The Man Behind Common Core Math
npr.org
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Lunch costs $14.45. You pay with a $20. If you calculate your change without borrowing you just did common core math. The best facet of common core is the amount of adults complaining they don't understand it. Rather than an argument against, it is exactly an argument in support of teaching kids multiple ways to think about math.
Borrowing?
EG:
$20 - $14.45 = ...
$6 ($0.45 excess)
$5.60 ($0.05 excess)
$5.55 ($0.00 excess)
$20 - $14.45 = ...
$0.05 ($14.50 total)
$0.55 ($15.00 total)
$5.55 ($20.00 total)Once you know the basics of how to do something you do not need to continue to get better at it if your computer can do it better for you. Learn something else with the saved time.
Edit: Quick example: Is like marveling that you can do arithmetic in your head with 100 digit long numbers. Impressive? Yes. Useful? Nope. Is actually less than useful because all that time wasted you could have used it to learn something else.
Meanwhile, the better students don't bother memorizing the rules, they just focus on solving the problem. Once they see how the problem is solved, those rules either come naturally, or are supplanted by some other process that also works.
This is not about parlor tricks, but about creative thinking. How do you determine whether your 'trick' works or not? How do you know if the problem is solved? Most students believe a problem is solved when they get the 'right answer' -- which often includes "doing what they were told." This is NOT how you identify a solution to a problem. The students who are left behind are the ones who never figure this out.
Compare that to how you could solve the problem in your head.
.01 + .70 + 6.00
For my example I bet you'd think 5¢ + 50¢ + $5.00 to compute your change.
Also, when you say the +0.01 and +0.70 there, aren't you implicitly borrowing anyway? It's just "easier" borrowing -- you say that 0.09 + 0.01 = 0.10, as opposed to explicitly borrowing the 1 to the second decimal and subtracting the 9. Similarly, you say that 0.30 + 0.70 = 1.00 instead of borrowing the 1 to the first decimal.
I can see why this makes mental maths easier, but I don't see that it is any deep conceptual improvement over the borrowing. Is one of the goals of Common Core to improve mental arithmetic? If so, then this makes sense. Otherwise, unless you properly explain why the two are equivalent, and why the other method is faster, it's more like a neat sleight-of-hand trick that might leave kids slightly more confused about why it is "better" than the borrowing method.
[Reference: Non-American, non-parent who knows very little about the American education system, but has some friends teaching in it.]
All math solutions will be equivalent. And it isn't a parlour trick. It's teaching kids to think about breaking down problems into smaller units and composing a solution. The rote algorithms work, but training kids to execute an algorithm won't help them understand.
The long form subtraction algorithm isn't a skill that carries over to multiplication. Breaking a problem into smaller components, composing a solution, and checking with your original estimate does carry over. And not just multiplication but programming as well.
Common core breaks down when you have to involve writing down the steps due to the size of the operands and there ordinary algorithms shine.
When faced with $20 - $14.45, I round up the $14.45 to $15 and subtract from $20. I have $5. Now, I think how much more I still have and that is $0.55. I add them together to get $5.55.
If I can write the answer, why would you dock points just because my way of doing this simple math is inefficient?
Common core is not about efficiency, it's about helping kids develop an intuitive understanding of how numbers work.
It turns out that a lot of children who learned how to subtract on paper with borrowing never learn how to do math in their head the way you described. Common core is an attempt to correct that deficiency.
So depending on some factors, your question might be answerable with either "about $5" "about $5.50" "$5" "$5.50" or "$5.55".
Which one is the one that will get the child a correct mark? No idea. But you can see any number of angry parents posting pictures of they're children's homework grades where "$5.55" is marked wrong even though it's the most correct.
Some people will argue that "well the subject was about estimation", well that still leaves the child with 4 possible correct answers, but school being school, only one of them will be counted as "correct" and anything else will be marked wrong.
It turns what's normally an error bounded estimation problem with degrees of accuracy into a binary right/wrong problem that looks exactly like arithmetic and is graded like arithmetic, but unless you have the curriculum guide with the answers in it, it's a crap shoot to figure out what the expected "correct" answer is.
Teachers don't sit around all day thinking up ways to trick students and anger their parents.
http://roundtheinkwell.files.wordpress.com/2013/10/the-math-...
What the hell is a "number sentence"?
What about #12? "What's the related subtraction sentence?" followed by four answers which all use addition.
What the hell is a "counter"? Should first graders also learn about incrementers and changing bases, carry bits and overflow flags?
