Why and how does verbal rehearsal help students?

When practicing Rocket Math, we ask students to say the whole problem and the answer for each problem while the checker listens. Two beneficial things are happening when students do that. (1) They are retrieving the answer from memory. As they go out and find that answer in their mind they are strengthening the neural connections between the problem and the answer. The more times you think about something the easier it is to remember. So that’s the first benefit. (2) The second benefit is the rehearsal of the verbal chain. A verbal chain is a set of words you often say together. In my workshops I always show how this works by saying the final words of the pledge of allegiance, “and justice for …” and leaving off the word “all.” The participants always help me out. Everyone can complete that final word of the pledge because those words “and justice for all” are a verbal chain. You cannot say “and justice for…” without thinking of the next word “all.” Back to verbal rehearsal of the verbal chain for a math fact. When the student says “Nine times seven is sixty-three” enough times, when the student rehearses it aloud it becomes a memorized verbal chain. Then in the future when the student says to himself or herself, “Nine time seven is…” the answer “sixty-three” pops into mind automatically. That popping into mind is the essence of automaticity and it is the goal of all that practice in Rocket Math. [You didn’t really think the goal was to get to Level Z, did you?] What we want is that when student are doing calculations later in school and life they only have to mutter the problem to themselves and the answer pops into their minds. Now they can do calculations and focus on the procedure and the problem rather than trying to recall the answer. That’s how all that verbal rehearsal pays off. And now you know!

Correct speed and manner of practice

Question: We are using Rocket Math in 3rd grade and it is taking much longer than it should for the kids to master a given set of facts. I observed in the room, and the thing I noticed is that the kids are moving through the paired practice section trying to do the problems as fast as they can and are not getting the solid practice they need. Ms. Apple says that she has modeled over and over the correct speed and manner in which to do the practice and the roles of each kid in the practice session. She also commented that the kids will get into an argument about if one of them paused or if they said it correctly or some other procedural issue. Any suggestions beyond more modeling that might help bring this part in line so that the kids get the practice they need?

Answer: Good questions. A few ideas here.

1) Be sure that the paired practice is long enough—e.g., at least 2 minutes and possibly 3 minutes. More practice is better and as they get tired, they will slow down a bit.

2) There is nothing wrong with going fast (everyone can listen faster than anyone can talk), as long as the checker is stopping to correct errors and practice hesitations. The teacher should be sure to model for the students, where she makes a hesitation, and the checker has to stop her to give her the correction procedure. Then as students are practicing, she should circulate, listening for correction of hesitations, and praise that highly, as the BEST thing you can do for your partner—give them extra practice on a fact that were slow in answering.

3) Set up the rule: The checker is always right. Any argument she should respond in the same way. “No arguing. The checker is always right!” This is fair because everyone gets to be the checker. No other policy is workable because there is no way to know and no time to investigate. Just always say, “The checker is always right.”

4) If checkers are having trouble keeping up, make sure that they always “track with their finger.” She will need to make sure that is part of the modeling, and that she praises that behavior when she circulates. “I see some smart checkers who are tracking with their finger!” I’m thinking these should help.

5) Make sure they are taking the un-passed sheets home and practicing there. Give rewards or post on a chart who is taking their sheet home and practicing (the same way) and bringing it back signed by the person who practiced with them. At home practice can make a huge difference, and siblings can do it as well as parents. And three to five days is an OK length of time to pass a set.

6) As a last resort, especially if students are spitting out the problems too fast for the checkers to even hear and everyone is doing it, the teacher needs to stop Rocket Math for a few days. The teacher will have to go back to modeling how to practice, [where she is the student and she picks a student to be the checker] and where the students have to show how the checker should make corrections, as was done in the beginning of the year. But now, with every student who is being her checker she should say the problems too fast to understand, and then teach the checker to say, “I’m sorry I can’t understand you. Go back and speak clearly so I can hear what you are saying.”

Hope this helps.

What’s so special about Rocket Math Flashcards?

Question: Okay, I have a question about the Rocket Math flashcards. I’m a retired teacher, doing some tutoring on the side now. I have TouchMath flashcards and Really Good Stuff flashcards. What is the difference from Rocket Math flashcards, other than your directions for use? Can the cards I have be used? I read somewhere on here that your goal is to help teachers and kids, not to just make money! LOL. Thanks!
Nancy

Answer: Good question. What’s So Special About Rocket Math Flashcards?

Remember: The best condition for learning is having a few things to learn in a sea of mastered material!

