Author: Dr. Don

Fraction & Decimal Equivalents Learning Track

Posted on by Dr. Don

List of Learning Tracks Continue to purchase

Fractional & Decimal Equivalents

This learning track gives students practice in identifying four kinds of equivalents.  All the equivalents practiced in this learning track are listed in the sequence shown at the top of the page.  In the virtual filing cabinet you can also print out the sequence. Note that this is Learning Track 16 in the Online Tutor.

Decimals that are equivalent to common fractions

The first type of equivalents students learn are decimal numbers to a fraction.  An example is 0.667 is equivalent to the fraction 2/3.  Decimals such as 0.4 = 2/5 or 0.25 = 1/4 or 0.125 = 1/8 are practiced.  Twenty-five of these equivalents are learned.  These are the most important items and are the equivalents that get the most practice.

Fractions in decimal form (tenths and hundredths)

A second kind of equivalent is that of a fraction in decimal form, such as 66.7/100 (which is equivalent to the fraction 2/3).  Another example is 4/10 which is equivalent to 2/5.

Fractions equivalent to division problems and vice versa

The other two kinds of equivalents show the interchangeability of division problems and fractions.  The fraction 2/3 is equivalent to dividing 3 into 2.  Conversely, dividing 3 into 2 is equivalent to the fraction 2/3.   These are introduced, but because they follow a rule, these are not tested as thoroughly as the decimals equivalent to fractions.

 

 

 

Rounding up to Millions Learning Track

Posted on by Dr. Don

List of Learning Tracks Continue to purchase

Rounding up to Millions

This learning track gives students practice in rounding to the nearest ten thousand, nearest hundred thousand and nearest million.  Students practice with numbers with varying numbers of digits, starting with 3-digit numbers and going up to 5-digit numbers.  The sequence of the kinds of numbers students learn to round is shown above.

Each worksheet includes four examples of rounding.

We give four examples of rounding at the top of each worksheet so that students can see how to round each type of number.  Then students work with their partner, who has the answer key, to round the numbers around the outside. The student says the “answer” which is the rounded number.  The partner corrects errors by saying the number and what it rounds to aloud, (e.g., “8,621 rounds up to 9,000”) and follows the same correction procedure: Ask the student to repeat the correct information three times, then back up three problems.

1-minute Daily test requires writing only 3 numbers

The Daily Tests do not require the student to write out the complete number.  Instead, they only have to write three digits of the rounded number.  This allow students to answer more questions in the one-minute test.

 

 

Rounding up to Thousands Learning Track

Posted on by Dr. Don

List of Learning Tracks Continue to purchase

Rounding up to Thousands

This learning track gives students practice in rounding to the nearest ten, nearest hundred and nearest thousand.  Students practice with numbers with varying numbers of digits, starting with 3-digit numbers and going up to 5-digit numbers.  The sequence of the kinds of numbers students learn to round is shown above.

Each worksheet includes four examples of rounding.

We give examples on each worksheet so that students can see how to round each type of number.  Then students work with their partner, who has the answer key, to round the numbers around the outside. The student says the “answer” which is the rounded number.  The partner corrects errors by saying the number and what it rounds to aloud, (e.g., “8,621 rounds up to 9,000”) and follows the same correction procedure: Ask the student to repeat the correct information three times, then back up three problems.

1-minute Daily test requires writing only 3 numbers

The Daily Tests do not require the student to write out the complete number.  Instead, they only have to write three digits of the rounded number.  This allow students to answer more questions in the one-minute test.

 

 

Educational apps should answer these six questions for the teacher

Posted on by Dr. Don

Educational apps should provide information on whether students are progressing and whether they are learning.  Teachers want to know how their students are doing and if they are benefitting.  Teachers need to know if students are engaging and if they find it too difficult.  Here are six key questions that all educational apps should answer for teachers.  Examples of how these answers would look come from the Rocket Math Online Tutor (RMOT).  This educational app answers these six key question in real time on the website and for download into spreadsheets.

(1) Are students engaging with the app?

Students only learn when they engage with an educational app.  Teachers need information on how many of their students are using the app and how frequently.  The RMOT has a page called “Review Progress” where this information is available.  The first info centers on engagement with a chart showing what percentage of the students are completing how many sessions over the last 14 days.  Students are rated “good” if they complete 12 sessions in 14 days.  That translates in the last two weeks to a ten-minute session every day at school and a four times additionally as homework.  That rates as “3 stars” or a grade of “B.”  In the example above, 65% of the students in the class have completed that number of sessions or more.  Also, 88% of the students are working at a steady pace, of 8 sessions over two weeks.  So 88% of the students are engaged enough to see benefits.

