Memorization of Basic Math Facts

Have you looked at Math Facts the Fun Way? This uses stories with colorful visualization, and almost always “sticks” quickly with LD kids who haven’t been able to learn math facts any other way. The addition kit is about $44 at http://www.citycreek.com (includes a consumable workbook). Since your son is highly visual, my bet is that this would work quite well. Kids who learn this way develop mental shortcuts with practice, and eventually are able to drop the visualization component.If you haven’t yet done so, you might want to take a look at the articles in the “LD in Depth” section of this website, under “Math Skills”. The article on Developing Fluency with Basic Number Facts can be enlightening. There is an article there (I think) on software for LD kids, including a math program that will print worksheets to specifications — such as only a certain number of problems on the page, different sizes of typeface, etc. Maybe you could start with just two different problems on the page.My dd had a problem remembering math facts until she went through PACE (http://www.mentalskills.com). PACE seemed to help with sequential processing a lot also, and has a good reputation for helping attention problems.Mary: My son is a second grader with Asperger’s Syndrome, dysgraphia, ADHD
: and a host of specific learning disabilities and language
: processing problems. He is an excellent reader (heavily dependent
: on sight word recognition and context clues, but able to decode
: when all else fails) and loves science and social studies. He is
: behind his peers in spelling and written expression, partly
: because of his dysgraphia and partly because he has poor visual
: sequential memory skills when applied to spelling words. His math
: abilities and disabilities are an enigma to all of his teachers.
: He was counting and was able to associate the numbers 1 through 10
: with their corresponding quantities before he was 2. He could
: identify numbers to 100 both receptively and expressively by the
: time he was three. His math ITBS scores in first grade were all
: above average, with a national percentile rank of 85% overall. His
: ability to solve word problems, count money, and generally
: understand math concepts is developmentally appropriate.
: Unfortunately, he isn’t learning to memorize math facts. We have
: been trying since kindergarten to teach basic sums and he just
: can’t seem to learn them. He uses manipulatives and number lines
: very skillfully and counts up and back in his head (or out loud)
: to arrive at answers, but virtually nothing is memorized. He even
: understands place value and the concept of regrouping, but he
: can’t memorize 3+6 or 2+5 to save his life. For some reason, he
: was able to memorize doubles up to 10+10 and he can solve any
: double plus one problem fairly quickly after a warm up of
: reviewing doubles, but the other facts are somewhere in a black
: hole. Adding or subtracting 0 and 1 aren’t too taxing, but mixing
: addition and subtraction problems on a page sends him over the
: edge and alternating between minus one and minus zero on the same
: worksheet is too challenging for him. If you gave him a dollar and
: told him tootsie roll pops were on sale at 2 for a quarter and
: asked him how much change he would get if he bought 6 tootsie roll
: pops, he would have the patience and ability to work through all
: the steps to get to the answer, but when he sees a worksheet with
: just numbers on it, he can’t get through it without becoming very
: upset. We were willing to wait patiently and let his math facts
: fall into place over time as he worked on a variety of math
: problems and activities, but he has made no progress in over two
: years. We have tried Kumon worksheets and they were great for
: handwriting but did nothing to help him learn math facts. Flash
: cards now send him into a panic. Off the shelf computer programs
: hold his interest at the simplest level but he quits as soon as he
: gets beyond the +2 level. Minute Math or anything with a timer is
: enough to make him break out in hives. What should we be doing to
: help him acquire this important foundation skill? Are there
: special computer programs that do for math what Fast ForWord does
: for language? Please keep in mind that unless he is enjoying what
: he is doing, he has the attention span of a house fly. Can anyone
: out there help me help my son?

