teaching

Why is a gifted student having trouble with Rocket Math?

Posted on by Dr. Don

Question: Hi, Dr. Don! Just had a question recently from a parent of a gifted child whose son is having a lot of difficulty doing Rocket Math! He understands almost everything conceptually in math (in the 99% on national testing) but he is not being successful working with a partner on his math facts. Have you had this problem in other places? I’m not sure if the problem is he really can’t focus on the facts, he’s stubborn and doesn’t like details (big picture thinker), etc. He’s a very social kid so the partnering doesn’t seem to be the problem. I would greatly appreciate any suggestions you might have that I could give this mother. She says that he is fine at home doing his facts with her without a timer. But I don’t like the idea of excusing any student from doing this valuable practice. Thanks for your thoughts. Linda

Answer: I’ve blogged a bit on some of these issues elsewhere on the Rocket Math website, but let me try to be more specific here. First, gifted kids are stunned to find out that they have to work hard to memorize math facts. They probably need three or four days of practice—which to them seems like failure.  They are like an athletic kid who excels easily at every sport but finds he needs to work out with weights as much as a klutz to get to be able to lift heavy weights—his natural talent doesn’t help in this instance. So kids who’ve never had to work to learn things before, really are annoyed by having to practice several days in a row.  But it is really good for them!

How is mom practicing with him at home? Can she video him doing the test “untimed?”  If the child is “writing facts” and “without a timer” then he may be figuring out facts over and over—but is not getting to instant recall. That’s why the oral peer practice is so critical—if there is even a slight hesitation the child is to repeat the fact three times, back up three problems and come at it again—until the answer comes with no hesitation. There is a fundamental difference between instant recall of facts from memory and strategies to come to the answer by thinking it through. My parent letter addresses how to practice.  On the other hand, if the student is able to write the answers to math facts at a fast enough rate to complete 40 problems in a minute, but only when he thinks he is not being “timed” then he needs to learn how to do the same thing when he is being timed.

If he is not learning with the daily practice, we have to ask, “Why not?”  Social kids sometimes socialize instead of practicing. Social kids also can convince their partner not to do the correction procedure. Or they just say the answers instead of the whole problem and the answer. Any of those things would result in not successfully learning the facts. The teacher would need to monitor the quality of the practice. My experience has been that when students are “stuck” or “having difficulty” even just one session of practice done the right way rigorously (with me) and they suddenly improve enough to pass or to recognize they can pass the next day with another session of rigorous practice.

Last of all, sometimes the writing goals are off because of some glitch in how you gave the writing speed test.  So the student might know the facts well enough but not be able to write them fast enough to pass the tests.  If the student can answer 40 facts in a minute in the current set (just saying the answers without having to say the problems) then the facts are learned to automaticity—and the goal in writing should be lowered to whatever the student has done to this point.

Hope this helps. You are right not to excuse this student from learning math facts to automaticity. He might be a stellar mathematician someday if he learns his facts well enough that math computation is always easy for him. If math computation remains slow or laborious he won’t like it enough to pursue it as a career.

Rush help to those who need it with an aimline

Posted on by Dr. Don

The sooner you provide extra help, the easier it will be to catch them up.  

How can you know when students need help to meet expectations?  Use the graph above, which is available from the Educator’s Resources page or here: One Semester Aimline.  It is also available in the basic subscription site, Forms and Information Drawer as an optional form. It is an “aimline” for finishing an operation (Sets A-Z) in one semester.  Schools that don’t start Rocket Math in first grade need students to finish addition in the first semester of 2nd grade and subtraction in the second semester.  This means that students who get stuck on a level for even a week need to be helped.

How an aimline works

If you indicate on this graph the week in which the student finishes each set in Rocket Math you can tell if the student is making enough progress, or if he/she needs to be getting extra practice sessions each day. If the student is working on a set above the line of gray boxes or on the line then progress is adequate–they are on track to finish the operation by the end of 18 weeks of the semester.  But if the student is working on a set that is below the line that means he/she needs intervention.

In the example above the student whose progress is shown in red is above the aimline.  That student has been passing at a rate that means he or she will finish the operation by completing Level Z by the end of the semester.  That student does not need any extra intervention.  In the example above the student in blue is falling behind.  By the fourth week that student has only passed Level C and so he needs to have extra help.

Intervene with better practice or with more practice

The first step would be to ensure this student has a good partner and is practicing the right way.  Sometimes students don’t stay on task or do not listen and correct their partner.  If the checker allows hesitations (while the student figures out the answer) and does not correct them immediately, the student will not improve.  The quality of practice is essential.  Fix the practice in class first and see if the rate of passing improves and the student starts to get up to the aimline.