  • Rocket Math flashcards are coded in sequence so that it is easy to have only 12 cards in the “working deck” at a time, and the right 12 cards at all times.
  • Only 3 of the “working deck” are new or “hard.”
  • When beginning addition and subtraction Rocket Math flashcards provide nine “name the numeral” cards so that students still have only three new facts to learn out of the first 12 cards in the working deck.
  • Students are taught to practice by saying the problem and the correct answer without any hesitation.
  • A “practice partner” follows a specified correction procedure any time there is an error or hesitation.
  • Rocket Math flashcards allow for a few short practice sessions (3-4 minutes) each day.
  • New cards are added to the “working deck” only after a “cold” run-through is 100% correct.
  • The “coded” cards indicate which cards are to be removed to make room for the new cards.
  • Mastered (removed) cards become the “review deck.”
  • “Coding” allows users to follow the Rocket Math sequence–which is very smart and helps students learn the facts more easily.

Some of these points are, in fact part of the directions and could be used with other flashcards sets. However, to do this with other flashcard sets would require one to add some known facts to the set for starting out, and for one to number the cards in the right sequence. Thanks for asking!

When to begin Rocket Math?

Question: I am the K-1 instructional coach for our district and I am looking for the contact information for a 1st grade teacher who has done Rocket Math in first grade. We have a building who will be piloting the program in first grade and would like some advice on what time of year is best to begin the program!

Answer: We don’t keep customer contact information to give out–our privacy policy does not allow that. [However, we are about to create a Rocket Math Ambassadors web page for teachers who volunteer to be available to take questions from other teachers about Rocket Math. We’ll announce it in Dr. Don’s Hints and Tips.]

Answer to your second question: You want to know when in first grade to begin the program. The answer to your question is that students can begin math facts in First grade as soon as they understand the concept of addition. This is the kind of information discussed in our Teacher Directions and in our Rocket Math FAQs here in letter “E.”

When are students ready to begin fact memorization in an operation?

When they “understand the concept” of the operation. “And how does one know that?” you might be asking. Well, we’re going to tell you. Drumroll, please. Children “understand” an operation when they are able to compute or figure out any fact in the operation. They can use their fingers to figure out the addition and subtraction facts. Or they can use successive addition to figure out the multiplication facts. Or they can use manipulatives and get the right answer. Or they can draw lines, or horses, or dots, or cookies  (We’ve seen it all.) and get the answer. Somehow, some way, given any fact in the operation, and unlimited time, the child can figure out the answer. Then the child is ready to begin memorizing.

This might be at the start of the school year, or might not be true until November–depending on your district’s scope and sequence. Hope this answers your question.

Monitor, monitor, monitor

As Dr. Anita Archer says, aside from teaching, the most important thing a teacher does is monitor students as they are working. This is doubly true during Rocket Math. Far from being a time to sit down while the students are happily engaged in “doing Rocket Math,” this is a time when it is imperative that the teacher must be up moving around and listening to the quality of the practice. Walking around the room to see that everyone appears to be on task is the minimum, but really stopping to listen to the students is the gold standard in monitoring. (Me, I have to squat down or bend over to be able to hear clearly.)

During Rocket Math the teacher should be tuning in and listening to pairs of students as they practice to be sure of several things. (1) Is the student saying the entire problem and the answer each time? (2) Is the student audible to the checker? (3) Is the checker tracking with his/her finger so you can tell if they are following along? (4) Is the checker correcting hesitations, as well as errors? [Give public praise, perhaps after the practice session to every checker you heard correct a hesitation–that’s a really big deal!] (5) Does the checker follow the three step correction?

The teacher cannot know whether or not practice is being done correctly without careful monitoring and listening to the pair of students as they practice. Praise the pair if they are doing it right. Then move on to another pair and monitor them. Keep moving to as many pairs of students as you can during the two to three minutes of oral practice.

By the way, look out for students who go once around and stop! This is supposed to be an endless task. That is why the problems now go in a circle around the outside so the students know to go on to a second lap if they can. The best teachers institute a signal (fist in the air for example) that shows which students have made it to the second lap during the practice time. That should be a badge of honor. It often means that the student has no hesitations on any of the newer facts and will be likely to pass that day. But hard work and diligent working–enough to get to a second lap should be rewarded in any case.

If the teacher finds that students are NOT practicing and correcting as they should it is time to go back to the beginning and model for students how they should practice and correct. More on that in another blog. For now, just be sure to monitor, monitor, monitor during Rocket Math.

Trying to teach reading by the light of a shared candle

How can a teacher run a math fact fluency program with access to only a couple of computers?

