Without the directions you may get lost!

Posted on by Dr. Don

What happens when teachers don’t have a copy of the Rocket Math Teacher Directions?  Bad things!  

When teachers don’t have the written directions to Rocket Math, the essence of the program usually gets lost.  Procedures get modified and modified over the years until they are not even close to what should be occurring. Sometimes we have found schools that are not even providing daily oral practice.  Other schools don’t give the answer keys to the peer tutors.  Other schools don’t give the writing speed test and make up impossible-to-reach goals for students.  We often see teachers implementing the “Rocket Math” program incorrectly and wondering why it doesn’t work.  We ask them if they have read the teacher directions, and they say they didn’t know there were any.  When teachers have never seen the directions, is it any wonder they don’t know what they are supposed to be doing?  Hear-say directions handed down over the years from one teacher to another just don’t convey all the important details.  Teachers need the directions!

This is why I’d like you to have my complete directions for free. Even if you purchased Rocket Math ten years ago and haven’t gotten the updated versions since then, you can have these directions for free.  I have them in three places.  I have the directions broken out into FAQs on their own web page here.  That’s easy for quick reference.

The second place I have the Teacher Directions is as a downloadable booklet you can print out and distribute.  The Rocket Math Teacher Directions for the worksheet program booklet is here.   Please print this out and give to your teachers, especially in schools that began implementing several years back.  Read them and have a discussion at a professional development time.  You will be astounded at how much your implementation differs.

The third place I have the Teacher Directions is in the “filing cabinet on the web” for those of you who have the subscription. In the “Forms and Information” drawer we have the booklet and the FAQs which can be opened and printed out.

In school-wide implementations of Rocket Math, principals or math coaches need to take a leadership role.  The Administrator and Coach Handbook gives you forms with what to “look-for” in a Rocket Math implementation.  If you use that to observe Rocket Math in your classrooms you’ll quickly see whether or not things are going the way they should.   If you have a subscription to Rocket Math you’ll find all of the chapters of the Administrator and Coach Handbook in the “Forms and Information” drawer of our filing cabinet on the web.

Please take the time to see that you or your teachers are implementing Rocket Math according to the directions.  Trust me, it works SO MUCH BETTER if you do.  I wouldn’t steer you wrong!

 

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.

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.

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 hesitations are allowed (while the student figures out the answer) and not corrected the student will not improve.  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.

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.

 

 

Developing test-taking strategies into habits.

Posted on by Dr. Don

Three important test-taking strategies that Rocket Math will turn into habits.

(1) Perseverance Pays Off

Students really need perseverance to get through today’s tests.  You want your students to really work hard and do their best! To have that kind of perseverance students need to KNOW that it pays off.  Sticking with learning and testing over and over until they win is a central lesson of Rocket Math’s daily practice and tests.  Most days, most students do NOT pass the One-Minute Daily Test.  They have to practice some more and try again the next day.  If they try hard and do their best on each day’s test, eventually they do pass.  This teaches perseverance like nothing else in the curriculum!

 

 

(2) When taking a test, work as fast as you can.  

Students doing Rocket Math learn that to be successful you have to work as fast as you can.  Their individualized goals require that they write answers as fast as they can write.  Students who pause to look at the clock or look around the room during the one-minute test simply do not pass.  This may be the only time of the day that students experience the need to work quickly and they get immediate feedback based on whether or not they do work quickly–and it is something they care about!  So they are motivated to work quickly.  It is important for students to have that kind of experience if they are to learn the general rule that you are supposed to work as fast as you can when taking a test.  

 

(3) Skip what you don’t know  

Have you ever watched a student waste valuable time working on a test item you knew the student wouldn’t be able to answer?  Nothing more painful.  Students need to learn to skip the items to which they don’t know the answer readily.  How are they going to learn that without practice?  Rocket Math has a progress-monitoring component–a weekly 2-minute timing you can see to the right. These weekly tests sample all the facts in the operation, including ones they haven’t memorized yet.  Therefore the strategy they should use is to skip the ones they don’t know yet, so as to answer quickly all the ones they do know.  If you explain this to the students, and they can develop this strategy while taking these weekly tests.   

