Is Common Core Math Good or Bad?

[tuckerkao]

Good: If you and your kids are frequently counting in binary, octal, dozenal and hexadecimal, Common Core Math offers the potential abilities to convert in between bases without using the calculators. Convert 1 dozen inches to 1 foot back and forth very quickly. Convert pound to ounce using hexadecimal methods.

Bad: If you are a decimalist who only count in 1 single math base, Common Core Math will cost you and your kids triple to quadruple amount of time to finish simple equations while not harvesting the best fruits out of it. Much like requiring someone who doesn't play video games to buy a $1,000 Video Card.


Example 1: [Decimal] 12 + 7 = 12 - 2 + 7 + 2 = 10 + 7 + 2 = 17 + 2 = 19 (much more complicated than just 12 + 7 = 19)

[Octal] 12 + 7 = 12 - 2 + 7 + 2 = 10 + 7 + 2 = 17 + 2 = 20 + 1 = 21 (convert math base in a smart way.)


Example 2: [Decimal] 254 - 87 = 3 + 10 + 100 + 54 = 113 + 54 = 167 (much more complicated than just burrowing digits)

[Dozenal] 254 - 87 = 5 + 30 + 100 + 54 = 189 (smart way to figure out dozenal subtractions)


I can totally understand why Bill Gates support the entire Common Core Math programs and invest in large amount of funds and efforts to develop it because he's the master of all the computers.

 

[Timsup2nothin]

All math is good.

 

[Ajidica]

Don't know, don't care.

 

[amadeus]

I don’t know, but the explanations I’ve read of it to parents came off as condescending and combative.

 

[civvver]

I don't think it has much application outside of engineering sciences. I think teaching kids how logic works is more important.

 

[Truthy]

As far as I know, Common Core emphasizes "understanding" a lot and doesn't say much about teaching methods. However, lesson plans and textbooks that conform to Common Core seem like they try to give kids a good sense that numbers and operations are always just things you can manipulate as needed, not things you need to memorize or solve directly. For example, instead of directly computing 24 * 5, you turn 5 into 10 / 2 and instead do (24 / 2) * 10 = 12 * 10 = 120. Or solve 17 * 6 by turning it into (10 + 7)(6) = 60 + 42 = 102. And they're taught things like division as repeated subtraction and so on.

To me, this is fine and well and could give kids a better understanding of math. And then when they start, say, multiplying polynomials in middle/high school, they realize it's just the same thing they've been doing all along.

However, it also seems like a lot of teachers complain that under Common Core, "math facts" that ought to be memorized aren't emphasized enough. For example, a kid will turn 17 * 6 into (10 + 7)(6), but then won't be able to figure out 7*6. Or by 6th grade, students are still manually doing repeated subtraction instead of just dividing, so it takes them forever to do anything. Another issue seems like it still boils down to decent problem solving, which is hard to teach. You have to quickly realize how to simplify a problem into easier subproblems. I imagine a lot of kids struggle with that and there isn't much teachers can do to help them.

It also seems like Common Core math techniques are all things people who are at least slightly good at math realize and adopt on their own at some point. And then I wonder if education policy people aren't just teaching children to emulate understanding, resulting in a lot of kids memorizing little math tricks and algorithms, but still having weak fundamentals.

 

[Manfred Belheim]

[Octal] 12 + 7 = 12 - 2 + 7 + 2 = 10 + 7 + 2 = 17 + 2 = 20 + 1 = 21 (convert math base in a smart way.)

Having never heard of common core math(s), can you explain WTH is going on here?

Edit: I mean I get that 12 + 7 = 21 in octal, I just don't see what is being simplified or converted by going through this series of substitutions.

 

[hobbsyoyo]

However, it also seems like a lot of teachers complain

IMO a lot of teachers complain about change, period. What is especially frustrating is any time a new system of teaching or for tracking learning is used, everyone immediately attacks it as a failing, unworkable system. The truth is that the nature of education means a new policy/system needs at least 5 years to show results, and I'd argue a full assessment really can't be done until you've had entire an cohort go through the updated system from birth through secondary school.

 

[civvver]

My 2nd grader struggles with this with regards to reading and writing. She has a fantastic memory and her reading vocabulary is large but when she encounters a word she doesn't know she doesn't know how to figure it out, at least not as well as she should. She struggles learning the techniques to analyze a word or spell it correctly, and is relying very much on rote memorization. She's better at it with math, actually has to employ counting and concepts to figure stuff out and it's the reverse, she has done very little memorization. I find it kind of fascinating that she hasn't memorized 12 + 7 for example but she'll employ a concept like well I know 10 + 7 = 17 and so I add 2 more, yet has memorized longer word patterns like environment or imagination. Yet if she encountered one she didn't know like Idk, concept, she probably couldn't figure it out on her own, since she would forget the strategy regarding ce sounds. Really trippy to me.

 

[Truthy]

IMO a lot of teachers complain about change, period. What is especially frustrating is any time a new system of teaching or for tracking learning is used, everyone immediately attacks it as a failing, unworkable system. The truth is that the nature of education means a new policy/system needs at least 5 years to show results, and I'd argue a full assessment really can't be done until you've had entire an cohort go through the updated system from birth through secondary school.

Parents too
Edit: in some cases, more than 5 years, too. For example, pre-school shows strong results for a few years, but the gains generally don't persist into puberty or adulthood.

 

[rah]

Or solve 17 * 6 by turning it into (10 + 7)(6) = 60 + 42 = 102.

how is this any different than?

