Dr. Don's Blog

We are not talking about this kind of skipping, but she is cute!

A customer asks:

One more question, if I may . . . (I did not see this answer in the manual or I was reading so fast I missed it!)

When doing the 1 minute or 2 minute tests, do the students have to do the problems in order? We have differing opinions on this, too! Some of us tell the students if they are stuck on one, don’t spend too much time and go on to the next. Others require that they do each problem in order as written. We are just trying to be consistent throughout all grade levels 1-4. Thanks so much for your thoughts and rationale.

Dr. Don’s answer:

A very good question. The answers are in the manual but it is sometimes hard to remember the information until you understand the rationale. So of course I am going to give it to you! The 1 minute daily test and the 2 minute timing are very different kinds of tests and so the rules are different.

The 1 minute daily test is a test of mastery–to see if the students have completely mastered all the facts up through that Set. So there should be no errors and nothing skipped. Some schools insist on left to right answering so that it is clear there was no skipping. If a student even wants to skip an item on the daily test–then clearly the student does NOT know all the facts to the level and should not pass. Hopefully clear.

On the other hand, the 2 minute timing, done once every week or two, is a progress measure (can you tell I’ve taught assessment classes?) to see if growth is occurring. So the test presents ALL the problems in the operation and asks whether the student can answer more of them in 2 minutes than he/she answered last week or the week before. We know there are items on the 2 minute timing that students don’t know to mastery. To answer the most possible in 2 minutes they should skip the ones they cannot remember and answer all the ones they know instantly. So it is not only OK to skip on the 2 minute timing, it’s a good idea.  As they make progress they will find more and more items they can answer instantly and so the number answered in 2 minutes will go up. The graph will show that progress–which is the outcome we want to see.
In short, no errors and no skipping on the daily one minute test. The 2 minute test we just count how many are correctly answered on the page and hope it goes up–and skipping is fine.

Cathy L. of Carterville, IL asks:

On page 17 of the manual it states that a student passes a set of facts by meeting or passing his personal goal without errors. In our school, 3rd grade, a student’s goal was 45 multiplication facts. The student got 54 problems but missed one — 1×2. He got that same problem correct several other times on the paper but missed one and the teacher said he had to try again. What are your thoughts on this? Thanks! We love rocket math!

Cathy, thanks for asking! And a big thank you for reading the manual!!!
Yes, we do say no errors. But, it is clear that the student knows the fact because he answered it correctly. The error is a “rate induced error” meaning he made it simply because he was going so fast. Research shows that students who “know” something can still make up to 5% rate induced errors. So there are certainly reasons to allow the student some leeway.
I’d lean toward leeway, but it might cause a problem because you are being inconsistent. [Many is the time my students made me regret a momentary lapse in consistency!] What about the next time he makes an error, or his next door peer? Students want to test the limits and so will force you to be consistent.
The good news is that there is very little chance of that happening again tomorrow, if you have the student do that set again tomorrow. In other words, he’ll get one more day of practice on that set of facts, which is certainly beneficial, and he’ll move on the next day. So all things considered, I’d ask him to try again tomorrow and see if he can’t meet his goal without any errors. It is better to 100% accurate even if that means you are a little slower. Hopefully you can see there is room for your own judgment, but there are consequences from being more lenient.

Public displays of progress (or lack of it) risk humiliating some students.

Many teachers want to increase the motivation in Rocket Math by publicly displaying students’ progress. [Few do it as beautifully as this solar system with individual rockets for each student.] But what happens to the students who cannot learn as easily as the fastest?

Getting an “A” grade motivates students to do more of that subject.

Teachers ask me how they should grade Rocket Math. The answer depends upon the point of grading. If the point is to motivate students, then take the passing tests and grade them based on accuracy.  Everyone is required to get 100% accurate in order to pass, so everyone will get an “A.”  But somehow that doesn’t usually satisfy people.  Here’s the problem.  Who is responsible for the success of students doing Rocket Math? The teacher is.  The students–not so much!