The second step is to include this student in a group of students who get a second practice session each day.  They would work in pairs and do another Rocket Math session each day.  Whether or not they take tests is unimportant.  What is important is that they do the oral practice with a partner who corrects their hesitations as well as their errors.  This could be done by a Title One teacher or assistant or a special education teacher or assistant.  It should only take ten minutes.

Assigning a Practice session as homework can make the difference

Another step is to involve parents if that’s possible.  Another practice session (or two) at home each evening would make a big difference.  Parents will need to know how to correct hesitations, but there’s a parent letter in the Forms and Information drawer for that.  Also note that siblings can do this practice as well, as long as they have an answer key.

You will be pleasantly surprised at how an extra few minutes a day of good quality practice can help students progress much faster at Rocket Math.  The sooner you intervene, the easier it will be for the student to catch up.

NOTE: There is an aimline for finishing one operation in a year.  It is also in the Forms and Information drawer and on the Educator’s Resources page of our website.  If you follow recommendations and do addition in first grade, subtraction in second, and multiplication in third you can use that aimline.  It won’t require intervening on so many students.

 

 

What about students who can’t pass in 6 tries?

Posted on by Dr. Don

A teacher writes:

Help! I’m feeling bogged down in Rocket Math. I have some students who have been working on the same sheet for over 10 times and are no closer to passing. What am I doing wrong?

Dr. Don answers:

The problem could be one of several things.  You have to diagnose what it could be.  I am assuming you have students practicing orally in pairs, with answer keys, for at least two minutes per partner every day (as shown in the picture above).  I am assuming you already have students, who do not pass, take home the sheet on which they didn’t pass and finish it as homework and practice with someone at home.  The extra practice session at home each day can be a big help and the students should be motivated to do that.   If this is the case and you still have a problem, below are two possible things that may be needed.

(#1) Need to improve practicing procedures.  Pick one of the students who is stuck and be that student’s partner while they practice orally.  Make sure they are saying the whole problem and the answer aloud so you can hear what they are saying.  Correct even any hesitations, not just errors.  Correct the student by saying the correct problem and answer, having them repeat the correct problem and the answer three times, then back up three problems and move forward again.

Diagnosis.  If, after practicing with you, the student does much better on the one minute timing and passes or nearly passes (this is what I usually found) then you know the problem is poor practicing procedures.  If your work with the student makes no difference (they don’t do better on the one-minute timing) and they seem equally slow on all the problems then it is not practicing procedures at fault.  Try #2

Solution:  Monitor your students closely during oral practice to see if they are all following the correct practice procedures.  If you have quite a few students who aren’t practicing well you may need to re-teach your class how to practice.  [Note: Even if they know how to do it but aren’t doing it right, treat it as if they just don’t know how to to do it correctly.]  Stop them and re-do the modeling of how to practice and how to correct for several days before allowing them to practice again.  If your students haven’t been practicing the right way, they won’t be passing frequently, and they will be unmotivated.  You have to get them practicing the right way so they can be successful and so they can be motivated by their success.

Solution:  If you have poor practicing with only a handful of students you might assign them to more responsible partners and explain to them that they need to practice correctly. During oral practice monitor them more carefully the next few days to be sure they are practicing better and passing more frequently.

(#2) Need to review test problems also.  The problems practiced around the outside are the recently introduced facts.  The problems inside the test box are an even mix of all the problems taught so far.  If there has been a break for a week or more, or if the student has been stuck for a couple of weeks, the student may have forgotten some of the facts from earlier and may need a review of the test problems.

Diagnosis.  Have the student practice orally on the test problems inside the box with you.  If the student hesitates on several of the problems that aren’t on the outside practice, then the student needs to review the test items.

Solution. If you have this problem with quite a few students (for example after Christmas break) then have the whole class do this solution.  For the next three or four days, after practicing around the outside, instead of taking the 1 minute test in writing, have students practice the test problems orally with each other.  Use the same procedures as during the practice—two minutes with answer keys for the test, saying the problem and the answer aloud, correction procedures for hesitations, correct by saying the problem and answer three times, then going back—then switch roles.   Do this for three or four days and then give the one-minute test.   Just about everyone should pass at that point.

Solution.  If you have this problem with a handful of students, find a time during the day for them to practice the test problems orally in pairs.  If the practice occurs before doing Rocket Math so much the better, but it will work if done after as well.  They should keep doing this until they pass a couple of levels within six days.

If neither the first or the second solutions seem to work, write to me again and I’ll give you some more ideas.

Are students really “friends?”