(2) Who’s been making progress?

Educational apps should keep teachers aware of which students are working and making progress.  RMOT teachers can enable a Daily Progress Report to be sent to their email.  This shows for each individual student how many sessions they started and how many they completed the previous day.  If students complete one ten-minute session at school, the teacher can see if any students completed an additional session at home. The Daily Progress Report also tells the teacher which students are making progress.  Student progress shows when they pass one of the 26 A to Z levels in each learning track, such as Addition, Multiplication, or Fractions.  Students can then celebrate their progress by coloring in that level on their Rocket Chart.

(3) How far have the students progressed?

Educational apps should show the teacher how far students have progressed in their learning objectives.  RMOT makes progress clear to both students and teachers because each learning track is broken into 26 A to Z levels.  As students pass levels on the way to Z, the app congratulates them and makes their progress obvious.  In addition, the Review Progress page graphically displays how far students have progressed in each learning track.  And of course, the students are encouraged to keep track of their progress on their individual Rocket Charts.  These Rocket Charts are so important to the students, it’s where the app came to be named “Rocket Math.”

(4) Is there evidence of student learning?

An educational app like RMOT should show evidence of student learning, not just completing exercises.  RMOT measures math fact fluency through giving students 1-minute races, or fluency tests, periodically as they work through learning tracks and whenever these are assigned by the teacher.  This data is collected and is always available to export as an excel file.  Above is an example of a class of 35 students who began the Addition learning track with an average fluency of only 5 correct problems per minute.  The students who have completed the learning track have an average fluency of 17 problems per minute.  This data is also shown in chart form on the top of the Review Progress page.

Teachers can also assign fluency tests periodically.  The RMOT Review Progress page also shows the scores earned in the most recent two fluency tests so teachers can quickly see if students are actually improving in their math fact fluency.  That’s why you have the education app, right?

(5) Who is making a good effort each day?

On the Review Progress screen the RMOT shows, for each student, the number of problems they answered during their 10-minute session.  Students who are applying themselves will answer over 100 problems in that length of time.  The teacher will be able to see which students are not applying themselves and not making a good effort.  Some students may need closer supervision, or more motivation to get much benefit from their time on the app.

When students actually apply themselves, they see themselves making progress and are motivated to make more progress.  All it takes is a session or two of good effort and they will realize this app is really helping them.

(6) Are students finding the app too difficult?

The RMOT app calculates a difficulty score for each student.  The app counts each time students have to “Start Over” in a part because they aren’t at mastery.  The app divides the number of “start overs” by the number parts passed.  If a students score is over 3.0, that means they have to start each part over three times to pass it.  That may be a little too difficult and they may need some help or intervention. Not all students do, but the app has options on how to make it easier for those who need it.  On the other hand if a student has a difficulty score less than 3.0, then it is not too difficult and they just need to have some help in developing perseverance.

A good educational app provides clear answers to evaluate effectiveness

The answers to these key questions help a teacher evaluate the effectiveness of an educational app.  The teacher needs to be able to answer these six questions.

  1. Are students engaging with the app?
  2. Who has been making progress?
  3. How far have students progressed?
  4. Is there evidence of student learning?
  5. Who is making a good effort each day?
  6. Are students finding the app too difficult?

When this information is available to teachers in an educational app, they can fairly evaluate its success and the benefits it is conferring on their students.

 

 

 

What Is Math Fact Fluency: Misconceptions & Mistaken Advice

Posted on by Dr. Don

Math Fact Fluency: What you need to know and avoid

Many common misconceptions float around in educational circles about math fact fluency. These misconceptions are mostly based on an incorrect reading of the research. Some common misconceptions are about:

  • what math fact fluency is,
  • if it is important,
  • how to teach it,
  • how to understand it,
  • and finally, how to assess it.

These misconceptions lead to wasting time on incorrect strategies to teach math facts and math games that don’t work. More importantly, these misconceptions have led to an epidemic of students lacking fluency in math facts.  Teachers in the upper elementary grades still see students counting on their fingers or using multiplication fact charts.  Having math fact fluency is a key foundation for future success in mathematics. Wasting time on these misconceptions is the main impediment to developing this in all students.  Let’s look at the correct conceptions and contrast those with the misconceptions as we go.

Conceptual learning must precede committing math facts to memory

Students must be taught the conceptual meaning of operations and of course, know their numbers, before embarking on the task of committing facts to memory.  What do we mean by the conceptual meaning of an operation?  When you give a basic fact problem to a student, such as 9 + 6, the student can represent the problem and figure out the answer.  Whether they use manipulatives, or draw lines, is unimportant as long as they understand the process and can get the right answer.  The same goes for subtraction, multiplication and division.  Students must be able to show the problem and derive the correct answer to have a conceptual understanding of the operation. Students need to develop a conceptual understanding before committing facts to memory.

