And one more thing for the left hand of darkness ( cute and safe sounding name for a 3rd grade teacher btw)
Our children are the most prized, loved and valued gifts. To ask me a concerned parent who just wants some answers to just trust you, when you are clearly offended so easily is the scariest thing I could imagine.
who knows maybe if someone tried to show me or anyone else that has my concerns how or why this way or these methods that we described about the subtraction, arrays (when that is clearly POV) and box or lattice multiplication is better instead of slinging slyly styled insults then maybe you could turn me around.
But instead all I am getting is. It’s better because we said so types of responses.
If you say that a specific way is better than the examples I have shown. Then show me why and how it’s better. Because I obviously don’t see how.
And please understand that I am just a concerned parent that can not get any answers and want my child to be taught the way that will benefit him most. And because we say so just isn’t good enough.
I get answers like it does this and that. With no explanation of how. How is it different from my approach?
How can any parent trust a teacher that would rather be offended by our doubt and argue a point in a because I’m a teacher attitude instead of easing our minds and explaining it to us. After all most of us grew up successfully holding down a career of some kind without having ever seen this. And now there’s is something new that no one can explain and we are just suppose to blindly trust this with the minds of our children?
And before anyone else takes offense and asks me if I would blindly trust a new way of building Bridges without a proof of concept the answer is no I wouldn’t
I do. In my defense, your writing can be pretty opaque: you’re misusing punctuation, peppering your writing with fragments, using unclear antecedents to your pronouns, and more. If you’ll write more carefully, I’ll read your writing more carefully.
For example, what the fuck am I supposed to take from this? Do you want an explanation of how subtraction via adding is “more logical”?
Because here goes.
It’s not “more logical,” but sometimes, and for many people, it’s a lot easier. When cashiers count up change, they’re subtracting via addition. Given the relationship between addition and subtraction, it’s a trivial process: you turn X-Y=Z into Z+Y=X.
For a simple example, contrast using the standard US algorithm for subtraction against using the subtraction-via-addition method, with the following problem:
1000-999=Z
The traditional algorithm asks you to borrow the 1 from the thousands place leaving 0 thousands, use the borrowed thousand to make 10 hundreds, borrow 1 from the 10 hundreds leaving 9 hundreds, use the borrowed hundred to make 10 tens, borrow 1 from the 10 tens leaving 9 tens, use the borrowed ten to make 10 ones, and subtract 9 from the 10 ones to get 1 in the ones place. You then subtract 9 tens from 9 tens to get 0 tens and 9 hundreds from 9 hundreds to get 0 hundreds. You’re done.
The subtraction-via-addition method asks you to add one to 999 to get 1,000. You’re done.
That’s an extreme example, but the method also simplifies most problems where you’re subtracting from a nice round number (i.e., a multiple of 10, 100, 1000, etc.). It’s much easier to do, say, 500-387 using the add-up method than it is using the standard algorithm, easy enough that most third-graders can learn to do it mentally in a few seconds.
I dunno. Maybe I am, but maybe you’re not understanding what’s going on.
See, that’s an example in which the standard US algorithm works beautifully. There’s no regrouping necessary.
Kids (and adults!) should have a lot of different methods to solve problems. Different problems cry out for different methods, and the best mathematician chooses the right method for the job.
I mean, I can explain it with this problem, but it’s not efficient with this one, and it’d be a helluva lot easier with a number line. Here you go.
First you gotta believe that subtraction can be used to find the difference–the distance–between two numbers. 10 is six away from 4, right? 10-6=4.
Now you gotta believe that the distance between two points doesn’t change depending on which direction you go. If 10-6=4, then 4+6=10. Going from mile marker 10 to mile marker 4 takes you the same distance as going from mile marker 4 to mile marker 10. Right?
So if we want to find 489-242=Z, we can instead find 242+Z=489. Answer’s gonna be the same.
