stapled into a booklet so students don’t have to go hunting for answer keys. Having the answer keys copied onto a distinctive color is important for teachers to be able to monitor paired practice. When students are practicing, each pair should have one student with answers (in that distinctive color) and the partner without the answers (on white paper). Any variation of this means the students are not practicing correctly—and that should be easy for the teacher to spot. Additionally, if a teacher is ready to begin testing and sees a hot pink paper on a desk, the teacher knows someone has answers in front of him or her.

(5) Student folders have the next sheet ready before starting practice time. Some system needs to be put in place so that the limited amount of time available for students to practice is NOT taken up with all students trooping up to the crate to get the next practice sheet each day. The recommended system in the Teacher Directions is to refill student folders when they pass a level, after school, with a packet of six sheets. That way the only time teachers have to handle folders is when students pass and they check the “pass” for errors and refill with a new packet. Many other ways of refilling student folders are possible, but no matter the process, students should have a blank practice sheet or set of practice sheets in their folder—which you would see when you check folders.

(6). Students have clear goals indicated on goal sheet. After students complete the Writing Speed Test, they are to have goals set for their daily 1-minute timing. The goal sheet should be stapled to the inside left of the student folder, the goal line circled, and the 1-minute goal written at the bottom of the sheet. The goal may be crossed out and a higher goal written in if the student has consistently demonstrated the ability to write faster than the original goal. Sometimes, teachers also write the goal on the front on the Rocket Chart, but the student’s goal should be clearly indicated. If not, it may be arbitrary or inappropriate (the same for all students, for example).

(7). Individual graphs are filled in because 2-minute timings are happening. Every week or two, students should be taking the 2-minute timings. These timings are a progress monitoring measure. They could be used for RTI or for IEP goals, or for any other time when a curriculum-based measurement is useful. At least they can demonstrate to us (and to the students) whether they are making progress in learning math facts in a given operation. As students learn more and more facts in the operation to a level of fluency and automaticity, they will be able to write answers to more facts in the operation on the 2-minute timing. Each time they take a 2-minute test, they should count the number correct and graph that on the graph stapled on the inside right of their folder. Each test is graphed in the correct column for whichever week of the month the test was taken.

(8). Individual graphs show upward trends as students are learning facts. Once students are taking the 2-minute timings regularly, it should be easy to see a trend. It should be going up, even if somewhat unevenly. For example, scores might go down after the long December break, but they should recover after a couple of weeks. If these graphs do NOT show an upward trend, something is wrong. Practice may not be being done for long enough (less than 2 minutes a day), or frequently enough (only three times a week), or students may not be practicing correctly (not fixing hesitations and errors). If only one or two students have flat graphs, those students will need something more. The individual graphs will be your indication that there is something amiss. You will just have to figure out what could be wrong. This should lead you to do some observations during Rocket Math® practice in that classroom.

Look at the Rocket Math file crate

(1). There is a crate or set of files for each operation practiced in the room. Each operation fills a crate and requires a different set of files. In any classroom where not all students are working on the same operation, there will need to be more than one set of files. Sometimes, teachers who have only one or two students in an operation may use the files of a neighbor teacher, but that should be only a temporary fix. The rule is that there must be a crate for every operation being practiced in that class.

(2). Rocket Math® crate is filled and organized from A–Z, complete with tabs. As of the 2013 version of Rocket Math®, every operation goes up to the letter Z. So each crate should have hanging folders with tabs showing the letters A though Z. Tabs are important to save time finding sheets and filling folders. If the files are a mess, out of order, no labels, or some letters are empty, valuable practice time will be used up trying to find the right sheets. If everything is labeled, and there are sheets in each file, then efficiency is a possibility. The Rocket Math store has tabs for sale if you need them.

(3). Rocket Math® crate has 2-minute timings numbered 1–5. In order to make sure that teachers do the 2-minute timing and monitor progress readily, they need to have class sets of the 2-minute timings (1 through 5) available in the crate. This is easy for you to check. If they are not there, it is likely that the 2-minute timings won’t be done as regularly as they should be. It is important for those timings to be done so you can see if all the students are making good progress.

