What's Wrong with American Math? (And can Common Core save it?)

Saint_ · Post by **Saint_** » Sun Jan 01, 2017 2:47 pm

American math is totally broken. Pretty bold statement, eh?

So how would I know? Ok...I'm not only a teacher, I'm an upper division math teacher. Which means that I should be dealing with the highest level of math and the most capable of students. I also should know my stuff (content area and discipline) the best of all teachers. After all, you don't have to know the Quadratic Formula to teach 3rd grade math, now do you? Moreover, since I have taught full time Day School (normal school) for 25 years, full time Night School (credit recovery and remediation) for 24 years, and Summer School (Intensive credit recovery) for 23 years, I have many more thousands of classroom hours than any other teacher I ever heard of.

So imagine my confusion and chagrin when, every year, I get students into my class after twelve years of public, private, and charter education (it doesn't seem to matter which, although some of the brightest have come from home schools. Sadly, they always seem to be sadly lacking in social skills)...and they, collectively, as a class, cannot tell me what 9 times 12 equals!

Things like times tables, fraction rules, and simple formulas for area and perimeter are nonexistent. Nightmarishly simple concepts such as the undefined division by zero, or why a certain type of fraction repeats when it is turned into a decimal bring a look of fear and confusion to their eyes. It's truthfully heartbreaking. Don't believe me? Go ahead, ask any 14 to 18 year old you know what 9 times 12 equals and you'll see what I mean. Ask them for the area of a circle, or even the square root of 121! (Warning: You will probably have to explain what a square root is)

Here's the problem, before we begin discussing whether or not Common Core is the solution to it or a detriment to it: American math students have completely lost their (what I call) "math sense." When you and I (and now I'm assuming you are as old as I am, around 60) grew up, we did all the math, by hand, without a calculator. (and believe me, our textbooks were actually more rigorous than today's! I still have a couple around for when I want to really challenge my classes)

When you do math that way, you develop an understanding of the basic principles of math, such as the fact that two large numbers multiplied together become and even larger number. Multiplying by a fraction makes things smaller, but dividing by one has the inverse effect. In short, you develop a sense to the patterns of math, and math is all about patterns. Just like speech and speech patterns, math is just a language we invented to describe things that cannot be described by words.

Now, why did American students lose their math sense? That answer is extremely complicated. Of course the obvious answer is to say, "They rely on calculators now at way too early of an age." Believe me, that has to be a part of it. But there are many other considerations:

1. The Breakdown of the Traditional Family - My mother was almost solely responsible for teaching me my times tables. But she was a stay-at-home mother 24 hours a day? What family can afford that now?

2. Poverty - With the breakdown of the family structure and the increasingly large gap of income inequality, not only do both parents work, but there is very rarely time together as a family to talk and teach. Especially around the dinner table where I once did the majority of my homework. With my students, and granted I work with low-income and poor students, not only is there no time together, there is often not even a space to work! What a luxury my own desk in my bedroom was!

3. Mandatory Advancement - The verdict is still out on whether retention is good or bad, (most say it doesn't work) but I can tell you that there was always one kid who had flunked the 3rd grade three times and had a mustache on the playground that was the most powerful deterrent to the rest of us to not flunk any classes. Poor JimBob... It used to be, if the school said that a student was nowhere near enough proficient to handle the next higher grade level, the parents bowed to our judgement. We gave that away. Now a student can flunk every single math class in their twelve years of school and still be passed forward! Their fate? They can't pass the standardized tests and they drop out. (Oh, and by the way, the teacher takes the hit for that!) How is that doing the student any favors. Education is trying hard to fight back with intensive and targeted remediation and practice, but sometimes, (I have the names of students I must spend extra time with written into my lesson plans) that's all but impossible in large classes.

4. A Lack of "Expectation of Education" in the home - Want to know which demographic succeeds where all others fail? Asian-Americans, even if they are first generation off the refugee boat! Want to know why? In their families, you are expected, from birth, to succeed and become educated. They are not OK with a "C" or even a "B". It's Doctor, Lawyer, or Engineer or you aren't a part of the family. Intense? You bet. Results? Yep.

