Can memorizing and drilling math facts backfire?

[twoforjoy]

I picked up some math games to play with my DS7 recently. I'm noticing--and this would seem to go against conventional wisdom--that he actually does a lot better with the problems that we haven't drilled and he hasn't memorized yet. The fact that we've actually reviewed and drilled and memorized, he freezes up over. So, he can tell me, just having to pause for a moment to think, that 13+5=18 (we haven't drilled or reviewed that) but will freeze up and go blank if asked what 2+5 equals.

 

If you have a kid who is strong conceptually in math, can attempts at memorizing and drilling facts backfire and undermine their confidence and ability? Because I feel like that's what's happening. I don't want to put my DS behind by not having him memorize his facts, but if he can quickly figure out the problems, is it really that important that he has the answers memorized?

[Pata]

Not memorizing can backfire, at least it did for us by the time she hit longer multiplication problems & long division. Her progress stalled out because she didn't know her facts. We've been using xtramath.org to drill her facts and I was shocked to see her scores on addition & subtraction, which I thought were solid. I really wish that I had put more emphasis on fact memorization much earlier, even if she didn't enjoy it because it makes math so much easier for them as they go on if they can automatically recall the facts. All that to say that this is just my personal experience and your child may be different :D.

Edited May 30, 2011 by Pata

[stripe]

I put the focus on understanding more than drilling, until it was very clear that they were understood, then I did both. I think the first semester of y1 of MEP is fantastic for this. I supplemented with Math Mammoth and other games, but that approach worked really well. Slow, though. But ultimately I'm happy with both the process and outcome, and it's made the transition to bigger numbers And multiplication and divsion fairly unremarkable.

[twoforjoy]

Not memorizing can backfire, at least it did for us by the time she hit longer multiplication problems & long division. Her progress stalled out because she didn't know her facts.

 

I guess this is my question: what does not knowing math facts mean? Is not having them memorized rotely the same as not knowing them? Can you say that a child who hasn't learned their facts by rote memorization but who is able to quickly respond to addition and subtraction problems knows their facts?

 

What does "know" mean when we're talking about math?

 

My concern is that my DS seems to have learned his facts pretty well on his own, conceptually. (We did Miquon for the first two years of homeschooling.) I'm worried that I'm messing up his progress by focusing on drilling and rote memorization, and undermining his confidence, because at least for now that's what seems to be happening.

Edited May 30, 2011 by twoforjoy

[Pata]

My dd had a conceptual understanding of multiplication & division. She knew how to find the answer using skip counting, with manipulatives or by adding/subtracting from the facts she did have memorized (ie. 8x8 by subtracting 8 from 8x9). The problem was that she couldn't do that quickly, so one problem would take 5 minutes to do, which becomes frustrating when you have 20 problems in your assignment. She needed to be able to recall her facts quickly, so that she could focus on the new information/problems she was learning to do. IMHO, she understood her facts, but didn't know them (meaning she couldn't answer them without thinking). As for addition & subtraction, I never drilled them because dd seemed to know them after using them a lot. She does know these facts, but the speed is not there yet, which I think has led to some of her recent frustrations with math.

 

I'm not really into rote memorization, as I believe that a conceptual understanding if far more important. That said, I have come to appreciate that rote memorization of math facts is extremely beneficial as long as there is already a conceptual understanding in place. It will help with their computation speed and lead to much less frustration in math.

[blessedmom4god]

We've been using xtramath.org to drill her facts and I was shocked to see her scores on addition & subtraction, which I thought were solid..

 

Thanks for sharing this link! I have been looking for a free site like this for awhile. I have been using the mathusee drill page for a couple of years with my kids but it doesn't keep track of speed(over time) or how well they know each fact.

Nicole

[ChrissySC]

I think that you need to work on mental math skills too. I do not think it is just the memorization that becomes the issue, but the ability to perform simple calculations in your head.

 

Are you skipping this portion of your math program? Not practicing the mental skills maybe? Just a thought ... HTH

[Chelli]

Thanks for sharing this link! I have been looking for a free site like this for awhile. I have been using the mathusee drill page for a couple of years with my kids but it doesn't keep track of speed(over time) or how well they know each fact.