Teachers must teach students how they are to practice and how the partner is to make corrections.  The teacher is supposed to walk around and monitor to see that the students are practicing and correcting the right way. The teacher is responsible to intervene and re-train the students in the proper practice procedures if they aren’t doing it right, not give them a bad grade.  As long as students are practicing the way they should they will learn as fast as they can.  The teacher is responsible for how much time students have to practice and how frequently they get to practice.  The teacher is responsible for arranging that parents know how to practice at home and for arranging that students bring the used sheets home daily for homework.  The teacher is responsible for making sure goals are set properly.  If a student is not progressing well with one practice session a day, the teacher is responsible for seeing that the student gets an extra practice session each day. So, if the point of grading is to communicate whether students have been responsible in doing their work, how can you grade students down if they are doing what they are told but the teacher hasn’t done what’s needed to make them successful?

Still, if you feel the point of grading is to communicate student progress or lack of it, regardless of who’s responsible, you could grade students on the speed of their progress. That would be fair, as long as everyone was clear that a student who was progressing too slowly and thereby got a low grade needs additional practice time rather than a scolding. I would recommend grading based on the assumption that students should pass at least a level a week. Take the number of days the class has done Rocket Math during the grading period and divide by 5 to get the number of full weeks students have had to practice Rocket Math. Take the number of levels each student has passed during the grading period and divide that by the number of weeks they had to practice. That will give you a percentage on which you can grade, using your school’s typical grading system.

Levels passed divided by the number of weeks practiced (calculated by dividing the number of days by 5).

A class did Rocket Math 40 days during the quarter, divided by 5 gives 8 weeks. A student who passed 7 levels during that time gets 7/8 or 87%, which is a B in most places. His partner passed only 6 levels in those 40 days so he got 6/8 or 75% which might be a C.
Another class did Rocket Math every day, 45 days during the quarter, divided by 5 gives 9 weeks of practice. A student who passed 6 levels in that time would get 6/9 or 66% probably a D. Another student who passed 11 levels in those 9 weeks would get 11/9 or 122% an A.

Any student with a grade below “C” should start getting an extra practice session each day to prevent falling behind further. In a classroom where students were practicing the right way each day almost all of the students would pass at least a level a week and all would get As.

Jennifer asks:
After getting Rocket Math up and running in our 3rd grade classes, we are wondering if students’ goals ever change. For instance, I have a student who scored 42 on the writing speed test but is having difficulty achieving that on the one minute timing (scores 37-39 consistently). We have other students who are struggling with this as well. Let me know if we reset goals at some point or if you have any other suggestions. Thanks!

Dr. Don answers:
Jennifer,
Thank you for asking such a great and important question. Lowering students goals generally should not happen. Goals should NOT be lowered because of a “knowing-the-facts” problem, meaning the problems seem hard or the student hasn’t mastered the facts (learned every single one of the facts to the point of instantaneous recall). Goals might be lowered if there is a “handwriting speed” problem, meaning they really cannot write as fast as we thought.

You can’t decide which kind of problem you have on the basis of “not passing” for a handful of days. In other words, until students have practiced orally with a partner who is correcting their errors and hesitations and has taken tests for more than six days, I wouldn’t even consider it a handwriting problem. Some students will get annoyed that they have to practice for three or four days, but that’s how we teach them the value of perseverance.

In theory if a student can write fast enough to fill in 42 boxes in one minute in the Writing Speed Test, then he/she should be able to answer 42 problems in writing in one minute. I know that everything doesn’t work out according to the theory. But it is important to remember that we expect that it requires two to three minutes of daily oral practice for several days to get to the point where the student can answer every single fact on the page without hesitation. And some students (they used to be referred to me as the special education teacher) require a second or third practice session each day for several days until they get those facts learned. So some students literally take ten to fifteen oral practice sessions before they learn those facts. We want to give those students two or three practice sessions a day so they won’t take all year to learn the facts. But only after they get the number of practice sessions they personally need will they be able to write the answers as fast as they can write.

