One of the best books I read early on when teaching math as an EL subject was Kitchen Table Math. The reason the book was so good is not so much that it prepared me to make my child a math wiz, but helped me understand the hurdles children have to overcome in order to grasp what is going on. It is way more than you realize and on top of that, the places where a child can get confused is likely infinite. Maybe that’s an exaggeration. but probably not by much. So in the early years - 2-3.5, every child is going to be different and you have to wait for stuff to " just click".
When I made the subitizing LR file, the impetus for that was reading about Moshi Kai. He remembers that the concept of a number finally clicked for him when his mother showed him 1 lion and then 2 lions and then 3 lions. She did not count items consecutively, she showed him groups of things and gave those things numerical meaning. This idea shows up in the Manual of Methods which is the Teachers Manual for the 19th century set of school books in the Eclectic Education Series. The Ray’s Arithemetic recommends that you:
-
Never show a child the numerical symbols until they are very comfortable with the concept of what the number means. For example: the number 7 is taught using manipulatives. The child should recognize 7 as 7 beans, 1 bean and 6 beans, 2 beans and 5 beans, and 3 beans and 4 beans or whatever manipulatives you are working with. 1- 10 are taught this way.
-
All math is oral until 2nd or 3rd grade. So the use of symbolic representation doesn’t show up for some time as the symbols themselves can cause further confusion.
-
Children who are learning to write should also not be forced to do sums. It takes up too much mental power. Therefore there is no written work until a child is comfortable with both writing and mental math.
Now this set of books, which is really skimpy compared to what you are used to, is small. Math is only done for 15-20 minutes a day. And when kids dropped out of school at the end of 8th grade they were capable of running a business, calculate and understand interest, manage the amount of seed needed to plant fields. In other words far more capable than most of us are even after college math.
One of the other problems with counting and touching things as you count is that the child gets the idea that the last item counted is the number instead of all the items in the group. So let’s say I have 5 raisins and we count them one at a time and slide the raisin across the placemat as we do so. When the child gets to the 5th one he will think that is 5. He assumes that you mean that raisin right there is 5. And there is nothing to distinguish a 3 from a 5 in that context. So the counting hasn’t helped any but rather added confusion.
These are just some of the ways a child can get confused and each child may have areas of confusion that are unique to that child. But since there are some that are very common like the child assuming that counting means touching stuff and saying numbers, we want to make it as easy for the child to succeed. And so we take out as many variables as we can. So if I were starting out with a 2-4 year old, I would make sure that the counting occurred in groups. So I would have a group of 1, and then 2, and then 3 and then 4 and then 5 raisins. Etc. And then line them up in rows with each row one longer than the previous one. And then count the groups. So you would touch the group of one and say “one” and then touch the group of two and say “two” and so on.
And an easy way to work on one to one correspondence is just have your daughter help you set the table. Do you have 4 in your family? Tell her you need 4 plates and 4 glasses. Etc. Then have her put one of each at in the right place. She will need help with this the first few times. But she will get it.
One last thing to encourage you. On one of Crewton Ramone’s teaching videos he says that if you can speak English you can do math. English is much harder. He’s probably right - but I didn’t always believe that. I take care of a little girl with Down Syndrome. She turns 6 tomorrow. She is working on some fairly advanced math for her age. She is multiplying, adding and subtracting, and doing algebra and squares and square roots. She is not struggling and she is having a lot of fun. Her biggest issue, which is her issue with all the things we do, is the fine motor skills. That is going to take way longer to address than math. She knows what squares and the roots mean. When I told her that when we play with squares some people think that is very hard. I told her that when she finds the number of one side, that is called a square root. And finding square roots is really hard for some people. Her response was terrific: “You kidding me.”
. I try to think that this is just a phase for my son and he might grasp the fun of math in few years but I’m afraid he might not love the math the way I do :rolleyes: .
(I don’t want them to be like me, because Maths are really important in life, and it kind of cripples me in that area). I am not showing to her my relations with maths and make it sound exciting every time we do something - but maybe she’s picking up on this - I don’t know…