I've posted 2 other threads on our struggles with math this year for DD1 and kindergarten.http://www.mothering.com/community/forum/thread/1290870/dyscalculia#post_16178379 and posts in the kindergarten thread. I have not had DD1 tested because I don't want to jump the gun or anything. We started kindergarten with the goal of counting to 100 and identifying written numbers to 100. This was what I learned in kindergarten and remember how it was taught well. Just rote counting and writing until we could write them without looking at anything. When DD1 began to show clear signs of struggle as I described in the linked thread, I lowered our goals to identifying the written teens and twenties. I have done all I know to do at this point. We've worked with felt numbers on a felt board, done rote writing, used a chalkboard, sidewalk chalk, she's counted to 100 as movies load on Netflix watching the numbers change, we've used a calendar, watched YouTube videos, Leap Frog Math Circus and Math Adventures to the Moon as well as the math sections in our school curriculum connect the dots, writing practice, color by number, etc...
Right now she can:
-Count to 30 without a problem
-Write numbers 1-10 without a problem
-Write numbers 1-20 with little problem (however she cannot tell you which numbers she is writing)
Today, I was having her read the calendar. It didn't matter how many times I told her that 2 and 6 is 26, she kept calling it 16, 17, 70. I've explained it every way I know how. I've followed recommendations. A friend of mine who is a math professor said that this seems more like a reading issue than a math issue, however, she is catching onto letters and their sounds without any problems. She will be reading in no time.
She still makes many of her numbers backwards, confuses 8 and 9 as well. I'm lost and worried that something is wrong. I would have thought that if not learned as a true skill then she would have memorized the teens and twenties by now. I mean if I say 2 and 6 is 26 she should be able to remember that a minute later - right.
So, what should I do next. We have 20 school days left. Should I drop the numbers altogether and just focus on shape concepts and such? (Our curriculum picks back up at one and moves quickly through the numbers for 1st grade.) Should I have her tested before we start 1st grade? I'm so frustrated and confused. :( I don't want DD1 to hate math.
Appalachian mountain woman, radical homemaker, homeschooler, childbirth educator, and doula loving her DH and three powerful little femmes. Deladis 8-4-05, Ivy 4-28-08, and Gweneth 7-21-12 HBA2C! -
She just recently turned 6, right? I think the difficulties you describe are within the range of normal for that age. It's possible that this is just a lack of readiness, and an issue of poorness of fit with the math curriculum / teaching style you're using. The difficulties you list seem to be mostly related to the reading and writing of numerals. In other words, they're related to the symbolic representation of numbers on paper. She's not really grasping place value at all yet which isn't unusual at this age. Forgetting that 2 beside 6 means 26 is totally understandable: without the concept of place value to slot that information into, it's just a meaningless bit of rote-memorization with no context.
I wouldn't abandon number-teaching at all. But I would change the approach to work as much as possible with her strengths, towards her areas of weakness. Is your math program manipulative-rich, multi-sensory, kinesthetic? If not, I'd definitely move towards those modes of learning for a good while, and stay away from stuff written on paper. Pick up a 10x10 counting frame / abacus. Use Unifix cubes, counters, pennies, beans, fingers, cuisenaire rods, dice, playing cards ... anything that will gradually firm up her association between a numerical amount (say, this many * * * * * * * * pinto beans) and a word ("eight") and a written numeral (8).
For instance, you can get an egg carton and use a sharpie to write the numbers from 1 to 12 randomly in the bottoms of the wells, and then challenge her to put the correct number of pinto beans into each well. Or put 13 pennies on the table and ask her to represent those pennies on the abacus. Give her bigger and bigger numbers of pennies. Teach her how to put them in piles of ten to make it easier to keep track of how many there are to match them up with rows on the abacus. You might also want to try a more kinesthetic approach like a number-line on the floor that she can walk along -- particularly a short (1-12?) number-line that includes dots to show amount as well as the number-symbols. Give her directions ("Go forward three steps, now go forward two more, now go backwards three: where did you end up?") and have her hop and answer questions about the numerals she steps on.
Just some thoughts and ideas I think might be worth trying. Have fun!
Mountain mama to two great kids and two great grown-ups
I found this "counting to 100" placemat at a local teaching store.
It has been very helpful to our son who is 5.5.
and 3 , in our happy secular
Just thought I'd comment, since you said you had the goal at the beginning of the year of teaching her to "count to 100," that I don't think this is a particularly meaningful milestone, even though it's one many North American curriculums get hung up on. In Singapore, for instance, the English-speaking nation with the highest math achievement scores, they don't get into numbers larger than 20 until the 2nd half of first grade, and first grade doesn't start until after the 7th birthday. And yet by 7th grade, Singaporean kids are a year or so ahead of North American kids in math learning, and miles beyond in achievement. They don't start later: they start smarter, IMO, with really really strong development of "number sense" in the 0-20 range, without the confusion of larger numbers. When that is supremely well learned through concrete, pictorial and symbolic learning using multiple modalities and learning styles, it's easy to apply it to groups of higher place value. Those foundations in the numbers from 0-20 are crucial. There's no need to hurry on.
To my mind counting to a hundred is a little like "singing the ABCs." Parents of bright 3-year-olds love it when their kids can do either of these things. But these skills really have nothing to do with early literacy and numeracy. For literacy it's all about phonemic awareness. For numeracy it's that foundational "number sense" with which is best exercised with tangible (0-20) numbers.
Some kids are fascinated with big numbers from early on and seem to intuit the place-value relationships at a young age. For these kids, there's no harm in encouraging them to work with big numbers. But there is a solid body of evidence from Asian nations that early (prior to age 7.5) mastery of counting to 100 is entirely unnecessary with respect to later math achievement. In some kids I don't doubt it can be counter-productive if it provokes anxiety and/or resistance.
