learning

Is Rocket Math frustrating your students?

Posted on by Dr. Don

If students (and parents) are really frustrated, Rocket Math is not being done the right way.

How should Rocket Math be done?

  • * Students should be practicing orally two or three minutes each day in school .
  • * Students should be practicing again at home for another two or three minutes.
  • * SOME students who need it, should be getting a second practice session during the day at school.
  • * When practicing the students should be saying the facts aloud and the answers.
  • * Students should be practicing with a partner who has an answer key.
  • * Partners should do the correction procedure if the student hesitates on any of the facts they are practicing.
  • * This practice should occur every day–not just once or twice a week.

With good practice several days running any child can learn those two new facts to automaticity and should be able to write the answers to those facts without hesitation–as fast as he or she can read the facts and write the answers. This is the point of Rocket Math and it works when done properly. How could this go wrong? Here are some things to look for that are WRONG!

  • * Testing only without the daily oral practice. Teachers sometimes prefer just giving tests and think this will accomplish the same thing, but it doesn’t. The learning occurs during the practice sessions with the partner. Without orally practicing students are not all going to progress as well as they should, and some will become very frustrated.
  • * Students who have bad habits that interfere with their ability to write quickly, such as erasing answers, counting on their fingers, looking at the clock, skipping around or writing answers in complicated patterns.
  • * Setting goals faster than students can actually write. (How this happens I haven’t a clue, but it does.) Students know the facts without hesitation but can’t write as fast as their goals demand. If they have practiced well for a few days and they can orally answer the facts without hesitation–giving 40 or more answers orally in one minute–reset their goals to what they have been doing and let them move on. Students don’t have to pass every day, but they should pass within six days.

Remember, the point is for students to practice the two new math facts on the sheet and add them to the ones they already know. As long as students can answer facts without hesitation (after reading the fact aloud they have the answer already in mind) then they know their facts well enough. This should not be driving anyone crazy and if we do it right it is fun and enjoyable–even though it is work.

Why should it take months to learn addition facts?

Posted on by Dr. Don

Because you need to remember these facts your whole life!

Learning all the addition facts well should take a while. What’s more, it is important to spread this learning task out over weeks and months. Why? Because the longer you spend learning something the better you learn it and the longer you remember it. Conversely, when you cram learning into a short period of time you will likely forget it soon. Remember, cramming for exams in high school or college? Remember, what you learned? Probably not.

Rocket Math is designed to motivate students to work through a long task of learning nearly 100 facts in addition. It is broken down in bite-sized pieces for a couple of reasons. One, so each piece is not too much to memorize (nobody can memorize ten similar things at once). Two, so students can experience success along the way. Little successes keep them motivated for the long haul, which is a key point.

Rocket Math is purposely demanding. We want student to learn the facts to the point of instant recall, without any hesitation. So we expect them to be able to write the answers to the facts as fast as their little fingers can carry them–without any having to stop and think about on the way. That is called the level of automaticity. One way to do this would be to simply require all students to practice for a week on each set. That wouldn’t be terrible, but it wouldn’t be motivating and it wouldn’t take into account learning differences–it wouldn’t differentiate properly. Some students can learn facts to that level in 3 or 4 practice sessions while others may take 10 or more practice sessions to get to the level of automaticity.

Practice must be focused on learning. It is very important that practice has to be focused on learning, rather than just “going through the motions.” It is critical that students realize they can move on as soon as they learn these facts, and not until then. If everyone moved on every week regardless of learning differences, it would be too soon (moving on too fast) for some students and too slow for others.

Students need to meet the rigorous tests of Rocket Math and it is optimal that they spend several days on each set. With 26 sets to master and 90 days in a semester, we should not expect students to master an operation in less than a semester. It is also acceptable for a student to take up to a school year to learn all the addition facts. If schools routinely taught addition in first grade, subtraction in second, multiplication in third and division in fourth grade, their students would find math computation a breeze. Even better, they would remember those facts, that took them a school year to learn, for life. Isn’t that really the point?

Is a goal over 40 fair or necessary?