Nicole

 

:iagree: Thanks soooo much for this website! I can't wait to let dd use this today. It looks great! This is why I love the HIVE :001_wub:

[Pata]

You guys are welcome! I actually found out about it from another thread, gotta love the Hive! I love that it sends me reports of her progress, so I can keep track of her without all the nagging :).

[Critterfixer]

If you have a kid who is strong conceptually in math, can attempts at memorizing and drilling facts backfire and undermine their confidence and ability? Because I feel like that's what's happening. I don't want to put my DS behind by not having him memorize his facts, but if he can quickly figure out the problems, is it really that important that he has the answers memorized?

 

In the situation you described, yes. He may confuse having something memorized with actual automatic recall from having done it so many times. I'd rather have my sons work out 2+5 with crayons or the abacus until they have done it so many times that they no longer need to do it. Memorizing the exact steps of how to ride a bike is not the same as riding the bike, falling, crashing, starting out slow and getting faster until you don't even think about how you do it anymore. Memorization of process comes from doing it over and over again, not just "saying" it over and over again.

I have seen many times this year that a child may well "know" his flashcards, but put that problem in another way (turn it into a word problem) and they didn't really "know" it. (I've even seen a child mess up with the manipulatives after he answered it correctly with the flashcards.) If he is comfortable with larger addition and struggling with simple stuff have him show you how he "knows" how to work the larger problem and have him apply the method to the smaller problem.

My guys are age 7.

[In The Great White North]

He needs to both understand it conceptually and have them memorized. When it comes to factoring binomials in algebra, he will be at a severe disadvantage unless he has the memorized backwards and forwards.

[Free]

I think that you need to work on mental math skills too. I do not think it is just the memorization that becomes the issue, but the ability to perform simple calculations in your head.

 

Are you skipping this portion of your math program? Not practicing the mental skills maybe? Just a thought ... HTH

 

I agree with this. It seems that your child has a natural ease with numbers and with doing mental math. I feel doing practice problems frequently will slowly lead him to memorize his facts.

[Spy Car]

I picked up some math games to play with my DS7 recently. I'm noticing--and this would seem to go against conventional wisdom--that he actually does a lot better with the problems that we haven't drilled and he hasn't memorized yet. The fact that we've actually reviewed and drilled and memorized, he freezes up over. So, he can tell me, just having to pause for a moment to think, that 13+5=18 (we haven't drilled or reviewed that) but will freeze up and go blank if asked what 2+5 equals.

 

If you have a kid who is strong conceptually in math, can attempts at memorizing and drilling facts backfire and undermine their confidence and ability? Because I feel like that's what's happening. I don't want to put my DS behind by not having him memorize his facts, but if he can quickly figure out the problems, is it really that important that he has the answers memorized?

 

Sure it can backfire. What you are witnessing is stress and the beginning stages of "math anxiety." What's likely to come next is "I'm not good at math" > "I hate math."

 

I think you understand this or you would not be asking. While developing an automaticity with math facts is important in the long run it is a huge risk to induce math anxiety producing means to get to that end. The costs far outweigh the benefits.

 

You can see this. There is no other explanation for why he can do 13+5 and "freezes" on 2+5 other than the beginning signs of math anxiety. It is classic.

 

There are other ways to work these math facts that are way less stressful (and less stressful means more effective). The Right Start game set is one fun way to reenforce a wide variety of math facts, and there are numerous electronic games and devices that can take the place of drill.

 

I would look for other means to work these skills. At least until any sign of anxiety over being drilled passes. Children can be eager to be drilled, and that is the stage where it is a useful activity. But when they do worse post-drill than pre-drill it is a clear sign that it is doing more harm than good.

 

Bill

[Spy Car]

I think that you need to work on mental math skills too. I do not think it is just the memorization that becomes the issue, but the ability to perform simple calculations in your head.

 

Are you skipping this portion of your math program? Not practicing the mental skills maybe? Just a thought ... HTH

 

:iagree:

 

Working the mental math skills strengthens the mind (as exercise) and the skills are "scaleable" to ever more complex problems.

