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MineralMan

(146,317 posts)
Wed Sep 23, 2015, 01:32 PM Sep 2015

Thinking about arithmetic and elementary school,

here's something I remember. A lot of time was spent drilling on the multiplication tables. Until you knew them, the arithmetic methods in use then for multiplication and division were impossible to perform. So, we drilled and drilled to burn those tables into our brains. For some kids, like me, that was no problem at all, and I learned them quickly, so math was easy for me. That was not the case for all kids, though. Many had real troubles memorizing those multiplication tables. They failed at elementary schools arithmetic, and continued to suffer in middle and high school. The standard multiplication and division processes only worked if you knew single digit multiplication without thinking about it.

We weren't taught additive methods or 10-box methods. We weren't taught to think about mathematics, really. We were taught the multiplication tables and some methods that used them to solve multi-digit problems. We didn't learn about number lines and different number bases. We didn't learn many of the things that are now taught as a matter of course. You either knew the multiplication tables or you did not. If you did not, you were out of the loop and had no backups to use.

I went through school in the 50s and 60s. That is how we were taught. That is how people had been taught for a long time. Everyone thought that was fine. It wasn't. Not for the kids who couldn't memorize and commit to instant recall of the multiplication tables. I learned a lot of other math basics on my own, and some new math was beginning to be taught about the time I graduated from High School in 1963.

I was a math whiz. I had a memory that was very sharp. Math was easy. Not everyone had that advantage, and I learned something later in life that showed me what it must have been like. In 1991, I got viral encephalitis and was in a coma in the hospital for a couple of weeks. When I came out of that coma, I had therapists who worked to test me for any deficits that were left over from my swollen brain. Things were pretty OK, except for one thing: I had lost the multiplication tables. They were gone. I could add and subtract just fine, but multiplication and division were gone. I simply could not do them. Nobody seemed to concerned, but I was. Other than that, I had no deficits, but that was a real deficit for me, personally.

Over a week, I reconstructed the multiplication tables in my head, using an mental additive method that I devised for myself. Like a third grader, I built the multiplication tables from scratch and drilled myself on them over and over again. By the end of the week, they were back in my mind and all of the problems were gone. Without them, though, I could not do multiplication and division at all. I used addition to recreate them and relearn them.

I realized what those kids in my elementary school who could not commit the multiplication tables to memory as I had done so easily. Now, I understand why schools are teaching a variety of math methods early to students. Everyone learns a different way. Simple rote memorization of things like multiplication tables doesn't work for everyone. For those people who struggle with that, new methods offer alternative solutions. They're not as fast and take more steps in some cases, but math isn't just learning tables by memory.

13 replies = new reply since forum marked as read
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Thinking about arithmetic and elementary school, (Original Post) MineralMan Sep 2015 OP
if your comments are about "common core" melm00se Sep 2015 #1
I think most schools help the students understand what they're MineralMan Sep 2015 #4
We are all the same, so we all learn the same way. HassleCat Sep 2015 #2
Yes. Teaching children using only one method MineralMan Sep 2015 #5
I also remember HassleCat Sep 2015 #7
I learned to read before starting school. MineralMan Sep 2015 #9
I learned the whole word method from billboards HassleCat Sep 2015 #11
There's also something called Dyscalculia jeff47 Sep 2015 #3
Exactly. Everyone uses calculators now, anyhow. MineralMan Sep 2015 #6
the problem with using calculators without learning the basic math hobbit709 Sep 2015 #12
Yes, well, of course. MineralMan Sep 2015 #13
The navy made us use slide rules HassleCat Sep 2015 #8
I was good with a slide rule, but welcomed the calculator with MineralMan Sep 2015 #10

melm00se

(4,993 posts)
1. if your comments are about "common core"
Wed Sep 23, 2015, 01:40 PM
Sep 2015

teaching techniques (especially around math), I have looked over the common core techniques and concepts and can see how it makes sense as it attempts to approach math as a computer does.

where common core has fallen flat is because the methods are dumped on students and parents and

1) students are expected to become proficient at it very quickly when they have been taught the "old" way up to that point

2) the schools, administrators and common core proponents have not done a good job in explaining/selling the "why" this methodology is being taught over the old methods.

