Common Core Standards

[fuelair]

Well, that would be nice. But many kids come from in home day care and they lack the social skills to enter KG, but in our district they learn fast.

our goal is to have them as readers by eh end of KG and be fluent in numbers.

And the reason that many states resist standards across the nation is they are rather lax.

Ah, functional schooling!!!!!And, I suspect they have fun doing it!!!

 

[Dancing David]

Congratulations?



I wasn't judging anything.



OK, there's no busywork in school.

I did not mean to offend, that just seems a really low bar, in KG there are plenty of skills to acquire in your example.

My reference to busy work was regards KG

 

[stevea]

Back when I went to elementary school, America was just getting over the disaster of "New Math". So I learned ordinary math, using times tables, and drills. And at some point, I became smart enough to figure out on my own why the standard algorithms were correct and effective.
...
It's certainly not the abstract woo that was New Math.

As someone who was actually taught "new math" in early grade school and who has a degree in pure math from a well respected Univ, I heartily disagree with your assessment of "new math".

Introducing material based on fundamental concepts is far better than the alternative of teaching the rote detail and then trying to introduce concepts later. So yes I learned discrete sets, unions & intersections of sets, Venn diagrams associativity, commutativity, number bases, modulo operation and boolean logic by 3rd grade and this foundation was indeed very helpful in university study of group theory, topology and concepts of abstract algebra and homology theory. Yes basic arithmetic was taught in grade school along side and used to motivate as example.

To me your preference of teaching rote arithmetic first, is akin to forcing piano students to learn to bang out a Chopin Sonata on their own, and only then teaching them about octaves, chords, major/minor keys and proper fingering and hand positioning. They need to unlearn their biases and bad habits before they can advance, and unlearning is IMO much harder than learning. Further, rote repetition avoids engaging the student's abilities at abstract reasoning.

A better analogy might be the way that most ppl including physicists have trouble overcoming their early intro to Newtonian mechanics, classical E&M and particle theory vs relativistic & quantum Mech. We are all crippled by biases that introduced early and are hard to unlearn.


I've no idea if "common core" per se is good/bad or indifferent, and frankly no one can know until some careful and controlled tests have been performed. It has aspects that sound very good, particularly the ability to measure results in a consistent way. I'm a little concerned that it may prevent progress in education by classifying exactly which 'unit's must be taught at each grade level. It seems over-restrictive in dictating a time-line rather than just unit goals.

 

[Minoosh]

I did not mean to offend, that just seems a really low bar, in KG there are plenty of skills to acquire in your example.

I use "entertained" as a kind of shorthand. As I indicated in a later post, "occupied" would be a better word. Along with that, "engaged." Which brings me to "challenged." To me those are all part of the package, and a lot of people have no idea how difficult it is to deliver this type of instruction.

Introducing material based on fundamental concepts is far better than the alternative of teaching the rote detail and then trying to introduce concepts later.

I don't see why it has to be either/or. I don't see any huge advantage to 18-year-olds counting on their fingers to add single digits. Memorization has its place, IMO.

I've no idea if "common core" per se is good/bad or indifferent, and frankly no one can know until some careful and controlled tests have been performed.

It sounds good in theory to have careful and controlled tests. However, teachers by and large are working in real time to serve real children. What "works" will be different for each of them.

 

[Jules Galen]

Well, that would be nice. But many kids come from in home day care and they lack the social skills to enter KG, but in our district they learn fast.

our goal is to have them as readers by eh end of KG and be fluent in numbers.

And the reason that many states resist standards across the nation is they are rather lax.

Madness. Your district is mad.

 

[pipelineaudio]

I'm seeing stupidly large amounts of homework, where the kids have zero free time, and yet they consistently don't know jack about anything, and then go on to vote the anti-science position any chance they get in our unconstitutional ballot system.

We need an education system that takes into account that most of the loads of crap the kids are being saddled with won't mean anything as 3d printing gets cheaper and cheaper and cheaper. The world is changing, and at least here in Hawaii, we've dug our heels into the 19th century, with the only nod to the modern world being putting wheels on kids' backpacks so they can carry more homework

 

[phildonnia]

An observation from the front:

One of the Common Core requirements is that students be able to explain how they solved a problem. Well, that seems fine as stated; I think that it's good to know how to defend your answer, or how to convince others that your answer is right. However in practice, this takes the form of tacking on to every problem: "Explain how you got your answer".