The misconception:  Continuing to require students to figure out math facts is all you need to do.  It will automatically lead to math fact fluency.  What is true is that students need structured teaching to develop fluency.

What is Math Fact Fluency?

Student solving a basic addition equation. Fluency is the second stage in learning.  In the first stage of learning, a learner develops accuracy, the ability to answer correctly given time.  Imagine not just math facts, but other learning, such as a musical piece or a dance step.  After some work you can do it, but slowly with a lot of concentration. You are accurate only. However, with a lot of practice you can do it correctly and quickly.  That is fluency or its synonym, mastery.  So fluency is accurate and quick, or efficient.

Math fact fluency is committing facts to memory and answering them by direct recall.  We want students to just remember the answer.

The misconception: Using “flexible strategies,” like the student in this picture, to figure out math facts is precisely NOT fluency.  It takes time to figure out math facts and so you are not quick.  You’re still at the accuracy stage. What is true is that to develop fluency students must use “recall” to get the answers, rather than “flexible strategies.” Time spent playing games or developing a variety of strategies is time that should be spent committing facts to memory.

Misreading the research

The research on students using strategies to figure out math facts came from following what students do when left to their own devices to learn math facts.  These students were not being taught correctly.  Their teachers did not help to commit a small number of facts to memory at a time.  Breaking this down into bite-sized pieces is necessary for memorization.  With no help memorizing facts, children were seen to get started by using various tricks to help themselves remember.

However, all evidence shows that such strategies for remembering are an intermediate stage in learning that is replaced with direct recall by proficient students and adults.

The misconception: Students must spend a lot of time developing various strategies for remembering math facts. There is no research showing this is a necessary stage.  We know that students who memorize facts directly have no problem if learning is structured correctly.  Common sense tells you that an intermediate strategy, that is later abandoned in favor of direct recall, cannot be necessary in the first place. In other words, if you aren’t going to keep using these flexible strategies, why learn them at all? Instead, students should be helped to memorize the facts by systematically giving them a small number of facts to commit to memory at a time.

However, being able to answer fluently is not enough.  Students need to keep practicing and learning so they can develop automaticity with math facts.

Math Fact Fluency should be developed into Math Fact Automaticity

Automaticity is the third stage of learning.  It only comes after fluency is developed and only with additional practice.  Not only can the learner do the task fluently (correctly and quickly), but does so without much, if any, conscious thought.  Imagine a member of a marching band who has to play a piece of music quickly enough to keep time, but also has to think about marching in step with the rest of the band.  That musical piece must be learned to automaticity so the band member doesn’t have to put much attention into playing the right notes.

Decoding in reading and math facts in math are both tool skills. These skills are but a tool to do a more complex task.  Tool skills need to be learned to the level of automaticity so the learner can focus on the bigger task.  Automaticity in decoding (reading words) is essential so that students can focus on the author’s meaning rather than figuring out the words.  Students who read slowly, puzzling out words one at a time, lose the gist of the passage.  Students use math facts to do higher order computation.  Therefore math facts need to become automatic so that the student has cognitive capacity left to focus on the larger problem or procedure.

The misconception: Playing games and knowing a variety of strategies for deriving math facts are essential for developing fluency.  The truth is that math fact fluency and automaticity are related to simple recall of facts and are developed through practice recalling facts.  On the other hand, after facts can be recalled instantly, lots of games and “number sense” type activities are easy and fun for students.

Why is Math Fact Automaticity Important?

Automaticity in recall of math facts is important because it enables students to…

  1. focus on the processes in which they are using math facts rather than on deriving the facts as they go.
  2. better follow instruction in the classroom without being distracted by trying to figure out math facts during the lesson.
  3. solve difficult problems and to complete math assignments quickly and easily.
  4. have more confidence in their math abilities.
  5. have more success in their future math classes and careers.

How to assess Math Fact Fluency and Automaticity

I know a piano player who can play “The Flight of the Bumblebee” almost faster than I can hear it.  He has clearly learned this piece to the level of automaticity.  That being said, he doesn’t have to play it fast and it’s better when he slows it down some.

Unfortunately, there’s no better way to measure the development of fluency and automaticity than by measuring the rate at which the person can perform the task.  There is a limit after which more speed makes no difference.  But there is also a lower limit below which you know the person does not have automaticity.  Research shows that direct recall of math facts happens in a little less than a second.  So if a student is reading a fact off a flashcard or on the screen, once they have finished reading more than a second has passed and their answer should be instantaneous.  If it takes two or three seconds after someone reads aloud the equation for the answer to come to mind, then that fact is not yet fluent or automatic.