If you aren’t sure that your implementation is developing these habits please feel free to download the  Teacher Directions.   If you have a school wide implementation of Rocket Math be sure you have the Administrator and Coach Handbook.

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.”

cheetah running fast

Timed Math Fact Fluency Expectations by Grade Level

Posted on by Dr. Don

Students should be automatic with the facts. How fast is fast enough to be automatic?

Editor’s Note: “Direct retrieval” is when you automatically remember something without having to stop and think about it.

Some educational researchers consider facts automatic when a response comes in two or three seconds (Isaacs & Carroll, 1999; Rightsel & Thorton, 1985; Thorton & Smith, 1988). However, performance is not automatic; direct retrieval when it occurs at rates that purposely “allow enough time for students to use efficient strategies or rules for some facts (Isaacs & Carroll, 1999, p. 513).”

Timed Math Fact Fluency Expectations by Grade Level

Most of the psychological studies have looked at automatic response time as measured in milliseconds and found that automatic (direct retrieval) response times are usually in the ranges of 400 to 900 milliseconds (less than one second) from presentation of a visual stimulus to a keyboard or oral response (Ashcraft, 1982; Ashcraft, Fierman & Bartolotta, 1984; Campbell, 1987a; Campbell, 1987b; Geary & Brown, 1991; Logan, 1988). Similarly, Hasselbring and colleagues felt students had automatized math facts when response times were “down to around 1 second” from the presentation of a stimulus until a response was made (Hasselbring et al. 1987).” If, however, students are shown the fact and asked to read it aloud, then a second has already passed. In which case you expect a timely response after reading the fact. “We consider mastery of a basic fact as the ability of students to respond immediately to the fact question. (Stein et al., 1997, p. 87).”

In most school situations, students take tests on one-minute timings. Expectations of automaticity vary somewhat. Translating a one-second-response time directly into writing answers for one minute would produce 60 answers per minute. However, Some children, especially in the primary grades, cannot write that quickly. “In establishing mastery rate levels for individuals, it is important to consider the learner’s characteristics (e.g., age, academic skill, motor ability). For most students, a rate of 40 to 60 correct digits per minute [25 to 35 problems per minute] with two or few errors is appropriate (Mercer & Miller, 1992, p.23).” This 35 problems per minute rate seem to be the lowest noted in the literature.

The Correct Math Fact Rates

Other authors noted research that indicated that “students who can compute basic math facts at a rate of 30 to 40 problems correct per minute (or about 70 to 80 digits correct per minute) continue to accelerate their rates as tasks in the math curriculum become more complex…[however],…students whose correct rates were lower than 30 per minute showed progressively decelerating trends when more complex skills were introduced. The minimum correct rate for basic facts should be set at 30 to 40 problems per minute, since this rate has been shown to be an indicator of success with more complex tasks (Miller & Heward, 1992, p. 100).” Rates of 40 problems per minute seems more likely to continue to accelerate than the lower end at 30.

What is the recommended time to finish problems?

Another recommendation was that “the criterion be set at a rate [in digits per minute] that is about 2/3 of the rate at which the student can write digits (Stein et al., 1997, p. 87).” For example, a student who writes 100 digits per minute expects to write 67 digits per minute. This translates to between 30 and 40 problems per minute. Howell and Nolet (2000) recommend an expectation of 40 correct facts per minute, with a modification for students who write at less than 100 digits per minute. The number of digits per minute is a percentage of 100, and you multiply that percentage  by 40 problems to give the expected number of problems per minute. For example, a child who writes 75 digits per minute would expect 75% of 40 or 30 facts per minute.

If measured individually, a response delay of about 1 second would be automatic. In writing, 40 is the minimum, up to about 60 per minute for students who can write that quickly. Teachers themselves range from 40 to 80 problems per minute. Sadly, many school districts have expectations as low as 50 problems in 3 minutes or 100 problems in five minutes. These translate to rates of 16 to 20 problems per minute. At this rate, students can count answers on their fingers. So, this “passes” children who have only developed procedural knowledge of how to figure out the facts rather than the direct recall of automaticity.

Conclusion

With the right tools, any student can develop math fact fluency and have fun while doing it! Students use Rocket Math’s Subscription Worksheet Program to practice with partners, then take timed tests. Rocket Math also offers math facts practice online through the Rocket Math Online Game. Students can log in and play from any device, anywhere, any time of day! Start a free trial today.