"Write a subtraction story..." What? Based on #12 it must be something about addition since subtraction sentences all use addition.
These are barely comprehensible to college educated people with multiple degrees. People who are used to math, critical thinking, who speak multiple languages and solve incredibly complex problems in their day-to-day. I've run this by nuclear engineers with multiple PhDs who couldn't pass this test.
It's absurd gibberish to a 6 year old.
http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/10/...
Air hockey doesn't use "counters" it uses a scoreboard or score keeper.
Number sentence is not what these are called. We're teaching children the wrong things. Now they have to learn the concept twice. Once wrongly, the second time correctly. It's objectively the wrong way to teach.
But I'm totally with you about teaching children that these are equations. I wouldn't be surprised if this curriculum or whatever was built by someone not comfortable with the word equation themselves, for whatever reason.
Is it? I'm fairly certain that teaching is one of the most difficult things that we try to do, and that almost everything I've ever learned has be taught 'the wrong way' and then corrected later. But then, I have a degree in physics, and everything I've been taught about physics has either been wrong or is open to being made wrong. I was explicitly told as a freshmen "nothing we'll teach you in this class is true."
It doesn't matter what those are called. All that matters is how they work.
If I called aerodynamic lift "flying power" and gravity "flying power" and I asked you to calculate the "flying power" of an aerodynamic body on another planet?
You might be able to sort it out as an 18 year old Physic freshman once you learned some context...maybe by your 3rd year in, but a 6 year old being introduced to this stuff for the first time?
It's a terrible way to teach somebody. It's like a Machiavellian approach to pedagogy: confuse and isolate the students so that only the best rise to the top.
I wonder if it'd be possible that this might have a positive effect in decreasing the gap between men and women in science related fields. Perhaps if we told boys and girls they were doing well with equations they'd grow up to be more comfortable with them. Instead of "I'm not good at equations and never have been and those sound hard" (since they only started using the word with tougher mathematics or maybe never at all), they could think "Equations? Psh, I've been working them over since I was in grade one".
Just an idea.
You appear to think your ignorance isn't because you have no familiarity with the concept but is instead because the concept is flawed. Your error is thinking that you at age six would have understood traditional methods as well as you do today.
Question one: the whole is six. The part you know is Five. What's the missing part? Do you really not understand this question?
Why is any of those numbers the "missing part" from 5 pennies and a 6 <whatevers> of cream, or laundry detergent, or whatever that is. What exactly is missing? Pennies or liquid?
Is 1 missing from the pennies to make it turn into a cup? How about 2? 3? 4? Or is the liquid the missing part? The cup obviously isn't full. How many more liquid <whatevers> to make the cup full? Can liquid not be whole? When I was six I was clearly able to observe that my cup of milk didn't split into parts. Is it the number of pennies I have to put in the cup to raise the level and make it full? How should I know that? There are 5 pennies, and they all appear whole. Is it supposed to be the price for the cup? Then the answer is 1, but only if "6" is the price. But there's no $ of cents symbol, I knew what those looked like 1st grade. If it's raw numbers, I should be subtracting 5 from 1 (there's only 1 cup).
I could use a "subtraction sentence" to figure this out, but according to #12, subtraction sentences don't actually use subtraction.
Shame on you for pretending to understand the question and assume you know what the answer is just so you could try to brow beat me with your assumed smarts.
Here's a subtraction sentence question for you, the first three letters of "assumed" are?
#1 on this test in particular made rounds in my neighborhood as an example of how broken CC maths is. One of the local PTA organizers actually gave this exact test out to a group of parents and made them take it (I live in the district that used this test). Not a single one passed it. I live in statistically the most educated metro area in the entire United States and not one parent could pass this 1st grade exam -- which was given just a few weeks into the year. Now either we're a neighborhood of mental deficients, or the curriculum is absolutely broken and on top of that it manages to entirely eliminate the only help most students can get to understand this garbage, their parents.
Here are a couple of examples from the standards themselves:
> Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
http://www.corestandards.org/Math/Content/1/OA/B/3/
This one seems to be leading to lots of "why are they asking this" questions:
> Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
http://www.corestandards.org/Math/Content/1/OA/B/4/
The confusion seems to be the transition from "understand the relationship between these two things" (what the standards ask for) and "you must do all subtraction in this weird way" (which seems to be how some people interpret the standards).
An amusing anecdote is that the schools switched over to traditional arithmetic (carrying, borrowing, etc.) during the weeks or months leading up to each standardized test battery.