5. Lastly, and perhaps most importantly: The Death of Reading - They closed down my school's fine, well-stocked library. Why? They needed another computer lab. They gave all the books away for free. Guess who picked them up? The teachers. The students wanted no part of them. I hear students brag all day long that they "don't read!"

Why would reading impact math ability and scores? Because for math you MUST have an imagination. Math is all about creative problem solving. That requires both logical thinking and abstract, imaginative reasoning. Everything my students do all day long is pre-imagined for them! Movies? Pre-imagined. Videogames? Sure they're interactive, but the game itself is pre-imagined. The internet? Pre-imagined. TV? Pre-imagined. Apps? Pre-imagined. I've learned not to ever start a sentence with, "Imagine that you..." because they have mostly lost that ability. What is one of the best ways to develop imagination? Reading.

Part II: Common Core

As much maligned as it is, you can see now that Common Core tries to do two things with varying degrees of success:

1. Encourage imaginative thinking and creative problem solving, especially relating to real world math. (In one of my old books, it shows a son and his father using a Trigonometry table and primitive surveyor's transit to level and drain cropland and their barnyard. No wonder we used to be so good at math!) In other words, restore 'math sense."

2. Make sure that everyone in the country is learning the same things at the same time so that if you transfer to another state, a serious problem in the mobile age, you won't be left behind or fall through the cracks of the system. hence the word "Common." The common we refer to is driven by what businesses have told us that they want students to be able to do.

Here's a good example of what I mean:

Old School: Find the Area of the 8 foot by 12 foot rectangle given: Area = Length times Width

Common Core: If a swimming pool is twice as long as it is wide, how many concrete bags would it take to make a 2 inch deep by eight foot wide border around it? (One bag of concrete equals one cubic yard of concrete)

See the difference? The second problem is not only massively more rigorous than the other, it takes place in the real world, and tries for skills that would actually be used on a job.

See the problem? With broken math skills, this is a nightmare for both teacher and student. Now take away a third of the classroom time we used to have for standardized testing. Now add in the fact that each student averages around 30 absences per school year these days...

tude dog · Post by **tude dog** » Sun Jan 01, 2017 3:37 pm

It isn't the math. I think your five other considerations: carries the day.

I don't have your vast experience but growing up we moved a lot and I went to a number of schools. Didn't need a scholar tell me about different demographics affecting overall student performance.

Common Core or old school doesn't matter if students don't have the motivation or good interest.

I can't comment on common core, but even from the CC example you gave you still need the basic old school basics.

Actually, the CC reminds me of algebra word problems which I always hated.

Take away their calculators and hand them slid rules their heads should explode.

Post by **LarsMac** » Sun Jan 01, 2017 3:50 pm

Seems to me that whatever "Common Core" actually means in education, it should mean defining the core requirements for basic education.

As Saint stated, if students cannot handle even the rudimentary tasks of multiplication and division, hitting them with either of those two example questions will lead to failure.

Once the basics are understood, then the adventure of finding solutions to problem is just a matter of how you think about the problem, and how you go about collecting the the information to solve it.

And, by the way, it seems to me that the Common Core example in the OP may need a little more thinking. Read the question and first decide whether you have enough information to actually determine a workable answer.

Saint_ · Post by **Saint_** » Sun Jan 01, 2017 4:11 pm

LarsMac;1504809 wrote: Seems to me that whatever "Common Core" actually means in education, it should mean defining the core requirements for basic education.

Yep. We talk about a "ladder" of skills. What we are seeing is students, who are actually intelligent and could use a formula and even understand what it does, but cannot add or subtract. It's like trying to climb a ladder when the first three rungs are missing.

One thing I have hope for is that we have been talking about sending math tutors down to the elementary grades to teach alongside the elementary school teachers. Elementary school teachers never received training on how to teach basic math in the past. They didn't need to, the math was so basic and most of it was taught by the parents anyway.

Now the math they are teaching is extremely advanced compared to what they were used to. (Linear equations in the 5th grade!) They are struggling with teaching math at a level even some of them are not used to.

Which reminds me, the level of math, overall, has increased by about two grade levels. Some of the math I teach my students in Algebra II was the same math I learned in my high school Calculus class. And some of it I learned the third year in Engineering College! One problem the other day, solving a system of quadratic and linear equations, I couldn't even find in any of the massive collection of textbooks I have accrued over the years! Did I say the elementary math teachers are struggling?! Sheesh!