“Unless he is enjoying what he is doing, he has the attention span of a housefly” —love the description; hmmm, sounds like most of my family.Some practical techniques for learning basic math facts: (1) verbal. Try simply reciting them in rhythm. No, no special tune, no special silly rhymes, no nothing — just distractors, and he can make up more than enough of those on his own. Just recite problem AND answer together in a rhythmic chant: One plus zero is one One plus one is two One plus two is three One plus three is four…very important points: ** don’t just give him the questions and have him chime in the answer; he’ll recognize very soon that it’s a counting pattern and tune out of the major point, which is *what* you are counting. Have him chant the list of ten sums with you, then aloneThis keeps some interest on the task, because he is talking and you are listening, and he is trying to get it perfect. I make a game-buzzer bzzzeep noise when kids miss, and then we start again. I make a chime noise when they get through correctly, and maybe give a token award such as a gold star.** You only need the ten sums from plus zero to plus nine; after that, place value takes care of it. The idea of memorizing up to twelve or twenty comes from the same era as slate pencils, when it was hard to write things down.** for kinesthetic help, he can move a hand or foot in time to the rhythm. Again, no fancy patterns as distractors, just beating a rhythm.** if this seems to work at all, work on *overlearning* it. After he is getting all ten sums in a row, all ten rows, have him do two or three rows a day, until he can say the whole table. Then have him practice it at least a couple of times a week for another month or two.(2) Visual: Again, one of the major points is to get rid of distractors. No bunnies, leprechauns, etc. Get 100 sheets of nice solid paper or light cardboard in 8 1/2 by 11 size, plain white. Write in large marker a full inch or two high one math fact at the bottom of each one. first card: 1 + 1 = 2 second card: 1 + 2 = 3 etc.Then illustrate these clearly with nice round dots, red for the first number and blue for the second (or any two good clear colours that the child can distinguish) Make the dots neat and as identical as possible by tracing something like a medicine-bottle cap. Colour the dots in solid. Resist temptations to decorate with happy faces or to arrange the dots in pretty patterns or whatever; the goal is to remove as many distractors as possible and pay attention to the far more profound and interesting patterns in the way numbers work together. The cards should be nearly identical except for the changes in number.Then put the first nine cards — the one plus (number) set, omitting zero which comes later in visualization. — along one or two walls of your study area.Give the child *orally* lots of one plus (number) problems, and have him go to the appropriate card and count up as he needs to. Then play for speed, to see how many he can do without going to the cards. When he can zip through this set, post the two plus (number) set, and so on.(3) Combined: the above two games — can you tell me the (number) pluses in order fast , and can you get the (number) pluses in mixed order fast without looking or counting — work even better when used at the same time.(4) Problems: Get on your computer and type up in 18-point lots of little problems that explore simple sums, first in sets of one plus (number), two plus (number), etc. and then mixed: Nog has one hog. He buys one hog. How many hogs does he have now? Matt has one cat. He finds two cats. How many cats does he have now? Jan has one fan. Ann has three fans. How many fans do they have together? and so on.Have the child write out the problem as well as the answer each and every time, ie 1 + 1 = 2, never just 2. Writing just answers saves thirty seconds now and wastes years of your life later when you have to go back and learn to write a logical development.**********************************************Trying for a happy medium here: YES, it is very important to learn basic number facts! The advanced concepts that you want and need to learn later are *based* on these number facts and a good number sense, and concepts without facts are like butter without the bread — too rich and no structure (on the other hand, facts without concepts are like bread without butter — dry and tasteless.) My tutoring students almost all got to need my services by being handicapped with their number facts. Several members of my own family have been handicapped by bad teaching of basic facts, and have had college and professional futures damaged.