Both the worksheet program and the online game help students master addition, subtraction, multiplication, and division math facts.

 

 

How should students practice math facts?

Posted on by Dr. Don

Students should practice with a checker holding an answer key. 

  • One student has a copy of the PRACTICE answer key and functions as the checker while the practicing student has the problems without answers. The practicing student reads the problems aloud and says the answers aloud. It is critical for students to say the problems aloud before saying the answer so the whole thing, problem and answer, are memorized together. We want students to have said the whole problem and answer together so often that when they say the problem to themselves the answer pops into mind, unbidden. (Unbidden? Yes, unbidden. I just kinda like that word and since I am writing this, I get to use it.)
  • A master PRACTICE answer key is provided—be sure to copy it on a distinctive color of paper (yellow in the picture) to assist in classroom monitoring. The distinctive color is important for teacher monitoring. If you are ready to begin testing and you see yellow paper on a desk, you know someone has answers in front of him/her. When you make these distinctively colored (there, I said it again) copies, be sure to copy all of the answer sheets needed for a given operation and staple them into a booklet format…one for each student who is working in that operation. For some reason (I actually know the reason) teachers always want to find a way to put the answer keys permanently into the students’ folders. DON’T. Students need to be able to hold these in their hot little hands, outside of their folders. Then answer keys will be the same regardless of the set of facts on which a student is working. So students working on multiplication will have the answers to ALL the practice sets for multiplication. This allows students from different levels to work together without having to hunt up different answer keys.
  • The checker watches the PRACTICE answer key and listens for hesitations or mistakes. If the practicing student hesitates even slightly before saying the answer, the checker should immediately do the correction procedure, explained below. (Let’s stop here. This is critical. Critical, I tell ya. This correcting hesitations thing is sooooo important. I mean really important. You can probably guess why. We need students to be able to say the answer to these problems without missing a beat — not even half a beat. So students must be taught that there is no hesitation allowed. Really.) Of course, if the practicing student makes a mistake, the checker should also do the correction procedure.
  • The correction procedure has three steps:
    1. The checker interrupts and immediately gives the correct answer.
    2. The checker asks the practicing student to repeat the fact and the correct answer at least once and maybe twice or three times. (I recommend three times in a row.)
    3. The checker has the practicing student backup three problems and begin again from there. If there is still any hesitation or an error, the correction procedure is repeated. Here are two scenarios:

Scenario One
Student A: “Five times four is eighteen.”
Checker: “Five time fours is twenty. You say it.”
Student A: “Five times four is twenty. Five times four is twenty. Five times four is twenty.”
Checker: “Yes! Back up three problems.”
Student A: (Goes back three problems and continues on their merry way.)

Scenario Two
Student A: “Five times four is … uhh…twenty.”
Checker “Five times four is twenty. You say it.”
Student A: “Five times four is twenty. Five times four is twenty. Five times four is twenty.”
Checker: “Yes! Back up three problems.”
Student A: (Goes back three problems and continues on their merry [there is a lot of merriment
in this program] way.)