The latter issue may be caused by a mindset that I have seen from some educators, namely that they are teachers/educators so parents and students should just blindly accept what is being presented to them because teachers and educators are the experts, not the parents.

MineralMan

(146,317 posts)
4. I think most schools help the students understand what they're
Wed Sep 23, 2015, 02:22 PM
Sep 2015

learning, but parents are often confused, since the methods, etc., aren't what they learned. So, they get upset. That's what I'm seeing, anyhow in objections to what people think "common core" is. Since I have no children in the school system, I don't know exactly how teaching is done, nor do I know whether all schools and all teachers are competent, but that was true even when I was in school.

Perhaps parents need an introductory course in how their children are being taught, or need to read the school materials their children are learning from. I'm pretty sure, though, that most parents will neither take a course nor read their children's materials. If they don't understand their children's homework, I'm sure that's very frustrating, but there is a remedy, if parents will take it.

I suspect that children are doing better at this than their parents are. A Google shopping search for "Common Core Math for Parents" turns up a bunch of materials to help parents understand the current math teaching methods. If I were a parent, I'd have one of these books or other media to help me understand so I could help my kids. Maybe schools could make these materials available to interested parents or parents could find them in their local library.

Simply railing against change does no good at all, really. A better plan is to learn to understand what is going on and why.

 

HassleCat

(6,409 posts)
2. We are all the same, so we all learn the same way.
Wed Sep 23, 2015, 01:43 PM
Sep 2015

Math has always been a problem in nearly every grade of school. When I was a kid in the 1960s, there were no alternative methods of instruction for students who didn't get it from the standard pedagogy. My friends' kids are learning math about three different ways, and I guess the idea is a sort of shotgun approach, blasting the kids with different methods to see which one works for different individuals.

This is very different from the earlier goal of making sure everybody learned in the same way, at the same pace, with the same methods and instructional materials. When I started Kindergarten, my parents were called in to meet with the teacher and the principal. They sat my parents down and told them, in a very accusatory way, "Your child can read!" This was double plus ungood, as Orwell would put it. They were violently opposed to children who thought they were better or special by learning to read before the other children. This is so funny, because now they would be concerned if a kid showed up at Kindergarten and could not read.

MineralMan

(146,317 posts)
5. Yes. Teaching children using only one method
Wed Sep 23, 2015, 02:26 PM
Sep 2015

leaves many without learning.

Like you, I could read very well already when I went to Kindergarten. The teacher didn't scold my parents, though. She gave me books to read while the other kids were learning pre-reading skills. Then, in first grade, my teacher gave me more books during the "Dick and Jane" lessons and I sat at the back of the class.

They were excited that I could read and encouraged me to do as much of it as I liked. So, I did. I learned way more from my reading than I ever learned in a classroom, throughout my education. Fortunately, my school system back in the 50s and 60s not only let me find my own speed, but encouraged me to do that.

 

HassleCat

(6,409 posts)
7. I also remember
Wed Sep 23, 2015, 02:42 PM
Sep 2015

The long-running debate about phonetic methods (phonics) versus whole word methods. I learned to read by the whole word method, but phonics was the exclusive method at the time, and it was OK with me because it appealed to my sense of logic. I seem to recall the battle reached its zenith in the 1990s, with teachers expected to choose a side and vow to fight to the death. My neighbor was a grade school teacher, and she reported that teaching careers were made or lost depending on which side of that battle you chose. I think now they use a combination of both methods.

MineralMan

(146,317 posts)
9. I learned to read before starting school.
Wed Sep 23, 2015, 02:53 PM
Sep 2015

My father said, "sound it out" when I'd stumble on a word. That was in about 1949, long before "phonics" became a thing. I already knew the alphabet, of course, so I'd "sound it out" until I found a recognizable word. It wasn't long, though, before I was reading using the whole word method. Somewhat later, in 6th grade, I got to take a speed reading class during the summer, and reading changed for me forever. From whole word reading, I learned to take in text in larger and larger blocks. It was a method made for me, it seemed, and I surprised everyone with my progress. It's not for everyone, though. I'm not sure what makes it work, but if it does, it's a life-changer, for sure.