(4). Teacher has a hard copy of the directions available for reference. The best place to keep the directions is right in the crate, so they are handy at any time. We have found that most of the time, when teachers are not doing things as they should in their Rocket Math® implementations, they don’t have a copy of the directions. When teachers don’t have the directions handy, they will ask a colleague how to do things. Unfortunately, this is like a game of telephone and typically doesn’t end well. Being sure that every teacher has the directions available for easy reference goes a long way toward proper implementation. It also allows you to pick up the directions when you are in the room and point something out to the teacher or to reference an appropriate page number in the directions in your notes to the teacher.

You can print the Teacher Directions from the virtual filing cabinet, in the Forms and Information drawer, under Rocket Math Teacher Directions.  You can buy printed copies from RocketMath.com/shop.  There are additional things to look for on the form but they are optional and go with supplemental parts of the curriculum.

Seven steps to an exemplary Rocket Math Worksheet implementation

Posted on by Dr. Don

You know already what should be happening.

This article assumes you have read the Rocket Math Teacher Directions yourself, so you know how things should run.  You can also read the Administrator and Coach Handbook for more ideas on how things should be running.  These helpful manuals can be purchased at their link, or available for free in the virtual Rocket Math Worksheet filing cabinet–in the Forms and Information Drawer. You’ll also need to have done observations using our observation form and checklist.    You should already know what things need to change–this is about how to make that happen.

How to make change happen.

These are recommendations as to how to get an implementation of Rocket Math® running smoothly, correctly, and effectively—without unduly annoying your teachers. How can you get every teacher in your building to abide by all the critical features of Rocket Math®? If teachers feel criticized, they will begin to resent the program and you. On the other hand, teachers (especially good teachers) are highly self-critical and, if they understand what should be happening, will enthusiastically self-correct a lot of details without you having to point out their errors. So here are seven steps to getting more of the enthusiasm and less of the resentment.

1. Choose one procedure to change at a time.

There may be several things not being implemented the way you would like (or as is outlined in the Teacher Directions). The temptation is to assign everyone to read the Teacher Directions and then follow them. Ask them to read the directions, yes, but they will need help to actually improve. To begin, just pick one concrete procedure that you want everyone to be sure to do the right way. Pick the most important one—as best as you can. Start with the top four of the observation form (shown here).

2. Talk about it first.

Always talk about needed details or techniques in a staff meeting before “noticing” the problem in any particular teacher’s room. If you see a problem in one or more classrooms, don’t ask those teachers to change as your first response. Instead, talk about what should be happening, in a staff meeting, without saying anything about those who weren’t doing it right. Describe clearly what you want teachers to do. Consider writing it down and passing it out as you talk about it. You may even need to have teachers practice it in a role-play scenario in small groups. This can be done for just a few minutes.

3. Give the rationale.

Whenever you talk about a feature or a technique you want teachers to do, explain WHY it is important. Explain it in terms of student learning. (The rationale is in the Administrator & Coach manual and in the Teacher Directions also.) Teachers want their students to succeed, so if you explain why it is important for the kids, the teachers will see the reason for doing it the right way. Have some discussion with the staff to make sure everyone knows both what you want and why it is important to learning.

Note: If you have a staff that doesn’t readily discuss, give them the questions you would ask, break them into groups to come up with an answer for each question, and have the groups report out.

4. Give a “heads up” that you’ll be observing.

At the end of talking in the staff meeting about the change you want to see, let everyone know that you will be visiting classrooms during Rocket Math® to see how things are going. If the change that you are looking for requires preparation, give a week’s notice. If it is just a way of doing things that can be changed immediately, start observing in the next day or two.

5. Follow through with praise first.

After observations where you see people doing what you wanted to see, be sure to tell them personally how impressed you are with their ability to implement a new idea so quickly or so well or with such enthusiasm. At the next staff meeting, after the end of the first observations, praise the people who are doing things well. If more than ¾ of your staff is doing it correctly, you can move on to observing for something new. If less than ¾ of your staff is doing the one specific thing correctly, then revisit the change and let your staff know that you will be visiting again within the next few days. Be sure to follow through with your visits.