As I understand it, multiple cycles of math teaching fads swept through the schools between when I learned math (a long time ago) and common core. There was a period in my locale when 8th grade math was taught in such a way that the bright kids tuned out due to boredom and nobody was prepared for algebra. Debate over the math curriculum actually swung a school board election!
(Many parents, including my spouse and me, quietly taught our kids "regular" math as we understood it, at home. I didn't know what "regrouping" was, but taught them borrowing instead. I fear that the result of widespread home coaching is that the "good" schools get rewarded for high test scores and poor families have no idea why their kids aren't learning math).
I don't blame anybody for being confused by the subtle distinction between standards, curriculum, and testing. We've heard all of the things that common core isn't. On the other hand, when some states began to publish their common core standards, I took a look at the math portion, and it seemed surprisingly "normal" to me.
As for Pearson, I wonder if one company owning both the curriculum and the testing process is a good thing.
I immediately sorted out from the context that "number sentence" = equation, while "story" = word problem. "counters" appear to be tokens to make arithmetic problems more concrete (people use "counters" in games and other things all the time). I got all the answers sorted out in less than a minute, though I am definitely puzzled by the "subtraction sentence" thing in #12...
Using simple terms for math ideas for first graders doesn't actually seem like a terrible idea, it sounds like an approach to bridge understanding.
It isn't a great quiz (#1 is poorly written and uses terrible confusing clip-art, #12 seems like an error), but if I had a penny for every poorly written math quiz American kids have been exposed to I'd be a millionaire. It's completely peripheral to Common Core or any other didactic approach.
If nuclear engineers couldn't sort this quiz out, I think that's a very compelling argument against nuclear power. This is not an incredibly complex problem, and any one capable of critical thinking should be able to use that to sort out that the quiz used simple terms for math concepts. I know little about Common Core, but this isn't a compelling case against it at all.
We're adults, we've been through school. We can make some assumptions. We can guess that a "subtraction story" like in #9 is supposed to be an explanation of the algebra problem (in 1st grade) 8 - ___ = 2.
Something like "I had 8 problems, but got 6 answers wrong. I only got 2 right."
We can establish that a subtraction story is tied to the concept of subtraction which is indicated with this symbol '-'. (I'm not going to address the picture).
We know, because we're smart 1st graders, that a story is made up of sentences. So a subtraction story, must be made up of subtraction sentences. And we know from concepts like the ones that built up to #9 that '-' is the symbol for subtraction and there's some kind of concept that an equation like 8-6=2 must be a subtraction sentence written with symbols and not words. Though this equivalence isn't easy for kids to get, which is why word problems are always so hard in maths pedagogy. But let's say I'm sharp and I get that.
Now reassess #12. The obvious related subtraction sentence, written with symbols, should be something like 7-3=4 or 7-4=3 (there's no context to let us know what we're subtracting from the lego diagram, so either answer should be correct). But we look down at the answers, and there's no '-' sign! In desperation we circle 'c' because it has all the right numbers, even if it doesn't make any sense conceptually...none of the other answers have numbers we can fit into the picture.
Now absurdly this is marked correct! Whew, my grade is saved. But my concept is broken. Subtraction sentences do not feature the symbol '-', they feature the symbol '+'. I'm 6, and I'm just being introduced to this, so what am I to think? Subtraction stories use '-' but subtraction sentences use '+'...even though stories are made up of sentences. So either my English class is wrong, or Math is wrong...
But wait. #6 uses "subtraction sentence" also, but the correct answer used a '-'! Now what am I supposed to think? We know what a number sentence is. We know what a subtraction story is. But we have no clue what a subtraction sentence is and the concept for what it is is utterly lost. Now instead of learning about subtraction, I'm an extremely frustrated 6 year old who gets through tests by random guessing instead of learning.
This isn't a bad exam, this is terribly pedagogy. As a former professional educator, my assessment is that this is the work of idiots who were purposely trying to sabotage 1st grade math education.
Here's what I think of #1 https://news.ycombinator.com/item?id=8820195
By topic #2, in 1st grade we've utterly and completely failed every child who took this test. They couldn't even get through a few weeks of school before we managed to alienate most of the class from math education and a large number of these kids will carry this around with them for the rest of their schooling.
You could argue that because Common Core was adopted, Pearson and all of the other curriculum/lesson planning content creators were forced to build out new, less vetted curriculum, which has not been battle tested. That would be true, but it's not specifically Common Core's fault. It's simply quality control issues for Pearson and others for not vetting their methodology.