How to Solve Linear / Quadratic Systems of Equations

Saint_ · Post by **Saint_** » Sun Jan 01, 2017 4:15 pm

LarsMac;1504809 wrote:

And, by the way, it seems to me that the Common Core example in the OP may need a little more thinking. Read the question and first decide whether you have enough information to actually determine a workable answer.

HAhahaha! Good Catch! I made that up in my head from what I remembered of a similar question, but I forgot to put in the Area of the pool! OK, assume the area of the pool is 200 square feet. (If you want to try to work the problem out!)

Post by **LarsMac** » Sun Jan 01, 2017 4:29 pm

There was a series of "math" puzzles flying around Facebook a while ago. Relatively simply math stiff, assuming you know simple math, I guess.

The questions were basic math equations for which the solutions required a basic grasp of the order of operations.

I was shocked to see that two people I knew to be fifth and sixth grade math teachers actually missed the answers.

Saint_ · Post by **Saint_** » Sun Jan 01, 2017 4:33 pm

Yeah, it was pretty depressing. I'd say 95% of my friends on Facebook, including family and other (non-math) teachers missed those kinds of problems. Stuff like:

10 + 10 x 10 + 10 =

and

6 ÷ 2 ( 1 + 2 ) =

Sheesh! (Although that second one is a bit tricky...)

Clodhopper · Post by **Clodhopper** » Sun Jan 01, 2017 4:54 pm

Oh Lordy...Can I remember any maths? Ok. I make the first one 120 and the second 1.

Have I remembered how to use BODMAS correctly?

Saint_ · Post by **Saint_** » Sun Jan 01, 2017 4:56 pm

Close. You got the first one right. By the way, I like your Monty Python "Life of Brian" quote.

Clodhopper · Post by **Clodhopper** » Sun Jan 01, 2017 5:13 pm

Augh! Then I won't start guessing the second.

Thanks regarding the MP quotation. One of my favourites

Oh and incidentally your comments on UFOs have stayed with me. I've no personal experience at all, but the testimony of someone with your experience has stopped me simply dismissing the idea of alien visitation.

Saint_ · Post by **Saint_** » Sun Jan 01, 2017 5:15 pm

Yeah, UFOs are one of those things that you just can't believe until you see one for yourself.

"I thought we were the Judean People's Front.."

"You idiot. We're the People's Front of Judea!"

Clodhopper · Post by **Clodhopper** » Sun Jan 01, 2017 5:30 pm

Splitter!

And to bed with a smile. Thanks

There's been little to smile about in the last year (and no sign of that improving in the year to come).

Post by **Bryn Mawr** » Mon Jan 02, 2017 4:33 am

Saint_;1504814 wrote: HAhahaha! Good Catch! I made that up in my head from what I remembered of a similar question, but I forgot to put in the Area of the pool! OK, assume the area of the pool is 200 square feet. (If you want to try to work the problem out!)

almost exactly three but it's a very small swimming pool

Post by **Bryn Mawr** » Mon Jan 02, 2017 4:37 am

Saint_;1504827 wrote: Close. You got the first one right. By the way, I like your Monty Python "Life of Brian" quote.

The second one is nine.

Post by **Bryn Mawr** » Mon Jan 02, 2017 5:16 am

Bryn Mawr;1504838 wrote: almost exactly three but it's a very small swimming pool

Damn damn and thrice damn - I calculated it to the length of the sides and forgot to make allowance for the corners.

With such a small pool that makes a significant difference and takes it up to 4 47/81 cubic yards

Post by **spot** » Mon Jan 02, 2017 5:34 am

Maths has a vocabulary and a grammar - BODMAS, mentioned above, is central to the grammar part. That and the vocabulary, made of the essential equations and numeracy, have been ditched in favor of "imaginative thinking and creative problem solving" when they really must be precursors. Without the grammar and vocabulary there's no point trying to think through any of the imaginative thoughts or creative problems because the only tools to hand are blunt inappropriate toys.

I do think there's an exception to this. Anyone who can get meaningful clear information out of Mathematica using real-world data has got the job, regardless of what the job is.

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 7:56 am

Hey you guys, what is your mnemonic for "BODMUS?"

