Thank you all so much for your replies. I dropped the whole number families thing and we are just working our way up and guess what.... I discovered she understands numbers much more than I thought she did. Yesterday, she said. With these numbers 10 is the most, but we may get to where 100 is the most... but it can't be because there is always 1 more... numbers never end. She understands what they represent! She does! Just doesn't understand their names. I'm going take it easy and we'll build up to counting to 100. Maybe by the end of this school year, who knows. I think I just have to remember to relax and that just because it says to do something in our curriculum, doesn't mean I have to. :)
I'm in tears - DD1 still not grasping numbers - Page 2
Curriculums are wonderful guidelines but it can be hazardous to allow them to rule your childs learning experience (after all, isn't this why most of us homeschool? Personally tailored learning?). It sounds like she is really doing fine, maybe a more relaxed and slow approach will help you both breath a sigh of relief.
I think it's essential to stop often and look ahead - seeing the many years a child will have for learning all the essentials. It really doesn't depend on starting so young and continually building on a set schedule. Homeschooling can provide the gift of time - time for ease and comfort with all the individual growth spurts and plateaus in all the different areas of learning. The important thing at your daughter's age is just finding out how enjoyable and satisfying it can be to learn about lots of different things, and a lot of that involves gaining a confidence in her own learning style and abilities. When you have anxiety about some of that, it shows and affects her own perceptions. She's very, very young - it won't affect the rest of her life or education if she doesn't know much of anything beyond the first 10 numbers, and it wouldn't even matter if she didn't know those yet.
I haven't told this story in a long time, but I've told it a lot here, so here goes again. My son was on panels of young adult homeschool grads at a couple of conferences. On one of those, he commented on how much faster and easier it is to learn things later rather than earlier - in days rather than weeks, weeks rather than months or years. He was referring to that process from the beginning right through to the teen years. There was a raucous outburst of laughter and applause from the front and center rows. Those were his friends and their parents, all cracking up and cheerfully applauding that someone was coming right out and saying what we'd all learned the hard way, because it's something a lot of people don't think to point out, especially in recent times when earlier and earlier formal studying is being done in schools and now in homeschool settings.
Years later, when he was in college, some friends of his in the dorm were Googling names of friends for fun. They were laughing hysterically and going around the dorm getting others to laughing and teasing him (just fun - not in a mean way) about this comment he'd made in an article I'd written: ",,,but you'd be surprised how much you can learn at my age in a few weeks compared to the few years it would take in your early teens." I didn't get it - couldn't understand what was so funny. He had to explain it to me - they said he was "bragging about being able to learn faster than a bunch of little kids." I still didn't quite get it. After more explanation, I got that it's just so obvious to them at their age that it's a whole lot easier to learn things as you get older that it was funny - whereas teachers and parents have somehow lost track of this to a certain extent.
So, I'd like to suggest that it can flow along in the coming years a lot more smoothly if you try not to think in terms of traditional age and grade expectations and instead just move along gently at her individual pace, letting her be the owner of her learning experiences as much as possible. When I look back, that's what I wish I had known to do in the very beginning. And I realize that right now there's that one anxiety on your mind, and there are always others coming along, so it isn't always easy. Lillian
If this helps any, my DD just turned 7 the first week of Sept 2011, and she is doing so much with logical math conceptualization, primarily because we didn't do the whole numbers-on-a-page thing. We have conversations all the time, especially when driving, about evens, odds, etc. and ask each other math riddles for fun, but I saw how her unfolding natural understanding came crashing to a halt when I faced her to a blackboard of the numbers and symbols. I reversed course because I remember that's what it did to me too at that age, leaving me in a bewildering sea of unrelated math "facts" to accept on rote and regurgitate without perceived purpose.
