Hands-on Homeschool: How important is it to memorize basic math facts?

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Math FactsI remember that when I was in third grade in public school (way back in 1980), I memorized math facts. My family had moved to Iowa from Oklahoma halfway through the fall semester, and the new school had a room at the end of the hall with a dinosaur of a computer (cutting edge back then) that we took turns using to play a math facts program.

It was a very simple timed flash card type program on a green screen. When we passed each level, the computer would print out a nifty certificate that I, for one, was very proud of. I think I still have some of those certificates. We spent all year memorizing math facts, and it was quite a competition among us more motivated students to see who could earn the certificates faster.

I didn’t realize at the time how important this was. I guess most public schools today don’t think it is important enough to spend much time on math facts because they think it is much more important to teach second graders algebra.

Math FactsThe subject of math facts is something I have been dealing with quite a bit in my homeschooling experience. When I pulled my older girls out of public school as they were going into fifth and sixth grades, I didn’t even think about going back to review math facts because they were both at the top of their classes. I thought they should have been way past that.

I realized about a year into homeschooling the girls that they really didn’t have the basic math facts memorized to automaticity (automatic response). In fact, Virginia’s teacher had taught her class a finger trick to multiplying by 9, and to this day, Virginia has to stop and do the finger trick to answer a times-nine question.

Later, I homeschooled a fifth grade boy that had been expelled and needed help. I realized right off the bat that the reason he was frustrated to the point of anger with school was that he was trying to do long division with no real knowledge of any of his math facts. Plus, he had been making good grades in math until that year. It is very frustrating to a child to make them go back and learn something they should have learned in second or third grade.

It seems that in most math classes today, students are taught math facts but never made to memorize them to a level of automaticity. Once they are taught (even if they are not truly learned), the teacher must move on in order to keep up with her scope and sequence.

This year my son Joel is in second grade. We are working with Horizon Math for 2nd Grade and Joel is doing well at it, but I realized that it moves very quickly through the math facts. He is already on multiplication, meanwhile he is still trying to memorize his addition facts. He has learned how to do addition and subtraction, but because he didn’t memorize them when he learned them in first grade, he got in the habit of using his fingers. This habit is extremely hard to break!

Rocket MathSo a few months ago I bought a math facts practice curriculum called “Rocket Math.” It was created for public schools and some of the schools around us in Oklahoma use it, however I don’t think they stick strictly to the program as it is written. Rocket Math is a ten-minutes-a-day, worksheet-based, supplemental curriculum designed for the sequential practice and mastery of math facts. To see sample worksheet pages, click here.

We have started with addition and are about halfway through. It is going slow because of Joel’s habit of counting on his fingers, even with problems that I know he already knows but feels the need to count. When we finish addition, we will start subtraction. I am hoping that since he doesn’t have any shortcut habits for subtraction yet, he’ll be able to memorize these facts even faster. We’ve been using this alongside an enjoyable math supplement series called Life of Fred Elementary Series.

I found the instructions for Rocket Math to be very enlightening. It has changed how I want my students to learn their math facts and cemented the “why” for me. So I want to share what the authors say about automaticity:

What is automaticity with math facts? (From Rocket Math)

“Automaticity is the third stage of learning. (Buckle up. We need to review a bit of Ed. Theory here. Ed who? No, Education Theory. Don’t worry, it won’t be painful, and it is really quite smart and interesting.) First we learn facts to the level of accuracy — we can do them correctly if we take our time and concentrate. Next, if we continue practicing, we can develop fluency. Then we can go quickly without making mistakes. Finally, after fluency, if we keep practicing we can develop automaticity.

Automaticity is when we can go quickly without errors and without much conscious attention. We can perform other tasks at the same time and still perform quickly and accurately. Automaticity with math facts means we can answer any math fact instantly and without having to stop and think about it. In fact, one good description of automaticity is that it is “obligatory” — you can’t help but do it.

Students who are automatic in decoding can’t help but read a word if you hold it up in front of them. Similarly students who are automatic with their math facts can’t help but think of the answer to a math fact when they say the problem to themselves. (See, that didn’t hurt much huh?)”