For those with a good intuition of the subject, it would be like asking someone to shoot a basketball free-throw, and then explain how they did it. The question is frustrating to everyone, and students invariably are coached on the correct answer to write in the blank, and everyone seems satisfied that we are teaching kids to have a deeper understanding.

With my own children, I have tried some experimental techniques at home. (I have no background in education, pedagogy or child psychology) Their teachers asked us to practice addition-facts with flash cards. I did not do this, but rather told them that counting on fingers is a perfectly correct and acceptable way to do addition. Since these kids are naturally lazy, they managed independently to discover commutativity and associativity, and to memorize the more frequent addition patterns.

 

[Minoosh]

Since these kids are naturally lazy, they managed independently to discover commutativity and associativity, and to memorize the more frequent addition patterns.

Tutoring a small group yesterday I had students match verbal expressions with the equivalent mathematical expression. As they culled out pairs of index cards, one boy was intent on rearranging the cards in orderly rows and columns. I was able to connect that to the idea of prime numbers - you can't make a rectangle out of 7 cards, or 13. As with your children, there was an opportunity to let them make that discovery.

Lead classroom teachers have a much harder job, IMO. They may be tasked with bringing 150+ students up to speed with "math facts." What you are doing, and what I have the luxury of doing, is harder to accomplish when trying to manage groups of 30 or more students at a time. As far as I can tell Common Core is about your kids, or anyone's, being able to explain that their finger-count indicates it doesn't matter what order you use to add numbers.

There's some pressure on teachers to *instill* this knowledge - to tell kids, this is the commutative propery; order doesn't matter in addition. I think it sticks better if they derive it for themselves as your kids have done. But, a lot of kids don't get much exposure to that at home.

 

[Paul C. Anagnostopoulos]

One of the Common Core requirements is that students be able to explain how they solved a problem. Well, that seems fine as stated; I think that it's good to know how to defend your answer, or how to convince others that your answer is right. However in practice, this takes the form of tacking on to every problem: "Explain how you got your answer".

This convinces me even more that the folks coming up with the core requirements and tests have no concept that some kids simply cannot do math. At least those kids have a vague chance with rote problems, but certainly not with explanations.

Again, I want to add three physical education requirements to the core.

~~ Paul

 

[Minoosh]

This convinces me even more that the folks coming up with the core requirements and tests have no concept that some kids simply cannot do math.

What do you base this statement on? Would it sound reasonable to apply this to other subjects, or are you making math the exception?

At least those kids have a vague chance with rote problems, but certainly not with explanations.

It's perfectly valid to say, "I counted with my fingers." You seem so certain kids won't be able to explain. What gives you that confidence?

I've had to deal with kids who said they couldn't do math when in fact they were doing it at the time!

 

[arthwollipot]

342 -
173
---
???

You can't take three from two, two is less than three, so you look at the four in the tens place. Now that's really four tens so you make it three tens regroup and you change a ten to ten ones and you add it to the two and get twelve and you take away three that's nine. Is that clear?

Now instead of four in the tens place you've got three 'cause you added one, that is to say ten, to the two but you can't take seven from four so you look at the hundreds place.

From the three you then use one to make ten tens and you know why four plus minus one plus ten equals fourteen minus one 'cause addition is commutative, right, and so you've got fourteen tens and you take away seven and that leaves five.

Well, six actually, but the idea is the important thing.

Now go back to the hundreds place and you're left with two and you take away one from two and that leaves...?

Everybody get one? Not bad for the first day.

Hooray for New Math, New-ew-ew Math. It won't do any good to re-view math, it's so simple - so very simple - that only a child can do it.

-Tom Lehrer (1965)

 

[SUSpilot]

342 -

173

---

???



You can't take three from two, two is less than three, so you look at the four in the tens place. Now that's really four tens so you make it three tens regroup and you change a ten to ten ones and you add it to the two and get twelve and you take away three that's nine. Is that clear?



Now instead of four in the tens place you've got three 'cause you added one, that is to say ten, to the two but you can't take seven from four so you look at the hundreds place.



From the three you then use one to make ten tens and you know why four plus minus one plus ten equals fourteen minus one 'cause addition is commutative, right, and so you've got fourteen tens and you take away seven and that leaves five.



Well, six actually, but the idea is the important thing.



Now go back to the hundreds place and you're left with two and you take away one from two and that leaves...?



Everybody get one? Not bad for the first day.



Hooray for New Math, New-ew-ew Math. It won't do any good to re-view math, it's so simple - so very simple - that only a child can do it.