Because our similar rule is "PEMDAS."

"Please excuse my dear Aunt Sally." for:

Parentheses

Exponents

Multiply

Divide

Add

Subtract

Or "Purple elephants must dine at sunset," "Pink Emus must dance at sunrise" "Please electrocute mu dirty, aggravating sister" or even "Please eliminate my disgusting arithmetic subject." as my students have created in the past.

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 7:57 am

Bryn Mawr;1504839 wrote: The second one is nine.

Correct you are!

Post by **spot** » Mon Jan 02, 2017 8:24 am

Saint_;1504844 wrote: Hey you guys, what is your mnemonic for "BODMUS?"

BODMAS - Brackets, Order, Divide and Multiply, Add and Subtract.

I don't think I use any sentence-mnemonic for anything, it's easier just to recall the thing itself.

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 8:46 am

So "Order" is your word for "Exponents?" Fascinating.

Post by **spot** » Mon Jan 02, 2017 9:32 am

I expect it's most often seen in "order of magnitude".

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 10:19 am

Of course! And why not?

Post by **LarsMac** » Mon Jan 02, 2017 12:09 pm

So, back to the title, What IS Common Core?

Most of the Social media mentions of Common core break down into two categories.

1. Silly math problem-solving methods that fail to make much sense

2. Parents and Teachers fluttering on about how stupid Common Core is.

Even the web pages dedicated to the initiative is difficult to understand as far as what it really means.

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 2:25 pm

LarsMac;1504870 wrote: So, back to the title, What IS Common Core?

Common: A curriculum for teaching the same math the same way to all students. Core: The core skills needed to be successful in businesses, modern labs, and industries as stated by the businesses themselves.

The common part tries to instill more of the missing "math sense" I talked about. The core part emphasizes lots of the higher math you need for modern technological jobs.

Most of the Social media mentions of Common core break down into two categories.

1. Silly math problem-solving methods that fail to make much sense

They don't make sense to most people, because most people were taught in a strictly algorithmic way. Just the formula and how to use it. Not how to make your own formula. It's the difference between driving a stick and an automatic. most people were taught to drive automatics, so they don't understand a manual transmission...much less how they operate.

2. Parents and Teachers fluttering on about how stupid Common Core is.

It's a bitch. Seriously. And people HATE change, even if it's for the better. You have to work at it and people, especially some teachers I know, get stuck in their ways. Ever hear your parents saying, "Well we never did that in our day!" But you sure as Hell knew that it was necessary these days. Sadly, Common Core is too hard for many of them, even some teachers, so they hate it even more. Nothing like having to do something that makes you feel like an idiot after you thought you knew everything, eh? Hell, even I struggle with it. I was trying to write some of my own problems today to emulate some of the assessment problems and I could only emulate 18 out of 20 of them! The other two were too hard for me to design my own! And I've been doing this for a quarter century!

Even the web pages dedicated to the initiative is difficult to understand as far as what it really means.

Yeah, that's because modern education loves their teacher-speak, which, to be fair, is more necessary now that we understand much more about how people learn and how to teach correctly. I can't even talk about what I'm doing without acronyms and educationese.

For example, I am currently analyzing the fail/success ratios for the TLI Short-Cycle Assessment in order to design my own assessment-driven student-led tactics to increase scores on the EOC Assessments which are vertically aligned with the PARCC graduation test. The Algebra II EOC is so hard that it is an ADC for the PARCC! (Sh1t like that is what's driving teachers away in droves!)

You want to know the difference between the past and the present:

Past: Solve this equation.

Present: Write your own equation that models this problem in the real world. Then solve it.

I'll add this: Everyone thinks they know education better than the teachers. I used to wonder why that was. I mean, I'd never presume to go up to a doctor or welder and say, "Hey, you're doing that wrong." I don't know enough. But everyone from parents to politicians has no problem telling us what to do.

Then there's the whole thing about privatizing education because, believe me, there's a lot of money in it. That's the most horrifying thing happening by far. Can you ever run a school like a business to turn out children on an assembly line like a product while watching the bottom line? It's bad enough we're already stamping a number on a student's forehead on a certain testing day and determining their future from it. What if that child has divorcing parents or a stomach ache?

