I drank some of the Kool-Aid, but not all of it.
As the school year starts up, I have seen a lot of posting on Facebook about how Common Core Math is the worst thing in the entire world for kids. Three months ago, I might have agreed with you, but here's the thing, I am a student in the College of Education working towards a degree that will allow me to work with students who have learning disabilities. And as such, I had to take a class called "Math Methods" which taught us how to use different techniques to work with those types of students.
I should stop and explain (in case you didn't know) more schools are adopting a multi-tiered form of special education services. This means that as much as possible, schools are including students who have mild to moderate disabilities in the general education classrooms rather than secluding them in a room all unto themselves. That being said, this emphasizes the fact that there are students with a wide variety of learning styles. Additionally, (as most everyone knows), the US continues to fall behind China and other countries in math skills as demonstrated on standardized tests.
There are two reasons for this. The first is that our culture says that being good at something is due to our intelligence--something that we're born with--but not necessarily from hard work. So if we have trouble learning something new, we are, as individuals, embarrassed. We blame it on not being smart enough. However, in Eastern Cultures, the struggle to learn and the process itself is celebrated, applauded even. Read more here: http://www.npr.org/sections/health-shots/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning. There is some merit to Tiger-Mom mentality, they praise the process, the hard work done rather than the "A" received. We, as Americans, tend to tell our kids they're doing a good job whenever they finish a task, rendering the praise someone useless for all the qualities we want our kids to end up with like grit and perseverance. You read that book aloud with very few mistakes? Good job.
The second reason that our kids struggle in math is that our weakness is in conceptual math. What might that be? It's more about how students deal with abstract concepts, varying ways the problems present. I grew up in an educational system that stressed procedure and practice with math. So, my algebra teachers would show us the step by step process to completing a problem and then give us 30 problems per night to complete. Where did we all struggle? Word problems--what we call Application problems now. You had to take what you'd learned a step by step process for and translate that into a problem consisting only of words. Who didn't groan when I said Word Problems? I groaned, and I haven't done any for awhile, aside from the occasional, "if I want to buy this item and it's 20% off, how much is it?" problem.
And yes, when I read all the ridiculous Common Core math problems asking "Why is it true that your answer is correct?" I thought, DUH.. what's the point of that? "I learned it by memorization, so what's the point of having the student answer why?" Well, there isn't anything really wrong per se, except that the average American person can't figure out how to do a Word problem unless they have a procedure in place a step by step way to come up with the answer. I'm not talking to you engineers out there, btw.
Think about this... if you have a job, and it's a rote job where you do the same thing day in and day out, and you're learning the job, and someone tells you to do something new, and it makes no sense to you, doesn't it help if the trainer tells you WHY you have to do it that way? or Why it has to be done? Doesn't it help broaden your perspective? Doesn't it help you solve other problems you may encounter along the way?
So the Common Core 1+2= ? and why? is really about training students to ask Why and How these things are true so they can continue to ask those questions as they approach more complex problems.
I challenge everyone who "hates Common Core" to actually read the standards themselves. Here is the website to help you find them. http://www.corestandards.org/read-the-standards/ The math standards are unique in that they have what they call "Standards for Mathematical Practice" which are as follows:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
I should stop and explain (in case you didn't know) more schools are adopting a multi-tiered form of special education services. This means that as much as possible, schools are including students who have mild to moderate disabilities in the general education classrooms rather than secluding them in a room all unto themselves. That being said, this emphasizes the fact that there are students with a wide variety of learning styles. Additionally, (as most everyone knows), the US continues to fall behind China and other countries in math skills as demonstrated on standardized tests.
There are two reasons for this. The first is that our culture says that being good at something is due to our intelligence--something that we're born with--but not necessarily from hard work. So if we have trouble learning something new, we are, as individuals, embarrassed. We blame it on not being smart enough. However, in Eastern Cultures, the struggle to learn and the process itself is celebrated, applauded even. Read more here: http://www.npr.org/sections/health-shots/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning. There is some merit to Tiger-Mom mentality, they praise the process, the hard work done rather than the "A" received. We, as Americans, tend to tell our kids they're doing a good job whenever they finish a task, rendering the praise someone useless for all the qualities we want our kids to end up with like grit and perseverance. You read that book aloud with very few mistakes? Good job.
The second reason that our kids struggle in math is that our weakness is in conceptual math. What might that be? It's more about how students deal with abstract concepts, varying ways the problems present. I grew up in an educational system that stressed procedure and practice with math. So, my algebra teachers would show us the step by step process to completing a problem and then give us 30 problems per night to complete. Where did we all struggle? Word problems--what we call Application problems now. You had to take what you'd learned a step by step process for and translate that into a problem consisting only of words. Who didn't groan when I said Word Problems? I groaned, and I haven't done any for awhile, aside from the occasional, "if I want to buy this item and it's 20% off, how much is it?" problem.
And yes, when I read all the ridiculous Common Core math problems asking "Why is it true that your answer is correct?" I thought, DUH.. what's the point of that? "I learned it by memorization, so what's the point of having the student answer why?" Well, there isn't anything really wrong per se, except that the average American person can't figure out how to do a Word problem unless they have a procedure in place a step by step way to come up with the answer. I'm not talking to you engineers out there, btw.
Think about this... if you have a job, and it's a rote job where you do the same thing day in and day out, and you're learning the job, and someone tells you to do something new, and it makes no sense to you, doesn't it help if the trainer tells you WHY you have to do it that way? or Why it has to be done? Doesn't it help broaden your perspective? Doesn't it help you solve other problems you may encounter along the way?