Why is automaticity in math facts important? (From Rocket Math)

“Automaticity with math facts is important because the whole point of learning math facts is to use them in the service of higher and more complex math problems. We want students to be thinking about the complex process, the problem-solving or the multi-step algorithm they are learning — not having to stop and ponder the answer to simple math facts. (Taking off their shoes and socks to count toes is a good indication that perhaps automaticity is not present!)

So not only do we want them accurate and fast (fluent), but we also want them to be thinking about other things at the same time (automaticity). One characteristic of students who lack automaticity in math facts is that their math work is full of simple, easy-to-fix errors. We used to call these “careless errors.” But these errors stem from not knowing math facts to automaticity — the student can either focus on getting the facts correct or on getting the procedures correct — but cannot focus on both at the same time.

So helping students learn math facts to automaticity will improve their ability to learn and retain higher order math skills — because they won’t be distracted by trying to remember math facts.”

What do you think about the importance of mastering math facts? What curriculum and/or tools are you using to help your children master their math facts? Or have you found a different approach that works for your children? We’d love to hear your thoughts and tips on this topic in the comments below.

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25 thoughts on “Hands-on Homeschool: How important is it to memorize basic math facts?

  1. Yes!! Mine are in second grade. Originally I was going to start them in on teaching textbooks this year. One thing after another happened though, an I’ve ended up just drilling addition and subtraction and now easing into multiplication with wrap ups, holey cards and dadsworksheets.com. And we supplement with life of Fred to round it out. I’m so glad it’s worked out this way, as we are getting close to instant response of correct answers. 🙂

    1. Thanks your comment. We just got Life of Fred and started it this week to go with Rocket Math! I love Fred already! I know we will feel very accomplished and fly through math once we have our math facts memorized to automaticity! It is worth all the practice.

    2. I am SO happy to hear that you homeschool moms realize the importance of memorizing the basic facts. Memorizing does mean automaticity, and the trend in public schools today is to offer various strategies to arrive at a answer for a basic fact, but not to memorize it. So, if children in public school can figure out the answers in a round-about, usually cumbersome way and that’s all that is required, then they will get a good grade. So many parents who have children in public school think their children are doing great in math because of their grades or because the teacher says they aren’t having any problems with the math curriculum. Little do they know, if their children don’t have the basic facts memorized, that their children will have tremendous struggles with higher level math. Memorized multiplication facts are the pre-requisite for fractions and fractions are the pre-requisite for algebra.

      There is a growing group of homeschoolers who think that conceptual and discovery math is the best and only way to teach it. This alarms me. I thought that homeschoolers were going to be our sensible mathematics stronghold! I just retired from teaching elementary school and I have to say that the public schools jumped on that bandwagon about 20 years ago and now look at their messed up math.

      Please, please, stick to your guns and stick up for memorized basic math facts! It doesn’t have to be robot-like or kill and drill. I always blended both conceptual and memorized basics and made it interesting. It worked out great…and you are probably doing the same. THANK YOU!

  2. I think this is super important. As a former public school teacher, I created my own drill-and-practice flash card system for the second half of first grade to make sure that my kids knew their facts – but my daughter came home not knowing hers – being supposedly had ‘passed’ the test for them. We’re now working our way through, memorizing and practicing, and we’re almost to the 10s. As you say, you can’t do any other math if you don’t have the facts down cold!

  3. Amen! As a business owner in the food industry we have had so many problems finding customer service people who can do basic math on the fly. It is an important skill to have in everyday life.

  4. Yes! I struggled like everything with division. Until I finally went back to multiplication and got some fluency. I still have to think pretty hard for subtraction.
    I didn’t take me long to decide that my children were memorizing math!
    My plan: Life of Fred and a variety of speed-enhancers. Maybe timed worksheets, computer games. We used to play Funnels and Buckets on an ancient DOS PC. It was so much fun. I wonder if anything like it still exists??

  5. I am thrilled that you posted this! I believe that it is very important to learn the basic math facts. After you can add it is more simple to multiply. After you can subtract it is easier to divide. Without the basics to build on, you do not have a foundation. I plan to teach both of my children memorization of their math facts. I would love to know if you know of any computer based games that offer timed drills.