  • This correction procedure is the key to two important aspects of practice. One, it ensures that students are reminded of the correct answers so they can retrieve them from memory rather than having to figure them out. (We know they can do that, but they will never develop fluency if they continue to have to “figure out” facts.) Two, this correction procedure focuses extra practice on any facts that are still weak.
  • Please Note: If a hesitation or error is made on one of the first three problems on the sheet, the checker should still have the student back up three problems. This should not be a problem because the practice problems go in a never-ending circle around the outside of the sheet. Aha…the purpose for the circle reveals itself!
  • Each student practices a minimum of two minutes. The teacher is timing this practice with a stopwatch…no, for real, time it! After a couple of weeks of good “on-task” behavior you can “reluctantly” allow more time, say two and a half minutes. Later, if students stay on task you can allow them up to about three minutes each. Make ‘em beg! If you play your cards right (be dramatic), you can get your students to beg you for more time to practice their math facts. I kid you not. I’ve seen it all over the country…really!
  • After the first student practices, students switch roles and the second student practices for the same amount of time. It is more important to keep to a set amount of time than for students to all finish once around. It is not necessary for students to be on the same set or even on the same operation, as long as answer keys are provided for all checkers. If students have the answer packet that goes with the operation they are practicing and their partner is on a different operation, they simply hand their answer packet to their partner to use for checking. I know what you are thinking. Yes, I realize that “simply handing” something between students is often fraught with danger. I was a teacher too. All of the parts of the practice procedure will need to be practiced with close teacher monitoring several (hundreds of) times prior to beginning the program. Not really “hundreds,” but if you want this to go smoothly, as with anything in your classroom, you will need to TEACH and PRACTICE the procedural component of this program to near mastery. Keep reading. I will tell you HOW to do this practice. (This is VERY directive.)
  • The practicing student should say both the problem and the answer every time. This is important because we all remember in verbal chains.
  • Saying the facts in a consistent direction helps learn the reverses such as 3 + 6 = 9 and 6 + 3 = 9.
  • To help kids with A.D.D. (and their friends) the teacher can make practice into a sprint-like task. “If you can finish once around the outside, start a new lap at the top and raise your fist in celebration!” Recognize these students as they start a second “lap” either with their name on the board or oral recognition — “Jeremy’s the first one to get to his second lap. Oh, look at that, Mary and Susie are both on their second laps. Stop everyone, time is up. Now switch roles and raise your hand when you and your partner are ready to begin practicing.”

Can’t I copy answer keys for half the students?

Posted on by Dr. Don

Shane asks: After the answer keys are copied onto colored paper, can’t I just make enough copies of answers for half the students? It seems that they will only be using the answer keys while working with a partner and therefore will only need 1 set of keys per pair.

 

Dr. Don answers: Lots of people think this, but here are four examples of issues that make it preferable for each student to have their own answer key, and yes, it should be on colored paper.

1) When students are absent you must pair two students but under the one-answer-key-per-pair both students could be “without” answer keys!  In both cases, their partner has the answer key and that folder is in their desk.

2) When someone comes in to help or volunteer, you want Johnny to practice Rocket Math with that person–but Johnny doesn’t have an answer key–his partner does. So Johnny has to go searching for an answer key.  If Johnny had his own answer key he could just get out his Rocket Math folder and go to work.

3)  The Title 1 or Special Ed teacher or instructional assistant might offer to do extra practice with a student, the student takes his/her folder down to the a place to practice–but doesn’t have an answer key.

4) Alex moves up to division, but his partner doesn’t have an answer key to division–another example where Alex needs his own answer key.

Can a few minutes of fact practice each day be harmful?

Posted on by Dr. Don

Practice is not harmful as long as students are successful.

The best way to practice math facts is by saying them aloud to a person who can tell you if you’re wrong or hesitant in your responses.  If you are wrong or hesitant, you should practice on that particular fact a bit more until you know it well. This is an effective way to learn anything, including math facts.  It is especially valuable if students are given a limited set of facts to learn at each step so they develop and maintain mastery as they learn.  If practice is set up carefully, and students get positive feedback showing they are learning and making progress, it is enjoyable and motivating for students.  This is the essence of Rocket Math.  How in the world could this be harmful?    Only by doing it wrong, and doing it wrong specifically in a way that students are not successful.

If teachers skip the practice and learning part and just give the tests–that would be harmful.  Students won’t get a chance to learn and will experience failure.  The daily oral practice is the heart of Rocket Math–it can’t be skipped!

Daily tests in Rocket Math determine if a student has learned the set of facts he or she is working on, and learned them well enough to have a new set to be added to memory.  If students are not proficient in the facts they are working on now (proficient means being able to say a fact and its answer without any hesitation) then they will become overwhelmed with the memorization and will not be successful.  So it is critical that teachers are certain (based on the daily tests) that students can answer all the facts up to that point without hesitation.  Otherwise they will not be successful and it won’t be enjoyable.

Goals for those daily tests must be based on how quickly students can write.  Slow writers must have lower goals. Fast writers must have higher goals.  Every student’s goal should be “as fast as her fingers can carry her” and no faster.  Arbitrarily raising those goals (expecting faster performance than possible) or arbitrarily lowering those goals (moving students on to the next set before they have mastered the previous set) will cause students to be unsuccessful.

