Anonymous wrote:

Anonymous wrote:Wow, if I had learned from the ground floor that there were lots of different ways to slice math problems, not all--but some--of which involve memorization, I might have been much more comfortable with math, and not have math anxiety as an adult. I'm very smart, but in other ways. And, yes, I did take calc AB in 11th grade, but had terrible anxiety about it.

This seems to me one of the points that people who argue against this thing don't (or can't) understand: people learn in different ways. Curricula built on Common Core strive to have children learn lots of different techniques--some using manipulatives, some using pictures, some using words or rote memorization--to give them the skills needed to figure out the best tactics later down the road.

FWIW, I had no problem with the directions on any of the worksheets posted here. And I think kids with these foundational skills will be able to use them later in harder more traditional math to answer problems quickly without anxiety.

Actually Common Core focuses heavily on language, putting all language impaired children at terrible disadvantage. I don't know one child doing well with these "standards" in special education.

+1

I agree with this. PP from above whose DS didn't understand the word "between." Math is actually one of his strengths, but when it becomes language heavy, he becomes impaired at that as well. A double whammy.

The language of math, even in word problems, is actually not that difficult. But for these children--really for all children--success requires the language to be very clear and precise. And what OP has shown is that many of the materials being passed off as CC fail utterly in the language department.

It would also help if those teaching it were explicitly made aware of language blocks many children may encounter in the way math is presented and be given effective strategies for dealing with it, a la the knife, spoon, fork exercise I described above.

I found Saxon math really good at this and by supplementing my DS with that at home I was able to help him enormously. But it was a lot to do with a child already tired from school and regular homework.

Anonymous wrote:Wow, if I had learned from the ground floor that there were lots of different ways to slice math problems, not all--but some--of which involve memorization, I might have been much more comfortable with math, and not have math anxiety as an adult. I'm very smart, but in other ways. And, yes, I did take calc AB in 11th grade, but had terrible anxiety about it.

This seems to me one of the points that people who argue against this thing don't (or can't) understand: people learn in different ways. Curricula built on Common Core strive to have children learn lots of different techniques--some using manipulatives, some using pictures, some using words or rote memorization--to give them the skills needed to figure out the best tactics later down the road.

FWIW, I had no problem with the directions on any of the worksheets posted here. And I think kids with these foundational skills will be able to use them later in harder more traditional math to answer problems quickly without anxiety.

Actually Common Core focuses heavily on language, putting all language impaired children at terrible disadvantage. I don't know one child doing well with these "standards" in special education.

Wow, if I had learned from the ground floor that there were lots of different ways to slice math problems, not all--but some--of which involve memorization, I might have been much more comfortable with math, and not have math anxiety as an adult. I'm very smart, but in other ways. And, yes, I did take calc AB in 11th grade, but had terrible anxiety about it.

This seems to me one of the points that people who argue against this thing don't (or can't) understand: people learn in different ways. Curricula built on Common Core strive to have children learn lots of different techniques--some using manipulatives, some using pictures, some using words or rote memorization--to give them the skills needed to figure out the best tactics later down the road.

FWIW, I had no problem with the directions on any of the worksheets posted here. And I think kids with these foundational skills will be able to use them later in harder more traditional math to answer problems quickly without anxiety.

Anonymous wrote:

Anonymous wrote:

This. These strategies are mental math tricks. Highly effective in understanding numbers. Countries who do well on PISA tend to emphasize these a lot more. I grew up in China and did all sorts of calculations like this.

I grew up in Russia. We had a very strong math curriculum and math culture when I was growing up. http://www.wsj.com/articles/SB10001424052748703740004574513870490836470

We did not do any of these tricks. We had a very strict, very rigorous system. We were not allowed to use calculators, at all. No multiple-choice answers EVER. We had to learn to prove all theorems ourselves. We had to memorize a lot of things. All the concepts were drilled, drilled, drilled to ensure we had a good foundation before moving on. I bet most of my Russian friends, after thirty years of not touching algebra or geometry will still be able to recipe Pythagorean theorem and solve a system of linear inequalities.

And no there was no way you would get to 7 by doing 4+4-1. My math teacher's favorite saying was "You shouldn't scratch a left year with a right hand", meaning that a math problem should be solved the simplest way.

I agree with PP. I don't see the link to critical thinking.

Well that is the point right there. You may not have a full recollection of your early childhood math foundations as much as you remember algebra. But, for your teacher to have used that quote, it would appear that, in addition to the drills (which we still do here too) you must have been shown that there were other ways and your math skills were refined to make you figure out on your own which was the best and fastest way. You may not remember the methods used in early childhood to give you this understanding that then enabled you to in upper level math to attempt to prove the theorems yourself. Here, by contrast, having only ever seen one way to do it and math facts drilled with no other skills or understanding added, our teachers would have had no reason to use that colorful quote. The process was expedited and the simplest method taught in a vacuum.