Posted on by Dr. Don

I hear teachers calling their students “friends” quite commonly these days.  While the use of the term “friends” is certainly harmless enough, it reminds me that there are extremely important distinctions between the way a person should treat friends and the way a teacher should treat students.  I don’t want to stop teachers from calling their students “friends” but I do think it is critical for teachers to know why and how they should not treat their students as friends.

The main reason that teachers should not treat students as friends concerns expectations.  With friends you’re nice to them and hope that makes them like you.  Then if they like you, they will be considerate of your feelings and treat you well.  Many beginning teachers expect that a classroom of students will be like a room full of friends.  If you are unfailingly nice to them, they will in turn be considerate of you and attempt to acquiesce to your wishes.  Unfortunately, this does not work.  Why?  Primarily because a teacher has to ask students to do things they’d rather not do and has to keep their attention on things to which they’d rather not pay attention.  In short, teachers are authority figures rather than friends.  Friends can get up and leave when they aren’t interested in what you’re doing, but students are required to stay.  Therefore teachers must treat students differently than they treat friends.

The first way that treating friends and students should be different concerns how a teacher reacts to student academic errors.  When a student answers a question incorrectly it shows they have a misunderstanding.  For example, a student says that the sun orbits around the earth.  That misunderstanding needs to be corrected to set the student “straight.”  A teacher who allows a student to continue with a misunderstanding is doing that student a disservice.  Errors should be corrected immediately, in a nice way, but as clearly as possible.  For example, the teacher says that although it appears as if the sun rotates around the earth, actually the earth orbits around the sun.  A good teacher may even take the opportunity to model how a spinning globe creates the illusion that the distant sun is going around us.  The student should be taught/told the correct understanding in as unequivocal a manner as possible and the teacher needs to check to be sure that the student learned the correct information both immediately after the correction and a few minutes later to see that the correct answer is retained.

When a friend makes a factual error, it is socially expected that you will not make a big deal of it.  It is socially inept to clearly and loudly correct errors of fact among friends.  At best one can simply not confirm an incorrect statement, but pointing it out as incorrect is just rude.  Teachers who treat their students as friends will make light of or gloss over errors, and they fail to teach students as a result.

Another way treating friends and students should be different concerns how a teacher reacts to student behavior.  Teachers need to learn to “catch ‘em being good.”  Teachers should look for students who are doing the right thing and should praise/recognize them by name, make eye contact and name the behavior they are doing that is exemplary.  “Alan has his desk clear, his textbook out and he’s ready to start learning.  He’s looking ready for college.”  Praising and recognizing appropriate behavior in the classroom helps prompt other students towards what they should be doing as well as reinforcing Alan.  It sends the signal of the behaviors the teacher values in the classroom and teaches students what’s expected.  At the same time the teacher should deliberately not give any attention to students who are not doing the right thing, who have not gotten ready to start.

With friends we are expected to give non-contingent attention.  We give them love and attention because of who they are, not based on how they behave.  One doesn’t turn away from a friend and deliberately pay attention and begin talking to someone across the room because you approve of their behavior more.  If you did that it would be too rude to your friend and it might hurt your friendship.  Instead, if your friend misbehaved at a party you would begin by attending to your friend, to see what’s wrong, or find out what you can do for them.  That attention reinforces your friendship and proves you’re a good friend.  In a classroom, teachers who respond to misbehavior as they would to a friend end up reinforcing the inappropriate behavior and they get a lot more misbehavior from all of their students.

There is a role for non-contingent reinforcement of students.  They need to know that the teacher cares about them as people.  The time for that is at neutral times when the student is not misbehaving, such as when entering the classroom, out on the school grounds not during class, or even when circulating the room.  Giving appropriate and friendly social attention to the student at times when they aren’t in crisis or off-task helps create good relationships within the classroom and is valuable.  In that circumstance “friends” is just what is wanted.

A third and final way that teachers should not treat students as friends is when students break the rules.  To establish order in a classroom there needs to be rules and consequences for rule-breaking.  Consequences need not be major or draconian, but they do need to be applied consistently.  If a teacher says, “Wait to be called on before you speak,” the teacher needs to not answer or engage with students who call out without raising their hand and waiting.  The teacher should ignore the student calling out and call on someone who raised their hand.  That needs to be consistently applied, no matter who the student is who calls out.  Students only learn to follow the rules when the consequences are consistent.

I wouldn’t recommend treating friends in this manner.  If friends blurt out and interrupt your turn speaking, we generally tolerate it.  When a friend breaks a rule, we don’t apply consequences.  We might complain to them.  We hope that our friendship will cause them to re-examine their behavior, but we’d rather “ask” them not to do it than apply swift consequences.  That is because we are ultimately not authority figures with our friends.  But teachers are authority figures and they therefore have to treat their students differently than they would treat their friends.  As long as teachers understand this, they can certainly call their students “friends.”

