8 ms·

Old Standards vs. Common Core: A Side-By-Side Comparison of Math Expectations

36 points by tempestn 11y ago

charlesdenault 11y ago
The first example is pretty bad. It could just as easily be "Each shirt costs $6. How much do 7 shirts cost?"
- minikites 11y ago
  It has to do with the particular phrasing of the question. The correct phrasing for your example would be, "Each shirt costs $6. How much money do you need for 7 shirts?" It may seem like a meaningless distinction but it isn't. The first phrasing sets you up to count, the second phrasing sets you up to multiply and grapple with what multiplication actually is.
  - userbinator 11y ago
    I don't see any real difference in phrasing. They both involve multiplication, and you can always use repeated counting to multiply. Could you explain more where the difference is...?
    - TheOtherHobbes 11y ago
      One requires math. The other requires English comprehension before you can work out what the math problem is. And in the "Write two equations..." example the English is very vague. There's no suggestion that what it really means "Show the steps you use to rearrange the equation as you work out what y is." As I read it, it's clearly not stating the real problem correctly. If you write two arbitrary rearrangements that are correct but aren't steps on the way to solving the equation, do you get marked down or not? The first example is clearly specious. What is being taught? The concept of multiplication, the memorisation of times tables for multiplication, or the use of multiplication to solve simple problems? I have no problem with a unified national curriculum, but I'd prefer it to be a unified national curriculum supported by hard evidence that it improves outcomes and understanding. This looks more like pointless tinkering around the edges - especially if the textbooks are really bad, as others have suggested.
      - userbinator 11y ago
        There's no suggestion that what it really means "Show the steps you use to rearrange the equation as you work out what y is." I did not get that meaning at all from the wording. (I'm not in the US.) My best guess was that it was a really open-ended question and any two equations with a solution of 11/3 would do, which seems like a rather odd thing to ask.
douche 11y ago
The examples given seem to be a bit of a strawman argument. Sure, asking a single, focused question tests less for understanding than the multi-part Common Core examples. But at least from what I remember, you'd be drilled on all the different permutations of these kinds of word problems anyway, so the net effect is the same. Also, I really don't see how their reasoning follows on their first example. 3 shirts, $4/per shirt = $12. 7 shirt, 6 buttons/per shirt = 42. All that multiplication is, on the integers, anyway, is repeated addition. The only real difference I can see is that you can do the first example on your fingers and toes, whereas you'd have to scratch some tally-marks in the dirt or on paper to do the second if you don't know multiplication tables. What I wonder about with these Common Core curricula, is whether students will ever get enough practice working through mathematics operations to really be comfortable with it. When I was taught math (and it really wasn't that long ago), we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, etc. Maybe five or ten minutes, every day; they were probably graded enough to make us do them, but not enough to really matter. Most of the Common Core style math worksheets I've seen require far too much rewriting the algorithm from mathematical notation into grade-school English to ever allow that kind of repetition.
- DanBC 11y ago
  > When I was taught math (and it really wasn't that long ago), we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, A child can do sheet after sheet of calculations and co-incidentally get the right answer, without having any understanding of what they're doing. They can manipulate these symbols because they've memorised a routine. But because they lack understanding they stumble when they move onto something more advanced - they need to forget what they thought they knew, re-learn it properly, and learn the new thing. I agree that the first example is a confusing example to use, and that there doesn't seem to be much difference.
  - nmrm2 11y ago
    You'd be absolutely astounded at the number of vector calculus students at highly regarded universities who: * identify a rote procedure to apply when a problem of a particular form is seen * execute the rote procedure * come up with "<equation here> / 0" * ... and then turn the thing in anyways.
minikites 11y ago
I've never personally heard any reasonable criticism of Common Core. The criticism tends to either be "The Federal Government is overreaching!" combined with some States Rights dogwhistling or "This wasn't the way I was taught and since this confuses me, a grown adult, I have decided that it's bad for children! [who have a completely different set of requirements and experiences] Are there any sane, evidence-based criticisms? Because Common Core seems like a decent improvement to me.
- debacle 11y ago
  The textbooks are crap and teachers, especially older ones in my experience, lack the proper training to teach the standard. These are more implementation problems, but as a parent they've been the biggest issue.
  - minikites 11y ago
    That makes sense. To dramatically oversimplify, the idea is fine but the execution is lacking?
    - saboot 11y ago
      I've recently looked at one of the current "Common Core" textbooks for freshmen math in my sibling's school district in California. It is very different from the style of learning I was accustomed to. The textbooks I had introduced a new topic in some introduction pages, gave practice examples, and then a few pages of exercises of increasing difficulty. In contrast "Integrated Learning 1" by CPM takes a very different approach. It is very much continuous where the "text" of a topic is interwoven with a couple problems to do. Class room exercises and experiments constitute a lot of the main lessons. This is in contrast to Khan Academy where the progression of math knowledge is easily understandable and the step-by-step approach for learning by example and doing is emphasized. I was a bit taken aback by this approach. I can see it possibly working better in a class room setting. However I did most of my learning by reading. I'm also concerned that this approach will make it more difficult for students to catch up if their previous math education was not great as this continuous flow style doesn't lay out which topics to study. I'm not sure, but I'm not currently convinced. I'll be seeing how my younger sibling fares next semester, especially as our parents are not great at math and his education has some large holes in it (which we are working on). Thankfully he really enjoys Khan Academy so I anticipate him using that more if Common Core falls short.