If I’m looking for Z in 242+Z=489, I can break it into a series of smaller equations. Imagine traveling from mile marker 242 to mile marker 489, stopping a lot of time along the way. If you add up all your little trips, you’ll get the distance of the big trip.
I’ll do a series of small, easy equations to nice round numbers. I can do all these bitty equations in my head, even if I’m 8. Here they are:
242+8=250
250+50=300
300+189=489
Now if I add those little bits together, I’ll get the answer:
8+50+189=Z
I’m gonna use a different trick now, decomposing the 8 to get 7 and 1, and add that onto 189:
189+1+7=190+7=197
I’m gonna use the same trick to decompose the 50 to get 3 and 47, and add that onto 197:
197+3+47=200+47=247
And that’s the answer: 489-242=247.
Now, some notes:
This is not the most efficient way to solve that problem. But it’ll work.
I wrote every single sub-step I could think of. In reality, a lot of those steps happen mentally (especially the number decomposition steps).
Even though this is an inefficient method for this particular problem, it’s a very efficient method for some other problems.
A number line both makes it much more intuitive, and also helps a lot of kids grasp what subtraction means. I speak from years of experience teaching this method.
I always tell kids that they need to choose a method that works for them. I only require students to use one particular method when I’m actively teaching that method to them; even if they don’t like that tool, it’s good for them to have it, in case they encounter the perfect problem for it.
First, that’s not my user name. Second, it is the name of one of the greatest and most compassionate novels ever written, and my actual username is a riff off that novel. Third, I don’t mind going dark as a teacher; today my third-graders learned about the murder of Julius Caesar at the hands of a terrified Senate. Fourth, THIS IS THE PIT, a part of the messageboard specifically designed for insulting people. I’m not going to call you a dumbshit here, but I’d be entirely within the board’s culture to do so. Finally, I don’t teach your kid, so stop with the vapors.
Did you read the entire thread before responding? Because I spent a long-ass time explaining shit like that back in September. If you didn’t read the thread first, expect a bit of blowback from impatient people like me who want you to use two ears before you use your one mouth.
(Huh. On the Internet you have two eyes but ten fingers. That explains so much. I digress.)
I know I meant to put 20 2’s I’m on my phone and I have big fingers. All the computers in the house are being used. Lol but thanks for pointing that out. But you can see how it works.
Madam Jo. Thank you for being the first polite person on here. I agree with what you’re saying. It just gets frustrating when I don’t want my child held back when he’s right. It definitely gets me passionate and makes me worry.
Left hand of darkness. Thank you for attempting to explain this. I do agree with counting change example. Something similar I do when subtracting involves adding as well but much easier. Which I will get to. First i don’t have any problems teaching a certain concept. But I don’t agree with marking answers wrong when my child gets the write answer.
For a barrowing scenario of say…
344
168
Knowing my son understand the concept of taking away. I felt ok showing him how I do it using adding…
I look ahead as see two barrows so I can feel secure in writing a 1 under the 3-1. Knowing that barrowing is taking place and the middle 4 will become a 3, I simply use compliments of 10
In the middle 6’s compliment is 4. Adding 4 to the top 4 is 8 minus the one I know is barrowed becomes 7 all done in the head. 8’s compliment is 2. 2 plus 4 is 6. 176 is the answer. Simple. And efficient.
Anyway thanks for at least trying to explain your position. Now that even you admitted the one example using the adding was not efficient. This is part of my frustration. That my son’s teacher can cut see this point and refuses to listen to reason. And I’m not kidding when I say she could not explain it. She literally said it just works because it does.
Now my grammar. I’m on a phone that puts me in an autocorrect nightmare. Do yes I miss punctuate and it causes other grammatical errors but thanks for trying to make others look dumb.
Oh and FYI I hope you are not really a teacher with that foul mouth. Regardless of the sites rules this thread clearly talks about math and school. So some could come to the conclusion that children are reading this. Like the one sitting beside me asking me why a teacher has such a potty mouth.