** On the other hand, why is it important for your child to do numbers-only worksheets?** These are totally artificial, not real-world (I always ask my students: When did you last go into a business and hear someone say “Oh my God, we have to get these worksheets filled in by noon?” *Nobody* out of school does worksheets.)I sometimes assign repetitive practice for overlearning, a necessary goal for automatic skill, like doing piano scales; but this is a refinement and/or last resort. IF (two very big ifs) your child is doing OK on grade-level tests and can retrieve the number facts in whatever way works for him at a speed that is consistent with his grade cohort, why is the filling in of useless paper a required ritual? Particularly a problem-solving person with a creative flair, as you describe him, can have his abilities turned off by being forced through this kind of wasted effort. Ask yourself what your real goals are — forcing him to fill in this paper because that’s the way it’s done, or having him grow up knowing numbers and liking to solve puzzles with them?Once more, I am *not* saying to ignore learning and automatizing facts, or to omit writing work on paper — just the opposite; but I am saying that filling in blanks is not a major life goal for most people, and this *method* of teaching can be reduced or totally omitted.Good luck, and I would be happy to hear progress reports from you.
: My son is a second grader with Asperger’s Syndrome, dysgraphia, ADHD
: and a host of specific learning disabilities and language
: processing problems. He is an excellent reader (heavily dependent
: on sight word recognition and context clues, but able to decode
: when all else fails) and loves science and social studies. He is
: behind his peers in spelling and written expression, partly
: because of his dysgraphia and partly because he has poor visual
: sequential memory skills when applied to spelling words. His math
: abilities and disabilities are an enigma to all of his teachers.
: He was counting and was able to associate the numbers 1 through 10
: with their corresponding quantities before he was 2. He could
: identify numbers to 100 both receptively and expressively by the
: time he was three. His math ITBS scores in first grade were all
: above average, with a national percentile rank of 85% overall. His
: ability to solve word problems, count money, and generally
: understand math concepts is developmentally appropriate.
: Unfortunately, he isn’t learning to memorize math facts. We have
: been trying since kindergarten to teach basic sums and he just
: can’t seem to learn them. He uses manipulatives and number lines
: very skillfully and counts up and back in his head (or out loud)
: to arrive at answers, but virtually nothing is memorized. He even
: understands place value and the concept of regrouping, but he
: can’t memorize 3+6 or 2+5 to save his life. For some reason, he
: was able to memorize doubles up to 10+10 and he can solve any
: double plus one problem fairly quickly after a warm up of
: reviewing doubles, but the other facts are somewhere in a black
: hole. Adding or subtracting 0 and 1 aren’t too taxing, but mixing
: addition and subtraction problems on a page sends him over the
: edge and alternating between minus one and minus zero on the same
: worksheet is too challenging for him. If you gave him a dollar and
: told him tootsie roll pops were on sale at 2 for a quarter and
: asked him how much change he would get if he bought 6 tootsie roll
: pops, he would have the patience and ability to work through all
: the steps to get to the answer, but when he sees a worksheet with
: just numbers on it, he can’t get through it without becoming very
: upset. We were willing to wait patiently and let his math facts
: fall into place over time as he worked on a variety of math
: problems and activities, but he has made no progress in over two
: years. We have tried Kumon worksheets and they were great for
: handwriting but did nothing to help him learn math facts. Flash
: cards now send him into a panic. Off the shelf computer programs
: hold his interest at the simplest level but he quits as soon as he
: gets beyond the +2 level. Minute Math or anything with a timer is
: enough to make him break out in hives. What should we be doing to
: help him acquire this important foundation skill? Are there
: special computer programs that do for math what Fast ForWord does
: for language? Please keep in mind that unless he is enjoying what
: he is doing, he has the attention span of a house fly. Can anyone
: out there help me help my son?