debacle 11y ago
The problem with Common Core, in my experience, has not been the math itself. It's the textbooks. The workbooks. The stubborn teachers. Math is math. Knowing more than one way to solve 345 * 14 is a valuable skill. I would rather my children learn it on a whiteboard than from a workbook, and I think generally the quality of the modern texts is very poor for actually teaching math. I also think the teachers are bemoaning the Common Core much more than they need to. Explicitly teaching the algorithms for mental math is important. Learning how to do the lattice method, even if it's not the preferred method for multiplication, is important. I've talked to far too many teachers who have complained unendlingly about the weakness of the standard, and all that the kids are being forced to learn. It feels very much like a "This is change and change is bad." mentality. Disclaimer: I haven't encountered the Common Core as a parent at a high school level yet.
- Asbostos 11y ago
  Teachers will complain about absolutely every change that's imposed on them. Perhaps it's because there isn't really an undeniable way to know what's good and what's bad (unlike most jobs where profits make that clear) so every teacher assumes what they're doing it good and any change must therefore be bad. Or maybe it's just a job that attracts people with that kind of personality.
  - bsder 11y ago
    > Teachers will complain about absolutely every change that's imposed on them. Often for good reason. Remember "new math"? Most of my math textbooks as a kid had things about ordinality and arithmetic in non-base 10 (generally base-12--why?--I have no idea) down as far as like Grades 4 or 5. It turns out that if you don't have a very clear grasp of your own arithmetic, you can't change bases very easily. Teachers who have been around for 20+ years have seen bad education fads through several cycles.
- angdis 11y ago
  I've looked at some recent high school algebra textbooks. What a disaster. These books are literally written by committee, the "author's" page in the front has a dozen headshots complete with bios. The content inside the book is a mishmash of color photographs, historical information, brain teasers and junk. The texts are distracting and takes away from what SHOULD BE an uncluttered exposition of the basics of mathematical reasoning.
niels_olson 11y ago
My mom is a college math teacher, previously a high school math teacher, and helped develop the current Texas standards. She knows a number of the folks who wrote the California Common Core and has high praise for it in principle. In practice, she is quite frustrated when she tutors my daughter. She has worked with her Over FaceTime, using Pearson's own remote tutoring app, and over a two week "Grammy Camp" in the summers. Thanks for posting the side-by-side. I wish they would tell the parents something like this, once per testing period or so. My undergrad is in physics and I too struggle with how to help when asked.
- bsder 11y ago
  > My undergrad is in physics and I too struggle with how to help when asked. In what way? Is it that you're trying to replicate an unfamiliar procedure or an unfamiliar concept. Maybe as an engineer I'm just unusual in that all of the Common Core procedures I have seen so far actually map to the way I calculate in my head. But, I've seen carpenters, woodworkers and machinists all calculate similarly when they do (normally they use advanced geometry to avoid calculating at all).
bsder 11y ago
I won't even touch the political reflexive negativity surrounding Common Core. However, the only non-political (I'm being nice ...) criticism I continue to see is in the mathematics. And it's always because of "word problems". Common Core likes "word problems" and reasoning a LOT. I have taught math. With very few exceptions, everybody hates word problems. Most students just want "Give me the question and give me the procedure so I can regurgitate the procedure. Don't make me think." They don't want to reason. You can see this even in senior year of high school in the US in science. Just try to get the students to explain why they are doing an experiment (In short: "state the hypothesis"). It's almost always a disaster. After a year, you might get a majority up to the point where they can actually state it coherently. I have this problem even with some really senior engineers when debugging things. "We did X, Y, and Z. They didn't work." "Um, okay, why did you do X, Y, or Z?" "Huh?!?!?!" "Why should X, Y or Z have worked? Is there a relation between X, Y, or Z and the problem? What is it?" <puzzled stares> So, I see the objections as positive evidence that the Common Core standards are doing their job. The fact that adults have trouble with some of these problems is no surprise. Most of them skated through reasoning and word problems themselves.
- DanBC 11y ago
  > You can see this even in senior year of high school in the US in science. Just try to get the students to explain why they are doing an experiment (In short: "state the hypothesis"). This starts very young. Most "science for kids" on the Internet is little more than "here's a demonstration of something, and here's a sciency explanation of what's going on". Most sites don't suggest making any changes to the setup, or ask any questions about what happens if you do stuff differently. (I'm keen to find good science content for children that does teach scientific method, so please let me know of any good sites).
- thraxil 11y ago