 

Bill

[Spy Car]

In the situation you described, yes. He may confuse having something memorized with actual automatic recall from having done it so many times. I'd rather have my sons work out 2+5 with crayons or the abacus until they have done it so many times that they no longer need to do it. Memorizing the exact steps of how to ride a bike is not the same as riding the bike, falling, crashing, starting out slow and getting faster until you don't even think about how you do it anymore. Memorization of process comes from doing it over and over again, not just "saying" it over and over again.

I have seen many times this year that a child may well "know" his flashcards, but put that problem in another way (turn it into a word problem) and they didn't really "know" it. (I've even seen a child mess up with the manipulatives after he answered it correctly with the flashcards.) If he is comfortable with larger addition and struggling with simple stuff have him show you how he "knows" how to work the larger problem and have him apply the method to the smaller problem.

My guys are age 7.

 

:iagree:

 

Well said!

 

There is something very different about an understanding that comes from repeatedly working the same set of interrelated "math facts" in a wide variety of different ways (from manipulatives, to basic equations, to world problems, to how much less/more, to bar graphs...on and on).

 

If you work them, and work them, and work them...they become "known" facts that are entrenched in the important upper-cognitive levels of the mind. This is "deep" knowledge.

 

The flash-card memorization is a short cut that only engages the lowest level of cognition. This is not activity that really works the mind, and the recall skills often fail when the context changes just a little. Where a child who has learned through testing their understanding in a great variety of ways is unlikely to be phased when thrown a multi-part problem that they need to keep straight in their minds. It is a very different skill base.

 

Bill

[FO4UR]

The end goal is automacity with the facts, but "memorization" can backfire. imho :iagree:with working with them until they are "owned" and letting the facts cement in the brain as a natural course of things. I think it was in RS materials that I read that flashcards are only fun for kids who don't need them...and my ds8 finds them fun only when he's the fastest and loudest (most obnoxious!!!:tongue_smilie:).

 

Some summer math fun = lay a bunch of craft sticks at the end of the driveway, and sit at the other end with flashcards. Hold up a card, and he has to run down and grab the correct number of sticks (5+7...5 in one hand, 7 in the other), and then tell you what it = If he has trouble, he can easily move 3 sticks over to make the 7 into a 10 and see the answer, but if he can do it mentally he will b/c it's fun running.

[DarlaS]

If you have a kid who is strong conceptually in math, can attempts at memorizing and drilling facts backfire and undermine their confidence and ability? Because I feel like that's what's happening. I don't want to put my DS behind by not having him memorize his facts, but if he can quickly figure out the problems, is it really that important that he has the answers memorized?

 

No.

 

Only memorizing can backfire, but memorizing anything (math facts, The Gettysburg Adress, poetry...) is a perfectly good thing to do. :001_smile:

[stripe]

I wouldn't consider it enormously important to memorize haiku in Japanese, which they don't speak. Poetry in languages they understand -- yes. Memorizing the quadratic equation at age 3, not so much.

 

SWB said she thought Charlotte Mason was wise when she said no child should memorize a multiplication table until he has made one.

 

I found a huge shift in thinking -- an improvement in thinking -- to stop and really understand. Then, with practice, memorization became easy.

[Critterfixer]

I wouldn't consider it enormously important to memorize haiku in Japanese, which they don't speak. Poetry in languages they understand -- yes. Memorizing the quadratic equation at age 3, not so much.

 

:iagree:Memorization comes so easy to young children. Mine have memorized double the poetry recommended by FLL, simply because they just soak it up. But I've learned something very interesting about my children and memorization this year. I've noticed that even after they have memorized a book we've read over and over, or a movie, or a song; they still want me to read it, to watch it, or sing it over, and over and over again. They are not tired of it, or sick of seeing it or of hearing the song play over and over. They literally seem to pick up on something new every time. Just because it has already been memorized does not mean that they have learned all they are going to learn from it. Even when a child has demonstrated that he "knows" a math concept, even after he has memorized it, he may still benefit from practicing it. If I remember right, just because I could play Moonlight Sonata, that didn't excuse me from having to play my scales. And I could mess those up!