: There are some good math sites on-line that offer games designed to reinforce the learning of math facts. If you e-mail me, I’ll send you the links.My son is a second grader with Asperger’s Syndrome, dysgraphia, ADHD
: and a host of specific learning disabilities and language
: processing problems. He is an excellent reader (heavily dependent
: on sight word recognition and context clues, but able to decode
: when all else fails) and loves science and social studies. He is
: behind his peers in spelling and written expression, partly
: because of his dysgraphia and partly because he has poor visual
: sequential memory skills when applied to spelling words. His math
: abilities and disabilities are an enigma to all of his teachers.
: He was counting and was able to associate the numbers 1 through 10
: with their corresponding quantities before he was 2. He could
: identify numbers to 100 both receptively and expressively by the
: time he was three. His math ITBS scores in first grade were all
: above average, with a national percentile rank of 85% overall. His
: ability to solve word problems, count money, and generally
: understand math concepts is developmentally appropriate.
: Unfortunately, he isn’t learning to memorize math facts. We have
: been trying since kindergarten to teach basic sums and he just
: can’t seem to learn them. He uses manipulatives and number lines
: very skillfully and counts up and back in his head (or out loud)
: to arrive at answers, but virtually nothing is memorized. He even
: understands place value and the concept of regrouping, but he
: can’t memorize 3+6 or 2+5 to save his life. For some reason, he
: was able to memorize doubles up to 10+10 and he can solve any
: double plus one problem fairly quickly after a warm up of
: reviewing doubles, but the other facts are somewhere in a black
: hole. Adding or subtracting 0 and 1 aren’t too taxing, but mixing
: addition and subtraction problems on a page sends him over the
: edge and alternating between minus one and minus zero on the same
: worksheet is too challenging for him. If you gave him a dollar and
: told him tootsie roll pops were on sale at 2 for a quarter and
: asked him how much change he would get if he bought 6 tootsie roll
: pops, he would have the patience and ability to work through all
: the steps to get to the answer, but when he sees a worksheet with
: just numbers on it, he can’t get through it without becoming very
: upset. We were willing to wait patiently and let his math facts
: fall into place over time as he worked on a variety of math
: problems and activities, but he has made no progress in over two
: years. We have tried Kumon worksheets and they were great for
: handwriting but did nothing to help him learn math facts. Flash
: cards now send him into a panic. Off the shelf computer programs
: hold his interest at the simplest level but he quits as soon as he
: gets beyond the +2 level. Minute Math or anything with a timer is
: enough to make him break out in hives. What should we be doing to
: help him acquire this important foundation skill? Are there
: special computer programs that do for math what Fast ForWord does
: for language? Please keep in mind that unless he is enjoying what
: he is doing, he has the attention span of a house fly. Can anyone
: out there help me help my son?