6. Follow through with individual help.

Once you are down to a small number of staff members who are NOT implementing the change you want to see, it is time to offer more help to each of them. Once you see for the second or third time that a teacher is not implementing what is expected, tell them what you saw instead, and ask what you can do to help.

Be genuine. More often than not, teachers do not implement correctly because they don’t exactly know how, but were afraid to ask. Ferreting out what the stumbling block is, finding out what’s getting in the way of a good implementation, is the best use of your time. Sometimes, just role-playing what to say or do is needed. Sometimes resources are missing or haven’t been requested. Sometimes a method of organizing better is the key. Often, another teacher will have the key as to how to implement something—so don’t hesitate to use peers to support one another.

You should know that Rocket Math® done correctly will work. If you can get a teacher to do this well, they will be reinforced by the results. Students will end up being more successful, and that is very rewarding to any teacher who really cares. Staying with a teacher until the details are right will end up being worth the time—for you, for the teacher, and, most importantly, for the students.

7. Celebrate 100% implementation.

Keep track of the new things you’ve asked to be changed. Keep track of how many teachers are implementing. Keep praising those who are coming on board. Finally, celebrate when everyone “gets it.” Find a memorable way to celebrate the victory. Some people even create a “bragging list” of all the new procedures that were implemented to mastery by all the teachers in the school.

The Online Game never teaches anything wrong.

Posted on by Dr. Don

Are your students complaining that the Online Game said they were wrong, when they were right?  This is similar to a problem we found with students and their checkers in the Worksheet Program. Bear with me a second while I explain.

In the Worksheet Program students often complain to their teacher that their checker made them do the problem over, even though they weren’t wrong.  Trying to adjudicate such a dispute is nearly impossible, as veteran teachers have learned the hard way.  The extra practice didn’t hurt the students and you’re going to be inundated with complaints if you try to adjudicate them. In workshops we always counseled teachers to respond to such complaints with, “The checker is always right.  Just do the problem over again.”

The extra practice that the Online Game) makes a student do is never harmful.  The problem and the answer that Mission Control gives is never wrong.  When students complain to you about the game telling them a right answer was wrong, just tell the student, “The game is always right. Just do the problem over again.”

The Online Game only says right answers, so it’s not wrong.

The correction procedure says both the problem and the correct answer.   Students may say, “But, that’s what I put!” They are not confused. They are just complaining that they were “unjustly” corrected.  An unjust correction is relatively unimportant compared to an actual error.

The program never says a student’s answer is “wrong.”  The game does a correction whenever it does not process the correct answer within the time limit.  The student may hit the correct answer just a fraction of a second too late to be processed by the game. Even though correct, the game will say “Time’s Up” and do a correction.

Sometimes a student misses the button they mean to hit, they make a “typo,” and the game buzzes and the screen shakes “no.” Sometimes, a glitch occurs and it skips ahead to the next problem and processes the last answer as incorrect. However, the game can only say a problem and its correct answer as those are the only words that are recorded.  There are no recorded errors.  For example the game will say, “Six plus two equals eight. Go again.”  After that the game waits for the student to enter the correct answer AND waits for the student to hit the checkmark. No amount of arguing, “But that is what I put!” or “But that wasn’t the problem I was answering” will change it.

The extra practice caused by an “unjust correction” is not harmful.

Students should listen to Mission Control while it is displaying and saying a problem and the correct answer.  Then the game will show the problem just stated without the answer.  Students will know what they should do. They should just enter the answer and hit the checkmark.  Students should just do the problem over again regardless of whether or not they think they entered the right answer.  The game never says anything incorrect and the extra practice won’t hurt them. While an unjust red “X” for an error seems terrible to students, it will not do anything other than give them more practice, which is good for them.

We  offer a $50 gift certificate to the store of your choice if you can capture an error by the game on video, as we have never seen the game make an error and can’t replicate the problem.

A mom congratulates her son at a baseball game.