Here is your big chance: begin to write your own curriculum, and do a better job. Upset the entrenched Pearson curriculum. Be the change you want to see
You might not like the idea of a "subtraction story," "math story," "counter," etc. I am not really a huge fan off the bat, though I'd need to research to understand the principles behind it before I made any strong judgment.
If you want to vent righteous fury somewhere, then attack Pearson, who wrote the quiz and introduced these terms. I'm all in for criticizing textbook companies - they are completely horrible leeches who produce minimum quality work to leech capital out of education funding in a totally parasitic and damaging relationship. They constantly release minor needless updates to books and end publication of past editions so districts can't replace books but regularly have to buy new full sets they don't really need.
However, you'd be misdirecting vitriol if associate this with Common Core, since both the inept greedy textbook publishers, and the math ideas in the ideas that bother you aren't actually a part of the standard, but have been around since before that standard ever existed.
I simply ask my kids, on those occasions where I can't suss it out on my own, what concept the teacher was teaching them about. I don't expect a perfect answer to that question - their teachers are instructing learners and not teachers after all - but the responses to my question usually give me enough context to recognize that they are just a new vernacular for the way my mind does math anyway.
(to save you the clickthrough: it's a single-page question consisting of a simple illustration of a day at the park...the prompt is: "Today in class your child practiced telling subtraction stories. For tonight's homework, your child will tell you 3 subtraction stories using the attached paper"...presumably, the child is supposed to look at the picture and observe, for example, that there are 10 trees and 9 birds, leaving 1 tree empty)
I stand corrected in my assumption: that is a bizarre question. I guess it depends on what was taught in class...if the class went over a similar question and walked through examples...then I guess it's a useful exercise...in the same way that I challenge students whom I teach programming to look at a real-life situation and think about how programming applies. Can 5-year-olds think like that? I seriously have no idea...I just came back from visiting my 1-year-nephew who apparently can recognize words in 3 different languages (English, Spanish, Vietnamese) and communicate common phrases (I'm hungry, I'm sorry) in sign language...admittedly, he still craps his own diapers, but still...I've forgotten how early-brain development can be.
Side note: Awhile ago, I asked why HN's Google pagerank was so low (something like a 4 or 5) Paul Graham has stated that the robots.txt on HN throttles Google spiders...and yet when I googled "north carolina common core dad"...the parent comment was one of the top search results. I guess HN's pagerank is moving up?
The big thing to remember is that Common Core doesn't actually dictate the implementation details people commonly complain about. It's possible that a particular state, district or school does something weird but that's like using some horrible enterprise Java monstrosity as an argument that object orientation is a bad concept.
That may be, but this is a bizarre question.
The problem and blame seems to keep coming up over and over again is that CC didn't have implementation control. Why not? Why didn't CC go out the door with a gold standard reference implementation publishers could license and a certification program for alternates?
The internet is full of crazy examples like this. Questions that will simply drive people away from math on multiple levels.
I'm not arguing that – only pointing out that they have a strong partisan motivation to spin this as mandated by Common Core, which parts of the conservative movement have been trying to spin as part of some Democratic conspiracy for years, rather than the more honest “Local teacher / school / district does something dodgy / buys substandard curriculum” story which wouldn't be of much interest to anyone outside of that particular city.
On the bright side, the PR result I just got in checking it, came back a seven (Reddit is an eight by comparison).
On the other hand, when we discussed money in grade school, we learned the "count up to nearest denomination increments. Was a bit harder to grasp since you have to think in coin denominations, but it's served me well since then at a few retail jobs.
Overall, though, the normal form of borrowing math has been more useful in my career than the denomination method. If you can't do normal borrowing math, advanced mathematics is going to be rough on you.
Nothing at all, in fact they are actually required to learn both ways. The idea that Common Core is replacing borrowing with left-to-right is just part of a reactionary misinformation campaign.
Educational reforms usually result in an ambitious curriculum being presented by underprepared teachers to unprepared students. And parents don't understand the homework and can't help.
For example, "New Math" ended with "Johnny Can't Add". I wish my kids weren't victims of the current round.
I stand by that comment. Given how many failed reforms there have been over time, how could these smart people not have predicted what has happened?
Right now we have a new set of standards. A new set of lesson plans. Every teacher has been retrained to teach in a new way. We have new homework going home with kids, which makes little sense to anyone. Kids learn to perform the operations, but do not seem to be mastering the concepts. There is an endless drum beat of positive messaging being sent home from schools. Parents that I talk to are..shall we say..less than convinced.
This is about the worst kind of big bang upgrade that you could have.