The misconception: It shows fluency if, after reading a fact off the card or a screen, a student has to think for 2 seconds to come up with the answer.  The truth is, we want direct recall which, after reading the fact, is instantaneous, less than 1 second.  Having to stop and think about facts is not automaticity and it means that students need more practice recalling facts, not figuring them out.

Best ways to assess math fact fluency

Interestingly, the fact that an individual may automatically recall the answer to one math fact does not tell you about their recall of other math facts.  Students memorize math facts better in small handfuls, not all at once. As they are learning we would expect students to be able to answer some facts instantly, but need more time to learn the rest. The ideal way to assess math fact fluency is with flashcards or a computer display. These tools help keep track of the ones that are answered instantly and which are not. So, it is not an all-or-nothing result, but determining which facts students know at a fluent level and which ones they still need to learn.

Giving students a sheet of 100 math facts to answer, some of which they know and some which they don’t, gives you a mixed result.  On top of that issue, there is the issue of how fast a student can write.  Most elementary students cannot write as fast as they should be able to answer math fact problems.  Expectations for fluency would be for students to answer math facts at between 66% and 80% of their writing speed.

The misconception: Students are either fluent or not. We know that learning math facts is not an all or nothing proposition.  Students learn facts individually by committing each fact to memory individually.  Students can have memorized some of the facts but still need to learn others.

How to Memorize Math Facts to the level of Automaticity

Students must first learn the concept of  the operation, such as addition or multiplication, before they begin memorization.  Once students can represent and figure out any fact in the operation, then they understand the concept.  Then they are ready to begin memorization.

A few at a time

Also as mentioned above, the only way to memorize the many facts in an operation is a few at a time.  One memorizes the words to a song one stanza at a time, or your lines in a play one response at a time.  This requires organization and a system to work through all the facts in some sequence so that gradually the students learn all of them.

With corrective feedback

When learning facts it is essential that there is corrective feedback, either from a partner or from a computer.  Someone or something needs to give the learner the correct answer when the learner is uncertain.  And someone needs to give the learner additional practice when there is a hesitation.  Computers can reliably do this. Student partners can, too, but they need some training, which takes little effort to learn.

Bring facts to mastery before teaching more

Next, there has to be a way to ensure that each small batch of facts has to be learned to mastery before the next batch is introduced to be learned. This is the principle of feeding mush to the baby.  One spoonful at a time, making sure the baby swallows the last one before giving them more. It is important to base the decision on when a student goes on to learn the next set when they’ve mastered the last set and not some pre-set schedule.

The misconception:  You can push a class of students through the facts at the same pace.  Truthfully, if you place learners in a position to try to memorize more before they have digested the previous sets you will cause proactive and retroactive inhibition.  The student will begin getting more confused and lose ground.

After memorizing math facts, use them daily.

After students have learned math facts to automaticity, they enjoy using them in computation, which they can do very easily now. Students who are automatic in math facts are happy to race through math computation.   They can also do mental math, which they now find fun.  Math games can be used to practice using math, not as a method to learn, but as a method to practice what has already been learned.

All of the interesting relationships among numbers (that are incorrectly touted as a method to learn math facts), can be engaged in after committing these facts to memory.  Second grade students who were in the process of learning subtraction facts, volunteered to their teacher, “These are easy because they are just the opposite of adding.”  Because they had previously memorized their addition facts, this aspect of number sense was perfectly obvious to them, without any instruction.  Memorizing math facts does not hinder number sense, it just makes it easy.

Find out more about the Rocket Math Worksheet Program for peer partner math facts learning

or the Rocket Math Online Tutor for computer-assisted math facts learning.

 

 

 

 

 

 

Learning Computation with Rocket Math Worksheets: A customer review

Posted on by Dr. Don

We strongly recommend the Rocket Math Learning Computation four tracks for any homeschool. We hope you find this review helpful.

JL Marcos family, Jacksonville Beach, Florida

When to use the Learning Computation Learning Tracks

Once your student has mastered the math facts (reached Level Z) in one of the four arithmetic operations, the Rocket Math Learning Computation worksheet Learning Track takes this student seamlessly all the way to the top of that operation’s ladder (at the top is the highest skill in that operation).
I recommend you start using the Learning Addition Computation track as soon as the student has mastered the Addition facts, and while the student continues learning the facts in the other operations. When the student masters the facts in another operation, start the Learning Computation track for that operation. And so on.

What’s in the Learning Computation worksheets?