Since staying away from all that, her boldness has returned, and she was able to tell me what happens when you add odds with odds and evens with evens, and odds with evens, AND WHY! I used the Socratic Method for us both, an honest inquiry together, because even though I was gifted at spatial reasoning skills, I could never learn math by having factoids and formulae poured into my head, and anything I didn't discover for myself, I didn't retain. So as a 38 year old, until my 7 year old and I explored the topic, I couldn't have rattled off whether you get an even number every time you add two odds, or why. We both figured it out together, and it was fun.
She still reversed letters and numbers, can count to 100 verbally but has a lot of trouble with written numbers past 20 also. And for whatever reason, I wasn't (and still am not) the least bit worried. In so many things in life, the ability to deal with the symbolic conventions of a thing, come AFTER the ability to think abstractly about the thing, and that's actually a good thing, because those who learn the symbolic conventions long before they can conceptualize, often come to equate the symbol with what it represents, and then see math as nothing but a complex and mysterious set of seemingly arbitrary conventions and formulae to obey mindlessly. That's how it's taught in school, and for me at least, and apparently my daughter, it's a good way to shortcircuit the emerging creative logical ability to conceptualize quantities and spatial relationships.
How many of us can say we understood a thing about what the trig formulae we had to memorize and utilize, represented in 3 real dimensions? How many of us could really see it in our heads, the reality of relationships that the flat formulae on paper were describing? And if we didn't understand what it was we were really doing with those numbers and conventions, it's not surprising if we forgot all the memorized operations soon after, because there was no innate sense to it.
Just as we don't learn our language by first learning to read, write, and spell, I think the natural ability to conceptualize logical spatial relationships and quantities, is best served by being allowed to develop a bit, before being transferred too much into a formalized system of nomenclature and symbolic representations. It's too easy that way, to miss the forest for the trees, like someone who was never allowed to cook alongside someone else, trying to plan and prepare a full meal out of nothing but a collection of written recipes. It might not hurt to step away from the recipe cards and just make some pancakes by feel, together, for a while. Maybe open-ended conversations on things of daily importance like the clock and calendar, how to divide a bag of treats evenly, etc would open a door for enthusiasm and confidence? If nothing is wrong (as you have had to painfully consider, though if it's wrong with your DD, it is with mine too!), then in time, the symbols will come, without trauma.
Best wishes. I hope I don't come across badly. I only hope that explaining how my DD is, and that there are some similarities, gives you a breath of hope. Sometimes perfectly bright kids just aren't ready for something that the outside world expects them to be. I was gifted at math and spatial reasoning, yet until geometry (which I aced effortlessly) I flunked every single math class, and got passed along to the next based on test scores, and I could not learn to tie shoes or tell left from right til I was 8 years old, and the only reason I learned to tie shoes then, was because I had a tie on my shoulder of my sundress, and was able to address the problem as a front-back rather than a left-right spatial problem. I could also conceptualize spatially in special ways, though I didn't share the same assumptions with normal people, like I would get confused when someone told me clockwise turned to the right. How could it turn to the right, when it actually depends on where the observer is positioned? Clock hands turn to the right from 12-1, but to the left from 6-7, and turn "up" from 8-9, and "down" from 3-4!
They always thought I was being a smart mouth, but I really had to keep asking teachers to clarify which of 6 different interpretations they meant, of something. But in areas where intuitive spatial awareness and reasoning was required rather than memorization, I could derive, solve, visualize, anything...within my own limits. I'm happy to say, I look forward to the adventure of discovery of reason, logic, quantity, properties of numbers, planes, and spaced, that lies ahead, and I don't plan on rote memorization being part of it, because it shuts down thinking.
Crunchynerd, you've given me faith for *my* family, and I think we're doing pretty well mathematically. My dd also "gets" multiplication, addition, subtraction (and touched a little on division once) and runs around announcing it to the family. I'm not opposed to workbooks, if they are presented like puzzle books and they are having fun, but your post has really helped me see the value of mental calculations over the written form, even if they are ready for the written form. To keep the bulk of math understanding grounded in visualizations.
My DD is 6, she can only count accurately up to about 15 and can only do addition up to 5. She is also not reading. We are not unschoolers btw but pretty structured. I am not worried about it... some kids just develop more slowly than others. As long as you are making consistent efforts over the school year, it's inevitable that she will start to learn more.
