The person responsible for the computer use for my kids school district has a .sig that reads something like “if you can google the answer, then you probably asked the wrong question.”
I’ve been helping a second grade teacher for the last few years with teaching her kids math. So, I’ve had plenty of time to think about the issues you raise an I’ll say that you’re dead on. I’m not there to stuff one way to multiply into the kids heads. I’m there to try to help them understand how multiplication works and what it means. The grid method shown in the video works great with some kids who struggle with other methods.
One of the nice parts of common core is that they tend to have several ways to solve any specific problem. So, it becomes less about memorizing one method and more about findind a way that works for each student. They can all get the same answer at the end of the day, but they may reach it using a different method. One of the benefits of this from my point of view is that there is a method that works for kids of all abilities. The clever kid can use a different (probably shorter but more complex) method than the child who’s not so good at math.
The old way of having one way to do any problem and if you don’t understand it, you get left out didn’t work. It caused kids to get further and futher behind until they either gave up or were given up on. If our goal is to help every child reach a larger portion of their ability, then this seems like a good way to do it.
I’m sorry if it means that mom and dad are going to have to learn something if they want to help their kids with their homework. They’re not going to get a lot of sympathy from me.
Common Core doesn’t have any ways of teaching anything. Common Core is literally just a set of standards of what a kid is expected to know by a certain grade level.
All of these methods are supposedly “aligned” with Common Core, but some are definitely moreso than others.
Anyway, my only complaint is when they teach to the methods. My daughter brought home a worksheet where she had to do it using a number chart. As a way to teach understanding systems of rules and spatial logic, it was great. But she could do 61 - 33 in her head a lot faster.
So she’s dutifully showing her work and it’s fine but definitely a bit annoying especially knowing this method is for visual learners which my daughter is not. It’s like they completely misunderstood the point of multiple intelligences.
Oh and it’s annoying having to be positive and encouraging about it because trust me the tediousness does make her like math less because it eats into her free time without any obvious benefits.
I don’t understand why the example in the article is factoring both numbers. Surely you can do either 30x12 + 6x12 or 36x10 + 36x2 in your head. You’re adding 360 and 72 either way.
I don’t have a problem with other multiplication methods being taught. However one very good reason for learning the traditional* multiplication method is for when you try to learn division. Try doing a division problem where you have to fill a scratch sheet of paper with lattice multiplication problems just to calculate the partial products.
My kids went through Everyday Math where the learned all these different methods designed to give them a number sense. Guess what, they followed the rules to these other methods just as blindly as the rest of us did in the good old days.
I think it all boils down to this old joke: There are 10 kinds of people who understand binary, those who do and those who don’t. (Ok I was going for those who get/like math and those who don’t. It sounded better in my head.)
yeah-yeah, I don’t remember the proper name for the method of multiplication we learned when I was in school. Sue me.
Vedic Math: Add the digits piecewise in some order to make enough digits, pad with a 9 sometimes.
Tantric Math: Make the numbers shine and decorate or decimate the digits 6 and up; but present no more than is asked.
Rudic Math: Check the answer 8 (or 8!, to taste) ways to be sure. Then never do that again.
Phone Math: Used to be showing the problem to the camera while a certain app was up; now, meditating on ARM-nature while considering the digits as a the corresponding release of a make of mobile, with revisions counting as decimal digits.
So…Cheating Craft (anime) is only good after middle grades? Oh well.
I don’t even think it’s a good algorithm to use! I can’t remember the last time i did long multiplication, and that’s not for lack of numbers to multiply (nor use of a calculator). Mostly i use combinations of tricks like he describes. That includes a mental area method, right down to visualizing bits of area.
I was never taught those methods as such but i have had a very good maths education.
How does it help with division? I’m pretty sure I don’t ever use long multiplication when conceptualising division, but i might be wrong (or others might use it).