  Totally agree on the importance of reasoning. Word problems though are often hated because they're so ambiguous in unintentional ways that don't really relate to the problem. Eg, in the middle school example on the page, when it says "She makes $4.40" do they mean net or gross? In this case, it turns out that only one of those gives you an integer answer, so you can work out what they meant, but it's not uncommon to see problems where that's not the case and you're stuck making a 50/50 guess. With the current emphasis on test scores, that adds a lot of stress.
jkingsbery 11y ago
Can't say I've been following Common Core too closely (my kids are 3 and 1 respectively, so there'll be a bit before it affects me directly). But these example questions just seem completely to be arguing with a strawman: The only difference in the elementary school question was bigger numbers. The first middle school example contains only one additional step (being able to do algebra instead of just arithmetic). The explanation for the "old way" contains the word "simple" gratuitously - you might as well say that the CC version of the problem only requires "simple algebra." For, the second middle school example, I definitely had questions that were multi-part like that in middle school. Also, each part is just applying the same formula a few different times - but the explanation given makes it seem like it's a whole new thing! The explanations for the high school example is really the worst one though. "This question is an example of solving equations as a series of mechanical steps" and "This question is an example of solving equations as a process of reasoning" mean basically the same thing, just one is put in a derogatory manner. The CC version of the question itself is also vague: can I pick any two equations that have the same solution? Should I pick equations that are the intermediate steps toward the solution? Does "y=5/3" count as one of the equations?
- contravariant 11y ago
  I also don't get their critique that the problems can be solved easily using simple mathematics. That's kind of the point of mathematics. Making the problems slightly more difficult (if it can be called that) doesn't really remedy the original problem, which is that they don't understand why something works.
- tempestn 11y ago
  Regarding the elementary one, there's a good reason for the larger numbers though. With 4x3, a student can get the right answer through a counting process. 1-2-3-4 5-6-7-8 9-10-11-12 For someone who hasn't either memorized multiplication tables or learned faster ways of working out the answer, that's likely the approach they will take. With 6x7 on the other hand, it's natural to look for a faster (better) way to solve the problem. I agree that the last question was vague / poorly state.
lordnacho 11y ago
If 3(y-1) = 8, then what is y? On what planet is this a high school math problem? How do people learn linear algebra and vector calculus in college if this is what they're at in high school?
- saboot 11y ago
  There are several level of classes at the middle and high school levels. Normally this would be taught in elementary school. But there are some students who do need to be taught this again in high school. There are a whole debate of possible reasons why, but providing the basic math avoids sticking them in classes which they are guaranteed to fail
  - sp332 11y ago
    Exactly - my "pre-algebra" class in 8th grade put me beyond the entire "Algebra" class when I started high school. And my calculus teacher in college wasn't very good so I coasted through 2 classes based on what I learned in high school and then flunked out of the 3rd because I finally ran into new ideas.
- protomyth 11y ago
  Well, they cancelled trig when I was in school because I was the only one taking it. It happens and there is no real excuse. As to how we learn in college? I gutted it out and did every damn problem I could. I would imagine that STEM is beat out of a lot of kids in elementary so it might just be the survivors are already used to doing the extra work.
- Jtsummers 11y ago
  This would be covered in Algebra I and pre-Algebra (under the old scheme, not sure what it falls under now). Those courses are typically taught somewhere between grades 7-10 (7 as the earliest for pre-Algebra, 10 as the latest for Algebra I) for most students depending on the particular track they're on.
catawbasam 11y ago
What I'm seeing with my Maryland 3rd and 5th graders is lots of focus on number patterns and word problems using the integers. I think they are also getting fewer, and sometimes harder, problems than they would have previously. Some of that is good. At times they really are being required to think more deeply. The problems I have seen are: a. Emphasis on explanation even when it doesn't make sense. In 2nd grade they brought home worksheets with 20-30 simple addition problems where they were asked to 'explain' each answer. b. Focus on a narrow range of topics, to the point where they are not always learning the basic vocabulary of mathematics. c. In particular, there has been very little attention given to geometry.
- tempestn 11y ago
  a. sounds like a perfect example of the concepts of CC being mis-applied. It might make sense to explain how they arrive at the answers in general, but separately explaining each answer is obviously nuts (and would have driven me crazy when I was in school).
sp332 11y ago
For clarity, these are the actual Common Core math standards. If it's not in here, then it's a problem with the curriculum instead of the Common Core. http://www.corestandards.org/Math/ http://www.corestandards.org/Math/
swills 11y ago
At the bottom of this page you see: All content Copyright © 2010 – 2015 Foundation for Excellence in Education Wikipedia says the Foundation for Excellence in Education is a think tank established by Jeb Bush and has received funding from Bill Gates, who I understand has also funded development of Common Core.
sixbrx 11y ago
"What are two different equations with the same solution as 3(y-1) = 8?" How is this scored if the student just adds 1 to both sides, then 2 to both sides, for the other two equations? 3(y-1)+ 1 = 8 + 1 3(y-1)+ 2 = 8 + 2 Is that a full-credit answer (it is technically correct)? Or do they want movement towards a solution? This seems very ambiguous as to what they want which I've noticed is common in CC questions.
cline6 11y ago
I will let this man do my talking. https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....

