Sometimes students need to review test problems also.

You know that there is a difference between the test problems and the practice problems, right? 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. Sometimes students have forgotten some of the older facts. For example, 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.

How you could diagnose for this problem. 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 summer break or after Christmas break) then have the whole class do this solution. For the next week, 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 or three 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 a week 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.

To prove whether students are making progress in learning math facts.

First of all, understand that the two-minute timings are NOT a teaching tool. They are an assessment tool only. Giving a two-minute timing of all the facts in an operation every week or two allows you to graph student performance. You graph student performance to see if it is improving. If the graph is going up, as in the picture above, then the student is learning. If the graph is flat, then the student is not really learning.

The individual graphs should be colored in by students allowing them to savor the evidence of their learning. The graphs should be shared with parents at conference time to prove that students are learning.

Progress monitoring with two-minute tests are a curriculum-free method of evaluating a curriculum. If you use the same tests you can compare two methods of learning facts to see which one causes faster growth. This makes for a valid research study.

This kind of progress monitoring over time is also used in IEPs. You can draw an aimline from the starting performance on the two-minute timing to the level you expect the student to achieve by the end of the year. (Note the writing speed test gave you goals for the two-minute timing which you could use for your end-of-year goal.) The aimline on the graph, when it crosses the ending date of each quarter, will provide quarterly objectives that will enable quarterly evaluation of progress–required for an IEP.

These two minute timings are a scientifically valid method of proving whether students are learning math facts, in the same way that tests of oral reading fluency prove whether students are learning to read. They can be used to prove to a principal or a curriculum director, for example, that Rocket Math is working and is worth the time, paper and money it requires.

Many students find integers confusing. If you add a negative to a negative are you getting more or less??? Over the years different “rules” have been used to try to remember what should happen. Rules such as “two negatives make a plus” or “opposite signs subtract.” Whatever is used to try to remember, it interferes with a student’s ability to quickly and reliably get the answers without having to stop and puzzle it out.

I have posted a series of free lessons online (links below) that use a vertical number line to take some of the confusion out of the process. Turns out there are a total of eight types of problems but all of them can be solved with the same process on the vertical number line. Intuitively on a vertical number line, up is more and down is less.

Using the vertical number line there are two rules to learn. Rule 1: When you add a positive or subtract a negative you go up on the number line. Rule 2: When you subtract a positive or add a negative you go down on the number line.

So first thing to figure out is whether you’re going up or down. Once you do that you simply make “bumps” going either up or down from where you start. That gives you the answer without any uncertainty. These lessons are quick (about 2 minutes) and identify a pattern of whether the answer is like the sum or the difference between the numbers. Once students can recognize the pattern they can begin to answer fluently and without a struggle.

To help with the work of learning to quickly and easily recognize each pattern in Integers Rocket Math now includes a “Mixed Integers” program in our Universal Subscription. (Click here to get a 60-day trial subscription for $13 –rather than the standard $49 a year.) Students use the vertical number line to work a problem. In this example: -6 minus (-4). Then they have a set of problems with the same pattern they can orally answer without having to use the number line.

As with all Rocket Math programs there is a 3 minute practice session, with a partner. Then the two switch roles. Then the practice is followed by a one-minute test. If the student can answer the problems without hesitations the level is passed. If it is still difficult the student stays with that level a bit longer. When a new pattern is introduced the tests will have a whole row of problems that are the same pattern. When that level is passed the next test will have two types of problems in each row. The next level has 3 types, then 4 types in each row. Then the problem types are mixed. This way the student develops fluency in recognizing the type of problem and how to derive the answer quickly.

Rocket Math has a money-back satisfaction guarantee. If you try this and find it isn’t everything you hoped, in terms of helping your students become fluent with integers, I’ll gladly refund your money. I’m betting they’re going to love it.

Rocket Math is an offshoot of an existing programme for schools designed to increase children’s speed and fluency in answering simple arithmetic. This app encourages frequent short sessions and is supported by plenty of information explaining its purpose and methods.

The purpose of Rocket Math is to build what its developer terms “automaticity” in arithmetic. A fluent reader does not need to decode simple and frequently encountered words letter by letter. The same can be true for frequently encountered arithmetic.

