Massachusetts’s Rejection of Common Core Test Signals Shift in U.S
nytimes.com
nytimes.com
This is so sad. The Common Core standards are designed very well. They emphasize understanding over mechanics. They've gotten surprisingly bad press from parents who don't understand math and don't understand the new methods which really are designed to build intuition and understanding. But even if you have to give in and go back to the old way of teaching, why ditch the new, high-quality test? I don't get it. Maybe the schools are all afraid of looking ineffective because they know they don't teach proper understanding.
The public employees unions basically run the state so when a topic that affects them comes up they get their way.
Bobby's teacher asked him what the value of the 5 in 582 is.
He answered that it was in the hundreds place. Did he answer the teachers question? If yes explain why. If no what is the right answer?
Bonus points if you can explain the intention of asking the value of a numeral in a larger integer.
The intention of the question is to find out if the child has understood the concept of place values, and I think the ambiguity of the question is there so that you can accept either answer that demonstrates that the child understands that the value of a digit changes based on its location, and that the location of the 5 in 582 notates a 'hundred' multiplier.
While I think the structure of the question might be off putting, asking about place values makes plenty of sense to me. I recall being taught place values in the mid to late 90s up here in Ontario, so it's not exactly a new fangled thing.
edit: used less broken sentences.
To me it's confusing as anything, because it implies that symbol values aren't really constant.
Isn't it easier to learn that symbol values are constant, but they're modified by position?
So the 5 in 582 is 5 X 100.
It's not "500", because conceptually that implies a different unique symbol.
One way emphasises a limited set of consistent symbols, and a small pool of symbolic operations. The other way suggests there's an infinite pool of symbols of varying values, and you're supposed to think of them as separate numbers when they're in different place groups.
The real point of math is generalisation and symbolic and functional economy. So I think the latter obscures what's happening instead of simplifying it.
Symbols defined using only references to themselves are notoriously difficult to understand.
When the student answers, "it's in the hundreds place", that tells me a lot. It really says, "I think I know the concept you are trying to test, and I would like to prove that I have mastered it, but the question you asked does not allow me to do so, as it is ambiguous as to whether you are testing my knowledge of the invariant symbol value of '5', the positional value of the third digit from the right in a decimal number, or the embedded multiplication inherent in decimal notation. As the value of '5' is the least complex of those three concepts, I have purposefully left it out of my answer, and I hedged the other two senses by explicitly saying the second and implying the third." Or in shorter terms, "I'm not sure exactly why you are asking me that, so I'm not sure whether to tell you five or five hundred."
As a result, I would say that answer is correct, but given in a form that exposes the inherent weakness of the question.
The symbol '5' has value five no matter where it appears. The radix-exponent-2 position has the same value no matter which numeral symbol appears in it. The student can best demonstrate knowledge of this generalization by performing radix conversions.
The '5' in hexadecimal number 0x582 is still worth five, but it is multiplied by position value sixteen exponent two rather than ten exponent two. The '5' is in the twohundredfiftysixes place rather than the hundreds place. So the symbol has net value five touhunnerfittysixes rather than five hundreds.
If you don't emphasize the separation between symbol value and positional value, you're actually encouraging a regression to the mental-math roadblocks of Roman numerals, where I, V, X, L, C, D, and M have distinct invariant values.
This is standard 1 (4.NBT.A.1)
https://books.google.co.uk/books?id=RvpzCQAAQBAJ&pg=PT160&lp...
Bobby has made a true statement that is related to the question, but hasn't completely answered the question. The correct is that the value of 5 in 582 is 500, and an even better answer would be "the value of 5 in 582 is 500 because the 5 is in the hundreds place".
This distinction is something that many teachers overlook. There is an excellent handbook for teachers called "Teach Like A Champion" [1] which emphasises that "Right is Right" - here is an excerpt:
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Right Is Right is about the difference between partially right and all-the-way right—between pretty good and 100 percent. The job of the teacher is to set a high standard for correctness: 100 percent. The likelihood is strong that students will stop striving when they hear the word right (or yes or some other proxy), so there's a real risk to naming as right that which is not truly and completely right. When you sign off and tell a student she is right, she must not be betrayed into thinking she can do something that she Cannot.