Positive Praise: Building Effective Teaching Habits

Posted on by Dr. Don

Positive praise is one of the most effective ways to encourage wanted behaviors from students. Because building habits is not an easy task, here are a few things you can do to start easily incorporating positive praise in the classroom.

  1. Be prepared with positive phrases
  2. Develop the most effective wording
  3. Start Small with two areas you would like to see improved behavior
  4. Practice in the Classroom and watch the effect it has on your students
  5. Grow and expand your positive phrases over time as you master the habit

Be Prepared with Positive Praise Phrases

I distinctly remember trying to help pre-service teachers build the teaching habit of positive praise. I would make suggestions and then observe. Trying to implement my suggestions wasn’t as easy as you would imagine – these teachers would glance in my direction and start the sentence “I like the way you’re . . .” and then trail off without knowing what to say.

Teachers want to use positivity and affirmation with their students, however, in my experience, they don’t always have the appropriate words ready to praise good behavior. Building the teaching habit of positive praise starts with getting the right words ready.

Recently I was reminded of this key component of building the new habit of making more positive statements. I wanted to personally develop this positive statement habit, but for some reason was not making the progress I had hoped for.

I quickly realized that I was making the same mistake I had watched the pre-service teachers make. I was unable to make more positive statements because I did not have any in mind that were ready-to-use.

To build the habit of making more positive statements, I would have to start memorizing some key phrases to keep on standby, ready to use when I needed them.

Positive Praise Example Phrases: How to Develop the Right Wording

The first step in positive praise is learning and developing the most effective wording. Using effective wording means you are getting through to your student, and clearly communicating that you appreciate the good behavior they are exhibiting.

Praise is most effective when it is prompt – when you deliver the praise in the moment. Can you picture a specific scenario in your classroom when many of the students are not doing as you asked, while a few students are dutifully following instructions?

This is the perfect scenario to use positive praise not only in rewarding students with good behavior but also encouraging other students to follow suit. Don’t be afraid to praise good behavior loud and proud for the rest of the classroom to hear!

Here are some examples of positive praise:

  • Look at Alan so smart sitting in his seat and showing me he is ready to learn. Way to go, Alan.
  • I see Beto is tracking with his finger while Claudio is saying the facts. That’s the way to help your partner!
  • Julia, you are so sharp having your eyes on the teacher, so you can learn!  I am impressed.
  • Stacy and Sophia know just what to do, they have their books open to page XX.  They are so on top of it!
  • Fantastic, Justin! You put your pencil down and are waiting for directions.  I can tell you’re going to college.
  • Stephanie is being such a great on-task student by working quietly and not talking.

Start Small: Pick Two Key Behaviors You Would Like to See More Of

Start out by choosing wanted behaviors from the two most annoying or frustrating scenarios you face as a teacher.  Stating small will help you build a consistent habit of giving positive praise.

Take these two wanted behaviors and build two praise statements you can easily use in-the-moment. Make sure the statement names the behavior specifically. Always include the student’s name, and keep it simple and affirmative.

Now, take a note card or piece of paper and write down these two statements. Don’t wait! Write them down now and keep this note in front of you while you teach. It will serve as a reminder throughout your day to incorporate positive praise as much as possible.

Practice saying these phrases aloud until you have them memorized and can recall them without having to think about it. The most important step in building this habit? Actually practicing positive statements in the classroom.

With these key components and diligent practice in the classroom, you will quickly build the habit of positively praising your students.

Positive Praise in The Classroom: Will it Make a Difference?

Fortunately, positive praise is free and can be implemented at any time throughout the school year. Start using positive praise now, and watch how your students respond.

Prepare yourself for giving positive praise when you are about to begin those frustrating scenarios. When the activity begins, look for opportunities to praise the behavior you are looking for when you notice students who are off-task.

You will see results when you use positive praise genuinely and with enthusiasm. You will know it is working if you watch for those distracted students taking notice of who is being praised. If you notice this happening, keep it up. The more praise you give for wanted behavior, the more that behavior will occur.