What best honors & motivates achievement?

Posted on by Dr. Don

Recognition only after real, actual accomplishments.

What makes for a great award, or great recognition that really motivates?  In the final analysis, recognition, like an Olympic gold medal, is not about what you receive–it’s about how hard you worked to get it.  If students worked hard, and accomplished something real and tangible, then the recognition they are given, regardless of its form, will be valuable and meaningful.  A paper certificate given out by an adult that represents weeks or months of effort, an honest accomplishment, will be highly prized. Those are the certificates that are posted prominently in the bedroom or on the refrigerator at home, because it was hard to get.

Recognition that is not given to everyone.

Remember this fact, when you want to honor student achievement at the end of the year.  If you give awards to every student, then an award means little or nothing.  If on the other hand, students know they had to work and put forth effort to earn the reward, then it is a real honor.  Rocket Math has many built in milestones of accomplishment that are great to recognize publicly.  Certainly completing an operation and getting a Learning Track Certificate, like the one to the left, is one of the most commonly celebrated achievements.

This student’s teacher shared this picture of the student and his Rocket Chart, proving his accomplishment as he moved up through the levels.  This is something to be really proud of, because it represents a real, tangible accomplishment.  Another accomplishment is when a student beats his or her individual best in two-minute timings.  Yet another tangible Rocket Math accomplishment is being able to pass two levels in one week or ten levels in a month!

Recognition for things the students know they can do.

What motivates students to try to achieve is (1) knowing what has to be done and (2) believing they can do it. This is another reason why recognizing real, tangible accomplishments works so well. If the other students can see what their recognized peer did and they understand what has to be done to get there, they are motivated to get some of that glory for themselves. Getting through Level Z of Rocket Math is something students know they can do, if they just keep working at it. It is hard to believe you will become Student of the Month, if you don’t know what the previous recipients did to achieve that honor. But if you know that working hard and practicing your math facts every day can get you there–then you can believe it is possible.

This is why Rocket Math motivates students.

Rocket Math was created to teach math facts to students.  They need this fundamental skill.  So that’s why it was created.  However, because Rocket Math has real, doable milestones that take work to achieve but that students can do, students are highly motivated by their accomplishments in Rocket Math.  They love it because they recognize their achievement.  If the teacher pays attention and also recognizes student effort and achievement, the students will be motivated to learn math facts.  Then math becomes a subject of pride and confidence, which is priceless.

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.

Don’t I need to teach doubles and other combinations first?

Posted on by Dr. Don

There is a lot of advice out there that teachers need to introduce different tricks to remembering math facts to help students learn the facts. Things like doubles, or doubles plus ones, or special combinations that add to ten are recommended to be taught to students. Teachers are exhorted to use many different kinds of exercises to teach these different ways of remembering facts. Is that necessary to do before memorizing facts as we do in Rocket Math? The simple answer is, “No, that’s not necessary.”
DoublesPlusOne
How do we know? What’s the evidence? There are two basic sources of evidence, one from experience and another from logic.
Let’s look at the logical reasons these are not necessary. The goal of Rocket Math, and any good math fact memorization program, is to develop automaticity in answering math facts. Automaticity means the student can instantly answer the fact, without any intervening thought process. So even if students first learn those memory tricks they have to be abandoned in favor of simply recalling the fact from memory.

An intervening thought process would go like this, “Four plus five is like four plus four but one more. Four plus four is eight , so one more is nine. So four plus five is nine.” But the goal of Rocket Math is to simply come to the point where the student reads, “Four plus five is,” and the answer, nine, pops into mind without another thought. Logic tells us that if the learner ultimately has to abandon the strategy, the only reason for learning the strategy is if it is needed as a transition. In other words, if students have to learn the facts to the point where they don’t use the strategy, then the only reason to learn the strategy is if they need it to get to the point of memorizing the facts.
This brings us to the second piece of evidence, experience. I know from experience tha students don’t need these strategies to learn the facts.  When I started using my original hand-written version of Rocket Math with my students with learning disabilities–it worked without them knowing other strategies!  In the past fifteen years thousands of children have learned math facts to automaticity using Rocket Math without learning those different tricks. If it were necessary, then they wouldn’t be able to do it. The reason it is not necessary is that students only have to memorize two facts at a time and that’s just not difficult to do. Give them plenty of practice with those two (enough so that they come to be able to answers as fast as they can write) and they will know the facts without some other (intervening) strategy.
So you don’t have to teach all those different tricks to students to remember facts. Just use Rocket Math, and make sure they are practicing the right way with corrective feedback from their partner. Their results will speak for themselves.