36 points by tempestn 11y ago

charlesdenault 11y ago

The first example is pretty bad. It could just as easily be "Each shirt costs $6. How much do 7 shirts cost?"

minikites 11y ago
It has to do with the particular phrasing of the question. The correct phrasing for your example would be, "Each shirt costs $6. How much money do you need for 7 shirts?" It may seem like a meaningless distinction but it isn't. The first phrasing sets you up to count, the second phrasing sets you up to multiply and grapple with what multiplication actually is.
- userbinator 11y ago
  I don't see any real difference in phrasing. They both involve multiplication, and you can always use repeated counting to multiply. Could you explain more where the difference is...?
  - TheOtherHobbes 11y ago
    One requires math. The other requires English comprehension before you can work out what the math problem is. And in the "Write two equations..." example the English is very vague. There's no suggestion that what it really means "Show the steps you use to rearrange the equation as you work out what y is." As I read it, it's clearly not stating the real problem correctly. If you write two arbitrary rearrangements that are correct but aren't steps on the way to solving the equation, do you get marked down or not? The first example is clearly specious. What is being taught? The concept of multiplication, the memorisation of times tables for multiplication, or the use of multiplication to solve simple problems? I have no problem with a unified national curriculum, but I'd prefer it to be a unified national curriculum supported by hard evidence that it improves outcomes and understanding. This looks more like pointless tinkering around the edges - especially if the textbooks are really bad, as others have suggested.
    - userbinator 11y ago
      There's no suggestion that what it really means "Show the steps you use to rearrange the equation as you work out what y is." I did not get that meaning at all from the wording. (I'm not in the US.) My best guess was that it was a really open-ended question and any two equations with a solution of 11/3 would do, which seems like a rather odd thing to ask.