Mountain mama to two great kids and two great grown-ups
Is her problem just with the symbolic representation of the numbers?
If you spilled a pile of marbles (or whatever) on the floor and asked her to count them, could she? Since she only counts to 30 right now, use an amount smaller than that. If she can consistently count out objects--that is "one to one" correspondence. If she can't do this, then the problem is greater than the symbolic representation. If she can do this. . . celebrate! Number sense is worth more imo than the rest.
Oh, forgot about the rote memorization part. Here is what helped my dd to be able to just count to 100. We taught her to count by 10s to 100. Then, we would have her use her fingers. First, she would just count (no fingers yet). When she got to ten, she held up one finger. She kept that finger up until 20 (when she lifted a second finger). Once she got the right ten-word (twenty, thirty, forty, etc) she could rapidly add the 1, 2, 3, etc to it. She was always pausing when she needed a new term for the tens. So, by teaching her to count by tens--and then associating a finger with each one, she was able to extend that to counting to 100 and eventually it helped with writing the numbers as well.
BTW, when we started this, her 1 to 1 correspondence was great with numbers up to 29 as well, her symbolic representation was awful, and her rote memorization was awful. Additionally, this is my dyslexic child, but I have NO idea if the dyslexia is what affected these areas of math or not. She is actually quite good at math, yet she still struggles with rote memorization (now of math facts), and she will sometimes still mess up written numeric expression (usually backwards numbers--sometimes the 3 looks like an E but once in a while she will still do mistakes like 31 is written as 13).
We use RightStart curriculum and one technique that really helped my kids learn place value was the "math way" of counting. (This was combined with work on the abacus, which I highly recommend so that the child can visualize what they are saying.) My kids could already rattle off the numbers the regular way up to 40 or 60 or something, but the "math way" really drove home what those numbers *meant*. It's very simple -- if your child can count to 10, she can get it with a little practice.
Count 1 - 10 normally
11 = "One ten, one" (You would show her on the abacus or with other manipulatives that "one ten, one" is one group of ten plus one extra.)
12 = "one ten, two"
13 = "one ten, three"
and so on. The teens can be extremely confusing for English speaking children because they don't follow the pattern linguistically. This way of counting avoids that problem.
20 = "two ten" or "two tens" if she needs that extra concrete literal-ness
21 = "two ten, one"
22 = "two ten, two"
Continue gradually until the child can count to 100 ("ten ten") Once she is proficient, then re-introduce the everyday words for the numbers.
Seriously, with this system, my dd could count her own money in Monopoly when she was 5 or 6. I would just tell her she needed to pay "seven ten, 5". At first she always payed with a pile of $10 bills of course! As she learned more about adding, she started to combine a 5-ten bill with a 2-ten bill, etc.
I also agree with the pp who said you should first establish that she understands one-to-one correspondence. That is foundational. I'm not an expert, but if a 6 year old did not get one-to-one correspondence yet, I might be thinking about learning disabilities. (?) The difficulty with counting beyond 30, writing numbers, and place value is more typical of young 6 year old challenges, I think.
These suggestions are right on the ball. You should absolutely shift your focus to CONCEPTUAL understanding of math at this stage, rather than SYMBOLIC representations. It's like putting the cart before the horse. Or to compare it with reading/literacy, it's like expecting a kid to be able to read in a language they don't yet speak.
From the way you've described it, it sounds like you're focussed on rote memorization of the oral terms and the written symbols, without any connection to their meaning. I love the analogy to the ABC song -- it's a fun song, but has really nothing to do with literacy. Singing the song doesn't mean they recognize the written letters, nor their phonemic roles. Counting to 100 just as a rote exercise is only an exercise in memorization. Not that there isn't value in exercising memory, of course... but it has nothing to do with MATH.
Instead, it should be the other way around. Once they've learned what counting MEANS, how it WORKS, then counting on forever becomes a no-brainer. They need to understand the PATTERN of it first. All you really need to understand is the order of 0 to 9, and then the concept of place value; that every time you go past 9, the '10' which is next becomes 1 more in the other space and 0 in the current space. Memorization is pointless, you can *figure it out*.
What likely happened in your own K class, was that you were able to *figure it out*... whether because there was manipulative/other activities that helped with that which you've simply forgotten about, or you were just one of the kids who cottons on to it quickly enough. You didn't necessarily have it memorized by rote. But after being able to recite it for a period of weeks or months by *figuring it out* as you went, then it did become memorized to the point where you didn't have to even think about it, and the oddities of memory have backed up that event a little bit so you're remembering it as the other way around. That would be my guess, anyway.
In most math memorization, the way it SHOULD happen (and how it is too often NOT taught in schools) is that kids learn how to figure something out FIRST, then through repeated practice they start to memorize just intuitively, then realize the speed advantage of memorization and if necessary do deliberate exercises to finish the process. It shouldn't be the other way around.
I'm another evangelist for Right Start math, most especially because of how it treats EARLY numeracy and math concepts. My daughter is only 4 and already understands place value pretty well... when she uses the abacus, she can count to 100 easily. She wouldn't be able to do it "from memory" yet, not by a long shot. But she understands the concept. Actually, we recently took the next step, of counting 100's! She was able to correctly figure out that if a chicken farmer has 200 eggs then gets 300 more eggs, they'd have 500 eggs, and she demonstrated it with 100's tiles as well. She can take place value cards and stack them to build 2 and 3-digit numbers, and name them (using "math language"). I just think it's a much more sensible approach.
Just wanted to say that you can buy the RightStart math games kit for $50. You don't need to buy the whole system. We are loving the games kit. It comes with everything you need. If it turns out to work really well for your dd, you might consider the bigger investment with the curriculum. Right now we use Singapore, but we love using RightStarts games.