Kindly use that education to choose less colorful language as my son in beside me.
Beside me because he’s pretty intelligent for his age and has been brought to tears over being made to look stupid in front of his peers when he’s anything but.
I wish some teachers would realize that this CCSS really is messing some children up mentally and destroying their self confidence.
My kid went from loving math to being brought to tears and dreading math class. And he’s not the only one. There are many kids that feel as he does. Kids that use to love math.
Anyway thanks to everyone else who at least wanted to help. I do appreciate it.
One final note…
These protesters are teachers.
There are 2 quick quotes I’d like one share from the site the image came from. I would pay the link but I don’t know if linking to Sue’s u are permitted so here are the quotes …
“One of the most outrageous features of Common Core education standards is the way they pit teachers against parents. Textbooks and curricula aligned with Common Core actively discourage parental involvement. . .”
And
“Common Core was not designed by teachers, but rather by bureaucrats who do not understand the classroom, and many teachers are among the loudest voices of opposition, angry at the way the standards prevent them from effectively doing their jobs.”
Teachers make up the largest numbers of people that do not agree with CCSS.
Would you be satisfied with a 3 class grading system “+” for did the problem correctly, “X” for got the answer wrong, “-” for got the answer correct but failed to follow directions. Because that is really what is happening here. As others are saying, getting the answer correct is only part of the what the teacher requires, and as a parent I’m sure you see the value of teaching the students to follow directions and that it would be reasonable to mark them down for failing to do so.
If a PE teacher said, today we are going to learn to do cart wheels and I want everyone to cartwheel across the room. If a child instead just walked across the room because it was more efficient than cartwheeling but achieved the same thing, I would expect the teacher to tell him that he was doing it wrong.
Not to compare apples to oranges, and I know this is not the same thing but it is at it’s core…
Would you follow directions for making a cake if you knew the directions would do more harm than good?
Same at the core because my son’s class has 22 children. After watching him message his peers 14 out of the 22 are experiencing anxiety and depression because they can see past what they are being force fed and it’s going against what they learned or learn naturally and it’s clear for anyone to see the problem. It’s all I’m saying.
But I’m finding this is like trying to convince a flat earther that the planet is round. They just don’t want to accept what’s right in front of them. I’m deleting my account here so go ahead and talk behind my back I wouldn’t expect less from the foul mouthed and uncompromising attitudes I see here.
I really feel for the future of our children when our educators can’t see past there own blinded convictions to see the problems that lay right in front of them.
I am sure not everyone that reads this thread is like this umbut it is what it is. I give up on here. But I’ll never give up on my child despite some teachers.
Maybe this will make more sense formulated in terms of higher grade math. When you learned conics, and specifically quadratic equations, I’m sure you probably learned:
Factoring
Completing the square
The quadratic equation
Of course, 3 is a generic solving of 2, but regardless. The fact is, while you can solve most problems with both of these, they have varying levels of efficiency. Factoring, when possible and for small numbers, is often extremely quick if you spend the time to get it down, it’s also the easiest to do in your head due to a number of factors. The quadratic equation is pretty easy to memorize and plug into your calculator if you can’t expend the mental energy to or the factors are not obvious.
Completing the square… well, it’s the process that yields the quadratic equation when all coefficients are variables, but learning it and being proficient at it is necessary for developing the intuition for why the quadratic equation works and getting general insights about how parabolas work.
Similar, when solving systems of linear equations there are a number of methods such as putting them in matrix form and executing algorithms such as conversion to RREF, or various heuristic methods that don’t apply in all cases but work extremely well when they do. Some of these methods are literally the same, but represented in different formats, yet are important because they’re used in separate mathematical domains (RREF being a brief intro to the field of linear algebra, and elimination being a more traditional algebraic approach).
In calculus, you were surely taught both u-decomposition and integration by parts, even when both can solve many problems equally well, because they’re better suited individually to certain problems.