Posted on by Dr. Don

A parent asks:
Our daughter has a goal of 50 problems in a minute. She is finding that hard as more of the answers in multiplication have two digit answers. Is this normal, and if so, should her target be lowered as a result? I don’t want to challenge her below her abilities, but is she actually learning less if she is only required to answer 40 to pass instead of 50?

Dr. Don answers:
You are right that a student who can answer 40 problems in a minute knows their facts well enough. Initially we did not have any goals over 40, but we discovered that a lot of older students (4th grade and up) can write a lot faster and are capable of having higher goals than 40 and can achieve higher goals with 3 or 4 days of practice.

There is a caveat on goals over 40, that is in the FAQs/Teacher directions in Part K. Here it is:
Please note: There is a special exception for students who are such fast writers that they have goals OVER 40 in a minute. On the bottom of the Goal Sheet, please notice the exception for fast writers. Students who have goals over 40 should try to meet those goals, but only for up to six days. As long as they are answering over 40 problems per minute without errors, they should be passed after six days. It is nice for those who can write faster to have higher goals, but we don’t want it to slow them down too much.

I have had people suggest to me that because of more two digit answers later in the sequence in Multiplication it slows students down and therefore goals should be lowered.  I would say, there is a case for keeping goals the same rather than raising them.  Here’s what the data show in terms the number of two-digit answers out of the 63 answers on a test:
Set B zero, Set D 23, Set G 37, Set K 43, Set N 46, Set Q 49, Set T 50
So there is a bit of a case to be made for the extra digits, especially if goals are raised really high during Set A or B.  The writing speed test is 50% two digit answers, but by Set G in Multiplication the test is a higher percentage of two digit answers than that.  So keeping the goals the “same” in Multiplication in terms of problems still means the challenge is increasing in terms of digits.  Watch out for any students who cannot pass within six tries/days with good practice.

The next caveat is that being able to answer orally 40 problems in a minute (just saying the answers) is fast enough to indicate no hesitations. So either orally or in writing to do 40 problems in a minute indicates a student is at mastery. In either case we would want the student to take six tries to meet a higher than 40 goal if they can. As I said in another post, we want them to practice 3 or 4 days on a set before passing, so we don’t need to pass them along before that.

The question is whether she can weather three or four days of practice without feeling like a failure. She shouldn’t, but compared to the passing every day she was doing before, it might seem like it.  Building up her stamina and getting her to take 3 or 4 days of practice on each set is optimal.

Why raise student goals for passing?

Posted on by Dr. Don

A parent asks:
Why does the teacher keep raising our daughter’s goal every time she does better on a test? She now has a higher goal than any other child in her class, and she can’t pass in one or two days like she used to. She is getting discouraged. Is this fair? Is this what you recommend?

Dr. Don answers:
Yes, this is what I recommend. I explain the recommendation on the Rocket Math FAQs page, item K, “What do I do about fast writers, slow writers, and do goals ever change?”

Your daughter’s teacher is following the directions which do say to raise student’s goals when they demonstrate the ability to write faster.  Two things tell me it is a good idea for the teacher to raise your daughter’s goal.
1) Before her goals was raised, your daughter was passing much faster than we would like.  Remember, the goal of Rocket Math is that students should know these facts by heart for the rest of their lives, so extra practice is a good deal.  Students who learn an operation in one semester (about 90 school days) are learning as fast as is necessary–and that is practicing for 3 to 4 days on each set of facts before passing. Tell your daughter that you don’t want her to pass until she has practiced for at least three days.  Help her to be patient and be willing to practice a bit longer.
2) Your daughter has demonstrated she can write faster than we initially thought.  We begin by setting individualized goals based on the writing speed test.  When students demonstrate the ability to write faster, we raise their goals.   The goal is to for students to practice until they know the facts instantly, without any hesitation.
If a student can write faster, but has lower goals, that student can be hesitant on some facts, and still pass.  This is not good, because they won’t get as much practice on those facts as they should have.  Eventually after passing several levels even though the new facts were not fully mastered, the student hits the wall.  They are too slow on a bunch of facts, and there are too many now to be learned.  (We can’t learn ten or more similar things at the same time.)  This is when students get stuck and can no longer move ahead.  This is not good.  To prevent this we need students to answer all the facts as fast as they can write.  That means if the student demonstrates the ability to write faster than we initially thought, the student should be expected to answer facts at a faster rate than we initially expected.  This varies by student, as some students can write much faster than others.
To ensure that students are answering fact questions as fast as their fingers can carry them, we encourage teachers to raise the goals closer to what students have actually done.  As long as students can still pass in fewer than six days, that is acceptable and better for them than passing every day.  Students who pass every day aren’t getting as much practice as we’d like.
Once students have goals over 40 however, the rules change.  More on that in another post.