    1. We have a math facts app on our ipad that works really well. My favorite game though is called TimezAttackz – it isn’t an app but a computer game. The little dragon has to go through a castle and giants come at him and you have to answer the multiplication question on his belly before you gets to you. It gives you the answer if you get it wrong and repeats until you pass. Joel loved it and started playing it on his own as a 4 year old when I was trying to teach the 5th grade boy his facts. Before Joel even knew what 55 was he knew that 5×11 was 55. He said five five, lol. They are beta testing other math facts – and Joel has played what they have of the addition. Definitely worth the money if your student likes video games.

  6. THANK YOU! I have been feeling frustrated with the never ending practice of math facts with Saxon 1 when it seems my friends who use Horizons and Singapore have moved on to other things. My husband who struggles with math wants to continue with Saxon. You have confirmed our thought that we sometimes push things on our children that they aren’t developmentally ready to learn without making sure the things they are ready to learned are concrete. I will stick it out the math facts!

    1. Definitely stick it out! I really think that once your children have the math facts down they will move through the curriculum much faster and with more confidence!

  7. I felt this way, but have been reluctant to push it on my girls. I have one who can almost do it, but the other uses fingers. I am also having to untrain them in the “new” math. I am in my second year of Homeschooling. They both were in public school long enough to be “ruined”. Everyday gets better, but still there are issues we are working on.

  8. My daughter has ADHD, CAPD, and dyslexia. She is a right-brained visual learner, but was never able to master her facts. We tried everything. There are some kids like her who just can’t memorize, but it’s not for lack of trying. It was hard for me to comes to terms with this, but she proves daily that she is able to do everything she needs to do and more, so if this is as bad as it gets, we are good to go. “)

    My Fave Highschool Site
    Let’s Homeschool HIgh School (www.letshomeschoolhighschool.com)

    1. Thanks for the comment, Jackie. I don’t know that much about those things but the great thing about educating your own children is that you can make sure they have what they most need to prepare them for life – whatever that is and whenever. She may pick up those facts later on when she is ready.

  9. Hmm..now you’ve got me thinking. My girls are both in second grade and are using Horizons Math too. They are doing great, but the younger one still counts on her fingers. It might be time for some memorization.

    Thanks for linking up to the Hearts for Home Blog Hop! Blessings!!

    1. We are at the end of Horizons Math 2 and they are already jumping into some algebra – he gets it but I think I am going to hold off on finishing and spend more time getting those math facts down. He gets frustrated trying to finish the page because of all of the addition and subtraction he is trying to muddle through (still using fingers). Thanks for the comments!

  10. We use Saxon math and it has a math facts component, which we work on every day. Some facts are remembered faster than others, but we keep at it every day. I keep reminding my son of exactly what you shared from Rocket Math: we need to memorize these basic steps so that, later, when the problems are more complex, we won’t have to waste time on the simple stuff like the doubles facts or the sums of 10 facts. It’s such an important set of knowledge that most people just ignore now. Thanks for bringing it up!

  11. Very wise words. I learned my math facts eons ago in school and still use them almost daily. Some of my grandkids have gotten less of the memorizing and more the algebra WAY too young and I so disagree with that. My homeschooling grandkids are memorizing the skip counting tables and I’m really glad for that. Plus we are working at showing them how those work with multiplication and working on times tables as well. Great advice.

  12. Rosanna >>>whatever that is and whenever. She may pick up those facts later on when she is ready.<<<

    You are so right. She has proved that with other skills so far. I guess I'll have to just keep my fingers crossed.

  13. Saw this post pinned on pinterest. My soon to be finished with second grade son is still struggling with his math facts. He is in tears often while doing math. I taught 4th grade over a decade ago and was frustrated then because many of my students had never learned their basic addition and subtraction facts and therefore struggled with multiplication and division. I’ve been searching for any ideas at all to help my son and will look into the things you have mentioned. We’re seriously considering homeschooling him next year and starting research now into curriculum, etc.

    1. If you want it to be fun I would suggest Math Blaster (for all operations) and Times Attacks for multiplication. Scholastic also has a fun computer math game. I have also stuck sticky notes with answers all over the walls and given him a nerf gun and then called out problems, then he would try to shoot the answer. Anything to make it fun and memorable.