Many teachers respond to almost-correct answers their students give in class by rounding up. That is they'll affirm the student's answer and repeat it, adding some detail of their own to make it fully correct even though the student didn't provide (and may not recognize) the differentiating factor. Imagine a student who's asked at the beginning of Romeo and Juliet how the Capulets and Montagues get along. “They don't like each other,” the student might say, in an answer that most teachers would, I hope, want some elaboration on before they called it fully correct. “Right,” the teacher might reply. “They don't like each other, and they have been feuding for generations.” But of course the student hadn't included the additional detail. That's the “rounding up.” Sometimes the teacher will even give the student credit for the rounding up as if the student said what he did not and what she merely wished he'd said, as in, “Right, what Kiley said was that they don't like each other and have been feuding. Good work, Kiley.” Either way, the teacher has set a low standard for correctness and explicitly told the class that they can be right even when they are not. Just as important, she has crowded out students' own thinking, doing cognitive work that students could do themselves (e.g., “So, is this a recent thing? A temporary thing? Who can build on Kiley's answer?”).
When answers are almost correct, it's important to tell students that they're almost there, that you like what they've done so far, that they're closing in on the right answer, that they've done some good work or made a great start. You can repeat a student's answer back to him so he can listen for what's missing and further correct—for example, “You said the Capulets and the Montagues didn't get along.” Or you can wait or prod or encourage or cajole in other ways to tell students what still needs doing, ask who can help get the class all the way there until you get students all the way to a version of right that's rigorous enough to be college prep: “Kiley, you said the Capulets and the Montagues didn't get along. Does that really capture their relationship? Does that sound like what they'd say about each other?”
In holding out for right, you set the expectation that the questions you ask and their answers truly matter. You show that you believe your students are capable of getting answers as right as students anywhere else. You show the difference between the facile and the scholarly. This faith in the quality of a right answer sends a powerful message to your students that will guide them long after they have left your classroom.
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> the teacher has set a low standard for correctness and explicitly told the class that they can be right even when they are not.
That "explicitly" word strongly suggests to me the author doesn't know what he's talking about.
If the question is "how do the Capulets and Montagues get along," the answer "they don't like each other" is not partially right, it is right. It is not detailed or sophisticated, but the question didn't ask for detail or sophistication.
If we're going to call an answer "partially right" because it misses some nuance that could be explored in greater depth, than we could play that game all day long with anything that has ever been written. For example let's take your answer:
> The correct is that the value of 5 in 582 is 500, and an even better answer would be "the value of 5 in 582 is 500 because the 5 is in the hundreds place.
Ok let's play this game. "Partially correct," I say. "First of all, the fact that a 'hundreds place' exists at all is thanks to the relatively recent invention of Arabic numerals around 500 A.D. and its innovation of a numeral for zero, which previous number systems such as Roman numerals lacked. Secondly, the reason the third digit represents hundreds is because we use base 10 numbers by convention, which likely traces back to our hands and their 10 fingers. Other bases are used in different contexts, most notably hexidecimal in software engineering, in which case the '5' would be in the 256's place, representing 1280. Thirdly, the convention of writing digits is most-to-least significant order appears arbitrary -- it is hard to argue that it is linked to the order of text directionality, since the same order is used in both left-to-right (eg. Latin) and right-to-left (eg. Arabic) writing systems."
Solid B+ answer though. Don't worry, I have faith in your ability to produce a truly correct answer someday.