17
X6
---
42
6
102

 

[Truthy]

how is this any different than?

17
X6
---
42
6
102

It's not, really. But that's because in my example I directly just split up 17 according to the tens places. You don't have to do it that way if you're able to break the numbers up in other convenient ways.

 

[rah]

It sound's like it just makes it more complicated. I get that it probably teaches the underlying concepts better, but the final result is what's most important since only about 1% of the population actually needs to understand the underlying concepts better I don't see the benefit that others claim.

 

[GenMarshall]

Looking at it, and math is not my strongest subject. I feel that it just complicated things even more. Just give me a formula and I’m happy as a clam.

 

[The_J]

It's a formula .

I had to look it up what this actually means. I've been doing this for ages.
It's just splitting up a problem into convenient subproblems. So... I'd say... what's the deal ^^?
(but then again, I have a PhD in a vaguely math related field, so I'm not representing the average)

 

[tuckerkao]

how is this any different than?

17
X6
---
42
6
102

Common Core Math slows down Decimalists(who only count in base ten) because this base isn't favorable to the divisions of 3 and 6.

Count by distance between numbers only very useful when calculating in other bases where people need to figure out the subtraction number between the new 10 and the largest single digit number.


[Dozenal] This example still not the best 1 to show the advantage.

17
×6
96

17 × 6 = 60 + 36 = 96 as 6 Dozens + 3 Dozens 6 = 9 Dozens 6


[Dozenal] When the new symbols involve in, Common Core Math methods show it's best strength, so no base conversions needed.

_17
×15
22Ɛ

17 × 15 = (10 + 7) × 5 + (100 + 70) × 1 = 50 + 2Ɛ + 100 + 70 = 100 + (70 + 50) + 2Ɛ = 100 + 100 + 2Ɛ = 22Ɛ

or 17 × 15 = 16 × 16 - 1 = (10 + 6) × 6 + (100 + 60) × 1 - 1 = 60 + 30 + 160 - 1 = 160 + 60 + 30 - 1 = 200 + 30 - 1 = 230 - 1 = 22Ɛ


Given the fact that the person hasn't fluently learned the basic multiplication tables in the new base yet.

 

[Truthy]

It's a formula .

I had to look it up what this actually means. I've been doing this for ages.
It's just splitting up a problem into convenient subproblems. So... I'd say... what's the deal ^^?
(but then again, I have a PhD in a vaguely math related field, so I'm not representing the average)

Yeah, exactly. I believe a lot of it boils down to divide-and-conquer approaches, where kids split things up into easy subproblems. And the idea is they need to have a good conceptual understanding of numbers to be able to do that. And that ability will help them in algebra later on.

Anecdotally, most people who have quantitative backgrounds (and a lot of people with any background?) are the same as you, here. It's how I do math both in my head and by hand. And I sometimes ask friends how they do mental math. It always involves some rearranging, breaking things up, or factoring, followed by quickly solving the subproblems and combining the results. Symbolically, it seems complicated, but actually it's very efficient. I don't think many people who are currently adults were taught to do arithmetic this way, but many people seem to adopt it on their own.

 

[tuckerkao]

but actually it's very efficient because you can do each of the subproblems in a small fraction of a second.

Common Core Math Fractions show on the pies which you divide them into 3rds and 4ths and visually very appealing.

Now in Dozenal, if I want to figure out 1/2 = 0.6, 1/3 = 0.4, 2/3 = 0.8, 1/4 = 0.3, 3/4 = 0.9, I have to do it in the common core math methods to avoid mistakes until familiar with that base.

It however won't make any sense to only factorizing the denominators of the fractions because people will immediately think back to Decimal instead of Dozenal.

The good question is that those who have invented Common Core Math, do they want the kids to learn at least 2 math bases in the future?

And the idea is they need to have a good conceptual understanding of numbers to be able to do that.

The best way to develop up strong conceptual understanding of the numbers is to count in different bases, unfortunately most people don't.

It's a formula .
I've been doing this for ages.
It's just splitting up a problem into convenient subproblems. So... I'd say... what's the deal ^^?

The deal for splitting up a problem into easier sub-problems is only necessary when reaching out formula in other math bases where you aren't familiar with, thus able to calculate pretty much in all the bases.

 

[hobbsyoyo]

Parents too
Edit: in some cases, more than 5 years, too. For example, pre-school shows strong results for a few years, but the gains generally don't persist into puberty or adulthood.

Parents are absolutely terrible in so many ways. I don't share here most of the abuse my wife and her coworkers are subjected to, but I did recently mention the police had to get involved due to threats against one of her coworkers. That was the worst recent example of abuse, but it's all too frequent and covers the entire spectrum of potential abuse from racist rants to sexual harassment and threats of violence.

 

[rah]

Yeah, exactly. I believe a lot of it boils down to divide-and-conquer approaches, where kids split things up into easy subproblems. And the idea is they need to have a good conceptual understanding of numbers to be able to do that. And that ability will help them in algebra later on.

Anecdotally, most people who have quantitative backgrounds (and a lot of people with any background?) are the same as you, here. It's how I do math both in my head and by hand. And I sometimes ask friends how they do mental math. It always involves some rearranging, breaking things up, or factoring, followed by quickly solving the subproblems and combining the results. Symbolically, it seems complicated, but actually it's very efficient. I don't think many people who are currently adults were taught to do arithmetic this way, but many people seem to adopt it on their own.

Yeah, when I think about it that's how I do it in my head, but on paper I'll do it the old way.
But then I'm a statistical programmer so I'm not the norm either.