So your system, which you remember as drill drill drill (because we tend to remember the least pleasant parts), actually might not have been solely drill and kill, but more like the system that is being introduced now, which is aimed at giving kids mental flexibility with numbers so that they can learn to prove the theorems themselves later on instead of just trying to memorize proofs without understanding them. It seems that your contemporaries might remember the theorems better than mine because you figured them out on your own making mistakes along the way (correcting mistakes begets understanding), then memorized them; we just memorized them in a vacuum, and most of us without understanding them.

I was very good at math, and very nearly majored in math, but I hit a wall. Now that I am re-learning along side my children, that wall is coming down, and I am reading math books for fun and understanding everything on a whole new level. I see the value in my children not only memorizing that 3 + 4 =7, but also understanding that 3 + (2+2) = (4 + 4) - 1. Learning and understanding that at age 8 will make algebra at 12 a breeze.

I think of it as if you were "teaching" a child how to build with blocks. Most of us were taught math as if there was only one correct way to combine the blocks to build a house. We could repeat the procedure to build the structure, some of us faster than others, but we couldn't discuss it, and we couldn't explain why it worked, and we certainly couldn't come up with another way to build it, especially once we moved beyond basic math and simple algorithms.

Kids today are being taught the language of building and that there there are many ways to combine the blocks to build many different structures, and that there are pros and cons to each combination which they can discuss and then make choices based on the situation they are in. Included in that is the memorization of math facts and key algorithms the way we learned it (or tried and true building patterns, to continue the analogy). But our kids are going to understand those algorithms and why the work so well much better than we did.

Because we are starting this mental flexibility early, with problems that are otherwise "easy" to memorize, parents are freaking out because they want to see their kids just get the "right answer" as quickly as possible. Which misses the point of learning math entirely.

Just my view of it.

Anonymous wrote:

I grew up in Russia. We had a very strong math curriculum and math culture when I was growing up. http://www.wsj.com/articles/SB10001424052748703740004574513870490836470

We did not do any of these tricks. We had a very strict, very rigorous system. We were not allowed to use calculators, at all. No multiple-choice answers EVER. We had to learn to prove all theorems ourselves. We had to memorize a lot of things. All the concepts were drilled, drilled, drilled to ensure we had a good foundation before moving on. I bet most of my Russian friends, after thirty years of not touching algebra or geometry will still be able to recipe Pythagorean theorem and solve a system of linear inequalities.

And no there was no way you would get to 7 by doing 4+4-1. My math teacher's favorite saying was "You shouldn't scratch a left year with a right hand", meaning that a math problem should be solved the simplest way.

I agree with PP. I don't see the link to critical thinking.

You are saying, "I didn't learn it that way, so teaching it that way is wrong."

Note that neither the Common Core standards nor any specific curriculum (as far as I know) says that you have to solve 3 + 4 as 4 + 4 - 1. However, it is one way to do it. It is not the simplest way (in the sense of the least steps), and it's almost certainly not the way that the child will do it once the child has memorized their math facts. But it is one way to do it. And if you can do it that way, then you understand more about numbers than if you just memorized "3 + 4 = 7".

Also, the Common Core math standards don't say anything about "critical thinking". This is what they are aimed at: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

http://www.corestandards.org/Math/Practice/

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Singapore math is as Common Core as any other CCSS aligned math.

+1

Singapore math is a technique. CC is a set of standards. Some schools use Singapore math to reach the standard. Some use other techniques.

I wonder if the same parents who refuse to understand this are the same ones teaching their kids that Catholics aren't Christians.

Well, if all schools who adopted CC are teaching the same strategies, then you can say it's a common curriculum.

No, you can't say it, or at least you can't say it and be correct. Here are the first-grade Common Core standards for using place value understanding and properties of operations to add and subtract:

CCSS.Math.Content.1.NBT.C.4
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

CCSS.Math.Content.1.NBT.C.5
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

CCSS.Math.Content.1.NBT.C.6
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

The standards do not specify which strategies the child should be able to use. The standards only specify that the child should be able to use models/drawings and strategies and explain the reasoning.

(Singapore Math is a curriculum, but otherwise I agree with that PP.)

Anonymous wrote:

OP here. I looked through all the recent papers. My DD does fine on actual computation. What she does not understand is the CC strategy. Because she's using her own strategy. So her school work looks kind of like this below.

She solves similar problems in Singapore math just fine, just because the instructions are not so confusing.

There is no such thing as "a Common Core strategy". If what you say is correct, then your daughter is not understanding THE INSTRUCTIONS ON THE WORKSHEETS THAT SHE IS GETTING. That might be because she doesn't understand the terms. In that case, you should work on the terms with her. Or it might be because the instructions on the worksheets are unclear. In that case, you should talk to the teacher.