Grow and Expand Your Positive Praise Habit

Now that you know how to promote a specific behavior with positive praise, you can systematically develop statements for all your troublesome areas.  Every time students are not doing what you want, think of what you want them to do instead.  Behavior analysts call those replacement behaviors. 

Positive praise can also be used creatively alongside other motivational tools in the classroom. When I began my teaching career I was in the habit of scolding behaviors I did not want. Early in my career, I learned the effectiveness of positive praise and began incorporating it into my daily routine.

When I saw the behavior I wanted I would give loud and proud praise for all to hear. I decided to couple this by adding marbles to a jar every time I gave praise, as an added motivational tool – so students could see how well they have been doing. It worked wonders on increasing wanted behavior.

Building new habits is never easy, but I can personally say that as a teacher, learning to incorporate positive praise into your teaching routine will not only help students learn, but it will save you a lot of frustration!

If you are currently looking for a job as a math teacher abroad, check out this link on Jooble.

Rocket Math Adds Beginning Numerals & Counting Program

Posted on by Dr. Don

A screenshot of Rocket Math’s Beginning Numerals counting worksheet showing how students choose the numeral besides the images to show how many objects are in an image.

Beginning Numerals and Counting

Dr. Don has created another math program and put it into the Universal level virtual filing cabinet at Rocket Math. This is a beginning program for kindergarten students and is to help them learn counting and numerals. That means they can’t learn on their own, the teacher must provide instruction. Teachers can use the counting objects kindergarten worksheets to effectively teach students to count objects aloud and then match the word with the numeral. You can see the top half of Worksheet A above.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet. Not a subscriber yet? Get the counting worksheets.

I Do: Demonstration of Counting

Each worksheet begins with a demonstration of counting objects and circling the numeral that matches. On Worksheet A, there are only the numerals two and three to learn. The teacher demonstrates (best with a document camera so all students can see) how she counts the objects and then points out that the answer is circled. Suggested teaching language is something like this,

“I can do these. Watch me count the frogs. One, two, three.. There are three frogs in this box. So they circled the three. Everybody, touch here where the three is circled. Good.

How many frogs were in this box, everybody? Yes, three.

Now watch me do the next box.”

 

We Do: Counting Together

In the “We Do” portion of the worksheet, the teacher counts the stars first as a demo and then with the students. Worksheet A you all just count three stars. Suggested teaching language is something like this:

“Our ‘We Do’ says to touch and count. Start at zero and count each star.

We are going to touch and count the stars. Put your counting finger on zero,

everybody. We are going to start at zero and count each star. Let’s count.

One, two, three. We counted three stars. That was great!

Let’s do it again! Fingers on zero, everybody. Let’s count. One…”

By Worksheet S the teacher and the students are counting 12 stars together.

The program has a page of teacher directions with suggested language for teaching the worksheets.

 

You Do: Independent Counting

A screenshot of the worksheet portion You Do, with a grid of three by five squares each with images to count and numbers to choose from.

In the “You do” portion of the worksheet (after learning the numerals with the teacher), the students are asked to count the items in each box and circle the correct number. They are not asked to form the numerals–that’s numeral writing skill. They just identify the numeral and circle it. Besides cute items, there are also dice to count, fingers to count, and hash marks to count–so students can learn multiple ways of keeping track of numbers.

Passing a level requires 100% accuracy. Students who make any errors should be worked with until they can complete the worksheet independently and get all the items correct.

 

Rocket Math’s Counting objects worksheets for Kindergarten

This Beginning numerals program will build strong beginning math skills for kindergarten students learning the meaning of numerals. Combined with Rocket Writing for Numerals it will set students up for success in elementary math.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet [use your link]. Not a subscriber yet? Get the counting worksheets.

 

 

Two students participating in one of Rocket Math's math fluency programs

How School Math Fluency Programs Work

Posted on by Dr. Don

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.

young boy wearing a blue striped shirt counting to seven on his fingersWhy 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.