Post by **Bryn Mawr** » Mon Jan 02, 2017 2:30 pm

Saint_;1504890 wrote:

Past: Solve this equation.

Present: Write your own equation that models this problem in the real world. Then solve it.

If you look back at the old style exam papers (Pre 1960?) then we've moved back to the way it used to be done.

A far better method as it promotes and shows understanding of the concepts rather than just manipulating the formulae

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 2:34 pm

Bryn Mawr;1504893 wrote: If you look back at the old style exam papers (Pre 1960?) then we've moved back to the way it used to be done.

A far better method as it promotes and shows understanding of the concepts rather than just manipulating the formulae

Bingo. You pegged it. That is Common Core to a tee.

(My theory is that sometime around the early to middle 1980s, we stopped being rigorous and started babying students. We stopped retaining students. Gave away a lot of our power to politicians and parents. We didn't do them any favors. They just skated by and then found out they couldn't innovate and compete globally.

Now comes the reckoning....)

Saint_ · Post by **Saint_** » Mon Jan 02, 2017 2:38 pm

Oh, by the way Bryn. If you hear people bashing Common Core, remember this: It's because they are afraid of it.

That includes myself.

Post by **Bryn Mawr** » Mon Jan 02, 2017 2:48 pm

Saint_;1504895 wrote: Oh, by the way Bryn. If you hear people bashing Common Core, remember this: It's because they are afraid of it.

That includes myself.

In all walks of life people fear what they do not know - as it becomes familiar the fear recedes.

Post by **LarsMac** » Mon Jan 02, 2017 2:50 pm

So, I just found that they have updated the Common Core web pages since my last visit.

I can see why teachers and parents might just be uncomfortable wit the idea.

This link is to the introduction to Grade one standards.

Grade 1 » Introduction | Common Core State Standards Initiative

My first thought was, Holy ****! You expect that from first graders?

And all the teachers are looking at their students, and just shaking their heads.

Post by **LarsMac** » Mon Jan 02, 2017 3:07 pm

Don't get me wrong. I quite agree that there needs to be some sort of common standards from which we choose to educate all the children so that whatever state they travel to, they can be expected to be at least fairly close to expectations.

I traveled a lot when I was a kid, in a new school, and often a new state, every year.

My first and second grade were in the Los Angeles region. We then moved to Northern Alabama. Third grade there was at a school built for the children of engineers and scientists working on the Space Program. After that I moved to a standard Alabama school district. The difference was remarkable. I had studied much of the 4th grade curriculum while in second and third grades. I ended up helping several other kids figure things out, until the teacher put a halt to that because I was "undermining her authority"

Suddenly I was a troublemaker. Oddly enough, THAT reputation followed me through the rest of my public school experience. North Carolina, Florida, and Georgia were very lackluster in their educational goals, and their teaching staff were authoritarian has-been coaches and little old ladies on power trip.

The only reason I stuck around long enough to get my diploma was because in those days poorly educated young men often ended up either in prison or on all-expense-paid extended vacations in beautiful Indonesia. My guidance counselor threatened me with both, quite often.

Had the states been more standardized, I may have continued my development and met my full potential. (I'm thinking MIT, Standford, Cal Tech, perhaps.) Instead, I fell off the grid from shear boredom before I even made my teens.

No sob story, just an observation. There are far too many people for whom I suspect that would be a familiar story.

Ahso! · Post by **Ahso!** » Mon Jan 02, 2017 3:24 pm

I had a pretty lousy time in school and in turn made it about as unbearable as possible for the school. I didn't want to be there and they didn't want me there. But I'm doing fine and I'm quite happy with my life. Then again, I'm the right gender and color too. Based on behavior and attentiveness there are lots of females and people of color at least as deserving of my life and have been denied it.

Wandrin · Post by **Wandrin** » Mon Jan 02, 2017 7:32 pm

I had a very good teacher in hs math. He could see that I was bored and would assign me special projects to work on, such as building a boolean algebra calculator out of junk parts. He would also give me books to read about the overlap between math and philosophy. He managed to get me excited about it and that was a huge help.

magentaflame · Post by **magentaflame** » Mon Jan 02, 2017 7:48 pm

Saint_;1504802 wrote: American math is totally broken. Pretty bold statement, eh?