Read Jules Verne’s ‘The Purchase of the North Pole’, where the plot is based on one character, a mathematician, accidentally dropping a few zeroes in a calculation.
While that is true, it misses some of the history. It’s called ‘common core’ becuase it’s the end ability that the students are expected to show. Before the standards required the students to show proficiency with a specific method of solving problems. So the difference is that they are now free to use different methods to solve the problem–as long as they can solve it. So, yes, Common Core doesn’t require the learning of these different methods, but the point of moving to Common Core was so that educators would be freed up to use other methods.
Yeah, I’ve seen that tendency in older teachers who are still stuck in the ‘what method are we supposed to teach’ mentality. They just can’t seem to get around the idea that it’s not the ‘method’ that needs taught, but the ability to reach the right result–regardless of how they do it. That being said, as long as a lot of time and effort isn’t wasted on it, it can be helpful for children to try methods which aren’t exactly their strength. While they may not end up using that method, they can be aware of it and open to problems having multiple way to be solved.
To me the simple explanation for all this is that many parents do not understand the difference between arithmetic and mathematics.
Arithmetic is mostly a set of tricks for getting the answer to calculations - algorithms if you like. Mathematics, at least at school level, is what you need to know to get to needing arithmetic. When you get to needing arithmetic you can do it in your head using simple algorithms or you can use calculating aids like tables, slide rules and computers. But knowing what to compute is mathematics.
Parents usually never saw the wood and they don’t like it if someone suggests that you can see the trees from a different angle.
California, in the 1960s, started teaching unconventional math to kids in junior high. That was the first wave of “New Math”, and it was criticized widely in the press and among parents.
So as a 7th grader, in math class, I was taught set theory. Which was ridiculed, of course, by conservatives and people who thought that only arithmetic was useful.
When I was 28, though, I got into computer programming (when it was still an apprenticeship profession) - and set theory is one of the foundational conceptual structures of data processing. It became more explicitly useful when relational databases were developed, but good programming always used set theory as a basic design tool My few weeks of studying sets in 7th grade put me permanently ahead of programmers who had never encountered set theory, or who had not bothered to actually learn it, and was useful during my entire career.
What are kids learning now that their parents don’t like but which will be a major boost to their futures? We don’t know. But learning math the way it is being taught now is far superior to the stunted and incomplete ways we used to learn about numbers.
The trouble is not that new techniques are taught, but that fundamentals like multiplication tables up to 12 are not taught, or set aside as the class presses forward. Multiplication tables are some basic shit that you use everyday, in real life, beyond homework. Rote knowing also makes life a lot easier inside the math class no matter what the level. So when teaching to the test and teaching to the method replace basic knowledge; well, that’s a problem, with no political component, it’s just bad teaching.
At the risk of being controversial, the only right way would be to start by teaching kids to multiply numbers of any size, in their heads, but only to 1 significant figure.
If we’re talking, and you ask me to multiply 1,018 by 883,428,319, what, I’m going to say “Eight hundred and ninety-nine billion, three hundred and thirty million, twenty-eight thousand, seven hundred and forty-two”? No, I will say “nine hundred billion”, because that’s how people actually talk about numbers.
And if you asked me to multiply 3 by 88, I might as well say “two hundred and seventy”. Unless you want to wait, and I can give you an answer that’s basically the same, but harder to remember, and more likely to be wrong.
So why not explicitly teach kids something nearly all of them can learn, which is good enough (if not better) in many situations, and still a good starting point if they go on to learn how to do it more exactly.
You could then score tests by the accuracy of each answer, so for an A+ you need to get all the answers exactly right, but for a B, kids can either try to learn the exact method, or they can become an expert at the simple method. That’s, like, two whole ways to not get labeled as a dum dum for the rest of your life.
The whole point is that number sense is reinforced even though they are blindly following the methods because the methods are less abstract than the old ones.
Sure, partial quotients division or an area model takes longer than long division, but who really cares? You want fast, use a calculator.