The thing with the multiple methods that are taught for simple operations like addition is that not all tools work equally well in every situation, and not all kids will be proficient with certain methods but may not know that’s actually their preferred method until forced to use it for a while. That’s a key part, oftentimes we find methods we originally find puzzling or offputting are actually our most used or best understood ones (in fact, at graduate level I’d counterintuitively say the proof and mathematical methods I use the most are the ones I first understood least because I had to put in so much effort to understand what made them tick).
Forcing yourself, or in this case, children under your wing to apply certain methods is meant to expose them to a wide range of tools and applications and make them gain proficiency, hoping that in the future after some blood, sweat, and tears, one or two will click with them and they’ll be better for it. Essentially, “throw it at a wall and see what sticks”.
Now if you want to quibble grading with me, sure, I’m not exactly a fan of the prussian school system we use. The grades, encouraging of conformity and indoctrination regarding submission to authority, and so on. But regardless, working through a bunch of different methods for doing one operation is not a flaw, it’s a boon.
This doesn’t discount that some teachers may be bad at their jobs and not clearly indicate directions, or are overly harsh in their grading, or don’t properly understand the methods they’re teaching. Maybe the materials they use or the training they got was bad (a lot of “Common Core” materials were produced by race-to-the-bottom textbook companies in a rush after the standards were formalized). But the notion of teaching a bunch of different heuristic methods to do simple operations is good.
In fact, LHOD’s example of addition is how I, a PhD student in CS who frequently does mental math, do addition in my head. Some of the “weird” methods for subtraction I do as well. Formalizing these methods exposes more people to them. Most of these methods are things people who are relatively proficient at mental math independently discover over and over, often not realizing they’re even using a neat heuristic method. Meanwhile, people who didn’t think up these methods get left behind trying to somehow do complicated but general algorithms in their head and getting frustrated (unless they’re one of the rare people who can legitimately hold all that in their head at once). You can solve that by… just telling people these methods exist when they’re first learning the material, and that’s exactly what’s happening.
To be clear, I really, really don’t expect most kids to see the utility of this. I constantly wish I could go back to High School and Early College with the literacy and mental maturity I have now because I feel like I’d get a lot more out of some concepts. Especially in English (which this thread is not about). While I think schools occasionally do a very poor job of motivating literary analysis techniques and with Spark Notes and such it’s become quite paint-by-numbers, there are a lot of concepts and techniques that I didn’t appreciate until I get more into analysis a good decade after HS. Things like “analytic lenses” seemed like head-in-the-clouds nonsense until I saw them thoughtfully applied many times in interesting ways much later in my life. I was in no way mentally mature enough to grasp a lot of those concepts.
Similarly, we can argue that a lot of primary and secondary education math is kind of a smattering of vaguely-related nonsense, most of which kids won’t even encounter again until college and if they do it’ll be such a faded memory it will need to be retaught anyway. I’m sympathetic to some curricula revisions due to this, but I don’t think these concepts fall under that umbrella.
Hah! It’s because of people like you who were convinced by a fake stamp that CC had to start using holographic stickers like NFL merchandise. Thanks a lot!
ETA: OOOOOooops! the post I responded too is from a while ago.
You’re trying to make me feel bad, because late on a Friday night you visited a messageboard where you have to be at least thirteen to participate, and you’ve navigated to the part of the board specifically designed for people to let loose with language and insults, AND YOU’VE BROUGHT YOUR EIGHT YEAR OLD SON ALONG WITH YOU?
That’s MY fault?
I mean, I’m pretty sure you’re lying in a lame attempt to guilt me. But that’s the charitable interpretation. If you’re telling the truth, this is such a significant parenting fail that it casts doubt on your understanding of–well, everything.
Kid, if you’re still sitting beside your dad, please turn to him now and tell him he needs to learn to set some boundaries for you. He’s really fudging things up.
Danvers, if you’ve really deleted your account, good on you. Be sure you don’t let your son have easy access to the grown-up sections of the Internet any more. It’s bad for him.