So how would I know? Ok...I'm not only a teacher, I'm an upper division math teacher. Which means that I should be dealing with the highest level of math and the most capable of students. I also should know my stuff (content area and discipline) the best of all teachers. After all, you don't have to know the Quadratic Formula to teach 3rd grade math, now do you? Moreover, since I have taught full time Day School (normal school) for 25 years, full time Night School (credit recovery and remediation) for 24 years, and Summer School (Intensive credit recovery) for 23 years, I have many more thousands of classroom hours than any other teacher I ever heard of.

So imagine my confusion and chagrin when, every year, I get students into my class after twelve years of public, private, and charter education (it doesn't seem to matter which, although some of the brightest have come from home schools. Sadly, they always seem to be sadly lacking in social skills)...and they, collectively, as a class, cannot tell me what 9 times 12 equals!

Things like times tables, fraction rules, and simple formulas for area and perimeter are nonexistent. Nightmarishly simple concepts such as the undefined division by zero, or why a certain type of fraction repeats when it is turned into a decimal bring a look of fear and confusion to their eyes. It's truthfully heartbreaking. Don't believe me? Go ahead, ask any 14 to 18 year old you know what 9 times 12 equals and you'll see what I mean. Ask them for the area of a circle, or even the square root of 121! (Warning: You will probably have to explain what a square root is)

Here's the problem, before we begin discussing whether or not Common Core is the solution to it or a detriment to it: American math students have completely lost their (what I call) "math sense." When you and I (and now I'm assuming you are as old as I am, around 60) grew up, we did all the math, by hand, without a calculator. (and believe me, our textbooks were actually more rigorous than today's! I still have a couple around for when I want to really challenge my classes)

When you do math that way, you develop an understanding of the basic principles of math, such as the fact that two large numbers multiplied together become and even larger number. Multiplying by a fraction makes things smaller, but dividing by one has the inverse effect. In short, you develop a sense to the patterns of math, and math is all about patterns. Just like speech and speech patterns, math is just a language we invented to describe things that cannot be described by words.

Now, why did American students lose their math sense? That answer is extremely complicated. Of course the obvious answer is to say, "They rely on calculators now at way too early of an age." Believe me, that has to be a part of it. But there are many other considerations:

1. The Breakdown of the Traditional Family - My mother was almost solely responsible for teaching me my times tables. But she was a stay-at-home mother 24 hours a day? What family can afford that now?

2. Poverty - With the breakdown of the family structure and the increasingly large gap of income inequality, not only do both parents work, but there is very rarely time together as a family to talk and teach. Especially around the dinner table where I once did the majority of my homework. With my students, and granted I work with low-income and poor students, not only is there no time together, there is often not even a space to work! What a luxury my own desk in my bedroom was!

3. Mandatory Advancement - The verdict is still out on whether retention is good or bad, (most say it doesn't work) but I can tell you that there was always one kid who had flunked the 3rd grade three times and had a mustache on the playground that was the most powerful deterrent to the rest of us to not flunk any classes. Poor JimBob... It used to be, if the school said that a student was nowhere near enough proficient to handle the next higher grade level, the parents bowed to our judgement. We gave that away. Now a student can flunk every single math class in their twelve years of school and still be passed forward! Their fate? They can't pass the standardized tests and they drop out. (Oh, and by the way, the teacher takes the hit for that!) How is that doing the student any favors. Education is trying hard to fight back with intensive and targeted remediation and practice, but sometimes, (I have the names of students I must spend extra time with written into my lesson plans) that's all but impossible in large classes.

4. A Lack of "Expectation of Education" in the home - Want to know which demographic succeeds where all others fail? Asian-Americans, even if they are first generation off the refugee boat! Want to know why? In their families, you are expected, from birth, to succeed and become educated. They are not OK with a "C" or even a "B". It's Doctor, Lawyer, or Engineer or you aren't a part of the family. Intense? You bet. Results? Yep.

5. Lastly, and perhaps most importantly: The Death of Reading - They closed down my school's fine, well-stocked library. Why? They needed another computer lab. They gave all the books away for free. Guess who picked them up? The teachers. The students wanted no part of them. I hear students brag all day long that they "don't read!"