When automaticity is achieved in arithmetic the answers are available in an instant. The advantages of this, beyond speed, are that it leaves more of the person’s mental processes available for other aspects of the problem. If a person does not have to think about achieving simple arithmetic answers, he or she can concentrate on the more complex and lengthier aspects of a problem.

Rocket Math the app follows on from a well-established programme of the same name based on traditional written resources. Repeat practice and a steady increase in the breadth of the covered arithmetic are at the heart of its methods.

Children are taken through a series of stages in which they are faced with a rapid succession of arithmetic questions. Remember, the purpose of this app is to build fluency in frequently encountered arithmetic problems, not complex ones. As such, the questions will be simple ones and, at first, until the breadth expands, there will be little variation in them. Only three seconds is allowed per question so, for some children, developing enough fluency to progress will be difficult but others will thrive on the challenge.

Answers are given by typing them onto a built-in number pad. The app is simple to use and looks attractive. Its space-travel styling and theme add a game-like feel although it is not a game. Speech provides a response to incorrect answers and provides encouragement between levels. It all works very well and provides the exact type of practice that it promises.

An unusual but useful feature is that the app enforces its little-and-often recommendations by insisting on a thirty-minute break after 5 minutes of play. As multiple sessions are likely to yield better results than a single, marathon session, this is an excellent feature that will prevent children from relying on a last-minute catch-up rather than a steady engagement with the app. This, combined with a useful breakdown of each child’s performance in the student report screen, provides reassurance to adults that their children are making the best possible use of the app.

A family of apps is available and potential buyers should think about which they need. Two of the apps cover addition and subtraction and two cover multiplication and division. Your choice here is obviously dependent on what aspect you would like to cover.

The remaining choice is between a school and a home version. They are identical in functionality except that the home version is free to download with a lengthy trial period. The school version has a flat, one-off, fee. Prospective teachers would still be wise to download the home version first so that they can appraise the app’s suitability.

If they choose to utilise the app within their school then buying the school version will be a simpler process than the in-app purchase of the home version. It will also allow schools to utilise the volume purchasing programme whereby they can receive a discount for buying twenty or more of the same app.

Parents will be pleased to see that the app caters for up to three children. As each child engages with the app, parents can check to see how they are performing and offer help, encouragement or rewards as they see fit. Some useful background information on the app’s purposes and usage are provided within the app itself and a more comprehensive overview of the Rocket Math ethos is available on the developer’s website.

All of the Rocket Math apps provide a learning opportunity that is tightly focused on realising their goal of improving children’s arithmetic fluency. As such, if this is a goal that you also share, you will find them good value and useful apps.

This topic of “know from memory” is something I have been digging into as a special educator. I wonder what your thoughts are about whether certain accommodations from these “know from memory” standards would actually be modifying the curriculum?

For example, if we used “extra time to respond” and the student had to use their fingers or some other method to count, would they then not be doing the standard?

This relates to where I’m at in middle school math, but I think that it’s reflected in the continuum of the common core maths.

Thanks.

Dr. Don’s response:

Actually, your example is very clear that it is not “knowing from memory.” You are describing “deriving from a strategy” or what I call, “figuring it out.” When you know it from memory, when you recall the answer, then you stop having to “figure it out.”

Knowing from memory and figuring something out are two very different things. I used to ask workshop participants to imagine sitting next to me in a bar and asking me for my name. What if, instead of saying, “Hi, my name is Don,” something different happened? What if, like the man pictured above, I was puzzled and said, “Wait a second, I have it here on my driver’s license.” Most people would likely turn their attention elsewhere while wondering what kind of traumatic brain injury I had sustained! They would very likely say to themselves, “OMG, that man doesn’t know his own name.”

The purpose of the verbal rehearsal that is a daily part of Rocket Math is to cement these basic facts in memory. Then when a student says to themselves, “8 times 7 is,” the answer pops into their mind with no effort. It takes quite a bit of practice to achieve that. However, the ability to instantly recall the answers to basic math facts makes doing mathematical computation a relative breeze. It make seeing relationships among numbers very obvious. It makes reducing fractions and finding common denominators easy. That’s why the Common Core thinks “knowing from memory” is so worthwhile. It’s why I began promoting Rocket Math in the first place.