I swear to god, it’s like everyone has a vested interest in keeping people bad at math. Adults that are currently bad at math want validation that it’s impossible and they never could have learned it and, perversely, seem to feel that being made to suffer through it in a super-specific way was character forming and all children need to go through it.
On the other hand, people that are good at math seem to think that all the techniques and understandings that allowed them to shine in 7th grade are sacred and that it devalues their own talents to just tell kids about them. The best way is to haul everyone through the painful and horrible process and then the naturals–the people that deserve it–will develop mathematical intuitions on their own.
I know I am being hyperbolic, but lord, I don’t understand actual antipathy to good math instruction.
I completely disagree with you, you are not being hyperbolic. (I agree with everything else.)
My friend’s mother was a fourth grade teacher, and she goes on about common core like it’s the worst thing ever.
She is bad at math. Like, really, really bad. Counting on fingers bad. And she was expected to teach math that she didn’t understand to kids that obviously didn’t understand it yet.
She would give the common core assignments with “malicious compliance”, going so far as to let her students know how stupid she thinks these methods are.
Great woman, and she is great with kids, and I’m sure that in other subjects that she knows and understands and likes, she taught well. But she failed them hard when it comes to math, at a fairly important age.
I don’t know how you are at math, LHOD, but you are obviously better than she was, and probably gave your kids a much better leg up on their math, but how much of that is undone if they get her next year?
Personally, I think that elementary school is inherently flawed in expecting teachers to teach all of these subjects, to which it really is impossible to be an expert in all of them, and fairly difficult to just be very competent in them all. You are certainly better at math than my friend’s mother, but there may be something that she teaches better than you do. That kind of inconsistency isn’t healthy for education.
IMHO, if I were to get to completely write education policy with any budget that I desired, the elementary school teacher would essentially be the babysitter. A very important babysitter, one that facilitates education. They would be in charge of the children, making sure that they are attending and attentive, assisting with any social or administrative issues. But it would be actual experts in the respective fields that would be actually teaching the subjects. People with an actual interest or even passion for the subject that they are teaching is going to get through to more students than a teacher who personally dislikes the subject and just wants to get through it to get to the parts of the curriculum that they do like.
Say that I’m a native French speaker, and an expert on French literature. I teach a college course on French literature, in French, to education majors whose French is mostly from two indifferent classes in high school. My students then go to teaching jobs, and are required to teach French literature to high school students. How effective will they be? Will they and their students enjoy the subject or material?
That’s where I think we are in terms of math education. People who are good at math, the process–and I will assume that most college professors teaching math courses are pretty good at it–speak Math, the language, fluently. Students in those courses generally know enough Math to ask how much a beer costs, or how far it is to the airport, but not enough to discuss poetry. Some will develop fluency, but most will latch onto just enough to pass the class. The ones who become fluent mostly don’t realize that they’ve learned to speak another language; they just internalize that Math is how one talks about math. When those students go on to teach math, you get teachers who don’t have a deep understanding of the material, or who understand the material, but don’t realize that they need to translate from Math to English. Either way, it’s a recipe for frustration and resentment, which are widespread in math instruction.
Anecdote:
I recently had a conversation with a very mathphobic teacher (a music teacher, so at least she isn’t directly infecting students with her phobia). She compared something to calculus, with the intent of conveying that it was impossibly esoteric…but she was sitting at a table with an electrical engineer (me) and a guy with a PhD in a mathematical field. Doctor Math objected mildly to the characterization, and the talk turned to math. I undertook to translate, because within minutes, both of them were looking confused and frustrated. They were speaking two different languages, and neither one quite realized it.
It turned out that no one had ever just told Mrs. Music, in plain English, what calculus is. Not the jargon, not the mechanics, just the bare purpose of calculus had never been communicated in a language she understood. Doctor Math was calling it the “mathematics of change”, which is true, but not helpful to her. The translation that worked was that calculus is the “math that breaks complicated problems into lots of tiny little simple problems”*, and five minutes of sketching on my whiteboard table based on that conveyed the basic idea of how differential and integral calculus do that. She still doesn’t know calculus, and would be intimidated by the mechanics of it, but at least she has an intuitive concept of it, so it’s no longer a scare word for her.