douche 11y ago

The examples given seem to be a bit of a strawman argument. Sure, asking a single, focused question tests less for understanding than the multi-part Common Core examples. But at least from what I remember, you'd be drilled on all the different permutations of these kinds of word problems anyway, so the net effect is the same. Also, I really don't see how their reasoning follows on their first example. 3 shirts, $4/per shirt = $12. 7 shirt, 6 buttons/per shirt = 42. All that multiplication is, on the integers, anyway, is repeated addition. The only real difference I can see is that you can do the first example on your fingers and toes, whereas you'd have to scratch some tally-marks in the dirt or on paper to do the second if you don't know multiplication tables. What I wonder about with these Common Core curricula, is whether students will ever get enough practice working through mathematics operations to really be comfortable with it. When I was taught math (and it really wasn't that long ago), we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, etc. Maybe five or ten minutes, every day; they were probably graded enough to make us do them, but not enough to really matter. Most of the Common Core style math worksheets I've seen require far too much rewriting the algorithm from mathematical notation into grade-school English to ever allow that kind of repetition.

DanBC 11y ago
> When I was taught math (and it really wasn't that long ago), we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, A child can do sheet after sheet of calculations and co-incidentally get the right answer, without having any understanding of what they're doing. They can manipulate these symbols because they've memorised a routine. But because they lack understanding they stumble when they move onto something more advanced - they need to forget what they thought they knew, re-learn it properly, and learn the new thing. I agree that the first example is a confusing example to use, and that there doesn't seem to be much difference.
- nmrm2 11y ago
  You'd be absolutely astounded at the number of vector calculus students at highly regarded universities who: * identify a rote procedure to apply when a problem of a particular form is seen * execute the rote procedure * come up with "<equation here> / 0" * ... and then turn the thing in anyways.

minikites 11y ago

I've never personally heard any reasonable criticism of Common Core. The criticism tends to either be "The Federal Government is overreaching!" combined with some States Rights dogwhistling or "This wasn't the way I was taught and since this confuses me, a grown adult, I have decided that it's bad for children! [who have a completely different set of requirements and experiences] Are there any sane, evidence-based criticisms? Because Common Core seems like a decent improvement to me.

debacle 11y ago
The textbooks are crap and teachers, especially older ones in my experience, lack the proper training to teach the standard. These are more implementation problems, but as a parent they've been the biggest issue.
- minikites 11y ago
  That makes sense. To dramatically oversimplify, the idea is fine but the execution is lacking?
  - saboot 11y ago
    I've recently looked at one of the current "Common Core" textbooks for freshmen math in my sibling's school district in California. It is very different from the style of learning I was accustomed to. The textbooks I had introduced a new topic in some introduction pages, gave practice examples, and then a few pages of exercises of increasing difficulty. In contrast "Integrated Learning 1" by CPM takes a very different approach. It is very much continuous where the "text" of a topic is interwoven with a couple problems to do. Class room exercises and experiments constitute a lot of the main lessons. This is in contrast to Khan Academy where the progression of math knowledge is easily understandable and the step-by-step approach for learning by example and doing is emphasized. I was a bit taken aback by this approach. I can see it possibly working better in a class room setting. However I did most of my learning by reading. I'm also concerned that this approach will make it more difficult for students to catch up if their previous math education was not great as this continuous flow style doesn't lay out which topics to study. I'm not sure, but I'm not currently convinced. I'll be seeing how my younger sibling fares next semester, especially as our parents are not great at math and his education has some large holes in it (which we are working on). Thankfully he really enjoys Khan Academy so I anticipate him using that more if Common Core falls short.

debacle 11y ago

The problem with Common Core, in my experience, has not been the math itself. It's the textbooks. The workbooks. The stubborn teachers. Math is math. Knowing more than one way to solve 345 * 14 is a valuable skill. I would rather my children learn it on a whiteboard than from a workbook, and I think generally the quality of the modern texts is very poor for actually teaching math. I also think the teachers are bemoaning the Common Core much more than they need to. Explicitly teaching the algorithms for mental math is important. Learning how to do the lattice method, even if it's not the preferred method for multiplication, is important. I've talked to far too many teachers who have complained unendlingly about the weakness of the standard, and all that the kids are being forced to learn. It feels very much like a "This is change and change is bad." mentality. Disclaimer: I haven't encountered the Common Core as a parent at a high school level yet.

