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Penny Arcade - Comic - The Grapes Of Math
Dog
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Penny Arcade - Comic - The Grapes Of Math
Videogaming-related online strip by Mike Krahulik and Jerry Holkins. Includes news and commentary.
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Them Spells are kicking in already
Not making a value statement about common core, mind you, but my point is that our own understanding of math is not necessarily the One True Way.
Them kicking spells.
you take two numbers and smush them together in very specific shapes until the right number comes out
I haven't seen a whole lot of actual common core stuff, but if it's all like this subtraction thing then I don't see what the big deal is. You do this same operation whenever you're paying for something in cash and need to break a large bill into smaller ones to get exact change. I might be a bit biased, though, as the school that kindergarten-me attended taught arithmetic on what amounted to an abacus.
Basically they are teaching everything as being movement on a number line.
Also, I just noticed the strip title. Fantastic.
I hate this.
It looks like it works pretty well for teaching the concept that addition and subtraction are opposites. But if I had to do multi-step addition like this every time I wanted to do a simple subtraction because that was the way I had been taught you do it, I would hate math too.
But maybe I’m misunderstanding and this is just the concept being taught and then they teach the other way later?
*shrug* I don't have first-hand experience with it, just complaints from family members who tried to help my nephews do their math homework. Found that picture doing a quick Google image search for an example.
On average
I think the example in the image was pretty egregious. That problem is way easier by subtraction than by figuring out the addition needed to make it work. It's even easier if you subtract 25 and add 1. Also the answer is probably apparent to most people without consciously doing any math. I'm sure that was why it was picked to make Common Core look horrible. My quick searching showed some Common Core problems that do subtraction by going backwards, and they seemed fine. In some ways probably better. I think viewing numbers as fungible substances to be grouped and broken down as needed probably gives people a better ability to do math. That 248 you have is also (100+100+48) or (250-2).
As an example of a subtraction that I think is easier counting up:
224-89=X
Using New Math you have to borrow twice, and I found difficult to do in my head.
Using Common Core it's obviously (?) 1+10+100+24. Which is 135, and I found easy to do.
They just need to cut out the middleman and teach those kids how to use an abacus
They're teaching kids how to break apart numbers so when they get to algebra and calculus and every single 80 year old algorithm that we consider "the old way" completely fails, they can actually know what the fuck is happening.
There's a reason that even simple math like algebra makes "no sense", it's because arithmetic is done entirely by shortcutting.
Anyway when I worked an inventory job we would often quickly count large quantities of stacked goods. It was second nature to me to see a stack of 12 cans, packed four high, with three missing, as 45. But a lot of people really struggled. So I can see teaching math spatially as very useful in real-world applications of math. At the same time being able to do it on paper quickly is useful too. So I guess I'd agree with those saying the new way is fine as long as you still teach the "normal" way.
Hey relax, I didn't say anything negative about it. I was just clarifying for fartacus that it was a newer, different method than the one in the video linked above by Sigma. In my second post, I was humorously noting that I'd learned about it secondhand from someone experiencing exactly the scenario outlined in the beginning of that Tom Lehrer song.
Kindergarten-me went to a Montessori school, and this image is super nostalgic. The fraction pies, the pythagorus thing with every 1 being its own piece, all those wire-threaded glass beads. I can still remember one of the other kids getting fucking shredded by a teacher because they'd thrown a 1000-bead cube across the room, when all the bead stuff had been discontinued and all they could get from the supplier were these dumb wooden cubes with painted dots. Also, assuming they still use them, Montessori schools do teach them to use an abacus. They just call it a "bead frame".
Ah, the song being old makes more sense. That subtraction-by-adding thing seems weird to me, but I think it's just teaching things in a different order. When I got into algebra we did a whole unit on moving things around a number line, but we never used it for arithmetic (beyond a few example problems) because everybody had already learned to do it the old way and/or had calculators.
Though the general look and concept is the same, the large and small bead frame materials differ from abacuses in pretty significant ways:
https://www.montessoricosmos.org/blog/2019/2/1/is-it-montessori-childrens-abacus-toy
Of course, the traditional abacus doesn't really look like the toy ones most people think of. They're in columns right-to-left, with only five beads in a column.
The separate bead is used to mark 5. It's a much more compact (and therefore efficient) way to do it as opposed to those with 10 (or 9) in each row.
Montessori is like this in so many different areas, with hands on materials carrying making up so much of the bulk of teaching. As such, remote learning has been extra challenging. Some things you can replicate at home, but others like the long division racks and tubes are more elaborate:
If regular math is wizardry, Montessori methods are alchemy.