If the checker does not listen and correct errors or hesitations, a student can practice incorrectly and learn the wrong fact.  They can also fail to get the tiny bit of extra practice they need on a fact that they can’t quickly remember yet.  If practice does not proceed as it should, then students will not learn as they should.  Lack of success will make facts practice onerous or counterproductive.  The teacher has to monitor students practicing carefully to make sure they are doing it the right way to be successful.

Rocket Math has very explicit instructions here and answers to FAQs here.  I have a 3 hour training DVD here.  I am available at don@rocketmath.com  to answer questions.  Practicing math facts ten minutes a day is NOT harmful, if we do it in the way that students are successful.

student counting on their fingers because they do not meet math fact fluency expectations by grade level

Facts practice: does it belong in middle school math?

Posted on by Dr. Don

It sure does, if you’re seeing this happen in your class!

Most middle school math teachers confide to me that their classrooms are negatively impacted by the number of students who stop to count out facts on their fingers.  Their issue was always what to do during facts practice with the other students who do know their facts.  It has taken a couple of years but I have put together a package of pre-algebra skills that are worth middle school students’ time practicing which are available in the Universal Subscription. Because the routine of Rocket Math is the same whether the students are practicing basic multiplication facts or learning equivalent fractions you’ll be able to manage all these different levels during the same ten-minute session.

Teachers know it is imperative that finger-counting middle schoolers get practice learning their facts.  Rocket Math is an excellent way to do that.  They will develop fluency and automaticity with the basic facts in an operation in a semester and from then on your lessons will be much easier.  Not only that, but a much higher proportion of the students will be finishing assignments.  There is a “Placement Probe” that can identify students who know their facts in about one minute. The students who know the basic facts of multiplication and division can be placed into the pre-algebra practice programs.

Factors Answers AFACTORS. Students probably ought to begin with the Factors program. What are the factors of 24? Answer: 1 and 24, 2 and 12, 3 and 8, 4 and 6. This is what students learn by memory from doing this program. Students practice with a partner, take a daily one minute timing, fill in a Rocket Chart, just like regular Rocket Math. Students learn all the factors for these numbers in this sequence: 12, 36, 24, 48, 18, 32, 16, 64, 10, 40, 20, 72, 8, 25, 50, 6, 21, 30, 60, 15, 45, and 100.

 

 

Fraction Number Line GEQUIVALENT FRACTIONS.  Students need to know that six-eighths is equivalent to three-fourths and that four-twelfths is equivalent to one-third.  While they can calculate these, it is very helpful to know the most common equivalent fractions by memory.  One of the most common problems students have in fractions is not “reducing their answers to simplest form.”  Equivalent fractions will help students commit 100 common equivalent fractions to memory.  Each set (A through Z) has four fractions which are displayed on a fraction number line.  Students frequently learn fractions equivalent to one,such as ten-tenths, as well as fractions that can’t be reduced, for example three-fourths is equivalent to three-fourths.  Using the fraction number line will help with student understanding of why those fractions are equivalent.

Integers ArrowsINTEGERS (Adding and subtracting positive and negative numbers).  Integers displays problems on a vertical number line and then teaches students two rules about how to solve problems that add or subtract positive and negative numbers.

Rule 1: Go up when you add a positive number OR subtract a negative number.
Rule 2: Go down when you subtract a positive number OR add a negative number.

Students gradually learn several variations of all four types of problems.  They practice with the number line on each page and then have a chance to build fluency on the top half of the page as they work with their partner.  You will probably not be surprised that there is a one-minute test on each set.  The goals are slightly different than before.  Students are to be 100% accurate and to complete at least 80% of their rate at answering simple addition and subtraction problems.

10s, 11s, 12s Multiplication and 10s, 11s, 12s Division facts are also available in the Universal Subscription.  If you have students who think they know the basic facts, but need review, putting them into either of these programs will review the 1s through 9s facts, teach them new ones and allow them to save face.

Among these five programs there are good things for ALL middle school math students to learn, even the more advanced students.  This will enable a math teacher to devote ten minutes a day to fact practice without holding anyone back.  Everyone will have something meaningful to practice during that time.  I think this could be a huge step forward for a lot of middle school MATH classrooms.