 

 

Students and teacher playing multiplication games with dice sitting in a circle in a classroom

Why Multiplication Games Are Awful & What to Do About It

Posted on by Dr. Don

As a university supervisor of pre-service teachers, I’ve seen my share of bad lessons.  Among the most painful were when student teachers would try to liven up their lessons to impress me by having the students do a math game.  My student teachers wanted their students to learn math facts and to do so in a fun way.  The picture above is typical of what I would see.  Here are the reasons that most multiplication games that the student teachers implemented were awful.

(For multiplication games that work in and out of the classroom, check out Rocket Math’s Worksheet Program and Online Game.)

Waiting for your turn at a multiplication game is not learning!

As you can see in the picture above, all but one of the students are just waiting for their turn.  They aren’t doing math.  The students are just watching the student who is playing.  No one likes waiting, and your students are no exception.  Any game that has turn-taking among more than two students wastes time.

Make sure your multiplication games are structured so all or most students are engaged and playing all the time.  You want students to have as much engaging practice as possible while practicing math facts at speed.  If everyone can be doing that at the same time, that’s optimal.  No more than two students should be taking turns at a time.

A multiplication game that allows using a known strategy to figure out facts (like finger counting) is not learning!

Learning math facts involves memorizing these facts so that students know them by memory, by recall.  Committing facts to memory is why there is a need for lots of practice.  If the game allows time for students to count on their fingers or use some other strategy for figuring out the answer to facts, then there is no incentive for students to get better.

In the lower left corner of the picture you can see one student counting on their fingers—which is better than just watching—but is not learning the facts, it is just figuring them out.  The most able students in an elementary school are able to memorize facts on their own when they tire of figuring them out day in and day out.  But the rest of the students will just do their work patiently year after year without memorizing if you don’t create the conditions for them to memorize facts.

Make sure that your multiplication games reward remembering facts quickly rather than just figuring them out.  Speed should be the main factor after accuracy.  Fast-paced games are more fun and the point should be that the more facts you learn the better you’ll do.

Multiplication games that randomly present ALL the facts make learning impossible.

It is a basic fact of learning that no one can memorize a bunch of similar things all at once.  To memorize information, like math facts, the learner must work on a few, two to four facts, at a time.  With sufficient practice, every learner can memorize a small number of math facts. Once learners master a set of math facts, they can learn another batch.  But if a whole lot are presented all at once, it is impossible for the learner to memorize them.

Make sure your multiplication games are structured so that each student is presented with only facts they know.  A good game presents only a few facts at a time.  As students learn some of the math facts, more can be added, but at a pace that allows the learner to keep up.  The optimal learning conditions are for the learner to have a few things to learn in a sea of already mastered material.

Rocket Math Multiplication Games

We designed Rocket Math games to help kids gradually (and successfully) master math skills. Students use Rocket Math’s Worksheet Program to practice with partners, then take timings. Students can also individually develop math fact fluency—from any device, anywhere, any time of day—with Rocket Math’s Online Game.

Math Teaching Strategy #1: Help students memorize math facts

Posted on by Dr. Don

Once students know the procedure, they should stop counting and memorize!

When it comes to math facts like 9 plus 7 or 8 times 6 there are only two things to know.  1) A procedure to figure it out, which shows that you understand the “concept.”  2) What’s the answer?

It is important for students to understand the concept and to have a reliable procedure to figure out the answer to a math fact.  But there is no need for them to be required to use the laborious counting process over and over and over again!  Really, if you think about it, even though this student is doing his math “work” he is not learning anything. 

Math teaching strategy:  Go ahead and memorize those facts.

(It won’t hurt them a bit.  They’ll like it actually.)

Once students know the procedure for figuring out a basic fact, then they should stop figuring it out and just memorize the answer.  Unlike capitals and countries in the world, math facts are never going to change.  Once you memorize that 9 plus 7 is 16, it’s good for a lifetime.  Memorizing math facts makes doing arithmetic MUCH easier and faster.  Hence our tagline

Rocket Math: Because going fast is more fun!

Memorizing facts is the lowest level of learning.  It’s as easy as it gets.  But memorizing ALL the facts, which are similar, is kind of a long slog.  Some kids just naturally absorb the facts and memorize them.

Math teaching strategy: Find a systematic way for students to memorize.