So the Common Core 1+2= ? and why? is really about training students to ask Why and How these things are true so they can continue to ask those questions as they approach more complex problems.
I challenge everyone who "hates Common Core" to actually read the standards themselves. Here is the website to help you find them. http://www.corestandards.org/read-the-standards/ The math standards are unique in that they have what they call "Standards for Mathematical Practice" which are as follows:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Okay, I'm really only going to talk about a few of these, and not too in depth. Can anyone argue with number one? I mean, seriously. "Make sense of problems and persevere in solving them." I challenge you with number 2 as well... "Reason abstractly and quantitatively." They don't want this generation of kids to just do this rote memorization thing we've been doing for years, they want them to have a hard core understanding of what the numbers represent whether they are items (manipulatives) or abstract concepts. I think number 5 is pretty key "Use appropriate tools strategically." I mean, come on. Who hasn't met the guy that used a screw driver as a hammer?
In addition to these "Standards for Mathematical Practice" there are the standards that build upon one another for each grade level and each domain of math. There are eleven domains, things like "Number and Operations Base Ten, Measurement and Data, Geometry," etc. Each domain builds upon previous steps, of course some of the domains interact in ways.
Here, I'm posting a few of the Kindergarten standards. You tell me what's wrong with them:
Count to tell the number of objects.
CCSS.MATH.CONTENT.K.CC.B.4
Understand the relationship between numbers and quantities; connect counting to cardinality.
Understand the relationship between numbers and quantities; connect counting to cardinality.
CCSS.MATH.CONTENT.K.CC.B.4.A
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
CCSS.MATH.CONTENT.K.CC.B.4.B
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
CCSS.MATH.CONTENT.K.CC.B.4.C
Understand that each successive number name refers to a quantity that is one larger.
Understand that each successive number name refers to a quantity that is one larger.
CCSS.MATH.CONTENT.K.CC.B.5
Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
Soooo... sounds okay, right? It says nothing about the WAY teachers get the kids to meet these standards, but the Standards for Mathematical Practice dictates that kids need to know WHY it works that way. Now, I know we memorization freaks like the old way. "It just is b/c it is." But first of all, isn't that like saying "It is what it is," which isn't that the most annoying phrase anyone can possibly say, ever? And here's the thing: IT'S NOT A REAL ANSWER TO THE WHY. The explanation part of this is translating the numbers into words... so they can eventually tackle the......WORD PROBLEMS. haha! So there!
And when kids are little, they aren't able to "picture" numbers, quantities. They do not have the brain capacity yet to understand that 5 is ***** things, to them numbers are like the alphabet, just squiggly lines they have to try to memorize and put together. So guess what they use to help young students understand numbers? MANIPULATIVES. That's right, ol' procedural math buddies of mine, that's how they get young kids to understand that numbers aren't just squiggly lines, they are representative of ITEMS. Whether that item is a watermelon, bananas or two sided chips, that's the purpose of the manipulatives.
So is any of the above BAD? It's bad for you parents of children who are working with a procedural math base, but is it really bad for your kid to learn to use manipulatives to get a more concrete understanding of math? And by the way, they do carry on with the manipulatives through most of sixth grade and sometimes into algebra. Because it helps make the concepts concrete in their young brains.
I have one more piece of evidence that teaching math this way is better than the old procedural way that we all learned it. And that's a study (I'm hoping to get a link to it to put here because there are nifty videos included of a child working on the problems both procedurally and then conceptually), that my professor showed us, which helped sell me on this idea. A fourth or fifth grade math teacher was teaching math conceptually, but for one lesson (on mixed fractions), she taught half of the class by having them draw out the fractions as circles which they cut into parts. So they could draw 9/4 as two circles consisting of four pieces each, and then write it as a whole number and its fraction. So that's 2 1/4--they could see the two whole pies and the 1/4 left over. The other half of the class, she taught them to divide the numerator by the denominator and then subtract to come up with 2 1/4 (that's the procedural way, in case you didn't remember).
The end of the first week, she quizzed both groups on that task, and they scored about the same. BUT (wait for it) when she re-assessed them on the skill 3 weeks later, the scores of the ones who learned it conceptually were significantly HIGHER than those who learned it procedurally. The kids who learned the step-by-step procedures FORGOT how to do it.
Boom.
So tell me again why you don't want your kid to learn math this way. Think about all the math you took in junior high and high school. How much of it do you remember? Are you just mad because you can't help your kids with their simpler math skills now? If that's the case, get yourself onto Khan Academy or do a YouTube search. There are TONS of video links for CC math. Since I didn't go to college for um, well, a long time after I graduated high school, I tested into intermediate algebra when I went back in. And I was able to pick it back up fairly quickly, but think about the kids that had a hard time learning the math the first time. I tutored a girl in Basic Math at Kent who couldn't persevere through the problems to pass the class... it took her three tries.
There is a lot you can say about Common Core. There really is, and I'm sure my little blog post will do little to dispel the negativity that's up. The parents writing on tests that when the kid gets a job they'll have to do things in the easiest way possible, blah blah blah. The kid isn't an adult yet. And there is a direct correlation between a person's math skills and their future career/income. The more math you have to take in college, the higher your income will be.
So the Kool-Aid I didn't drink about Common Core is the amount of testing that they require to see if progress is being made. I think that having similar standards across the states is okay--as long as we aren't all forced to use the same methods to teach those standards (which, in most cases, we aren't). Teachers still have the option to teach the way they want, but they have to think more about how to address the learning goals. And I do not see anything wrong with that.
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