As a programmer, I have never seen a "one size fits all" system that can both bring up bad programmers and also provide good programmers with the autonomy they need to continue to be good programmers. Common Core is a "one size fits all" system to a much more complex problem.
This would be more convincing if there were some examples of good textbooks that were scrapped, or good textbooks period. The textbook procurement process in the US has been appalling for longer than most readers of this forum have been alive.[ http://www.textbookleague.org/103feyn.htm ] Never mind that the best evidence available suggests that unsccooling, i.e. providing no systematic instruction to children whatsoever leads to a delay of one year in educational outcomes. Primary school hardly seems worth it unless the point is not education but teaching children to sit down, shut up and do as they're told. [ http://www.researchgate.net/publication/232544669_The_impact... ]
I have little to say about Common Core, since I haven't been following it, though I am seeing a lot of the same knee-jerk reactionary criticisms that are grounded in a sense of traditionalism and desire to focus on rote learning rather than any understanding of math, which we should be careful about.
This was already the problem. Parents didn't learn anything either, they just learned to perform the operations. If they _had_ learned the concepts, they would have no trouble understanding their kids' new homework.
Not so.
I understand the concepts perfectly well. The problem that I have is that there are multiple ways that I can map my understanding of the problem to the needlessly overcomplicated homework question in front of me. And if I can't figure out which of those ways matches what my child was taught, I can't tell my child which pointless and silly way of answering it is the "right" one.
You can object that this is opposite to the intent of the Common Core initiative. But it doesn't change the fact that this is the implementation of the Common Core initiative that my children actually have to deal with.
This is explicitly what Common Core is designed to fix -- Common Core is designed to break K-12 math's traditional focus on rote arithmetic and instead focus on learning math as abstract reasoning and multiple different solution strategies.
That you would include this barb in your comment shows that you're more arguing against the concept of changing standards, and not against Common Core itself. That's not an indefensible position, and you do consistently argue from that stance throughout your comment, but I fail to see how it's constructive. The US is ranked ~30th in math worldwide -- obviously things need to be changed. Perhaps there are better ways to change our standards: what would you propose?
The fact that it is designed to do so does not mean that it succeeds in any way. What I see is the replacement of rote arithmetic with the rote repetition of formulaic statements that are not connected to actual understanding. This is not an improvement.
That you would include this barb in your comment shows that you're more arguing against the concept of changing standards, and not against Common Core itself. That's not an indefensible position, and you do consistently argue from that stance throughout your comment, but I fail to see how it's constructive. The US is ranked ~30th in math worldwide -- obviously things need to be changed. Perhaps there are better ways to change our standards: what would you propose?
I would suggest incremental improvement, not revolutionary change. The education establishment has a long history of revolutionary change, and knows exactly how to go about it. This always turns out badly. The much safer way to go is to incrementally improve, with constant feedback and repetition. It doesn't feel day by day like progress, but it has much higher odds of actually succeeding.
What our educational system has done is the equivalent of throwing out a major software system, and rolling out a new one. Such big bang upgrades seldom go well, and the larger the system the worse the disaster that follows. Even if you can wind up in a situation where success can be declared, huge amounts of damage are done.
I'm not saying it's good or bad to teach math that way, it was just not communicated well and still isn't. Math has been replaced with math+critical thinking. It's as if English class now also included Latin. Maybe good, maybe bad, but it's a whole different class.
> It's as if English class now also included Latin.
I think a better analogy would be "it's as if English class now included critical thinking." Or "it's as if Science class now included critical thinking." Or "it's as if History class now included critical thinking."
All of those sound unambiguously good to me.
In college I'm always asking students to analyze the results to applied calculus questions and it can be a struggle and a revelation. You mean these numbers have meaning?!
The infrastructure is not in place to teach those concepts successfully. The question "explain why ancient calendars used 60-day units" is no more elucidative than "explain why a week has 7 days" or "explain why the French Republican Calendar and the International Fixed Calendar failed to survive" or "meditate for 2 hours on the number 60".
I am saying unequivocally that it is bad to teach math that way. A kid does not have enough pre-existing knowledge of any ancient calendars for that association to help rather than confuse. If you're going to do that sort of thing, you have to tie into something that all kids at that age already know about. So really, you can only count on the stuff they have already been taught in school.
I don't recall, exactly, when I was taught about ancient calendars in school. Oh, wait, yes I do--it was never. I do recall someone asking once why a circle had 360 degrees in it, and the answer was, "It's essentially an arbitrary convention; we'll always be using radians in this class anyway."