A lot of students don’t learn the facts and keep counting them out over and over again.  They just need a systematic way of learning the facts.  Students need to spend as much time as necessary on each small set of facts to get them fully mastered.  If the facts are introduced too fast, they start to get confused, and it all breaks down.  Each student should learn at their own pace and learn each set of facts until it is automatic–answered without hesitation and without having to think about it.  This can be accomplished by everyone, if practice is carefully and systematically set up.  It should be done, because the rest of math is either hard or easy depending on knowing those facts.  And don’t get me started about why equivalent fractions are hard!

 

Math Teaching Strategies #2: Ensure math facts are mastered before starting computation

Posted on by Dr. Don

Rocket Math can make learning math facts easy.  But even more important it can make teaching computation easy too!  One of the first teachers to field test Rocket Math was able to teach addition facts to her first grade class, and then loop with them into second grade, where she helped them master subtraction facts as well.  She told me that because her second graders were fluent with their subtraction facts, they were ALL able to master regrouping (or borrowing) in subtraction in three days.  What had previously been a three week long painful unit was over in less than a week.  All of them had it down, because all they had to think about was the rule for when to regroup.  None of them were distracted by trying to figure out subtraction facts.

Math teaching strategy: Get single-digit math facts memorized before trying to teach computation.

When math facts aren’t memorized, computation will hard to learn, hard to do, and full of errors.

When math facts aren’t memorized, computation will be hard to learn.   I used to think computation was intrinsically hard for children to learn.  Because it was certainly hard for all of my students with learning disabilities.  But none of them had memorized the basic math facts to the point where they could answer them instantly.  They always had to count on their fingers for math.

When I learned more about the process of learning, I found out that weak tool skills, such as not knowing math facts,  interferes with learning the algorithms of math.  When the teacher is explaining the process, the student who hasn’t memorized math facts is forced to stop listening to the instruction to figure out the fact.  When the student tunes back into instruction they’ve missed some essential steps.  Every step of computation involves recalling a math fact, and if every time the learner has to turn his/her attention to deriving the math fact they are constantly distracted.  That interferes with the learning process.

When math facts aren’t memorized, computation will be hard to do.   Having to stop in the middle of the process of a multi-digit computation problem to “figure out” a fact slows students down and distracts them from the process.  It is easy to lose your place, or forget a step when you are distracted by the difficulty of deriving a math fact or counting on your fingers.  It is hard to keep track of what you’re doing when you are constantly being distracted by those pesky math facts.  And of course, having to figure out facts slows everything down.

I once stood behind a student in a math class who was doing multiplication computation and when he hesitated I simply gave him the answer to the math fact (as if he actually knew them).  He loved it and he was done with the small set of problems in less than half the time of anyone else in his class.  Children hate going slow and slogging through computation. Conversely, when they know their facts to the level of automaticity (where the answers pop unbidden into their minds) they can go fast and they love it.  That’s why “Because going fast is more fun!” is the Rocket Math tag line.

When math facts aren’t memorized, computation will be full of errors.  When I learned more about basic learning, I found out that the frequent student errors in computation were not simply “careless errors.”  I thought they were because when I pointed out simple things like, “Look you carried the 3 in 63 instead of the 6.” my students would always go “Oh, yeah.” and immediately correct the error.  If I asked them they knew that they were supposed to carry the number in the tens column, but they didn’t.

I thought it was carelessness until I learned that such errors were the result of being distracted.  Not by the pretty girl next to you, but by having to figure out what 7 times 9 was in the first place.  After going through the long thinking process of figuring out it was 63 they were so distracted that they carried the wrong digit.  Not carelessness but distraction.  Once students instantly know math facts without having to think about it, they can pay full attention to the process.  They make far fewer errors.

In short, don’t be cruel.  If you have any autonomy available to you, first help your students memorize math facts and then teach them how to do computation in that operation.  In other words, teach subtraction facts before subtraction computation.  If you help them get to the point where math fact answers in the operation come to them without effort, you’ll be amazed at how much easier it is to teach computation, for them to do it and at the accuracy with which they work.