We also use RightStart Math, like an earlier poster. I was also going to suggest you name with tens, not by the "name" of the number. So, there's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, then 1-ten one (for 11), 1-ten two, 1-ten three........and you can continue this all the way to one hundred: 9-ten eight, 9-ten nine...
That may help her grasp the concept of the numbers, especially if you use manipulatives to demonstrate what you're saying. Then, when she really gets it, you can tell her the short-cut secret names for the numbers, and it will make more sense and be less arbitrary.
But, she is still really young, try not to worry too much.
Your child might be visual and not audial so repeating sound might not do much to her.
I have a visual child, I am visual myself and I remember by associating things with pictures.
When I was teaching her numbers from early on this is pretty much in the nutshel the process how I can recall how I did it:
1. I would touch objects in the pictures in children books and count. as I was touching.. one.. two.. three .. four.. five.. six.. and with each numver I
would touch a ladybug or what not.. untill I counted all of them... It is easier if you have objects of the same kind...
with time a child associated the process of cunting with objects as countig does not exist in vacum, counting always represent something..
2. I had a book that would beautifully move a child through pages and on each page she would have to find all objects of the same kind
up to number shown.. page one.. one cow.. page two two chickens,... page three three horses.. page four .. four bread loaves.. etc..
3. We would count steps as we would go up and down the steps every day.. one two three.. first I would do it and then when she was
old enough she would do it.
4. At some point I also bought a book for kids.. counting to ten ladybugs.. etc..
there are lots of books like that one that have a beautifl rhyming like "ten little ladybugs were sitting on the wine.. then came a birdy and there were nine.."
of course nobody eats anyody and stuff, I would not stand a book like that.. at the end all ladybugs are back home beacause they never are itten in the first place..
so there is ten again...
Those books very nicely reinforce the concept of association number with object and what it reall;y means. nubers are abstract and it is difficult to grasp
if not associated properly..
If a child gets it up to ten then all other numbers is just a breeze but to really make it sink in is tricky in the first place.
My sister had a problem with my niece remembering number 12, just plain blank on it. She was so upset over this and yealled at her sometimes.. now she is second grader
with flying colors and great at math. Just that my sister was not knowing how to teach her the numbers and only thought of memorizing sounds.. this is really short
success as all math is easier if a child is presented concept in visual way wherever possible. Otherwise kids do fail sooner or later... as they just try to memorize
to the point of exhostions the concepts. I was thought like that, my husband was thought to understand and expalind.. so now I rethought myself the whole concept
of math and see what difference makes for me the whole deal.
Lastly, get some counters, I got some super cheap mini erasers at oriental trading page, I could not afford counters at hte time and htey were not anywhere near
as exciting.. so I got with erasers, we got set that had bees, ladybugs, butterflies and something elese.. and I would use it all the time..
It is so much fun to do that.. my kiddo woud count bees, ladybugs, compare which group was bigger at first without knowing how many more.. as this is tough too
and now she can use it for how many more things.. and for estimates and things like that.
You really have to make the counting work first and then once she will really understand what it is it will be easier for her to relate numbers that they go just
like alphabet and havet to go one after another and then you can practice which letter is before.. let's say C and which is after.. and then do the same
on numbers,.. first small ones t hen bigger ones.
here is link to counters
we got this set that is super mini size of a penny each one so it is perfect, and it does not smell or anything and it is big enough to do basic math
I love them.my Lo loves them.
Best of luck and don't give up. It just take time and repetition. Yet don't make it a task, make it fun, ask her all the time to count something with you and
do it with her as you go at first.. "oh let's count all the bottles in this box.. and touch each one as you count!" "oh look, you have so many dolls, let's count
them together. Oh now let's see how many books we have on this shelf..
life is a math... we are surrounded by it and it can be easy if it is real thing, if it is shown to a child that we count things all the time then it is so easy to t hem.