It's a bit trippy to me that it's literally been 25+ years since I've laid eyes on Montessori gear and it hasn't changed at all. Well, I guess they probably use plastic for a lot of the stuff that used to be wood/glass/metal. People used to cut themselves on the regular with slices of the 10-piece fraction pie.
I've heard on more than one occasion from more than one person that they often still teach the "shortcuts" that many of us learned as kids. I think the common core method is good as well since it teaches them how to break the problem up so that they can better grasp what is happening. We all learned about borrowing and carrying using the traditional method, but I wonder how many kids truly understood WHY they were doing it when they first learned it.
Besides, let's be honest here. I have to perform basic addition and subtraction all the time in my job. I never write it out in the traditional OR the common core method. I use a damn calculator. I'm sure a very high percentage of adults do the same. We basically all carry one around in our pockets these days. The only time I don't use a calculator is if I want to give my brain a workout and figure it out it in my head. If I do that, then my mental approach is honestly closer to the common core method.
-Tycho Brahe
Okay, I might be just a tad biased here.
I do think there are probably some discrete math concepts that could be taught at a much earlier age.
And yeah, parents will hate when things are being taught that they can't do. And honestly, learning at home is no substitute for a dynamic and brilliant teacher, who is (under)paid for doing this work, although there is something to be said about self-directed study.
I never really got into any math studies in high school that did anything out of base 10 and boy it sure seems like the Common Core method makes it super easy to adopt base 8 and others and use the same tools to get answers.
People keep posting about the old ways and how mystifying it was for someone to move onto algebra/trig/calc from it, and I'm over here like "what are you talking about, you didn't learn things like using least common denominators to solve fraction problems in arithmetic?" I mean, the school district I went to had a lot of pretension, but didn't they explain concepts like how you can break down and rearrange numbers in a problem at any point before you got to algebra? Common core didn't exist yet AFAIK (this was the 80's & 90's), but we definitely learned about how you can restructure a problem to make it easier. For that matter, in 1st or 2nd grade they'd do stuff like using these plastic blocks to illustrate the mechanics of place value (sugar-cube sized pieces for 1's, sticks of 10 for the tens, 10x10 panels for hundreds).
I'd love to see how much calculus could be snuck in at a grade school level. Probably not any of the complex math, but it shouldn't be too hard to have students draw on graph paper and count the squares.
Again, I'm over here thinking "the problem wasn't the old math per se, the problem was poor math curriculums". I can't remember what we used it for, but I know we did something with graphs in elementary school, long before we were learning about slopes or curves.
One thing to note is that Montessori education doesn't really have homework, in the traditional sense. Your homework is often literally "home work", aka chores. Or things that can apply stuff they learn in school to real life (pairing up socks, cutting up pizza/pie into fractions, making change to buy things) or just simply reading.
Which is fantastic, because I don't what the FUCK to tell my kids half the time when they ask me questions about doing math. I have strong math skills, but they speak an entirely different language than I do. I have seen this approach in some schools outside of Montessori schools as well. Basically, if they're still learning when they're at home, school failed them. School is for teaching and home is only for occasional practice.
I think this is the "Common" part of "Common Core." Before, teaching was all over the place. You could have radically different approaches from state to state or even within. CC was an attempt to find good approaches and get them implemented everywhere. Also, CC isn't actually as prescriptive as people think. CC actually targets what students should know and what students should be able to do at each grade level. There is no curriculum actually specified in CC.
It's also not a federal law. Each state adopted CC individually. And each state and local unit is responsible for deciding how they will meet the benchmarks all the states agreed on together.
But it's been a convenient political cudgel. The real basic truth is that teaching is hard, especially without parental and financial support.
This was the thing I struggled with in math. I could do the work, and apply what we were learning to other situations, but I always had difficulty connecting the terminology with the methods. Like I would look at a problem and figure out how to solve it, but for me, being told to use [almost any term besides quadratic formula] to solve a set of problems was like getting directions from Charlie Brown's teacher. I just had this weird mental block when it came to a lot of the nomenclature.
Old math problem: A logging company can cut 145 acres of trees in 8 hours. If the trees are on average 200 feet tall, what is the cubic footage they clear in 25 hours?
Modern math: A logging company can cut 100 acres in a day. Write an essay on how logging harms the environment.
also yeah, I'm sure there's a youtube video out there showing old methods of teaching multiplication or lord knows long division and lol
that's why we call it the struggle, you're supposed to sweat