Why would reading impact math ability and scores? Because for math you MUST have an imagination. Math is all about creative problem solving. That requires both logical thinking and abstract, imaginative reasoning. Everything my students do all day long is pre-imagined for them! Movies? Pre-imagined. Videogames? Sure they're interactive, but the game itself is pre-imagined. The internet? Pre-imagined. TV? Pre-imagined. Apps? Pre-imagined. I've learned not to ever start a sentence with, "Imagine that you..." because they have mostly lost that ability. What is one of the best ways to develop imagination? Reading.

Part II: Common Core

As much maligned as it is, you can see now that Common Core tries to do two things with varying degrees of success:

1. Encourage imaginative thinking and creative problem solving, especially relating to real world math. (In one of my old books, it shows a son and his father using a Trigonometry table and primitive surveyor's transit to level and drain cropland and their barnyard. No wonder we used to be so good at math!) In other words, restore 'math sense."

2. Make sure that everyone in the country is learning the same things at the same time so that if you transfer to another state, a serious problem in the mobile age, you won't be left behind or fall through the cracks of the system. hence the word "Common." The common we refer to is driven by what businesses have told us that they want students to be able to do.

Here's a good example of what I mean:

Old School: Find the Area of the 8 foot by 12 foot rectangle given: Area = Length times Width

Common Core: If a swimming pool is twice as long as it is wide, how many concrete bags would it take to make a 2 inch deep by eight foot wide border around it? (One bag of concrete equals one cubic yard of concrete)

See the difference? The second problem is not only massively more rigorous than the other, it takes place in the real world, and tries for skills that would actually be used on a job.

See the problem? With broken math skills, this is a nightmare for both teacher and student. Now take away a third of the classroom time we used to have for standardized testing. Now add in the fact that each student averages around 30 absences per school year these days...

Its not just you.....as a parent i became increasingly frustrated.

My boys didnt know their times tables in grade five . I cracked it and made them learn at home by rote......GET THIS! A note came home to say that i should stop!

Apparently they should learn to 'understand whats behind the math rather than just repeat the math theyve heard.

What a load of cobblers . I knew my times tables by grade two.and figured out naturally what it had to do with fractions. High shcool for my boys had particular year groups (obviuosly under this curricular instruction) that struggled with maths....even the brighter kids . It serms the teachers eere reteaching maths that these year groups shouldve known in primary school.

ZAP · Post by **ZAP** » Mon Jan 02, 2017 8:12 pm

I am appalled when my 3 daughters whip out their little calculators (now on their phones) to figure out a simple tip on a check in a restaurant. They look at me in dismay as I do it quickly in my head. But I was always in first row in the Math classes, usually in first chair, and so were my 2 older brothers. My daughters are not dummies. Oldest is a teacher, 2nd is a microbiologist, third is an RN. It just seems that the calculator is the acceptable easy way of doing things today.

Post by **LarsMac** » Mon Jan 02, 2017 8:13 pm

magentaflame;1504924 wrote: Its not just you.....as a parent i became increasingly frustrated.

My boys didnt know their times tables in grade five . I cracked it and made them learn at home by rote......GET THIS! A note came home to say that i should stop!

Apparently they should learn to 'understand whats behind the math rather than just repeat the math theyve heard.

What a load of cobblers . I knew my times tables by grade two.and figured out naturally what it had to do with fractions. High shcool for my boys had particular year groups (obviuosly under this curricular instruction) that struggled with maths....even the brighter kids . It serms the teachers eere reteaching maths that these year groups shouldve known in primary school.

Yeah. You need to know the Math BEFORE understanding what's behind it. (In My Not-So-Humble Opinion)

Saint_ · Post by **Saint_** » Fri Jan 06, 2017 8:32 am

magentaflame;1504924 wrote: Its not just you.....as a parent i became increasingly frustrated.

My boys didnt know their times tables in grade five . I cracked it and made them learn at home by rote......GET THIS! A note came home to say that i should stop!

Apparently they should learn to 'understand whats behind the math rather than just repeat the math theyve heard.

What a bunch of crap! Times tables are so basic the only way they can be learned is by rote! Saying to stop is the equivalent of saying, "Stop teaching your child word like "is" and "the" because we only want them to know nouns. I certainly hope you told that teacher or school, "Forget you, I'm teaching my children any way I want, whatever I want, and any time I want!"

