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I'll put on my musician/music teacher hat for a moment. Muscle memory in music or dance is when the person goes on automatic pilot. One is not consciously thinking about their movements to play the scale or do a double pirouette. When someone uses their fingers for counting, they are consciously thinking in order to solve the problem (pressing 2 fingers and then pressing another 2 fingers solves the problem that now there are 4 fingers all together. When I play a Bb major scale on the piano, I don't think about when to tuck my thumb and cross over the middle finger, I just play it without counting, without thinking, without naming the individual notes. Using fingers to count can be done very quickly, but it's still an act performed consciously. I learned how to play that Bb major scale on the piano when I was 7. I rarely play the piano now, but if I tried to play that 2 octave Bb major scale, I am sure that I could still do it without thinking (once every 10 years, if I'm in a piano store. I'll run through a few major and minor scales and somehow I still remember when to start on the 5th or 4th finger).
When I taught first and second grades, I didn't tell the kids not to use their fingers. I taught them to use their fingers more quickly and efficiently. I also emphasized memorization. For example, when they learned to multiply by 3's, we all counted to 30 by threes many times each day until they had it memorized. Those students who needed to use their fingers to multiply 6 x 3 were welcome to do so, but they only used six fingers. They didn't keep adding three (one at a time), adding three, adding three, . . . But after they learned to count by sixes, they could get there on only three fingers. Most kids eventually just remembered the answers.
I figured instead of spending time trying to force the kids to do the addition and subtraction without fingers, I'd teach them to be efficient, then use the saved time to teach more stuff.
Some of the middle-school - and older - kids that I tutor now do figure 6 x 3 on their fingers, one number at a time. I don't know what their teachers have told them about fingers, but it's common for junior highers to still be using them for problems like 11 - 8. That shouldn't be necessary, but it isn't something I focus on.
Multiplication and division are more important to memorize than addition and subtraction, because those waste more time if you don't know them. Using a calculator just makes the situation worse when they get to higher math. It turns simple problems into much more complicated ones, as well as making it more difficult for kids to follow along when they are being taught.
She may want them to use manipulatives...here's a picture of some on this website. When my sons were young we had cuinsinaire rods & some of the others for them to use. And then there is a point where the child needs to be able to transition to mental math. But concepts are much easier to learn with manipulatives.
Is she encouraging her to use actual manipulatives instead of her fingers? There was a theory making the rounds for a while, along the pacifier v. thumb sucking lines, that because the fingers are always available the child will be less inclined to feel intrinsic need to learn (memorize) the facts.
From what i understand there are no other manipulatives and the teacher is not getting back to me on it either. I'm definitely not a proponent of her memorizing rather than thinking- at this age at least. The process of understanding what she is doing, how it works, why it matters is what I am concerned about. And when looking at common core it seems that is what is prioritized as well. I wonder if it's for the purpose of speed.
From what i understand there are no other manipulatives and the teacher is not getting back to me on it either. I'm definitely not a proponent of her memorizing rather than thinking- at this age at least. The process of understanding what she is doing, how it works, why it matters is what I am concerned about. And when looking at common core it seems that is what is prioritized as well. I wonder if it's for the purpose of speed.
Yes. My daughter's teacher explained that while the textbook does encourage thinking, by the next chapter, the child is expected to have the basics memorized. A friend of mine is a 3 grade teacher and she confirmed this as well. The students were encouraged to think about how multiplication works, but by the end of the chapter, it has to be memorized. From what I remember, my daughter was expected to learn her multiplication facts in 2 weeks.
From what i understand there are no other manipulatives and the teacher is not getting back to me on it either. I'm definitely not a proponent of her memorizing rather than thinking- at this age at least. The process of understanding what she is doing, how it works, why it matters is what I am concerned about. And when looking at common core it seems that is what is prioritized as well. I wonder if it's for the purpose of speed.
I’m not talking about the child being forced to memorize through “drill & kill” but the child subconsciously deciding to commit the answer to memory to aid themselves in answering the question in the future. The truly best practices in education are almost always doing both whether it is phonics v whole word or manipulatives v number facts, or in other words, understanding v information. It is the blending of the two that creates the best results, not forgoing one and just concentrating on the other. Training the brain to retain information is a crucial skill and the best developmental window for that is the primary years.
I have a friend who is intelligent enough that she earned several degrees in a STEM field that to this day has to sing the alphabet song to herself to put anything beyond the E or F in alphabetic order because somehow she never transferred the actual alphabet to memory when young like most people. It’s amusing to watch her silently mouth the song, now that I realize that is what she’s doing, but at the same time it takes her much longer to accomplish the task than someone of her intelligence should spend and there are people who would hold her in lesser regard if they knew that’s what she has to do.
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As someone who used math in Psychology when teaching the Statistics unit it was incredibly frustrating that kids couldn't do simple multiplication without hitting their calculators or even figure out averages from a column of single digit numbers.
Counting on fingers goes in and out of practice. We were (physically) discouraged in the early 1960s from doing it (and the left handers were reprogrammed to be righties. This was public school) but when I student taught in the almost late 1970s kids were using their fingers and when I began teaching in the mid-80s it was in full swing. By the time I retired in 2014 (or '15 depending on how you date it) the kids could only do any math if they had a calculator.
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