Like math, everyone learns language skills differently. Lucky kids have parents who work with them to find the right combination. Schools can't always do that, especially when there are 30 kids in a class, all trying to learn as best they can. Parents can fill the gap, but have to be engaged and have the time and talent to help. That combination doesn't always exist, sadly.

 

HassleCat

(6,409 posts)
11. I learned the whole word method from billboards
Wed Sep 23, 2015, 02:59 PM
Sep 2015

We lived in the resort town of Chetek, WI. You probably know where it is, about 50 miles north of Eau Claire on Hwy 53. At that time, the highway was a two lane affair, and there were billboards everywhere for bars, cabins by the lake, etc. And Burma Shave signs! Can't forget those. As we rode along the highway, I would demand to know, "What's that sign say? What does that one say?" The whole word method at its most basic.

jeff47

(26,549 posts)
3. There's also something called Dyscalculia
Wed Sep 23, 2015, 02:14 PM
Sep 2015
https://en.wikipedia.org/wiki/Dyscalculia

You can think of it as dyslexia for math.

In people with dyscalculia, the "old way" of teaching math just does not work at all. If you ask me "What's 5 + 7?", I have to think about it. As a result, I was always in remedial math.

Until they let us use calculators. Then I was suddenly put on the advanced math track. I could do algebra, trigonometry and calculus easily in junior high/high school. But when I got those problems to the point of actually adding or multiplying the resulting numbers, I could not (and still can't) do it well and relied on calculators to do the basic math.

From the little I've seen of the "new" way of teaching math, it make a lot more sense in my screwed-up brain than the rote memorization from my school days.

MineralMan

(146,317 posts)
6. Exactly. Everyone uses calculators now, anyhow.
Wed Sep 23, 2015, 02:30 PM
Sep 2015

At one time, I could manually find the square root of any number. Damned if I can remember the method now, though. By the time I was in college, the first calculators with a sqrt function were available, so there was no need for that manual method. Before too long, the slide rule also went into the garbage, once scientific calculators were available. I dropped out of college for four years in 1964. By the time I returned, the slide rule was history.

I still have my old book of logarithm tables. Not much use for that any more.

Math has become more theoretical, even in elementary school. It's taught more in a way that helps people understand concepts, rather than simply calculation methods. That's how life operates today. Nobody needs to know calculation methods really any more. They can be useful, to be sure, but there's a calculator on every device I own, even my old flip phone cell device.

I still use the old methods when I need to get a quick view of something, usually in my head, as an estimate, but if I do actual calculations, I use a calculator or enter the numbers in Excel if I have a long list of numbers to add or do other operations on. I enter the formula and Excel does the calculations, including some very complex ones that would take me hours to complete.

I like modern technology.

hobbit709

(41,694 posts)
12. the problem with using calculators without learning the basic math
Wed Sep 23, 2015, 03:00 PM
Sep 2015

is that I've seen people just put whatever the display shows after hitting the = key. I at least have some idea of what order of magnitude the answer should be in.
Saw a kid add up 9 two digit numbers on the calculator and get a 4 digit answer. He couldn't understand why I said that answer was wrong and he made a mistake somewhere.

MineralMan

(146,317 posts)
13. Yes, well, of course.
Wed Sep 23, 2015, 03:03 PM
Sep 2015

I think that's what they're teaching - basic math. They're trying to teach kids to understand what it is they're doing and why. That's confusing to adults who learned another way.

I learned the old way, and am very good at estimating results, as you mention. But, I also did enough math in college to understand what is underneath the calculation algorithms we use. I was lucky to have started out as an engineering major.

 

HassleCat

(6,409 posts)
8. The navy made us use slide rules
Wed Sep 23, 2015, 02:44 PM
Sep 2015

This was in the mid 1970s, when calculators were considered unreliable. I never did master the slide rule, and using it was harder than the math itself.

MineralMan

(146,317 posts)
10. I was good with a slide rule, but welcomed the calculator with
Wed Sep 23, 2015, 02:58 PM
Sep 2015

open arms. I gained more precision and much more speed. I don't even like to think about how much my first TI scientific calculator cost in real dollars. It was an SR-50, with tiny little red LED display. If I remember correctly, I paid about $180 for it. What a marvel!

I bought a much more recent one the other day at Goodwill for $5 that even had graphing features. $5.

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