The four Learning Computation tracks are divided into “skills.” Each skill in each step of the ladder, in the natural order in which one is to learn them. Dr. Don has created five worksheets for each skill in each Learning Computation track.
For each skill in each operation, Dr. Don has prepared the following:
1… The most detailed and helpful and concise instructions for that particular skill, for the teacher/parent to learn how to teach it.

I think the four LC tracks are amazingly valuable because they help learn the different skills…
1… thoroughly because there are plenty of problems to practice specifically the new skill
2… seamlessly because the jump from one skill to the next is almost imperceptible, so it is an easy jump to take
2… A set of five numbered worksheets. The top half in each Learning Computation sheet has problems with new skill learned in that particular five-sheet step. The problems in the bottom half of the worksheet are a review of the immediately prior skills.

How to use the Learning Computation (LC) Worksheets

How does one use it? Easy. We simply started with skill 1 sheet 1 and then follow onto sheets 2, 3,4, and 5. Then, you move on to skill 2 sheet 1, etc. If, by the time your student is in sheet 5 of a given skill, you think they have not mastered it, then you go back a few sheets or even to sheet 1 in that skill.
The teacher’s script tell you exactly how to teach the skill–it asks the student questions about each step in the process, so they learn how to think about what they are doing.  The script has sections where it reduces the amount of prompting you provide, until by the end of the five sheets the student is totally doing it on his own or her own.
There are placement tests for each operation which gives you a chance to see which skills are already mastered and where he or she begins to make errors.  The placement tests would allow you to skip some of the skills your student already knows, and begin where he or she has difficulty.  But it isn’t required.  We were happy to just go in order without using the placement test.

Doing Learning Computation in several operations

When our student was doing Learning Computation (LC) in three operations (addition, subtraction and multiplication, and was still learning division facts), we would do all three LC tracks each school day, but only the left or the right half of the sheet in question. So he would do the left half of addition, the left half of subtraction, the left half of multiplication. That way he was not doing too much each day, while still using the recently learned facts and learning the skill at hand.

Learning Computation makes it a painless process

At the time of this writing, we have completed the Addition and Multiplication LC tracks. LC tracks Subtraction and Division still ongoing (subtraction because it is by far the track with largest number of different skills; division because he started it not too long ago). For our student and for us this has been and still is a painless process. We like very much that there is plenty of practice of the new skill in each set of five sheets, so that he is most of the time ready to move to the next skill by the time he finishes the fifth sheet.
For us, working on learning computation for several operations at the same time has been a great way for our student to refresh and use the math facts he worked hard to master.

Why purchase these supplements to the Rocket Math Online Tutor?

Posted on by Dr. Don

Why supplement the Online Tutor?  The Online Tutor works best if your students are motivated and your teachers have all the support they need.  Purchasing these two key supplements will make the Online Tutor far more effective.  Make sure your purchase gets the job done.

(1) Motivate your students to use the Online Tutor.

The Wall Chart motivates within the classrooms.

Motivated students will use the Rocket Math Online Tutor more frequently and make more progress. The Wall Chart can motivate students on a daily basis.  It motivates by having students work together to reach a common goal.  Students receive stickers when they pass a level and get the honor of adding their sticker onto the class chart. The teacher sets goals for rows filled by a certain date.  If the class fills the rows before the date, the teacher rewards the class in some fashion.  (You can read the suggestions for use here.)

The Wall Chart helps monitor engagement easily.

As a math coach or administrator, the Wall Chart helps you quickly assess if a class is using the Online Tutor.  Visit a classroom, look at the Wall Chart, praise the class for their efforts and give them a principal “Principal Free Space” by adding a different colored sticker of your own.  Then you can revisit the class in a week or two and easily see how much they have accomplished since your last visit.  Then you can praise the class and the teacher, or show a little disappointment if it is not happening.  This supplement to the Online Tutor is very helpful.

The Super Hero Rocket Math cape helps motivate across the school.

When students complete a Learning Track (or other milestone of achievement), they get to wear one of the Rocket Math capes around school, at lunch or out to recess.  Everyone can see that they have accomplished something in Rocket Math.  It’s especially effective for students who haven’t been getting onto the Online Tutor and so haven’t had a chance to wear the Super Hero cape.  It’s also great for adults to notice and praise the student who has accomplished something in Rocket Math.  Healthier for students than candy prizes and it is re-usable.

 

(2) Provide support and guidance to your teachers.

Teachers need support, help, and guidance to make the most of the Online Tutor.  This support package provides help in four ways.  This is in addition to the video series “Making the best use of the Online Tutor.”