The trouble with making memorization part of math lessons is that it could very well occur naturally and STILL, the child might not have a full grasp of the concept. Yet, it is quite easy and natural to assume that because he can demonstrate that 2+3=5, and can say from memory 2+3=5, and even remember that two and and odd number is always the next odd number, that HE KNOWS IT. Mine can do all this. BUT, if they are faced with a word problem they still need to draw out the pictures and they will hand count every picture to calculate the answer. They may KNOW IT by a number of different ways, but they still don't. They are still learning.

[stripe]

Exactly. I had a child who seemed to be able to parrot some of the facts but didn't know how to use them. At all! Much to my great surprise. I switched to MEP and was happy, especially with year 1's first semester. The second semester of y1 got repetitive, but the first semester was really an interesting examination of numbers under 10. Understanding could not be faked.

 

At one point I was a bit sick of doing the same basic additions (5+2, 8+3) over and over again, each time as if it was something new! I really felt like I was going to go insane. But then I read in Mater Amabilis, the suggestion to do a math program daily plus 5 min of drill. That helped. I found it to be enough, when done consistently, yet not so much to be boring. Especially since the drill can take different forms, including card games and computer games (such as this nice site).

[Pata]

If you work them, and work them, and work them...they become "known" facts that are entrenched in the important upper-cognitive levels of the mind.

 

This is what I thought and this is what we did, mental math exercises, word problems and work them, work them, work them. Dd's conceptual understanding is fantastic, and I'm very happy about that, but her speed is not there, especially in multiplication & division. There is value in using rote memorization of the math facts after the conceptual understanding is in place. We've been working on consistently drilling facts for several weeks now and I've already seen an improvement in her speed and confidence. For me, not doing rote memorization of facts produced math anxiety because she couldn't recall the facts quick enough to feel like she knew how to do the problem.

 

IMHO, make sure his conceptual understanding is there by working all the problems with manipulatives. Once that is solid (he'll set the manipulatives aside on his own when it is), work on mental math and drilling the facts. Knowing all the facts down cold is equally as important as understanding the why's behind it. Together they produce a solid math foundation.

 

For reference, we've completed Singapore's CWP book 1-3, Miquon's orange, red, blue and green books and are currently working through Singapore's Primary Math 4A including the mental math exercises.

[Spy Car]

This is what I thought and this is what we did, mental math exercises, word problems and work them, work them, work them. Dd's conceptual understanding is fantastic, and I'm very happy about that, but her speed is not there, especially in multiplication & division. There is value in using rote memorization of the math facts after the conceptual understanding is in place. We've been working on consistently drilling facts for several weeks now and I've already seen an improvement in her speed and confidence. For me, not doing rote memorization of facts produced math anxiety because she couldn't recall the facts quick enough to feel like she knew how to do the problem.

 

IMHO, make sure his conceptual understanding is there by working all the problems with manipulatives. Once that is solid (he'll set the manipulatives aside on his own when it is), work on mental math and drilling the facts. Knowing all the facts down cold is equally as important as understanding the why's behind it. Together they produce a solid math foundation.

 

For reference, we've completed Singapore's CWP book 1-3, Miquon's orange, red, blue and green books and are currently working through Singapore's Primary Math 4A including the mental math exercises.

 

It is all a balancing act. I've said before that once concepts are learned that there is a value in developing fast recall. The problem can be how one does that. When means are used that cause a child to "freeze" there is stress, and this can cause math anxiety. Is if possible that at some point not having a good grasp of math recall can cause anxiety too? Sure.

 

My concern is how one gets to (or towards automaticity). For addition and subtraction in particular I think working the mental math skills is essential and memorization can be a shortcut that is counter-productive vs learning though practicing mental math skills.

 

With multiplication and division there is likely to be more of a reliance on rote memory.

 

Remember in this case the child was "freezing" on 2+5 (a drilled fact) but getting 13+5 (an "undrilled" equation), this to me is evidence that the means of drill are causing anxiety. Not a good thing.

 

Does that mean not using some method to sharpen recall? No. Even drill (for kids who are almost there, and enjoying the process) has merit. But when the drill is counterproductive I would look to other means.

 

Bill