Spending time on the difference between the phrases “a 5 in the hundreds place” vs “5 hundred”, when both the student and the teacher understand them to mean the same thing is a waste of people’s focus. Instead the student could be doing something much more interesting, such as examining what the digits would mean in a base twelve system, discussing how a number is transformed when multiplying/dividing by ten, learning what happens to the digits in higher places when working with modular arithmetic, learning how to use an abacus to keep track of the place values, or developing an algorithm to transform back and forth between explicit counters like pebbles in a dish and their written decimal representations, etc. etc.
On the other hand, the question asked of droopybuns’s daughter is sort of interesting from a philosophy/sociology/pedagogy point of view. There’s not really much math content in it, but getting students to think about the ways the social context shapes expectations about right answers and effective ways to navigate a society full of bureaucrats with sticks up their asses is definitely worthy of discussion.
Finaly spoke with the teacher:
Bobby is wrong.
The "value" of the 5 is 500. They are learning number placement right now: 582 = 500 + 80 + 2
So the thing she is supposed to say is that the 5 is in the hundreds place, so it should be equal to 500.
I loathe that they assign the word "value" when the concept is contextual. The value of 5 is axiomatic, as is the value 582. When I explained this, the teacher's only response was to argue that this standard is almost verbatim outlined by the school district. <s> It must be right then! </s>
This teaching risks proving that 5=500.
Markmcc has an excellent counterpoint to my frustration, and I plan to use it to explain the objective of the question to my daughter.
“What quantity does the symbol ‘5’ in the decimal number ‘582’ represent?”
Then the answer is unambiguously ‘five hundreds’.
But I think you've hit the nail. As in the article, the primary problem discussed is selling Common Core to parents and the no sale is generally "I don't understand this" coming from the parent. Whether Common Core is better or worse, it is not surprising that a new methodology is unfamiliar to adults trained under an older rather orthogonal one. That's what mostly drives the politics of public education and politics of public education is why your young relative had homework in the first place despite little vetted data supporting its imposition.
Disclaimer: My first reaction to Common Core was similar to my first reaction to Montessori - what the fuck are they doing, that's not the way I was taught. My current position is likewise the same, the results have been great and I am still not an expert in primary education despite my lack of effort to become one.
Emphasizing understanding at the expense of mechanics for basic arithmetic skills is a mistake. Especially, for kids at that age who are just beginning to develop these cognitive skills.
In addition, like the poster, glesica, mentioned below, the questions are often vague and tricky word problems where most of the work is just guessing what they are asking.
My son hasn't actually learned any arithmetic skills beyond what he learned in kindergarten.
Maybe it works better as kids get a bit older but I have found it to be a disaster.
It gets better in second grade. Our daughter has two timed tests a week that are just cranking through addition and subtraction. It's most likely in preparation for the first MCAS math tests they'll take next year in third grade, but I like them practicing straight up math problems.
There is still the focus on doing the problem just like they were taught, and taking points off for not drawing counters. There is still the work involved in figuring out how the concepts are described so I can help her do the homework.
But it did get a little better, at least for us.
So how is this really better? I'm not getting it.
The first 12 years of my education actively sabotaged the latter at the expense of the former. That was wrong. Humans are poor symbol-manipulation machines, and I'm ecstatic the math classes aren't treating them as such anymore.
I have to question this. Humans seem to be natural symbol-manipulation machines. We use this skill all the time in language (spoken early in childhood, written later).
100 years ago we were probably the best symbol-manipulation machines around. We learned to build better ones than us, and now we're pretty poor when compared to such machines.
My son has neither developed a solid understanding of the concepts that common core emphasizes nor a more mechanical ability to manipulate arithmetic expressions.
My anecdotal observation is that most kids at that age are not quite ready to absorb many of the concepts emphasized.
Instead they require gaining some familiarity of the basic elements of arithmetic and what they represent before pulling them apart more.
In general, I believe you are correct that most parents who are opposed to the common core also don't understand mathematics, but that's just a symptom of the abysmal way that mathematics is taught[1]. Common core tries to fix this but it falls short because it doesn't actually try to address why children aren't performing well, just gives another way for things to things to go wrong.