(First) Get a one-hour remote in-service training session with Dr. Don

Dr. Don will train your teachers.  Teachers can get either initial training or to get a refresher on the key points of how to implement the Online Tutor. Rocket Math will waive the normal $250 charge for the one-hour session.  Schedule the training on the Rocket Math website here.  Training is flexible and can address any issues you have experienced as well as preparing you if you’re new.

(Second) Receive a Weekly check-in/training Zoom call with Rocket Math staff

You will be able to schedule a weekly Zoom call with one of the helpful Rocket Math staff.  Usually you can set up a 15-minute call, but it can be longer if needed.  You can ask any questions or get trained on any aspect of how to use the Online Tutor.  You can rotate the calls among schools or staff for them to ask questions.  This will be a great way to get help on troubleshooting issues or a way to brush up on training.  We won’t require these calls every week–they are only offered as a resource.

(Third) Get one of your teachers Certified as a Rocket Math expert through 20 Zoom sessions

We offer the Certified Teacher Program #3102  for $600, but one teacher’s training is included here.  You choose the teacher on your staff to become Certified. In the first session we will explain how the Online Tutor works.  Then in each of the 20 sessions, together we will watch a student of the teacher’s choosing do an Online Tutor session.  The teacher will learn how the Rocket Math Online Tutor works and how it helps the teacher monitor what’s going on with the student.  The final wrap-up session we’ll answer all your questions and get you posted as a Certified Rocket Math Teacher on our website. A Rocket Math Certified teacher will be a great resource to your staff as they will have experienced all the issues that other teachers will be able to learn from.

(Fourth) Receive direct White Glove access for IT help

We will give you a direct number to call to reach a member of the highly trained and exceptionally helpful Rocket Math staff to help you with IT problems.  We aren’t available 24/7, but we are available during school hours on school days.  Often we can explain or walk you through how to deal with IT issues that come up and fix it on the spot.  Sometimes we will have to research the problem or we will have to fix a glitch.  We will fix those glitches ASAP and get back to you with a solution.

 

Student not progressing in Rocket Math Online Tutor? How to diagnose the problem. Part One

Posted on by Dr. Don

Progress in Rocket Math Online Tutor means passing levels in a Learning Track and then completing a Learning Track.  Students who are not progressing in Rocket Math will get discouraged.  The point of this educational app is for students to learn math facts by memory, by instant recall, instead of having to figure them out.  If students are not progressing, something is wrong.  Here’s the things to look for in order of how likely they are to be the problem.

Problem 1: Not completing sessions

Students can start a session and work for only a couple of seconds and then quit.  If students are not completing sessions then they are not doing enough practice.  They will not make progress unless they complete sessions regularly.

If you open the Review Progress tab and scroll down to the listing of your students you will see a column titled Sessions in last 2 weeks.  For each student, for the last two weeks, you can see how many sessions they completed each day as well as how many they started.  The data showing here tells you the student is starting sessions, but not completing them.  They are only ten minutes long, so they can do it if you tell them they should.

Solution 1: Require students to show Session Completed screen.

Rocket Math has a screen that proves students have completed their session each time they do Rocket Math. It comes up at the end of  the ten minute session.  This screen will stay up if they do not log out.  This is designed so you can require your students to show you they completed their session.  Because is will stay there, you can check them out (maybe use a clipboard?) and know they have completed their session.  Completing sessions is the first step in learning math facts and making progress.

Problem 2: Not working during sessions

Most students seem to understand that going as fast as they can with Rocket Math is the road to learning their math facts.  Most students like going fast and when Rocket Math helps them learn these facts they are motivated to develop mastery.  They realize it will make their lives easier when they have to do any arithmetic for any reason.

However, some students focus their efforts on trying to avoid learning and working. These students may log into Rocket Math but then go on to do something other than work on learning their facts.  These students will not spend much time practicing even when they are logged in.  They won’t of course, make much progress and that will be discouraging for both them and the teacher.

On the Review Progress screen, you can see each day how many problems students have answered in their ten-minute session. Student should be able to complete over 100 problems in a full ten-minute session, if they are working steadily.  Students who complete less than half that many problems are spending a lot of time doing something other than practicing math facts.

Solution 2A: Circulate and watch students while they are using the Online Tutor

If possible, monitor students closely while they are doing the Rocket Math Online Tutor.  Walk around, look over their shoulder and see them answer a couple of problems.  Pat them on the back, literally or figuratively, and move on. Praise people who are working hard, and do it aloud so other can here you.  Comment on anything you see, so they know you are watching and know you care how they are doing. Keep moving around the room so you can see everyone.  Keep circulating so that they know you will be coming by frequently.  If you do that you won’t have anyone off task.  If you did this for a month or two, you would build in good work habits and then you wouldn’t need to do it all the time.  If you never do this, you have no idea what is going on in the back corners of your room!