*Yes, I’m aware that this could be said of other branches of math, but it’s really core to calculus, and more importantly, it’s what she needed to hear in order to receive the concepts. It was the elevator pitch for calculus.
I’m curious to hear what LHoD has to say about it, but I don’t think I agree that elementary teachers need to be separated by content. Most of the raw content is not that hard (by definition). What an elementary teacher needs is to understand is how littles think, how things look to them, what they confuse, misunderstand, etc–and what misconceptions will go unremarked now but lead to problems later. You also need to know how to motivate them, how to pace things, etc.
Now, it may well be true that you can’t expect an individual to know all that for every subject within a grade–and I think by 3rd or 4th grade, a lot of schools do start having one teacher teach the math for a cluster, one teach the ELA, and one do, say, science and social studies. The three classes rotate kids. But the issue isn’t that you need an abolute content specialist in there. You need someone who knows both the content and the pedagogy.
You also need people willing to learn new things and they need to be provided with the resources and the time it takes to learn them. So often, there’s an excellent new program but it’s presented in a 2 hour workshop by someone who doesn’t understand it. Teachers know it’s likely going away in a year, anyway, so they don’t put hours into figuring it out on their own. Then, it does go poorly, so it’s canned after a year, perpetuating the idea that everything “downtown” shoves down your throat is a useless flash in the pan.
But what’s weird is that when you say 'Here’s a much better way to teach French. Tons of research shows we can teach it in a way that will make it more useful and intuitive and less painful", people flip out. “I drilled flashcards! I had to write lists of irregular verbs until my pencil wore out! I don’t understand my kid’s homework! It’s not miserable or repetitive in the way mine was! And while it’s true I can’t speak of work of French today, I am positive that the way it was taught to me is the best way to learn it!”
I think the “I don’t understand my kid’s homework!” is the biggest part of it. Adults are supposed to be Authorities to kids. They’re supposed to Know Things. Not knowing the thing the kid is learning makes them feel undermined and powerless, which leads to fear and resentment of the new thing that makes them feel that way. They want to go back to the old thing, which was bad, but which no longer has power over them.
Of course, they could say, “I don’t know–let’s figure it out together” when their kid asks them about it, but the first part is a sticking point for some people, and learning math again is a sticking point for others. So instead, they bitch about it, try to sabotage it, and hope it goes away.
I don’t say that the teachers should be segregated by content, but be assisted in content. The people teaching these subjects should be interested in them, passionate, even, in order to convey to the kids that this isn’t just some dry subject that they need to learn in order to pass on to the next dry subject that they need to learn in order to pass on to the next…
They should see the uses of math and science, practical things that they can do with the knowledge that they obtained that day in class.
In my ideal world, they would be in the classroom every day, but even if they are only able to be an hour a week or so, that would still be an improvement.
My experience is that we didn’t start changing classes until Junior High. Elementary, I was in the same room all day. (With the exception of PE or art or music, I guess.) 30 years ago, so things may well have changed.
I don’t know that you need an absolute content specialist either, but you do need someone that is actually interested and passionate about the subject. Not everyone is inspired by a passionate teacher, but even fewer are inspired by a bored teacher.
In my ideal world, teachers would also be getting paid far more than they are currently, and be given more resources to expand their education and certifications.
Out of curiosity, do any of you ever use things like numberphile or standupmaths to present information in an interesting way that may get kids interested? Do you have something that you prefer?
And the worst part is that some of the ways of learning that they object to are ways that they were in fact taught as elementary students, they just don’t remember it, and now object to it because they don’t understand it.
They don’t even have to admit that they don’t know. They can just say, “Let’s work it out together.”