[0]: https://medium.com/i-math/why-5-x-3-5-5-5-was-marked-wrong-b...
[1]: https://www.maa.org/external_archive/devlin/LockhartsLament.... (a classic)
"I know it’s frustrating but respect the teachers. They are qualified experts on child education. They have the best intentions for the students in mind. This teacher made a decision based off a lot more information about the student and class setting than we can tell from a photo. We don’t have to agree with it, but we can respect it." ...Why, exactly? Because they're experts?
That's hardly redeemed by the following, "If you are confused, ask them why they did something before you discredit a teacher on the internet."
I have had coworkers, all degreed electrical engineers, show me some of their children's homework and ask me to figure it out, because they couldn't. Similarly, many existing teachers weren't trained in any of this, just told to go do it.
The ideas behind common core are not bad ideas, but the execution has been woeful.
Never mind if a child comes in severely behind in reading or math skills and you spend much of the year working to improve those skills. Most teachers actually can't, now, because their state mandates exactly how they will progress through the curriculum. Schools require teachers to file lesson plans. Don't follow the exact content of that lesson plan on a given day, because you find you need to cover something in more detail or cover something the kids already should know, but don't? You might be formally reprimanded if your administration finds out.
My own mother, a career high school economics, accounting, and high-risk (meaning kids whose parents were extremely poor/in jail/other combinations of bad home situations) teacher, always said, "I am here to teach kids, not subjects."
> Notice that the second problem is marked incorrect as well. Why is it important that 4 x 6 is 4 rows of 6, instead of 6 rows of 4? Not only does this adhere to the definition, it also teaches students the correct order for diagramming matrices, which is rows times columns.
This sort of slavish devotion to arbitrary conventions is really tiresome, and I think it promotes the wrong sort of thinking about math.
Every time I see one of those questions going around like "4+8÷3(5)=?", it drives me nuts. People look at these equations and point to rules taught in school, or examples in textbooks. They see math as a set of rules, rather than a means of communicating. The fact is, an equation should never be written that way, because as shown by all the arguments about it, the intent of the author is not understood by all readers.
The problem is that these sorts of questions just demand that students mechanically follow a bunch of rules.
As a parent who has had to deal with these "experts" for years, I can't help rolling my eyes at this nonsense. Respect the teachers? I certainly respect many individual teachers, some of whom are wonderful, but this is a demand that we respect the special expertise of a group that pays politicians enormous sums of money to block any attempt at evaluating that expertise.
I have respect for groups of experts that vigorously weed out all but the top performers from their own ranks and willingly submit themselves to external competition to demonstrate their expertise, not those whose policy instead is to pay lawmakers to prevent anyone from removing the poor performers and to outlaw competitive threats to their monopoly.
First grade stuff is here [0]. Reading through these ideas, I don't really see anything wrong with them other than the standard is clearly written by a committee and is useless for actually doing anything. Very nebulous language that sounds nice and has some good intentions but isn't concrete, as you said. So, as long as we gear these principles appropriately for the abilities of the kids, we should be fine.
So you have to look at the execution. Which is most visible in the avalanche of "look at this bullshit worksheet my kid brought home today" posts that angry parents put up. I think those speak for themselves. As I said, they're often so arbitrary that they make little sense.
[0]: http://www.corestandards.org/Math/Content/1/introduction/
I, too, have been thinking about this a lot. My perspective is as a brand new dad who is sitting here looking at his 11 day old son and wondering how best to educate him. The standards aren't the curriculum, but as far as my son is concerned, what's the difference? It's all a big ball of nastiness that I don't want to expose him to. My wife and I are looking into homeschooling or private education to avoid Common Core and the rest of the insanity that is prevalent in public schools.
There's also a packages curriculum problem, which is basically a combination of the problems that exist worth oligopoly educational material regardless of the standards plus the same kind of transitional problems that impact teaching, where people will don't understand the outside of the standards address developing materials to be used under the standards.