Also let me point out that if a student did not start at “A” this year, (meaning some of the facts on the test were learned last year) then the problem may be with the older facts on the test. These facts are not being practiced in the oral practice around the outside. If the student is hesitant on any of those facts, then the student will need to do oral practice on the “test” as well as on the outside for a few days. See my recent video about that.

One way to “check” to see if you have a “handwriting problem” or a “knowing-the-facts” problem is to individually test a student orally. Have the student say the answers (just the answers not the problems) to the test for one minute. If the student makes any errors, or is hesitant on some of the facts or if the student answers anything less than 40 problems orally in one minute, then the student just needs more practice and probably practice on the test as well as around the outside. In other words, you know you have a “knowing-the-facts” problem.

If the student answers all of the problems on the test without error and answers more than 40 in the one minute, then the student knows those facts well enough to be at mastery. Now you know you have a “handwriting problem” rather than a “knowing-the-facts” problem. Now you have a reason to consider lowering the goal to the best that the student was able to do after four or five practice sessions. So the student you mention, if he has practiced for six days, and when you test him is able to orally answer more than 40 problems on the test in one minute without error, then you could lower his goal to 39, since that seems to be the best that he can do.

Alison asks:
Hi Dr. Don,
Quick question for you. A student has passed out of an operation while in first grade. The next year his new teacher moves him back to addition based on his two minute timing score. Should a student ever be made to go back and redo an operation based on two minute timings or once they have passed out they should get to stay? Should the two minute timings be used that way? I just reread the teacher directions but am unclear about this. Thanks for any insight on this.

Answer
Alison,
Sorry, there are no quick questions with me! The teacher directions did not specify any criteria of performance on a 2-minute timing upon which to put a student “back” into an operation. Really, I don’t know what that criteria would be. The 2-minute timings can’t really be failed, as they are just used to measure progress. There are few absolute criteria other than “as fast as his fingers can carry him” when it comes to math fact fluency. The criteria that represents “as fast as his fingers can carry him” in first grade is no longer the case in second grade–and the student can be expected to do more. But that does not mean that the student must start over practicing addition again, because if he went through the levels of Rocket Math Addition he probably knows the addition facts pretty well.

More to the point, we want that second grader to learn subtraction during this school year, so he is ready for multiplication facts in third grade. So I would say that given that the student has worked through the levels in Rocket Math Addition based on last year’s writing speed, he would benefit MOST from working through subtraction at this point.

If a second grade student gets through subtraction before the year is out, then it would be a terrific idea to have that student go back and get faster at Addition. Students can always get faster at math facts, but we don’t want to hold them back from learning the other operations unless they really haven’t had a chance to finish learning the prior operation–based on the fact they didn’t get through all the levels.

Also, it is not a good idea to test students at the start of the school year on math facts and then make placement decisions based on that performance. Students are bound to be slow after the summer. [As noted in another post, we wouldn’t want to put them back to beginning of an operation based on slow performance at the end of the summer.] Instead, let them practice for a week or two and bring those facts back into the forefront of their minds before deciding that they have to start all over again. On that basis (a slow test performance after the summer before any chance to practice) almost every student would have to do addition over again, year after year. And as the student’s writing speed increases every year, the goals would increase and the challenge would be increased, making it a real job to get through the levels each year. The student might never get a chance to learn subtraction, multiplication, division, factors, integers and all the rest of the programs they should learn.

In today’s society with computers and calculators ready at everyone’s fingertips—is memorizing math facts really that important? To be clear, we are not talking about whether students should spend a lot of time practicing calculation. While one could make a case that a lot of practice getting fast at long division, or even accurate at long columns of addition problems, is no longer valuable, quite the opposite is true for memorization of single digit math facts. Memorizing math facts is probably even more important today than it was 50 years ago.