While the high-level goals of the curriculum may be pedagogically sound, by the time that the course materials make it down to the classroom level, the original intent has been thoroughly diluted by the people trying to implement them.
I always did quite well in math, but sitting there at the back of the class messing around with stuff at the end of the book, I found that teachers tried so damn hard to make the content easier, and in the process made it harder. I could figure out how what they were saying corresponded to the material, because I already knew the material, but could not see how anyone else would understand it. Few did.
That said, "Common Core" is probably fine, as usual the implementation quality is just much more important than any particular methodology. (just like "object oriented programming" etc).
There's not really any evidence that the approach in Common Core will improve student's math achievement scores, and lots of evidence that it's been an abysmal failure. Instead of confused students ignoring the subject, we now have confused, frustrated, miserable students, a generation of which will now hate mathematics more than the one that came before them. The only thing CC has achieved is in alienating an entire generation of students from the critical skills of math.
The article makes the argument that the absurdity of the implementation of CC is a result of local standards overriding a national, well thought out program and that the CC creators are powerless to fix things. I call hogwash. Set up a textbook certification program: publishers have to pay some nominal fee to these guys to review the book and give it a seal of approval that "yes, this book fulfills what Common Core intends". Use that seal as a quality signal, books without the seal should be considered next to garbage and books with it are assumed to be better.
They should also have written their own reference K-12 curriculum, providing a gold-standard example of what it should look like. Publishers can license that curriculum and publish it unmodified or they can license it and add (but not subtract) chapters to handle local requirements.
That these things weren't done, on what's supposed to be a national educational reform that was "a lot of work" boggles the mind.
It reminds me of various specification-by-committee standards that are all over the tech world. They're laid out in document somewhere, with no reference implementation and no certification that some other implementation really is compliant and we end up with a decade of lost time while every developer tries desperately to get their image to line up just right in half a dozen different browser rendering engines, or get their query to work right in a dozen different SQL standard databases to work the same.
For example one of my children could not factor in the way I was taught with the trees, but another way was presented and it totally clicked for her. For one of my sons he could not do long division in the manner I was taught, but another method worked for him instantly. He showed me and I even liked it, cause I remembered how hung-up I had been about getting the correct digit at each step myself.
I also like how it seems to have this component about reasoning. To many people math is arithmetic, but it really is not that. The problem is that there are kids where requirements were different. So for example now a third grader is supposed to have memorized multiplication table, but there were schools that never did that before. Or a sixth grader is now already supposed to have done some geometry, but the school only did it in 8th grade or HS before. There is no route to fill in the gaps during this transition in many schools it seems.
Anyone who has ever spent anytime teaching knows that when you first start out, you have to figure out a lot of stuff when teaching a new curriculum, but by the time you've taught the material 2-3 times [0], you start streamlining things and getting more efficient. The time you spend retooling almost always comes out of your personal time. i.e. from hours beyond the 40-50 hour work week.
After you know a curriculum well, you end up with more personal time. Introducing new standards, means a new curriculum and a new curriculum means a lot of unpaid personal time from teachers if you want them to really adopt it and teach it well.
I just don't see a new curriculum working well unless it comes with the notion of paid extra-time that you know teachers will have to put in to succeed with the new curriculum. It doesn't have to be a lot, but simply 5-10 more hours each week and a bonus equal to 10-25% of their salary to make up for the additional time would probably work. The only key would be that there needs to be a way to measure that teachers are putting in the extra time to really learn the new curriculum and apply it instead of collecting the bonus for putting in the minimum effort.
At the end of the day, it you don't budget both time and money to learn any new curriculum, it's either going to fail or be met with resistance from teachers who feel like they already have a system that works for them and their students.
[0] either in the same semester or school year because you teach multiple groups the same material or after 2-3 semesters or school years of teaching the subject to one group at a time
Moving on, I think the article mentions the problem of getting good textbooks. This has always been a huge problem, I think. In India, there is a trinity of syllabi: one recommended by the Federal (Central) Govt. (CBSE), one by a consortium of private schools (ISCE) and each individual state's syllabus. So, a school does not have the independence to create its own curriculum, it has the choice of adhering to these 3 systems. It does have the independence of choosing textbooks; however, there are also officially prescribed books, and many teachers teach from them only because they cover things that are often asked in the standardized tests.
So, I don't know if it does good to have just one system, and not give schools access to more options.
I don't think there is one official way of teaching that is "Common Core."