Motivating by creating success

Posted on by Dr. Don

Cool rewards, such a getting to make a human Rocket ship on the playground (above), work best if students expect to succeed.

There is sometimes a chicken-and-egg problem with rewards for success. If students are not being successful, just offering new rewards won’t necessarily motivate them. Especially if they have come to the point where they don’t expect to succeed. Then a two-pronged approach to motivation is needed.

A very smart instructional coach and principal I know, recently decided that Rocket Math was not progressing the way it should in their school. Students weren’t passing frequently enough, weren’t excited, and weren’t getting motivated. These two instructional leaders realized that their teachers needed help to effectively motivate their students AND they knew the students needed to experience more success to get motivated. So rather than just offer rewards, they set up special practice sessions so students could get “two-a-day” practices for a week.

The principal and instructional coach made a special challenge week (all 1st-5th grades in this school do Rocket Math). During this week each class had a second ten-minute time during the day for Rocket Math. Immediately after their first practice session of the day, the instructional coach and principal checked the folders of any students who thought they passed, so that if they did, they would re-fill their folders with the next set, allowing them to move on immediately during the second session. Students who didn’t pass knew they had a second chance that same day. At Rocket Math we know that two practice sessions in one day is very powerful and leads to faster learning! The instructional coach and principal also held some extra enthusiastic “Rocket to the Office” practice sessions for selected students who needed the extra boost.

Prizes were announced at the start of the challenge week. The student in each class who passed the most levels during the week would get a $10 Barnes and Noble gift card. The teacher whose class passed the most levels in the week won lunch on the principal. And the class that won (by passing the most levels) got a special secret prize, which you can see above. The picture was posted in the school newsletter, on the school website, and the school’s closed Facebook page.

The brilliant thing about the challenge week was that the excitement of the prizes were reinforced by the extra practice sessions, boosting success at the same time as providing extra motivation. That is effective instructional leadership, par excellence.

Do CCSS expect math facts memorizing?

Posted on by Dr. Don

Yes!  Without question, CCSS expects students to know math facts “from memory.”  Students should not be counting on their fingers nor having to stop and think about basic math facts.

CCSS.Math.Content.2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
CCSS.Math.Content.3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Worksheets alone will not get students to that place–it requires oral rehearsal of math facts until there are no hesitations.  That happens best with the kind of peer practice that Rocket Math is designed to provide.
Click here to see my basic math fact recommended benchmarks to use with Rocket Math to implement the Common Core.

What’s wrong with this picture?

Posted on by Dr. Don

If you are seeing this in your school, you need Rocket Math!

Recently I gave my pre-service student teachers at Portland State University an assignment to do screening tests of basic skills in their placements. I was shocked to see how few of the screening tests showed students who were fluent with basic, single-digit math facts, where they could answer math facts as quickly as they could write. When children cannot answer math facts quickly and easily they are placed at a unnecessary disadvantage when it comes to doing math.

It is true that learning math facts takes time. No one can learn all of them in a matter of a few days or a week. It takes most students daily practice for months to learn all the facts in an operation. But when you consider that we require students to attend school five hours a day for years and years, it is pretty shocking to realize how many children do not have fluent mastery of math facts when they get to middle school. When the job can be done in ten minutes a day, and every child could become fluent in all four operations of addition, subtraction, multiplication and division by the end of fourth grade, why isn’t it?