Timed tests are not the important part of Rocket Math.

The “active ingredient” in the Rocket Math prescription, the thing that makes it work, is not timed tests. Timed tests don’t actually teach and often don’t really help students develop fluency. The usual timed tests of a random selection of all the facts can assess fluency in math–but they don’t work to develop it!

The “active ingredient,” the thing that makes Rocket Math effective, is verbal rehearsal. When students practice with their partner the students read the facts and RECALL the answers from memory and say them aloud. That verbal rehearsal is what cements them into memory. Reading the fact and recalling the answer from memory strengthens the neural connection.

Why do we give the daily tests in Rocket Math? Not to teach, but only to assess whether the facts introduced thus far have been learned well enough for the student to have new facts added to what they are learning. Individual students learn at different rates. Some students need only a couple of days of practice to memorize two new facts while others may need several days. The purpose of the daily tests is just to see if the student needs more practice time, or is ready to “swallow” some more facts.

As I note in my basic training presentation, “It’s like feeding mush to a baby. You have to make sure they have swallowed the last mouthful before you give them more.” See an explanation in this You Tube video in our Rocket Math channel: https://youtu.be/J8cWSDG0Di8

Do you want your students to learn OR are you just keeping them busy?

It’s OK if you need busywork.

It’s critical to keep some of your students occupied in order for you to have the peace and quiet you need to teach other students. Those free math worksheets of random facts are fine for busywork, provided students already know the facts.

(and this is a big but) if you want students to actually learn facts, you need math worksheets that are more systematic than the usual fact practice worksheets. A random mix of problems (on those free math worksheets) is fine for practicing what you already know, but it is USELESSfor learning new facts.

Students who don’t know their facts are left painfully counting on their fingers to do their “work.” This just wastes their time and makes them come to HATE math.

I know, because I made my students do it for years. 🙁

I discovered that with systematic practice students can actually learn math facts!

In order to learn new facts students must concentrate on a few they don’t know and practice those particular facts until they know them “by memory” without having to figure them out. After students have learned those they can then tackle a few more. That’s the only way to learn a bunch of facts. That’s what Rocket Math does. Watch this video to see it in action.

Rocket Math worksheets are not free, but they will actually teach.

Each sheet (A-Z) adds two new facts and their reverses, making the process of learning them painless. By the time students have worked their way through the A-Z worksheets of an operation they know the facts “by heart” or as the Common Core calls it “by memory.”

If LEARNING is your goal, you’ll need something more effective than the free math worksheets.

Rocket Math has a MONEY-BACK guarantee.

If you spend the $13 to get a trial subscription and you decide Rocket Math doesn’t work or you don’t want to use the program, we’ll gladly refund your money.

Plus

Students have more fun and learn better when they are practicing orally, with a partner so they can get corrections and extra teaching on any facts they don’t know well. That is part of how Rocket Math works. So it won’t just be busywork. Your students will actually learn the facts and be proud of it.

Here are 5 ways to get help with the procedures for successful Rocket Math implementation.

1.) Use the ***NEW*** search function. At the upper left of the blue navigation bar is an icon of a magnifying glass. Click on that and a search bar opens in the middle of the page. Click within the search bar and you can type in whatever you are looking for. It will bring up blogs, parts of the directions, basically anything I’ve written on the subject–which is a lot. You can get pretty specific very fast, so try this first. I’m very excited to have added this feature this week, which is why it is top of my list!

2) FAQs. Look at the Rocket Math FAQs page. Click on the linked words to the left, or navigate to it. The FAQs page is the third item under ABOUT in navigation. The FAQs page displays all of the questions from the teacher directions, and my answers, so you can scroll down to the topic you need quickly. However, all the FAQs will show up in the search function as well.

2.5) The FAQs are also available in the Rocket Math filing cabinet. They are in the top drawer, the “Forms and Information” drawer of the filing cabinet. There are titles of the FAQs so you can open and print any one you wish. Good for sharing with other staff.