The texts currently labeled Common Core are mostly copy-and-paste remixes of existing material.
The exams labeled "Common Core" are unfortunately similar. They don't test the standards as written. For math, a discussion at http://www.washingtonpost.com/blogs/answer-sheet/wp/2014/11/... . Unfortunately, a theme seems to emerge of Pearson tests written to test Pearson materials, some of which have a "Common Core" label.
That seems like a really serious flaw. Did the teaching community at least make and share their own?
The typical cycle for curricula, teaching strategies, and/or discipline plans in schools:
1) OMG the kids aren't learning better change everything!
2) District, state, or both pick some new system and pay some consultants and various companies a bunch of money.
3) Administrator presents plan to teachers: Here's the new system. Half of it's not finalized yet. Should be done in a year or two. We're not implementing some parts of it because they make me uncomfortable. The old way is stupid and sticking to even the parts of it that work well for you will result in my making your life miserable and eventually trying to fire you. You'll need to re-write all your lesson plans to conform to the new system. Here's a mountain of new paperwork for you. No, you can't stop filling out any of the old paperwork.
4) A couple years pass
5) Goto 1
1. Introduce a new test with an unfamiliar blend of questions, new style questions, etc. but don't give teachers extra time to actually receive updated textbooks, update their classes, etc.
2. Start giving the test to students immediately before they have any experience with the new format
3. Use the result low test scores as proof that things were really bad before
4. As everyone gains experience with the new system, attribute rising scores entirely to the brilliance of the new model. Give bonuses to district / state officials.
5. Once scores plateau at roughly the previous levels after a few years, start talking about repeating the process. At no point should you seriously consider tackling the structural problems preventing holding perennially under-performing groups back.
And yes, teachers do share lesson plans, both online and within their schools.
Lesson plans from big companies like Pearson, on the other hand, are good because they come from businesses. However, there's a conflict of interest because many of the same companies write the exams. Worst of all, none of these companies actually develop teachers' abilities to teach. That's not really the fault of the companies; we just don't do that here in the US.
Teacher development is almost nil for a lot of K-12 teachers in the US, compared to Japan or Finland. The average US teacher is in the classroom 1080 hours a year and it's something like 600 in Japan and Finland. That 480-hr-per-year difference is spent on development and prep.
And yet there are a lot of really excited and entrepreneurial teachers and they're making and sharing all sorts of material. See TeachersPayTeachers, for instance.
There is also an initiative to fund CC BY licensed educational content that school districts can use without getting milked by textbook publishers http://k12oercollaborative.org/
The erasers are essential. The knowledge particles wiped off the greyboard are physically transferred to the student, and are then absorbed through the skin. The knowledge slowly decomposes, releasing about a microsatori of electromemetic radiation, and the waste metabolites are exhaled into the room to create an atmosphere of learning.
Needless to say, I will never be permitted to design a school program from the ground up.
An often reasonable way to ensure that you can mechanically apply a problem solving technique (which is related to, but absolutely not the same thing as understanding the maths) is to make a program that does it. Trying to learn maths by programming it is a terrible idea.
Just this morning I've been looking at Riemann's geometry; learning that through the medium of writing a program to "do it" would be painful. I don't even know what it would mean to write a program that "does" Riemann's geometry. I suppose I could write a program to apply some equations, but that's not learning the maths at all. That's automating some equation solving and it teaches me nothing about the maths.
What "problem solving technique"? There's no algorithm you can mindlessly remember and use it to create algorithms. Making a program that solves the problem is the highest possible understanding.
>I don't even know what it would mean to write a program that "does" Riemann's geometry
That's because it's an abstraction, not a problem to be solved. In the same way you can't write a program that 'does' functional programming, you can only program in a functional way.
Well, I guess writing an AI which can solve problems in Haskell would be an exception. I bet you couldn't remember its code and execute it in your head, though.
http://www.corestandards.org/Math/
I would encourage anyone who is really interested in this issue to spend some time reading, or even skimming just a few sections. I find the standard is generally quite readable (conceding that it's a non-trivial commitment to read more than 1 grade level, but then again, there's a lot to know about math...) and I also tend to agree with many of the ideas in it.
I've been disappointed, but in hindsight not very surprised by the anti-intellectualism in the public response to the common core. I'm more surprised to see similar anti-intellectualism here. I expect better from you, HN!
It's true that the common core places more emphasis on critical, analytical, and sometimes even abstract thinking than the "traditional" math curriculum (whatever that is...). But as people who read hacker news, doesn't that sound good to you?