As I said in another posting, I was told to not worry about the facts. In her IEP she is allowed to use a calculator. I was concerned at first, but the point was if she is not having difficulty with the computation, the procedure will be easier to learn. If you are struggling with 8X7 you can easily forget how to work fractions or anything else. Unfortunately in the lower grades there is a lot of pressure to memorize all facts. She was not diagnosed until the 4th grade and we began implementing her IEP immediately. She is now in the 6th grade and knows her multiplication better than her addition and subtraction. (i.e. she was told to memorize add & sub, multiplication she used a calculater.) The repition without pressure was a big factor I’m sure.

OK, I look at this as a former/present student, as a parent, and as a teacher of math at high school and college levels.As a former/present student, I wasn’t much on memorization and still am not. I still tend to reverse, drop out, etc. things like numbers - long or lists. (Yes, I have a BA Honours Math and am most of the way to a pure math master’s, and yes, I still reverse digits in phone numbers.) But having **patient** people spend some time reciting the times tables over and over and over again helped me tremendously. Mostly the teacher and some help from my mother. I have confidence with numbers and do complicated calculations in my head (really freaked out the real estate lady re-calculating mortgages …)and this is a HUGE time-saver. I’ve already calculated the total prices of three different types of floor tiles and pictured my kitchen and made a decision while the salesperson is trying to bring up his computer screen. Also, the brain needs exercise; having learned to memorize the times tables, I found it easier to memorize other things, because I had learned the trick. As a parent: My daughter inherits many things honestly, from my hair and eye colour to my reversal habits. She unfortunately had a primary school of the “hurry up and wait” variety; you had to learn the tables right now, this week, or else, but then if you tried to go ahead in the problem-solving that was bad because you weren’t cooperating with the group. She got a distaste for learning math facts, and it has carried over and caused her much difficulty. She still has to count mentally to multiply. She does OK for a couple of years, and then hits a brick wall. She had to re-do calculus, then did OK for a while, and just this semester ran into trouble with mathematics of physics — a problem as she was planning to be a physics major. Each time she has had to convince herself that it was important for her to learn the facts and go back and teach them to herself. It would have been a lot easier if she didn’t have the mental block against learning facts when they are presented. Even if you have to work on it and it takes a lot of time, it’s worth having that skill and not hitting the brick wall down the road. As a high-school/college math instructor, I’ve seen nightmares and could tell you educational horror stories all day. Just one story on calculators: community colleges all nowadays know that “Algebra 2” on a transcript doesn’t necessarily mean the teacher or the student were doing any algebra, so they all give placement tests. The majority of entering college students end up at junior high level, pre-grade 9, and have to take “developmental” zero-credit pre-algebra and algebra 1 before they can handle even the most basic college credit classes. So one particular college’s Disability Support Center let learning-disabled students use calculators on the placement tests. OK on the algebra tests and other problem-solving and conceptual tests — if the students have problem-solving knowledge, fine. However, the placement test for the lower level was a *computational* test. It was largely whole numbers, and anyway modern graphing calculators could do the fractions also. So the LD students were tested only on pushing buttons. When they hit the college classroom, they simply were not ready for the level of the class, and they were failing dismally. Then the instructors were severely criticized for not being willing to accommodate. The whole setup was a guaranteed failure and setback for the LD students, who could have done well if they had been placed by their actual math knowledge. What I’m trying to say here is that it’s a judgement call. Is the student learning the conceptual processes, or just pushing buttons like a trained monkey? Is the student getting some thinking skills out of the class or just filling up reams of paper to satisfy the grade-by-weight school philosophy? Is the student looking at the numbers on the calculator and learning number sense by repetition, or just copying mindlessly? I have no problem with an algebra or calculus student using a calculator; in fact graphing calculators are required in most courses these days. But when I try to work on a problem with a student, and he pulls out the calculator and starts pushing buttons literally before he has even finished reading the question, I know that we have a serious case of not thinking, and we have to put the machine away and filter some ideas through the mind first.: As I said in another posting, I was told to not worry about the
: facts. In her IEP she is allowed to use a calculator. I was
: concerned at first, but the point was if she is not having
: difficulty with the computation, the procedure will be easier to
: learn. If you are struggling with 8X7 you can easily forget how to
: work fractions or anything else. Unfortunately in the lower grades
: there is a lot of pressure to memorize all facts. She was not
: diagnosed until the 4th grade and we began implementing her IEP
: immediately. She is now in the 6th grade and knows her
: multiplication better than her addition and subtraction. (i.e. she
: was told to memorize add & sub, multiplication she used a
: calculater.) The repition without pressure was a big factor I’m
: sure.