Using calculators and computers to do complex calculations for us is smart. That’s why a lot of time practicing how to do this by hand may no longer be necessary. Using a calculator saves time and it’s more accurate—except when we make an error in data entry or in the formula we have used to do the calculations. At that point, we must have already done a quick and unconscious mental calculation of the probable answer, so that we see the error. Catching errors in a calculator’s answer requires a ready knowledge of math facts. If you can’t catch your calculator errors then you’ll continue to make more and more of them. Furthermore, if you must use a calculator to compute single digit math facts (because you don’t know them) you will be incredibly inefficient at all math operations. So the ready availability of calculators makes the need for quick mental math facts more important than ever.

Another reason for knowing math facts fluently has to do with fractions. Understanding the manipulations of fractions that should be learned in upper elementary or middle school depends upon automatic recall of multiplication facts. Students who don’t know the multiplication facts fail to see when they should reduce facts like 8/24 or 12/16. They don’t recognize that 6/9 and 16/24 are equivalent fractions, or see why they are when it is pointed out to them. They struggle figuring out the lowest common denominator between thirds and twelfths, let alone between thirds and fifths. Many children are doomed to failure in learning fractions, decimals and percents simply because they lack a fluent knowledge of multiplication facts and the relationships built upon them. That failure makes it nearly impossible for them to succeed in algebra. And we all know that if you can’t “pass” algebra your chances of getting into a four-year college are slim to none.

Instantaneous recall of math facts is also important because it enables students to see patterns in numbers. We know that recognizing patterns is essential in math, but few teachers realize that recognizing patterns in numbers is dependent upon knowing math facts. The pattern 2, 4, 8, 16, 32, 64 is readily obvious to students who know the multiplication facts—but not at all obvious to those who don’t. The pattern of 49, 40, 32, 25, 19, 14, 10, 7, 5, 4 is obvious to students who can mentally subtract, but not to those who can’t.

So there are several reasons that knowing math facts to a level of automaticity is important to future success in higher levels of math. But is it really necessary to embark on an organized process of memorization? Won’t students just naturally become more and more fluent with the facts—once they’ve learned how to figure them out? The answer is no for many children. Because there is less emphasis on calculation in today’s math, students have less opportunity to practice using math facts on arithmetic worksheets than children did 50 years ago. Without practice to build up that immediate recall it becomes more important than ever to have in place a good method of memorizing those facts.

Question: We have purchased and are implementing your program at my school and LOVE it! Our staff wondered what tips/techniques you suggest for implementing the program to students with special needs?

Answer: Rocket Math was designed to be effective as it is with special needs students–but only if it is done according to the directions. I have used it successfully in special education classrooms. All the details of how it should be used are especially critical for special needs students. Some of the aspects are especially important.

One key with special needs students is to monitor their writing speed carefully. One should be sure to give the writing speed test and make sure that they follow the time limits. It’s not unusual for special needs students to try to squeeze in a few more responses on timings after time is up, because they are used to not being able to perform as expected. Of course, if a special needs student does that on the Writing Speed Test their goals would end up being impossible to meet. So be careful there. This may involve consultation between the special education and general education teachers so that goals don’t get too high causing lack of success.

Writing speed is an issue for many special needs students, and they often have great variation in how well they can perform from day to day. I would recommend caution about moving “up” the goals for special needs students. Perhaps you could wait until they have beaten their previous goal two or three days in a row, before raising the goal. You just want to be sure they can consistently write that quickly.

It is important not to give lower goals to special needs students, as they need to reach automaticity the same as everyone else. What will be different is the amount of practice they will need to achieve the goal. Where other students can develop automaticity with the four new facts in a couple of session a special needs students might need ten or fifteen practice sessions. Rather than spread that practice out over two or three weeks, special needs students should get more than one practice session (of two or three minutes duration) each day. Remember, don’t make sessions much longer than three minutes or students will burn out.