-Tom Lehrer (1965)

Except the teacher wanted it done in base 8. That's like base 10 - if you don't have any thumbs!

 

[Minoosh]

Except the teacher wanted it done in base 8. That's like base 10 - if you don't have any thumbs!

I think I've seen the thing the Tom Lehrer thing, set to music on YouTube. The traditional algorithm for subtraction, when I was in grade school, made sense when combined with conceptual work on place value. I wouldn't call that "new math"; it was established long before 1965.

I do remember work involving other-than-base-10 math and that was pretty useless for my computational needs at the time. On another thread, a poster maintains that base 2 is far more useful for computer applications.

This idea we have to reinvent the wheel every few years strikes me as counterproductive. As I said before, it keeps textbook publishers in business.

 

[arthwollipot]

Except the teacher wanted it done in base 8. That's like base 10 - if you don't have any thumbs!

"If you're missing two fingers" is the exact quote.

No video exists of this performance, but from the audio, there had to be some visual gags about counting on fingers involved.

 

[arthwollipot]

This idea we have to reinvent the wheel every few years strikes me as counterproductive. As I said before, it keeps textbook publishers in business.

From what I've seen - and I could be wrong about this (it isn't even my country) - what they're doing with arithmetic is teaching mental shortcuts.

For example, when I want to add 56 and 78, I was taught to add 6 and 8 to get 14, carry the one, add 5 and 7 to get 12, add the carried 1 to get 13, making a total of 134.

Today, I add 50 and 70 to get 120, then add 6 and 8 to get 14, which I add to 120 to get 134.

The first method is better on paper, especially when you can show your work, but the second method is quicker and easier to do in my head. The thing with the number line and the crescents that everyone is wtfing about seems to me to be very much like the second method.

 

[Minoosh]

The thing with the number line and the crescents that everyone is wtfing about seems to me to be very much like the second method.

There's a little bit of synergy, if you have your own method that you can relate to the commonly taught algorithm. I'm not familiar with "crescents." I'd say being able to apply alternatives algorithms to get the right answer is good for deepening one's math understanding. Like, after adding 9, expect that the digit in the ones place will be one less than the the digit you're adding 9 to.

It sounds awkward to verbalize. IMO American kids do put up some resistance to these extremely basic shortcuts. I doubt it's an issue in China. Yet, the U.S. consistently gets higher marks for innovation, while in China there's a little bit of a social movement against "rote memorization."

As it relates to education reform, my opinion is: Don't throw the baby out with the bathwater. Memorization isn't the only tool at our command, but it has its place.

 

[arthwollipot]

I'm not familiar with "crescents."

I'm referring to this:

 

[DallasDad]

I wouldn't mind if my kids had been taught explicitly that 427 - 316 is the same as (400 - 300) + (20 - 10) + (7 - 6). If the concept of positional notation is taught, optimization strategies are trivial, and best left as exercises for the students. Those who are mathematically inclined (or just curious and not sleeping in class) will find lots of shortcuts. All students should be able to demonstrate an understanding of "borrowing" and why the standard algorithm is correct (e.g., one cannot take 9 away from 3, so regrouping is needed).

If one must use crescents and number lines when teaching the concepts, fine. I don't think they help -- in fact, I can claim 2 for 2 anecdotes with my own kids that they just confuse the issue by obfuscating, rather than demonstrating, the idea of positional notation. But requiring children to solve problems using crescents or number lines bear a faint whiff of ridiculousness. It's a conceptual crutch, a teaching tool, not a replacement for the standard algorithm.

 

[JDC]

I'm referring to this:

[qimg]http://i.imgur.com/N3CePB6.jpg[/qimg]

Dear Jack,

On the number line you took away 3 hundreds ok but then you only took away 6 instead of 16.

Next time try to take away 3 hundreds, then take away 1 ten and then take away 6 ones.

So taking away 316 is like taking away 3 hundreds, then 1 ten then 6 ones.

Keep practicing, you'll get it!

Cheers,
Jeff

 

[Dancing David]

This convinces me even more that the folks coming up with the core requirements and tests have no concept that some kids simply cannot do math. At least those kids have a vague chance with rote problems, but certainly not with explanations.

Again, I want to add three physical education requirements to the core.

~~ Paul

Hi Paul, this is SOP for the 'extended response' in the ISAT test that Illinois has used for at least ten years.

The teachers go over it with the students and have sample rubrics on the walls in poster forms. So for our state it is nothing new.