Asbostos 11y ago
Teachers will complain about absolutely every change that's imposed on them. Perhaps it's because there isn't really an undeniable way to know what's good and what's bad (unlike most jobs where profits make that clear) so every teacher assumes what they're doing it good and any change must therefore be bad. Or maybe it's just a job that attracts people with that kind of personality.
- bsder 11y ago
  > Teachers will complain about absolutely every change that's imposed on them. Often for good reason. Remember "new math"? Most of my math textbooks as a kid had things about ordinality and arithmetic in non-base 10 (generally base-12--why?--I have no idea) down as far as like Grades 4 or 5. It turns out that if you don't have a very clear grasp of your own arithmetic, you can't change bases very easily. Teachers who have been around for 20+ years have seen bad education fads through several cycles.
angdis 11y ago
I've looked at some recent high school algebra textbooks. What a disaster. These books are literally written by committee, the "author's" page in the front has a dozen headshots complete with bios. The content inside the book is a mishmash of color photographs, historical information, brain teasers and junk. The texts are distracting and takes away from what SHOULD BE an uncluttered exposition of the basics of mathematical reasoning.

niels_olson 11y ago

My mom is a college math teacher, previously a high school math teacher, and helped develop the current Texas standards. She knows a number of the folks who wrote the California Common Core and has high praise for it in principle. In practice, she is quite frustrated when she tutors my daughter. She has worked with her Over FaceTime, using Pearson's own remote tutoring app, and over a two week "Grammy Camp" in the summers. Thanks for posting the side-by-side. I wish they would tell the parents something like this, once per testing period or so. My undergrad is in physics and I too struggle with how to help when asked.

bsder 11y ago
> My undergrad is in physics and I too struggle with how to help when asked. In what way? Is it that you're trying to replicate an unfamiliar procedure or an unfamiliar concept. Maybe as an engineer I'm just unusual in that all of the Common Core procedures I have seen so far actually map to the way I calculate in my head. But, I've seen carpenters, woodworkers and machinists all calculate similarly when they do (normally they use advanced geometry to avoid calculating at all).

bsder 11y ago

I won't even touch the political reflexive negativity surrounding Common Core. However, the only non-political (I'm being nice ...) criticism I continue to see is in the mathematics. And it's always because of "word problems". Common Core likes "word problems" and reasoning a LOT. I have taught math. With very few exceptions, everybody hates word problems. Most students just want "Give me the question and give me the procedure so I can regurgitate the procedure. Don't make me think." They don't want to reason. You can see this even in senior year of high school in the US in science. Just try to get the students to explain why they are doing an experiment (In short: "state the hypothesis"). It's almost always a disaster. After a year, you might get a majority up to the point where they can actually state it coherently. I have this problem even with some really senior engineers when debugging things. "We did X, Y, and Z. They didn't work." "Um, okay, why did you do X, Y, or Z?" "Huh?!?!?!" "Why should X, Y or Z have worked? Is there a relation between X, Y, or Z and the problem? What is it?" <puzzled stares> So, I see the objections as positive evidence that the Common Core standards are doing their job. The fact that adults have trouble with some of these problems is no surprise. Most of them skated through reasoning and word problems themselves.

DanBC 11y ago
> You can see this even in senior year of high school in the US in science. Just try to get the students to explain why they are doing an experiment (In short: "state the hypothesis"). This starts very young. Most "science for kids" on the Internet is little more than "here's a demonstration of something, and here's a sciency explanation of what's going on". Most sites don't suggest making any changes to the setup, or ask any questions about what happens if you do stuff differently. (I'm keen to find good science content for children that does teach scientific method, so please let me know of any good sites).
thraxil 11y ago
Totally agree on the importance of reasoning. Word problems though are often hated because they're so ambiguous in unintentional ways that don't really relate to the problem. Eg, in the middle school example on the page, when it says "She makes $4.40" do they mean net or gross? In this case, it turns out that only one of those gives you an integer answer, so you can work out what they meant, but it's not uncommon to see problems where that's not the case and you're stuck making a 50/50 guess. With the current emphasis on test scores, that adds a lot of stress.