    2. Please check out Color Coded Multiplication from Margo’s Math and More. It is a supplement to any math curriculum you use and it focuses strictly on the multiplication facts. Color cues and a series of great activities make the multiplication facts “memorable”. Created by a teacher who was frustrated by the absence of teaching the basic facts to mastery in most of today’s math programs. You will get personalized service and guidance by a simple phone call or email. The website: http://www.margosmathandmore.com.

      Hope everything works out for your son.

  14. I am SO happy to read that many of you consider the memorization of math facts to be important.

    I taught elementary school students for 30 years, up to 2011, and saw the steady decline in math acquisition and the steady increase in math anxiety. (for both teachers and students).

    This all started when memorization of basic facts was put on the “back burner”, then ignored, and finally discouraged and replaced with the enthusiastic promotion of “thinking like a mathematician”. In other words, let’s do away with conventional ways to compute and devote our energy to innovative ways to problem solve.

    When it came time to do multi-step multiplication, fraction work, pre-algebra, the students had faced their own roadblock. They didn’t have the foundational knowledge necessary to be able to succeed in doing this level of math.

    I came up with a little program that worked extremely well. My plan had neurological underpinnings for memory and psychological incentives for maintain student interest. It was called Color Coded Multiplication by Margo’s Math and More. This was a very simple program which used color cues to aid in the memorization of multiplication facts. Once my students mastered these facts, math became much more do-able for them.

  15. Thank you for this post, very interesting. I teach Pre-cal and AP Calculus at a low-performing public school. The math department’s focus is entirely on getting students to pass the Algebra I state test (the mantra is “we are all Algebra I teachers!”). After 2 years of teaching I am finally being allowed to lead a department meeting on vertical teaming and what students need moving forward to college-level math. I want to emphasize that even though the STAAR test allows use of a graphing calculator and a formula sheet, not all instruction has to be that way! It is so difficult to take students who have never been asked to graph anything by hand or memorize a formula and prepare them for an AP exam which has no formulas provided (not even more complicated ones like volume of a cone) and allows a calculator on less than 1/3 of the test.

    1. How are the students with their knowledge of basic facts?Do they have them memorized for automatic recall? As you know, math is a cumulative, relational subject-every process is built on the previous one and relates to it in some way. No matter how complex or advanced a formula is, you must use all or some of the basic operations (addition, subtraction, multiplication, division) to solve the problem. Mastery of the basic operations is a must! Memorized addition facts are the prerequisites to subtraction. Memorized multiplication facts are the prerequisites to division, fractions, and algebra. Not having these facts memorized is an obstacle in the pursuit of higher math and moving toward college math.
      If you’re feeling a little dismayed, take heart because you are not alone.
      In 2013, Cliff Mass, professor at the University of Washington stated ,” Nearly ¾ of Seattle Community
      College students require remediation in math……and….Over 100 Seattle students were not able to graduate high school because they couldn’t pass state-mandated math exams. Seattle’s math curricula was poor at all levels. The curricula minimized the development of basic skills and rarely brought kids to mastery.”
      The National Opinion Research Center at the University of Chicago surveyed area algebra teachers. Their chief complaint was that students came to them unprepared in basic mathematical skills and concepts.
      Here are some other statistics from the National Math + Science Initiative:
      *Only 44% of 2013 U.S. high school graduates are ready for college level math.
      *Only 42% of American 4th graders and 35% of American 8th graders performed at or above the proficient mathematics level in 2013.

      From “The Emerging Education Reversal in the United States: National and State Level Trends (University of Nevada)
      For over 200 years, educational attainment in the U.S.has climbed, with the largest gains occurring
      recently from 1940-1980. Beginning in the mid-2000’s, attainment among adults has flattened. A closer look at this educational “ceiling” reveals that the educational gains of the population have not only stopped but are beginning to decline. The reversal emerged for the newest members of the adult population around 2000. In addition, college completion rates, although not yet reversed, are slowing dramatically.
      Is it a coincidence that the constructivist/method of teaching math without the memorization of basic facts began picking up popularity in the 1980’s and was almost the exclusive way to teach math by 1995? Were the adults referred to here the students of this type of curriculum? Could this be one of the contributing factors for this education attainment reversal?

      On the bright side, a study published in the Journal of Neuroscience (2013), proved that when solving simple arithmetic problems, students who rely on memory rather than problem-solving do better on more complex mathematical problems, such as those found on the PSAT.

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