It's also important to know that the Common Core standards are a set of expectations, and that's actually all they are. They are not worksheets or standardized tests. If you see a bad "Common Core" worksheet, it is a bad response to the Common Core, but it isn't actually the Common Core itself. If you want to criticize the Common Core itself, choose a part of the document above and criticize it. Or failing that, criticize the process that led to its creation and dissemination. But criticizing a few oddball problems is not a powerful argument.
My own criticism-in-hindsight is that the Common Core is trying to do two things at once. Maybe it would be succeeding better if it only tried to do one of them at a time.
The first is to provide a nationally standardized set of grade level expectations. Many people have an interest in this goal because it makes it easier to prepare teaching materials for a large group of students, and to compare education effectiveness across regions. In an alternate world, this could have been done descriptively instead of prescriptively. The standards could have simply described what was happening in the largest fraction of the country's classrooms.
The second goal is to improve math pedagogy in the U.S. and bring it up to the best international standards, including tying math more strongly to critical, analytical, and abstract thinking skills. This is a prescriptive goal.
If the standard was a process, we could have started with 1, and moved to 2 incrementally. But I suggest this only half-heartedly, because I think 2 is a great goal, and I think the Common Core (as a document) does a pretty good job of it.
Now to be clear about my own biases:
I don't have any children (school age or otherwise). If my first exposure to the Common Core was seeing my child assigned problems that looked unfamiliar, unimportant, or even that I didn't know how to do, I'll concede that I might have reacted negatively too.
I do have a physics Ph.D. (i.e. math background), I do think and care a lot about how people understand math, and I do work on a software tool that tries to help children think about (part of) math more powerfully.
I don't have much personal exposure to "Common Core", but I've found when all the implementations turn out as shit, the blame usually lies with the specification.
My personal opinion is that a lot of this overloading on processes and bizarre approaches to presenting problems (and don't get me started on the form of homework assignments and tests) is because we're out-pacing the natural cognitive developmental process. For example, take the sample chapters that were on the front page a couple days ago from "Math from [Age] 3 to 7" [1] you can see a very interesting approach to building math skills. But even in that case, the author is rushing developmentally advanced tasks which are more likely to result in frustration and giving-up than engagement and learning.
Fundamentally, most learning does not occur while a teacher is speaking. The more absurd lengths the teacher goes to "explain" some concept, the less likely any child is to actually learn it. The more foreign the concept is by the time the kids get home, the less likely it is to be mastered.
I have a daughter in Kindergarten, but fortunately not one that follows CC. I just spent some time reading through /Math/Content/K/ on corestandards.org. Most of it is, IMO, complete trash and not at all aligned with how kids in kindergarten actually learn this shit. As a "spec" it's writing is sloppy, poorly defined, and highly ambiguous. If this is the starting point, I'm not at all surprised the resulting lesson plans are worse than nothing.
I also spent some time reading /Math/Practice and it struck me how all these things that CC is presenting as "Standards for Mathematical Practice" are not at all how children conceptualize mathematics, or cognitively approach the task of solving a math problem. Many of the stated practices are directly contrary to how children will naturally want to approach and solve a given problem, and I can imagine exactly how teachers faced with "instilling" these practices would get to exactly where we find ourselves.
I respect that you took the time to read the document, but your criticism isn't very specific. Are you bothered by the fact that it uses words that aren't appropriate for Kindergartners to describe what they should know? Or that it says what they should know, but not always how to teach it?
I think the "spec" analogy is a good one. The goal of a spec is to lay out requirements, not implementation. Same idea here, which strikes me as the right choice.
The actual expectations are to know a few things about counting, numbers, and shapes. That seems developmentally appropriate to me (admitting that I don't have much recent experience with kids this age).
What do you think Kindergartners should know?
Re: the practices part, these same practices are mentioned at every grade level through high school. I agree that the practices sound way too advanced for Kindergarteners, but the goal is to get students to do them well by the end of high school, not by the end of Kindergarten.
I continued to read through 5th grade math curriculum, and really I think it's completely the wrong approach for how children should learn the material. It's hard to summarize everything I dislike about it in just a few sentences. Mainly I think the process should be much more natural. This isn't something that really has to be taught, through 5th grade at least it all comes naturally in the right environment. So the approach is backwards; it's not 'here are the list of skills which should be taught and mastered at each grade' it's here are the ways we foster learning over this 6 year period.
The whole approach of setting these micro-goals, the whole thing is far too low level. When a spec starts at such a low level, it becomes a prescriptive checklist, not a spec.