Sometimes, teachers have been taught in their schools of education that helping children memorize things is somehow harmful. With that belief, teachers won’t try to do something systematic like Rocket Math. But after a year or two teaching, especially upper elementary grades, and struggling to teach higher math concepts to children who are interrupted by finger counting in the middle of every single computation, teachers learn that belief is simply wrong. Children are helped immensely by memorizing basic math facts. It enables them to have “number sense,” to easily appreciate the relationships among numerals, and to easily do computation.

Probably the main reason more students are not taught math facts, to the level they need, is that teachers are not aware of a tool that can help them do that. They don’t know that students enjoy doing learning math facts when it is done right. They don’t know that it can be done as a simple routine that takes ten minutes a day. They don’t know how easily students can master all of the facts. In short, they don’t know that Rocket Math exists. Someday a friend of theirs will tell them, because that is how Rocket Math spreads–by word-of-mouth.

If you read this, and you have never seen Rocket Math in action, you may be skeptical. Tell you what, write to me and if you need to see it in action to believe me, and don’t have a friend using Rocket Math, I’ll send you a free subscription to try it out.

What does CCSS mean by “know from memory?”

Posted on by Dr. Don

Knowing from memory means not having to think about it.

Two of the best standards from the Common Core State Standards are on our home page:

By end of Grade 2, know from memory all sums of two one-digit numbers and

By the end of Grade 3, know from memory all products of two one-digit numbers.

These standards name the most important elementary math skills of all, because they are the foundation of all further work in mathematics.  But what does it mean to say students know math facts “from memory?”  It means that students don’t have to stop to figure it out.  Say for example a student is adding nine plus seven. A student can figure that out by thinking that because 9 is one more than 8 and 7 is one less than 8, the answer to 9+7 would be the same as 8+8, which is 16.  This is a smart strategy for figuring out the answer, but knowing it from memory means the student simply remembers the answer is 16.

So if second grade students know from memory the sums of all single digit numbers, they can answer any of those problems without hesitation, without having to stop and think about them.  That takes practice, to build up the neural connections, so that students remember the answers instantly without some intervening thought process.  That’s what Rocket Math is specifically designed to do.  Practicing figuring out the answer to facts is NOT the same thing as recalling them from memory.  So any practice procedure that allows students a long time to answer facts, allows hesitations, will not be very helpful in achieving that status of “knowing from memory.”

The peer practice procedures in Rocket Math require the “checker” to follow a “correction procedure” whenever there is a hesitation.  If the student has to stop even for a second to “think about it” they need more practice on that fact to commit it fully to memory.  The “correction procedure” provides that extra needed practice.  Having students complete worksheets on their own will NEVER eliminate that “stopping to figure it out.”  That is why the oral peer practice in Rocket Math is essential.  And that is why Rocket Math really will help students come to “know from memory” all sums of two one-digit numbers.

How do students correct in Skip Counting?

Posted on by Dr. Don

Principal Luebke writes:
Dr. Don,
We have some fast Rocket Math students at our school. We want them to keep working and improving all the time. I want some students to start the skip counting function. What is the correction procedure while practicing? Do the checkers say the next number is ___, start over? Thank you,

Dr. Don answers:
Great question! There should have been some special directions in the Skip Counting Drawer for teachers. I fixed that this morning. Here’s what I posted there.

How Students Should Practice SKIP COUNTING

Students should practice by saying the skip counting series in order from memory. They learn the harder series in parts, so they only have to say the part they are learning at that point. For example, in Set G students are to learn the first four numbers of the count by 9s which are 9, 18, 27, 36. When practicing in Set G, the checker says: “Count by 9s to 36.” [That’s exactly what it says on the little cloud at the base of the rocket, making it easy for the checker!] The student then says, “Nine, eighteen, twenty-seven, thirty-six.” Of course, in Set H the student says the 9s to 63, and then in Set I all the way to 81.
Saying series in the same order every time is very important as it creates the verbal chain. Eventually, after many repetitions, an amazing thing happens. Whenever the student starts to say the first part of the skip counting series the rest of the series will pop into mind unbidden. (I try to use the word “unbidden” at least once in everything I write – just because I can.) This automatic coming-to-mind is called “automaticity” and is the goal of practice.