Solution 2B: Post names of those answering the most problems

If you are teaching something else while students are working, you won’t be able to monitor them while they are working.  However, at the end of the day you can go to the Review Progress page.  Scroll down to the individual student rows and scroll over to the Problems Answered Today column.  At the top you can barely see a little gray arrow and a stack of tiles.  Click it once and it sorts from the lowest up to the highest.  Click it again and sort it from the highest down as you can see in this example here.  Then you can post the names of the students who answered the most problems.

Just before students begin working on Rocket Math the next day stand up and read aloud the names and praise those students who are really working hard.  “I know these students are working hard because of how many problems they were able to answer yesterday.  They are going to get really smart and know their facts.  Can you do better?  I’ll see tonight who can do more than 100 problems!  Maybe your name will go on the board tomorrow!”

And of course, you should have a talk with anyone who is doing very little.  They could always do an extra session of Rocket Math during recess or after school if they can’t get more done during the regular time.

 

Still not progressing?  See Part 2

If your student is working hard and completing 5 to 10 sessions a week, they will most likely be making good progress and passing several levels each week.  If they are working hard and still not making progress go on to Part 2 of this blog.

 

 

Student not progressing in Rocket Math Online Tutor? How to diagnose the problem. Part Two

Posted on by Dr. Don

If you have not, please read and implement Part One of this blog post.  You have seen that your student is completing 5 to 10 sessions a week and is working hard the whole time (answering a hundred or more problems each session).  But still the student isn’t making good progress passing several levels a week?  Let’s look deeper into the problems.

Find out if it is too difficult for this student

When students make three errors or three hesitations in a part or a phase of Rocket Math, we have them start over and repeat those problems. In the Review Progress tab, in the individual student rows is a column titled “Difficulty.”  The Online Tutor calculates the difficulty score  by dividing the number of times the student had to “start over” or repeat a part by the number of parts passed.  We expect that students will usually have to start over once or twice in a part, earning them a difficulty score of “1 or 2”  However, if they have to start over an average of 3 times per part, (a difficulty score over 3.0) then it may be too difficult for this student.

In the Review Progress tab, you can look up the difficulty score for any student.  Or as was done in the picture here, you can sort the difficulty column to see the students with the highest difficulty scores at the top.  Then you should watch the students who are having high difficulty scores while they are working to see what the problem is.

Problem 3: Problems using the keyboard quickly

Some students, especially those under 8 years old, are not as adept at using a computer keyboard as they need to be for the Online Tutor.  At the standard speed, answers must be entered within 3 seconds for a one-digit answer with only an additional second for subsequent digits. Some students cannot use two hands so they can quickly hit the answer and the enter key. Searching for and tapping separately with one hand both the numerical keys and the enter key will be too slow–they will have a lot of start-overs. If you watch such a student work, you will see that they know the right answer, but cannot get it input on the keyboard in time.  This will frustrate them and slow down progress.

Solution 3A: Have the student use a touch screen

Using a touch screen is much easier than a computer keyboard.  For children under 8 years old, or students who are having difficulty entering the answers they know getting them a touch screen device should solve the problem.  To test if this will solve the problem, put the free Rocket Math app on your phone, log in for the student and let them do a session on your phone.  If they do better (have fewer start-overs) then you know how to solve the problem.  Touch screens are becoming more common, so we’re hoping you can locate one for the student who is having trouble.

Solution 3B: Slow the Online Tutor answering speed

If a touch screen option doesn’t help–the student is still frustrated then you can adjust the speed required by the Online Tutor.  This will help an individual student who is having trouble keyboarding the answer quickly enough.  Here are the directions (and caveats) about changing the speed of answering. https://www.rocketmath.com/online-tutor-knowledge-base/b-too-hard-or-too-fast-check-the-difficulty-score/

Problem 4: Student is not ready for the Learning Track

Students who are not ready for the Learning Tracks will have a lot of difficulty progressing through the Online Tutor.  Students won’t succeed who have not learned the basic prerequisites, such as understanding the operation they are trying to memorize.  For example kindergarten students who don’t know how to add two groups of objects (by counting) aren’t ready for LT 1-Addition.  Before students understand addition and subtraction they should not be memorizing the facts.  Generally we want first and second graders in Learning Track 1-Addition followed by LT 2-Subtraction.  The same thing goes for multiplication.  Students need to understand what multiplication means and be able to “figure it out” before being asked to do LT 7-Multiplication. After this concept is learned in third or fourth grade is a good time to begin LT 7-Multiplication followed by LT 8-Division.