Asa asks:
Don, My school doesn’t currently have a fluency program in place and I’d really like to implement one as I think it’s a real need for my kids. I have 65 5th grade students. I don’t have access to technology on a 1 to 1 basis in my classroom. I have a couple of computers and a few ipads. Where would be good place for me to start?

Dr. Don answers:
Hi Asa,  What you describe is like trying to teach reading by the light of a shared candle! Until you have computers (or iPads) for everyone, using computer based programs to provide facts practice won’t work! A paper-and-pencil program is really much more realistic.
The paper-and-pencil version of Rocket Math works really well. Because students work with each other in partner practice they enjoy it. The daily one-minute timings are a good challenge, and the fact that they only have to learn two facts on each set means within a few days they can pass a set. Filling in the Rocket Chart from the bottom up gives them a sense of accomplishment and they learn an important life lesson–that studying and practicing can help you learn!
For one teacher the cost of a Basic annual subscription is $29, so it’s not too expensive to start.

Listen to the Rocket Math in a Nutshell presentation on our home page www.rocketmath.com for a good quick idea of how this runs. Next print out and read the Teacher Directions from our Free Resources page here. Then when you have a clear idea what you’ve got to do, go ahead and get the Basic Subscription. You’ll be glad you did.

Oh, in case you don’t see this word of advice, with fifth graders start everyone on multiplication (even if they are counting on their fingers.) Fifth graders who aren’t fluent with the basic facts are a case for triage!!  If they never memorize another operation other than multiplication they might be able to make it through fractions and other pre-algebra topics if they know multiplication facts–so that is the place to start.

How to get parents to help you

Dear-ParentsOne-Page

If students practice math facts a couple of times a day throughout the year, they will never forget them! Parents will help you if you give them the tools, which you can easily do with Rocket Math. Start with a letter to parents telling them what you are doing. We have included a two page parent letter from Dr. Don on our subscription website. If you would like to personalize a letter we also have a one-page letter in Word that you can edit and make your own here.  We also have one in Spanish here.

The letter is a good start for parents to know how to practice. You can also use back-to-school night as a time for a couple of students to demonstrate how to practice, so parents are shown how to do the practice at home.

Now that parents know what to do, be sure that all your students are taking home their used practice and test page from Rocket Math each day. Students should complete the test and then get a parent or someone else in their family to help them practice around the outside. Then they could also practice the test, as long as they aren’t looking at the answers. This extra practice session at night will make a big difference in how fast students pass a level. You might even let the students in on the secret. (One teacher I know announced publicly to the class that they weren’t supposed to practice at night because it would give them an unfair advantage, but then individually told each student she’d make an exception, in their case. Soon the whole class was practicing each night diligently!)

Use the “Thank You to my Helper” achievement awards so that students can take them home and thank their helper when they pass a level. Ask students who is practicing at home, and then you could call home to thank those parents for their help. You will be amazed how these things will increase the amount of help you get from home and thereby improve the success of Rocket Math in your classroom.

Trying to use the app to support the paper-and-pencil Rocket Math

Customers would like to be able to use the app to help their child pass a certain level in the Rocket Math paper-and-pencil program at school. They are thinking that if their child is on Set L in the paper-and-pencil version at school, they should be able to set up their child to practice Set L in the app, which will help them pass the same level at school.

Actually the program does not work that way. Instead the Rocket Math app has everyone progress through the levels in order, starting at A and only gradually working their way up to Level L. Why isn’t it possible to just focus on Set L in the app? We could have set the app up that way. Why didn’t we? Answer: Because it wouldn’t help!

The test in the paper-and-pencil version of Set L is MOSTLY about problems from sets A through K. The test on Set L is a random mixture of all the problems learned in sets A through K. See the picture? The new facts in Set L (7×9 and 9×7) only appear five times in the test of 56 facts. But, those facts do show up 16 times in the practice on Set L (around the outside). That practice is how the new facts are learned.

Students can bring home the worksheet from Set L. Each day they don’t pass they should bring the used worksheet home for homework. They should practice with the most recently introduced facts around the outside of the test. They can even practice reading and answering all the facts on the test if they like. Orally practicing the facts in the test on Set L is probably the best way to focus practice for passing the paper-and-pencil test.

The Rocket Math app randomly selects problems from the set of facts that should be known because they have already been learned. Practice within the app will never be the same two times in a row, but it will be sampling of the right problems. Practicing on the app teaching the facts and adds to student’s knowledge. It is good for them, but it can’t guarantee they will pass the paper-and-pencil test the next day.