3) Rocket Math YouTube channel. You can go to the Rocket Math YouTube channel. Click on the linked words to the left, or search for Rocket Math in You Tube. If you scroll down the page you can click on “View Full Playlist” and then you’ll be able to see all the topics that are available. Right now there are 37 videos, but that could change if we add some more.

4) DVD training. Order the Workshop Training DVD (#2004) for $29 This is the whole training from Dr. Don filmed and broken into chapters. It is over 3 hours and gives a lot of rationale for the procedures we recommend. Very helpful if Rocket Math is new for your staff. Really important to do things as recommended. Having coached this in many schools for many years, I can promise you it will go better if you follow the directions!

5) Contact Dr. Don. Really. You can call me (800) 488-4854 during west coast school hours and I’ll probably be able to answer the phone directly. It’s a joy for me to talk about implementing Rocket Math with teachers, so don’t be shy. But if you don’t reach me, please send an email to [email protected] rather than leave your phone number because during the school day teachers are very hard to reach. I’d rather just write an answer in an email so we don’t miss each other. And if it is a new question I’ll probably turn my answer into a blog that can be found through the search function.

As I am planning my daily schedule I am looking for how long I should set aside for Rocket Math each day. What do you suggest?

Dr. Don answers:

If you allocate 15 minutes a day for Rocket Math that will be enough. You might have trouble meeting finishing that quickly in the beginning before the routine is established. But once the routine is set there is no need to take more time than that–each partner of the pair is practicing for 2 to 3 minutes and the test takes only one minute. Don’t try to have everyone correct their partners papers as that will take too long. Making sure that students practice every day with their partner is critical to success, so anything that makes you feel “we don’t have time for Rocket Math today” is harmful to student learning.

The other key is to be sure to teach students how to practice with each other. If you can train your students to correct hesitations you will accomplish a lot with your Rocket Math practicing time. Please take a look at my video on “How to teach students how to practice.” Take the time allocated to Rocket Math for the first several days of school and follow this teaching procedure. It will pay off for you all year long in improved learning during Rocket Math time.

A number of math programs around the country introduce math facts in families. Now Rocket Math does too!

A fact family includes both addition and subtraction facts. You can see to the right 25 examples of fact families such as Set A; 3+1, 1+3, 4-1 & 4-3. The sheet shows the sequence of learning facts in the new Rocket Math program Fact Families 1s-10s (+, -). Each set that students learn from A to Y adds just one fact family to be learned, so it isn’t too hard to remember. (That’s the Rocket Math secret ingredient!)

Learning math facts in families, is gaining in popularity these days. Logic suggests that this would be an easier way to learn. However, the research is not definitive that this is easier or a faster way to learn facts than separating the operations and learning all addition facts first and then learning all subtraction facts. But learning in fact families is a viable option, and I wanted to have it available for Rocket Math customers.

Flash news!! Someone looking for a master’s or doctoral thesis could do a comparative study of students using the fact families vs. the separated facts in Rocket Math. This could easily be a gold standard research study because you could randomly assign students to conditions within classrooms–the routine is the same for both–just the materials in their hands is different! Just sayin’…

I separated out the 1s through 10s facts from the 11s-18s, because this seemed enough for one program. It would be a good and sufficient accomplishment for first grade. I have heard that some first grades prefer to keep the numbers small but to learn both addition and subtraction–so this program accomplishes that.

I added Fact Families 1s-10s (+, -) to the Universal subscription in April of 2017 bringing the total number of programs in the Universal subscription to 14 (the basic four operations and ten more!). By the fall of the 2017 school year I should have the rest of the Fact Familes in addition and subtraction available. [In time for you to do that gold standard research study!] The rest of the addition and subtraction fact families, which students could learn in 2nd grade, would be the Fact Families 11s-18s (+, -). As always, new programs are added to the Universal subscription without additional cost as soon as they are available.

I most sincerely want students to be successful and to enjoy (as much as possible) the necessary chore of learning math facts to automaticity. Please give me feedback when you use this new program, Fact Families 1s-10s (+, -), as to how it goes for the students.