Solution 4: Stop Online Tutor and teach more basic math skills first

Students younger than these guidelines or who are cognitively delayed below these mental ages may not be successful with the Online Tutor learning tracks. If they aren’t successful, you’ll need for them to develop more basic math skills before using the Online Tutor.

 

 

 

 

 

 

Can individualized computer-delivered instruction be effective and easy to manage?

Posted on by Dr. Don

When instruction is below the student’s level (sometimes called zone of proximal development) they don’t learn anything they didn’t already know.  When instruction is over the student’s level they lack the prerequisite information to understand the lesson, and so they don’t learn as well. If you have the luxury of a homogenous classroom, thank your administration for making it possible to teach whole group. Most teachers don’t have that luxury and need to deliver instruction to many different levels because instruction needs to be individualized for the student.  It’s relatively easy to have individualized assignments that students can successfully complete and practice what they already have learned. What’s difficult is to have effective individualized instruction, where they are learning something new they did not know.  Computer delivered instruction can be effective, if there are five keys components to the software.

1. Testing for placement or promotion

The software must place students in the correct starting point for their instruction. That requires some kind of testing.  Either some kind of placement test is needed or the software must allow students to “test up” through and out of material they already know. This testing should be the same as the testing for corrections and for mastery.  Any teaching program that doesn’t have a testing component is not focused enough to be effective. Without testing you cannot know what students have learned.  Without testing the software cannot know that it has taught anything.

2. Good Quality Instruction

The software must impart the information to be learned to the students. Even in practice-type programs, such as math facts or spelling programs, the software should tell students what they need to learn.  It may seem simple, but it is critical for students to learn.

For more complex topics, the instruction, the telling of the information, should be as clear and simple as possible, and to the point.  It should be given in small bits, followed quickly by testing to see if the students learned the information (see correction procedures).  Too much information and not enough testing or checking for understanding and a program will be ineffective.  Unfortunately, sometimes “educational” software does not do a good job of teaching, the exposition is not clear enough.  The testing and correction procedures must be in place, so that the exposition will be seen to be ineffective and can be corrected.  Hopefully, the software developers used the feedback of initial trials to improve the lesson delivery.  In any case, the school or parents need to check the testing to see if the software is effective in teaching what it claims to be teaching.

3. Testing and Correction procedures

The software must include some immediate checking-for-understanding type testing after each bit of instruction. If that testing shows that a student has not learned the objective, the program must have a correction procedure in place.  It needs to be robust enough to ensure that the student learns the bit of information that was missed.  An effective correction will re-give the initial instruction and then immediately check for understanding.  A good program will repeat this step as many times as needed for the student to be able to correctly answer and show their understanding.  Then the program should intersperse something else and then re-test the student a couple of times more.  Then the information can be assumed to have been learned until mastery testing, which comes next.

4. Mastery-based promotion

Before students go on to learn another part, chapter, concept or unit the software must test them for mastery of all the objectives in this segment.  Mastery-based promotion means the student doesn’t go on to the next thing until the student has demonstrated mastery of the current material.  Instruction should, of course, be broken down into manageable size pieces, but each piece should be mastered before teaching additional content to be learned.  That requires a test of some sort.  Lack of mastery means the part needs to be repeated until it is mastered.  Demonstrating mastery on the test will result in the student being promoted on to the next segment of instruction.

 

5. Logical instructional sequences

Instruction must proceed through carefully thought-out, logical sequences.  Students must learn the prerequisites and learn them to mastery before they can take on a new skill.  Instruction must proceed carefully and thoughtfully so that students are never expected to know something that has not been previously taught and taught well.  Many topics that teacher and students find difficult to learn are simply a result of having several prerequisite skills that have not been brought to mastery ahead of time.  For example, long division requires that students have mastered subtraction, multiplication and division facts, as well as estimating and place value.  When several of those skills are not properly developed, long division become quite difficult to teach.  If the instructional sequence is sound, then each new step will not happen before the prerequisite skills are mastered.  When they are in a logical sequence and they are mastered, the new step will be relatively easy and will be learned quickly.

With these five components in place, computer delivered instruction can indeed be effective.  Students will be learning and the purchasers can see that students are learning based on the mastery testing in place.

Easy-to-manage requires that all the above are automatic

The above five components are necessary for instruction to be effective. They should be handled automatically by the software.  The testing and corrections, the re-teaching and the mastery testing, all should happen automatically and without fail.  When the instructional sequence is sound and students master each bit as they go along, then it will be easy-to-manage for the teacher.  For an example of an effective instructional program for math facts, see the Rocket Math Online Tutor.