The student should say the series in order without any hesitation. I really mean NO hesitation! Now I will say that a few different ways to prove that I am really serious. I want students to practice these series until they are as automatic as saying their name. If even a slight pause is needed to think of the answer, I want them to practice until it comes to mind without any effort at all. This will enable them (after these series are learned) to easily learn multiplication facts and go on to concentrate on the higher functions of math.

CORRECTION: Each time an error or hesitation is made, the helper/checker should follow the following correction procedure. It is really important to do this correction procedure. The correction procedure is part of that “secret important stuff” that makes Rocket Math work.
1. Helper states the whole series up to that number, for example: “Nine, eighteen, twenty-seven, thirty six.” (If the student has said the right answer but hesitated somewhere in the middle, the helper can confirm it by saying, “Yes, that was right, but you hesitated, so let’s practice that some more. Nine, eighteen, twenty-seven, thirty-six.”
2. After the helper says the series once, the helper and the student should say the series together twice. “Say it with me: Nine, eighteen, twenty-seven, thirty-six. And again, nine, eighteen, twenty-seven, thirty-six.” Then have the student repeat the skip counting series three times.
3. Go back and do the previous series [just one, not three!], which is enough so this series comes up again before the student forgets it. (Rinse and repeat as necessary.)

Note that this same correction procedure is to be used each time there is an error or hesitation. If the student hesitates again after they went back one series and started again, just repeat the correction procedure. Say it together twice, then three times without help, go back one series and start again. Repeat this practice until there is no hesitation. Extra practice on a series, to lock it into memory, is important work and should not be considered a bad sign. THAT is what we are doing here—LEARNING!!

Must students say math facts in a certain order?

Posted on by Dr. Don

It is actually more important than you might think, that students practice by reading facts in a consistent way.

Rachel asks:
Hi Don,
After using Rocket Math for a week, I have a question. My daughter often reverses the order of the numbers when reading off the facts (i.e. 1+5 when it’s really 5+1). Of course, this doesn’t affect the answer in addition, but I wondered if I should correct her? She sometimes does it upwards of 50% of the time. Anyway, I just wondered if I should be concerned about her reversing the numbers, and if so what I should do about it.   Thanks, Rachel

Dr. Don answers:

If I were still running a school I would be offering you a teaching job right now! What a good question! So your daughter is doing something that most people do, which is trying to simplify the task and ignore the difference in the order. Because 5+2 and 2+5 are both 7 why not just think of them as the same thing?***

However, there is a risk. If a student always says “five plus two is seven” and never says it the other way around they will not have the jingle-like memory of “Two plus five is…seven” in their brain. Then when they encounter 2 + 5 and read it aloud to themselves the answer won’t pop into mind automatically. They would probably puzzle a second, realize it is the same as 5+2 and then know the answer is seven, but it won’t be automatic. [That by the way is what I’m trying to illustrate in the picture above, which isn’t Rachel’s daughter!] We want that automatic answer to pop into mind, unbidden, without having to think about it. In other words, we want it so that when your daughter says to herself, “Two plus five is…” the answer “seven” pops into her mind without having to think about it.

Whew, this is a lot of rationale, but I know you can follow me. This means that you want to treat reading the problem in the wrong order as an error. When she reads the problem in the wrong order (says “Two plus five is seven” when the problem reads 5+2) correct by saying the problem in the correct order with the answer. You say, “Five plus two is seven.” This, by the way is why our correction procedure is for the checker to say the whole problem and the answer, so the checker can correct the order of reading the problem without causing confusion. Then have her repeat it three times and go back three problems.

She of course, will tell you, “But, it’s the same!” Just reply with, “You have to say it the way it is written.” You can tell her I said so!

PS. When you get to multiplication, this gets even more tricky, because there’s a good case to be made for reading multiplication fact problems up, because that’s how we say them when we are doing multi-digit multiplication problems. But that is a whole other blog!

***Interestingly, when doing the Rocket Math app, the learner/player is presented with both facts in the same set–mixed between the two as they are being learning. When I am playing the app, I find I can’t remember if I got both of those to answer or just one. Although the app gives both, I just put them together in my mind to make it easier, and don’t even notice the order.