I would encourage special education teachers to provide their students with an extra practice session each day in the special education room as well as the one the students have in their regular classroom. I would also encourage special ed staff to work with the parents (or siblings) to show them how to do another practice at home each evening. If the parents of special needs students can be recruited and trained to provide extra practice at home–done positively—it can make a huge difference in the rate of learning. Three short sessions each day would enable a slow performer to be able to pass in five or six days—within the expectations for all the other students.

It is very important that practice procedures for special needs students be monitored and done exactly as written. It is hard to overemphasize the importance of the proper and complete correction procedure for special needs students. Besides teaching the parents or siblings how to do the practice, it might be valuable for special education staff to monitor how the practice sessions in class are going. Often special needs students are not good at self-advocacy or leadership and if their in-class partners are not following the procedures the special needs students will need help to correct the problem.

Finally, we know that special needs students have had a history of failure at academic tasks. Therefore they often lack perseverance and give up rather more easily than we’d like. This implies that special needs students are more dependent upon the motivational procedures to keep them going. Unfortunately not all general education teachers make full use of Rocket Math’s built-in motivational procedures— such as coloring in the rocket chart, using the Rocket Math Wall Chart, or using the achievement awards. Special needs students may need all of these things to keep them going and not giving up.

The special education staff should work to provide some extra reinforcement if the homeroom teacher is not doing a lot. Even if there is no Wall Chart being used in the regular classroom, one could be put up in the special education room, and all the students on that teacher’s caseload could come in and put up star stickers as they pass levels in their regular classrooms. The special educator could set goals and have celebrations with his or her special needs students when the stickers pass the goal mark. In addition, a special education teacher can give out achievement awards to his or her students when earned, even if the general education students don’t normally get them in the classroom. One of the most important would be the “helper award” if the special needs student is getting practice at home.

While none of these things involves modifying the directions for special needs student, it is important to use ALL the tools provided in Rocket Math to ensure the success of special needs students. The extra effort involved in using all of the tools carefully may need to be undertaken by special education staff to make sure it all happens.

Don’t try to stop students from finger counting. Students count on their fingers as a strategy to figure out the answer to facts they do not recall. If they are counting on their fingers you know for a fact they don’t recall the answer. (Or they don’t trust their recall of the answer and are just checking!)

By helping students memorize the facts through daily practice in Rocket Math they will come to the point where the answer occurs to them before they finish counting on their fingers! Remember, that when practicing Rocket Math students have to be able to say the answers to the problems with no hesitation. They do it over and over as they are practicing with their partner. If they do hesitate, their partner should be correcting them, having them repeat it three times, and then back up and try it again. So our goal is to instantly know the answer to the facts.

When students recall answers to facts before they finish counting their fingers, they will NATURALLY replace finger counting with the much faster recall strategy. That is your goal rather than suppressing the only strategy some students have! And for the students who are “just checking”–i.e., they do recall the answer but they check anyway to be sure, after they check enough times almost all students will become sure and stop it. Rocket Math teaches that as well because students cannot pass the levels until they stop using their fingers, so they will learn to give up that strategy.

This is a VERY important principle for teachers to know. It is most important in the realm of classroom management. One of the most important principles of classroom management is that you should teach students what you want them to be doing in all situations rather than focusing on all the millions of things they should NOT be doing. The goal is to teach a replacement behavior that keeps them busy, that you can praise, and that gets them focused on accomplishing their goals. You teach students to track with their finger when others are reading instead of NOT: looking around the room, playing with their fingers, poking their neighbor, reading ahead in the book, tying their shoelaces, etc. You teach students to stand in a line looking at the back of the head of the student in front of them rather than NOT doing all kinds of other things. Teaching students what they should be doing also allows you to praise them for doing it. Teaching your expectations allows you to set them up for success and show them how to do the right thing. Teaching good behaviors that replace bad behaviors instead of trying to simply suppress the bad behavior is an important principle of effective teaching. Once a teacher learns to think this way they are on the road to having a happy and successful teaching career.

Teaching students to instantly recall the answers to basic math fact questions is just another example of that.