Students should NOT be expected to “pass” a set of facts in the paper-and-pencil Rocket Math the first day or two of practice. It is better if they don’t. They should spend three or four days practicing before they get fast enough to pass. Spending time practicing is the best way to cement in their learning. The goal is that students can remember those facts for life. If they practice on the app and practice at school, the end result will be that they know the facts better for the rest of their lives. The more time students spend practicing math facts, the better off they will be. That is FAR more important than getting through Rocket Math quickly.

That being said, after going once through the levels A through Z of the Rocket Math app (or the paper-and-pencil version), there is nothing wrong with going through it again if they have the time and the willingness.

Add a bonus session for students who don’t pass quickly

In most schools there are a few children who are not making good progress with Rocket Math. They don’t pass as quickly at each level. Assuming that students are practicing the way they should with a partner (teachers should monitor this closely), and their writing goals are reasonable (sometimes they become unsustainable), you may be looking at students who need more than the usual amount of practice. Some students do need two or three times more practice than their peers. Sadly, these are often the students who do not practice at home either. So the question is how to get them the extra practice they need to keep up with the class. Luckily, Rocket Math lends itself to arranging extra practice.

A school’s first option should be a cross-graded Rocket Math “Bonus” session some time during the school day. Students can work at all grade levels and in all operations in this group. Students should all come with their folder containing all they need. Students should be assigned to the Rocket Math “Bonus” session after not passing a level within four or five practice days.

A teaching assistant or para-professional might be able to run this session, depending on their classroom management skills. It would be better to have the Title I or Special Education teacher run these sessions. This kind of remedial work will really help students.

Students would bring their Rocket Math folders from class to the “bonus” session—because their folder should include their answer key and everything they need to practice. Students do not need to be in the same grade or on the same operation to be partners because the answer keys needed are right there in the folder.

In the bonus session, students would practice with a partner for two or three minutes the same way they do in class. Then the two would switch roles. But then, instead of taking a written test, they could practice again orally but this time on the TEST for one minute and then switch roles. That way no paper is used up and no paperwork is required of the person running this session with students from several classes. The students should be done in less than 15 minutes. This extra practice if done properly and every day should help students to pass within a very few days.

Of course, students with IEPs in math should get a bonus session during the time they are with the special education teacher. And Title I students should get a bonus session with the Title I teacher. But the bonus session should be available based on need rather than labels or categories.

Kids who write their numbers backwards

Here is a question submitted from a Rocket Math user, who would like to know if kids who write their numbers backwards or reversed, should be corrected.

“My school is using the Rocket Math program. We are wondering if you would accept reversals on Rocket Math papers? By the way, I love your program.”

Becky, thanks for your question. Many teachers wonder whether they should accept reversals or backwards numbers, when children are writing out answers to math problems. The answer depends upon the type of reversed numbers. Bet you didn’t know there were two distinct types of reversals, did you?

The benign reversals are single digits written backwards. A backwards 7 or 2 or 4 or 6 should not alarm you greatly. Up until the school years children have learned that a thing has the same name regardless of its orientation. A chair turned upside down or turned left to right is still a chair. Upside down toys are still the same and you learn to recognize things as being the same regardless of how it is facing. Then suddenly in school some things, particular symbols, have to be facing a certain direction. Learning which way the seven has to face, is best accomplished by a patient teacher who points out which way sevens have to face. Extra practice making 7s the right way would be a good idea.

Pre-correcting for the error by writing a model at the top of the paper for students who are persistently getting it wrong can be quite effective. And of course, the quickest learning results from lots of praise for “making these sevens face the right way.” But refusing to accept a 7 as the correct answer because it is facing the wrong way is at best unnecessarily discouraging and at worst, may be confusing. Some students may think they got the wrong answer and conclude that 3 plus 4 is not seven!

On the other hand, there is another kind of reversal that must be treated as an error. The unacceptable reversal is when the digits are written in the wrong order, as when fourteen is written as a four and a one (41) and nineteen is written as 91. This kind of reversal represents a misunderstanding about place value. In addition the student has actually written the wrong number, so he/she must learn that is a different number. “No, that’s not right. You wrote twenty-one and three times four is twelve. Twelve is written like this, 1-2.” Again, it would be smart to give some practice writing numbers from dictation–especially those pesky teen numbers. Modeling on the board or overhead first, followed by practice of a small set of numbers would be most effective.

So, single digits facing the wrong way can be accepted as the right answer, even though you work on correcting the way the numeral faces. But two digit numbers must be written with the tens digit on the left ALL the time.

I can’t leave this topic without pointing out that your students may also be reversing their zeros, ones and eights–but you just can’t tell!