The problem with Common Core is that it phrases questions like yours using weird words and focuses on specific procedures instead of the correct answer (or a range or reasonable answers).
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.
Common Core doesn't phrase the questions in weird ways. The standards are clear and don't tell you how to teach. Much of the training around it and essentially all of the curriculum (repackaged old stuff, new section headings on the same crap) is terrible. But that's the corporatization of education and the poor support for professional development of US teachers at work, which we allow to happen regardless of curriculum content.
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.
I have degrees in philosophy and Classics, speak multiple languages, and am "used to math and critical thinking."
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.
Believe it or not. #12 is not an error. Now put the semantics of that sentence in your hat and reevaluate the entire test and the concepts that went into the test. Think about it from a pedagogical standpoint.
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.
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.
I think the problem is, you are (with merit) criticizing Pearson for a crappy test. This isn't specifically Common Core's problem, this is Pearsons problem for a pretty awkward approach to Common Cores standard.
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
Had I been in the class perhaps I'd have understood what the requirements of the quiz were and understood what a "subtraction story" is. Looks like the kid who flunked that quiz did sort that one out.
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 couldn't find the phrase "number sentence" on the Common Core standards website, no idea where that comes from. Possibly from Pearson Education inc themselves?
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.)
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).
My kids started grade school a few years before common core was launched, and I remember "number sentence" was already in use. I, too, struggled to find out what a number sentence is. They also spent a fair amount of time with "you must all do subtraction in this weird way" and similar stuff.
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 would be embarrassed, not proud, of my inability to understand really fucking simple math aimed at young children.
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?
You don't appear to understand the question either, unless you go around subtracting pennies from cups of liquid.
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.
Number sentence is an equation explained using words a six year old understands. Children use counters all the time. Ever played air hockey? I'm not sure how that would be confusing. A number story is a word problem.
I don't see why the heck we don't just teach them the word equation instead of pretending they're too simple to understand the concept and add a word to their vocabulary.
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".
Nobody uses these terms to describe these things. The fact that you described the crazy way CC calls things with more familiar terms is specific evidence of that.
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.
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.
It does matter what they're called if they're not called something consistently. I've shown elsewhere in this thread that "subtraction sentence" has two entirely opposite meanings...on the same test.
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.
Well vernaculars differ and a counter is a totally intuitive way to describe the air hockey score keeper. I'd be hard pressed to call it a score board especially since the keepers are on opposite sides of the table generally.
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.
Parent is thinking about an electronic scoreboard. Parent's problem problem is that they assume anything different from their idiolect is stupid and wrong.
Those weird words and procedures are taught to the students. My kids understand them just fine. It's the parents who aren't in the classroom getting the instruction that goes along with the homework that are complaining.
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.
While I don't doubt some teacher at some school somewhere on america may have done something ill conceived, do you have a source? A quick Google found some common core work on estimation which was multiple choice, clearly geared towards understanding magnitude.
Teachers don't sit around all day thinking up ways to trick students and anger their parents.
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.