jkingsbery 11y ago

Can't say I've been following Common Core too closely (my kids are 3 and 1 respectively, so there'll be a bit before it affects me directly). But these example questions just seem completely to be arguing with a strawman: The only difference in the elementary school question was bigger numbers. The first middle school example contains only one additional step (being able to do algebra instead of just arithmetic). The explanation for the "old way" contains the word "simple" gratuitously - you might as well say that the CC version of the problem only requires "simple algebra." For, the second middle school example, I definitely had questions that were multi-part like that in middle school. Also, each part is just applying the same formula a few different times - but the explanation given makes it seem like it's a whole new thing! The explanations for the high school example is really the worst one though. "This question is an example of solving equations as a series of mechanical steps" and "This question is an example of solving equations as a process of reasoning" mean basically the same thing, just one is put in a derogatory manner. The CC version of the question itself is also vague: can I pick any two equations that have the same solution? Should I pick equations that are the intermediate steps toward the solution? Does "y=5/3" count as one of the equations?

contravariant 11y ago
I also don't get their critique that the problems can be solved easily using simple mathematics. That's kind of the point of mathematics. Making the problems slightly more difficult (if it can be called that) doesn't really remedy the original problem, which is that they don't understand why something works.
tempestn 11y ago
Regarding the elementary one, there's a good reason for the larger numbers though. With 4x3, a student can get the right answer through a counting process. 1-2-3-4 5-6-7-8 9-10-11-12 For someone who hasn't either memorized multiplication tables or learned faster ways of working out the answer, that's likely the approach they will take. With 6x7 on the other hand, it's natural to look for a faster (better) way to solve the problem. I agree that the last question was vague / poorly state.

lordnacho 11y ago

If 3(y-1) = 8, then what is y? On what planet is this a high school math problem? How do people learn linear algebra and vector calculus in college if this is what they're at in high school?

saboot 11y ago
There are several level of classes at the middle and high school levels. Normally this would be taught in elementary school. But there are some students who do need to be taught this again in high school. There are a whole debate of possible reasons why, but providing the basic math avoids sticking them in classes which they are guaranteed to fail
- sp332 11y ago
  Exactly - my "pre-algebra" class in 8th grade put me beyond the entire "Algebra" class when I started high school. And my calculus teacher in college wasn't very good so I coasted through 2 classes based on what I learned in high school and then flunked out of the 3rd because I finally ran into new ideas.
protomyth 11y ago
Well, they cancelled trig when I was in school because I was the only one taking it. It happens and there is no real excuse. As to how we learn in college? I gutted it out and did every damn problem I could. I would imagine that STEM is beat out of a lot of kids in elementary so it might just be the survivors are already used to doing the extra work.
Jtsummers 11y ago
This would be covered in Algebra I and pre-Algebra (under the old scheme, not sure what it falls under now). Those courses are typically taught somewhere between grades 7-10 (7 as the earliest for pre-Algebra, 10 as the latest for Algebra I) for most students depending on the particular track they're on.

catawbasam 11y ago

What I'm seeing with my Maryland 3rd and 5th graders is lots of focus on number patterns and word problems using the integers. I think they are also getting fewer, and sometimes harder, problems than they would have previously. Some of that is good. At times they really are being required to think more deeply. The problems I have seen are: a. Emphasis on explanation even when it doesn't make sense. In 2nd grade they brought home worksheets with 20-30 simple addition problems where they were asked to 'explain' each answer. b. Focus on a narrow range of topics, to the point where they are not always learning the basic vocabulary of mathematics. c. In particular, there has been very little attention given to geometry.

tempestn 11y ago
a. sounds like a perfect example of the concepts of CC being mis-applied. It might make sense to explain how they arrive at the answers in general, but separately explaining each answer is obviously nuts (and would have driven me crazy when I was in school).

sp332 11y ago

For clarity, these are the actual Common Core math standards. If it's not in here, then it's a problem with the curriculum instead of the Common Core. http://www.corestandards.org/Math/ http://www.corestandards.org/Math/

swills 11y ago

At the bottom of this page you see: All content Copyright © 2010 – 2015 Foundation for Excellence in Education Wikipedia says the Foundation for Excellence in Education is a think tank established by Jeb Bush and has received funding from Bill Gates, who I understand has also funded development of Common Core.

sixbrx 11y ago

"What are two different equations with the same solution as 3(y-1) = 8?" How is this scored if the student just adds 1 to both sides, then 2 to both sides, for the other two equations? 3(y-1)+ 1 = 8 + 1 3(y-1)+ 2 = 8 + 2 Is that a full-credit answer (it is technically correct)? Or do they want movement towards a solution? This seems very ambiguous as to what they want which I've noticed is common in CC questions.

cline6 11y ago

I will let this man do my talking. https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....