There is a program called touch math that may help. It teaches by adding dots to the numbers at specific places on the number itself. Over time, the student learns to associate or “sees” the dots on the numbers with out them being there. This may help him since he needs concrete ways to solve a problem. I am not sure where to get it, but I will ask a friend I know who has used it where it came from.My son is a second grader with Asperger’s Syndrome, dysgraphia, ADHD
: and a host of specific learning disabilities and language
: processing problems. He is an excellent reader (heavily dependent
: on sight word recognition and context clues, but able to decode
: when all else fails) and loves science and social studies. He is
: behind his peers in spelling and written expression, partly
: because of his dysgraphia and partly because he has poor visual
: sequential memory skills when applied to spelling words. His math
: abilities and disabilities are an enigma to all of his teachers.
: He was counting and was able to associate the numbers 1 through 10
: with their corresponding quantities before he was 2. He could
: identify numbers to 100 both receptively and expressively by the
: time he was three. His math ITBS scores in first grade were all
: above average, with a national percentile rank of 85% overall. His
: ability to solve word problems, count money, and generally
: understand math concepts is developmentally appropriate.
: Unfortunately, he isn’t learning to memorize math facts. We have
: been trying since kindergarten to teach basic sums and he just
: can’t seem to learn them. He uses manipulatives and number lines
: very skillfully and counts up and back in his head (or out loud)
: to arrive at answers, but virtually nothing is memorized. He even
: understands place value and the concept of regrouping, but he
: can’t memorize 3+6 or 2+5 to save his life. For some reason, he
: was able to memorize doubles up to 10+10 and he can solve any
: double plus one problem fairly quickly after a warm up of
: reviewing doubles, but the other facts are somewhere in a black
: hole. Adding or subtracting 0 and 1 aren’t too taxing, but mixing
: addition and subtraction problems on a page sends him over the
: edge and alternating between minus one and minus zero on the same
: worksheet is too challenging for him. If you gave him a dollar and
: told him tootsie roll pops were on sale at 2 for a quarter and
: asked him how much change he would get if he bought 6 tootsie roll
: pops, he would have the patience and ability to work through all
: the steps to get to the answer, but when he sees a worksheet with
: just numbers on it, he can’t get through it without becoming very
: upset. We were willing to wait patiently and let his math facts
: fall into place over time as he worked on a variety of math
: problems and activities, but he has made no progress in over two
: years. We have tried Kumon worksheets and they were great for
: handwriting but did nothing to help him learn math facts. Flash
: cards now send him into a panic. Off the shelf computer programs
: hold his interest at the simplest level but he quits as soon as he
: gets beyond the +2 level. Minute Math or anything with a timer is
: enough to make him break out in hives. What should we be doing to
: help him acquire this important foundation skill? Are there
: special computer programs that do for math what Fast ForWord does
: for language? Please keep in mind that unless he is enjoying what
: he is doing, he has the attention span of a house fly. Can anyone
: out there help me help my son?

My daughter is ADD with a visual processing issue. We have used touch math for adding and subtraction since first grade. My most wonderful math tutor taught it to her when not much else would help. She eventually memorized most of her math facts for addition, but we still rely on it for subtraction and those few addition facts that just won’t stick. Also, it’s a good crutch for those stressful stuations where her facts just seem to desert her.”There is a program called touch math that may help. It teaches by adding dots to the numbers at specific places on the number itself. Over time, the student learns to associate or “sees” the dots on the numbers with out them being there. This may help him since he needs concrete ways to solve a problem. I am not sure where to get it, but I will ask a friend I know who has used it where it came from. “

EMAILNOTICES>noAll these are great ideas but if, by 4th or 5th grade, the student still has trouble remembering math facts, then by all means use a calculator! As long as the student is thinking about the problem and not plugging in numbers blindly then what’s the problem?

: All these are great ideas but if, by 4th or 5th grade, the student
: still has trouble remembering math facts, then by all means use a
: calculator! As long as the student is thinking about the problem
: and not plugging in numbers blindly then what’s the problem?I have no problem with calculators but some teachers do. It’s a debate that rages on in math teaching circles. I think a similar debate occurred when they invented the ball point pen but slowly, over years, the advocates for quills died out and one rarely hears from them anymore. Those who are opposed to the use of calculators will too.

PASSWORD>aabL3A4qSQ7sAWe used Touch Math for some math facts but loved Math Facts the Fun Way (now using it for the multiplication tables) Highly recommended. Kathleen

: All these are great ideas but if, by 4th or 5th grade, the student
: still has trouble remembering math facts, then by all means use a
: calculator! As long as the student is thinking about the problem
: and not plugging in numbers blindly then what’s the problem?Well, tht IS the problem.There is this hard-to-define but extremely important thing called “number sense”. I have had classes full of students decide it was easier to multiply than divide and tell me happily that my pocket camera was ten meters long. If numbers and measures aren’t real to you, you will write and accept this kind of nonsense.In advanced algebra, students use — and should use — graphing calculators. But when they pull out the calculator and start punching buttons before they ahave even finished reading the problem — and they do this constantly in my classes — then they are absolutely guaranteed to get a totally ridiculous result. Then they get this hurt-puppy look and whine, they did everything “right” and why am I so mean as to say they are wrong.The problem is that they are pushing buttons madly, not thinking at all. If we are going to try to teach math without thinking, we should all give up and introduce classes in Chinese poetry instead; they’d get more out of it.