Which will likely cause the whole thing to fail, and then we'll be on to the next "revolutionary concept" in education, and the whole mess starts again. Meanwhile, educating real small humans suffers.
Has Common Core improved student achievement?
Any one in software should know, as a first principle, that you cannot test your way to quality.
> I've read a bit more about Sudoku, and even played part of a game.
Not the wisest way to go about solving a problem.
I do admire his courage in leaving this up all these years though.
Compare/contrast with Peter Norvig's sudoku solver[5].
[0]:http://ronjeffries.com/xprog/articles/oksudoku/
[1]:http://ronjeffries.com/xprog/articles/sudoku2/
[2]:http://ronjeffries.com/xprog/articles/sudokumusings/
[3]:http://ronjeffries.com/xprog/articles/sudoku4/
[4]:http://ronjeffries.com/xprog/articles/sudoku5/
[5]:http://norvig.com/sudoku.html
Norvig tests his code, too, but he begins by seeking to understand the problem, not by writing tests first and hoping to end up with a quality product.
For math, the methods are sound -- they are trying to train you to do stuff in your head and build innate understanding. But the implementation of these methods is the opposite... forcing students to conform to the one true path imposes mechanical process on what should be a positive experience.
In other subjects like English, IMO the new methods are just dumb. They are training a generation of Buzzfeed readers. The intense, high stakes focus on assessing conformance to the methodology eliminates coursework in things like social studies and history that applied/reinforced reading and writing skills.
I've noticed that in my kids common core based middle school experience. Nothing is ever applied. Cover sections of the test and move on. Half of his day is reading, writing, and math. Everything else fits in the other half of the day. It is a strange sort of cargo cult mentality, the purpose of life is to do well on an infinite number of basic skill tests. But never apply those skills to anything other than endless testing.
Aside from applied classes everyone used to take like history, there are also no electives anymore. He got to select band, choir, orchestra, or music theory. That's all. I would imagine there would be no way to common core the electives I took as a kid, photography, science fiction, technical drafting, science classes.
Its a "top school" in a "top district" but that ranking probably has a lot more to do with parental demographics than curriculum design.
Most of the bad press around Common Core is coming from teachers, not parents.
Ada the language is awesome. In particular it requires you to be VERY specific about types, as well as things like pointer aliasing, but it also gave you enough flexibility to manage this complexity, in the form of generics and parameterized types akin to Standard ML's but in an imperative language. So why was it so universally loathed and detested?
Part of the reason is resistance to change. But another part -- a BIG part -- is shitty compilers. Before GNAT came along, Ada tooling was expensive and sucked balls. All vendors had to do was conform to the standard and they had the possibility of winning DoD contracts without having to compete on ease of use, performance, or non-bugginess.
So it is with Common Core. Common Core is a standard only and it may be a good one, but it's not going to solve the problem of curriculum authors shitting out bad curricula and passing it off in the school board simply because it "meets the standards". That's a structural problem and requires fundamental changes in how education is procured, distributed, and administered in the USA.
People who conflate the standards and the curricula are abundant in discussions on Common Core, and it bugs the crap out of me.
You want to talk about the Common Core? Keep the for-profit sector out of it, and then we'll talk.
It's a little silly to point fingers at unions and parents whilst ignoring Pearson in all of this -- unless you work for Pearson, I guess.
As an example, my elementary school in the mid-1990s was required by California to buy new math textbooks, and even though the school didn’t want any of the ones that qualified, thinking the books they already had to be better and the mandated books to be complete crap, they had no choice but to buy the new books because otherwise the school would lose the entire yearly book budget from the state (there was a bit more diversity in the allowed books for other subjects, so they did want those). As a bunch of dedicated, opinionated teachers, they refused to use the new inferior math books, but mandates are mandates so they bought them and put them in a box in a closet in the library. Great for the publisher, huge waste for everyone else.
http://www.mcsweeneys.net/articles/what-we-talk-about-when-w...