And if it's an issue with the instructions on the worksheet, then this is not a Common Core issue. This is an issue WITH THE MATERIALS YOUR DAUGHTER'S CLASS IS USING. There were unclear worksheets before the Common Core standards, and there will be unclear worksheets long after the Common Core standards are gone.

(Capital letters for emphasis.)

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Singapore math is as Common Core as any other CCSS aligned math.

+1

Singapore math is a technique. CC is a set of standards. Some schools use Singapore math to reach the standard. Some use other techniques.

I wonder if the same parents who refuse to understand this are the same ones teaching their kids that Catholics aren't Christians.

Well, if all schools who adopted CC are teaching the same strategies, then you can say it's a common curriculum.

Except they aren't all teaching the same strategies! In a district, yes. Often in different districts that have the same textbooks. But in every single district across the country no.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:These threads always drive home for me how much we need higher math standards, whether CC or otherwise. A generation of parents who, for the most part, barely understand math, and yet still want their kids to learn it just like they did.

Barely understand? I'm computer scientist. Do you know the level of math knowledge that requires? Do you know how I'm able to do it? Because I had a strong math foundation at school.

And I've written and published papers, using the strong reading foundation I had at school. That doesn't mean that I know how to teach a child to read. In fact, life is full of similar examples: I've given speeches, but I can't do speech therapy. I play the piano, but I can't teach piano. Knowing how to do something and being able to teach somebody how to do it are related but different skills.

+1

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Can you give examples of the kinds of problems your first grader has been given? My first grader is currently doing math mountains and word problems, not complex stuff for a parent to figure out at all.

Here are a couple of examples she gets from school. This is the kind where I go "what the f--- ?" On the bottom one I think they were told by the teacher to use only two numbers, not three. She wouldn't have thought of this herself.

The first one I would have skipped and told the teacher we decided not to do it because it was stupid. The second one should have been 3+3=6 6-3=3 I would think.

On the first one, it looks like your DD does not really understand what is meant by doubles, count on (a new term to me), and then of course double minus or plus one. It could of course be that she does understand, but the worksheet is asking the child to do two different things with each problem at the same time: solve the problem and identify what type of problem it is. And adds in the confounding problem of assigning colors to the type of problem. I could see where a child would have difficulty with shifting gears for each problem. Possibly okay if there had been sufficient build up--that is, plenty of exercises where the child had only to identify the three types of problem--by colors that were used consistently for each type--without solving.
them.

The second pag is a bit faint but it looks like she got it right. Bravo!

^^Above response was with regard the picture to the second worksheet posted with the message at 23:16, not to the later work sheets.

I agree the instructions are confusing. I could only enlarge the second sheet. It says, "Write to make a ten. Then add." Unless the process is explained well by the teacher in advance, coming to the worksheet cold would be very difficult for many students.

The problem is the student doesn't just make a ten. There is another step: the number used to make the ten for the first number must be subtracted from the second number, then the ten is added to the reduced second number. Confusingly, in the second problem, the second number in the equation is the one used to make the ten.

Why couldn't the first line in the picture say: Make a ten from the 9. _9___ + ____ = 10. Subtract the number you used to make the ten from the seven to find the difference 7 - _____ = _____. Add the difference to the ten ____ + 10 = ___.
So 9 + 7 = _____.

Could it be a failure of the teacher to not explain the process well?

I think people sometimes really underestimate the role of language in beginning math. I remember my language impaired DS having great difficulty with concepts like name a number between 3 and 10. He really didn't understand the meaning of between. My BIL who has done a lot of work studying math teaching recommended I spend some time with him on doing the following (I think this comes from Saxon) "game:" I placed a knife, fork and spoon on the table and asked him to place the spoon between the knife and the fork, the fork between the knife and the spoon, etc.

After a few short sessions of this over a few days, he was easily able to name a number between 3 and 10. I remember feeling how miraculous this exercise seemed.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Can you give examples of the kinds of problems your first grader has been given? My first grader is currently doing math mountains and word problems, not complex stuff for a parent to figure out at all.

Here are a couple of examples she gets from school. This is the kind where I go "what the f--- ?" On the bottom one I think they were told by the teacher to use only two numbers, not three. She wouldn't have thought of this herself.

The first one I would have skipped and told the teacher we decided not to do it because it was stupid. The second one should have been 3+3=6 6-3=3 I would think.

Sorry, couldn't see the photo when responding. Since it was addition only it was what I originally thought 6+3=9

3+3+6=

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Can you give examples of the kinds of problems your first grader has been given? My first grader is currently doing math mountains and word problems, not complex stuff for a parent to figure out at all.

Here are a couple of examples she gets from school. This is the kind where I go "what the f--- ?" On the bottom one I think they were told by the teacher to use only two numbers, not three. She wouldn't have thought of this herself.

The first one I would have skipped and told the teacher we decided not to do it because it was stupid. The second one should have been 3+3=6 6-3=3 I would think.

Sorry, couldn't see the photo when responding. Since it was addition only it was what I originally thought 6+3=9