Saint_ · Post by **Saint_** » Fri Jan 06, 2017 8:35 am

LarsMac;1504926 wrote: Yeah. You need to know the Math BEFORE understanding what's behind it. (In My Not-So-Humble Opinion)

There's two kinds of math as we all know. Computational and Abstract. We all use computational arithmetic daily to add figures, estimate prices and sums, and keep track of measurements. We don't need to know squat about why arithmetic works to use it. Just like you don't need to be able to build a car engine to drive a car!

Abstract math, the ability to design new systems, circuits, invention, and solve new and unusual problems does take a higher level of reasoning, but there's plenty of time to get better at that in college and life.

Post by **LarsMac** » Fri Jan 06, 2017 9:19 am

Saint_;1505056 wrote: There's two kinds of math as we all know. Computational and Abstract. We all use computational arithmetic daily to add figures, estimate prices and sums, and keep track of measurements. We don't need to know squat about why arithmetic works to use it. Just like you don't need to be able to build a car engine to drive a car!

Abstract math, the ability to design new systems, circuits, invention, and solve new and unusual problems does take a higher level of reasoning, but there's plenty of time to get better at that in college and life.

The whole point of things like the times tables is that you don't have break out the calculator every time someone says something like "I can sell you 12 tomatoes at 8 cents apiece." or " I use 30 gallons of fuel to go 450 miles. Is my car really getting 22 miles per gallon?"

Ahso! · Post by **Ahso!** » Fri Jan 06, 2017 9:29 am

Why can't the seller just offer a total price? For the other example, the numbers might not be so rounded. Even among people who graduate, numbers may not be as simple for some.

Calculators are fine. What's the big deal? They're a tool that is used more so for some and less so for others.

Post by **Bryn Mawr** » Fri Jan 06, 2017 9:43 am

Ahso!;1505060 wrote: Why can't the seller just offer a total price? For the other example, the numbers might not be so rounded.

so one stallholder says "I've only got nine toms but you can have those for seventy five cents" when the other is saying "sure, they're yours for ninety six cents" - however you state it you need to be able to calculate one way or the other.

Ahso! · Post by **Ahso!** » Fri Jan 06, 2017 10:03 am

Bryn Mawr;1505062 wrote: so one stallholder says "I've only got nine toms but you can have those for seventy five cents" when the other is saying "sure, they're yours for ninety six cents" - however you state it you need to be able to calculate one way or the other.If money's that tight the only calculation the person needs to make is where to find another job.

ETA: I'd give em two bucks and take them all. Though Toms are not my kind of thing.

Post by **LarsMac** » Fri Jan 06, 2017 10:10 am

Ahso!;1505060 wrote: Why can't the seller just offer a total price? For the other example, the numbers might not be so rounded. Even among people who graduate, numbers may not be as simple for some.

Calculators are fine. What's the big deal? They're a tool that is used more so for some and less so for others.

Well, you can use your calculator if you want. One of my early jobs was working in a lumber yard. we'd get orders for so many board ft of 2x4, or so many Sq ft of 1/2 inch plywood.

If I had to break out my calculator for every order, I'd probably still have customer waiting in line for me to get there stuff.

Calculators are a fine tool, but then if you don't really know the math behind how to use them, you can get into trouble with them, too.

We were renting a house, and when we were preparing to move out, the landlord had some people come take measurements to replace the flooring.

One walked in looked around, estimated the square footage and gave a price that was 1.75 / sq ft for 960 sq ft.

The second guy came in broke out his tape measure, measured all the rooms, took his calculator and figured out a price that was 1.60 / sq ft for 1200 sq ft

The landlord and I broke out a tape and measured every room which would be re-floored. Our measurement? 958 sq ft

Guess which contractor got the job.

Ahso! · Post by **Ahso!** » Sat Jan 07, 2017 4:23 am

Ahso!;1505063 wrote: If money's that tight the only calculation the person needs to make is where to find another job.

ETA: I'd give em two bucks and take them all. Though Toms are not my kind of thing.Not that there's anything wrong with that, mind you.

FourPart · Post by **FourPart** » Sat Jan 07, 2017 7:48 am

Bryn Mawr;1505062 wrote: so one stallholder says "I've only got nine toms but you can have those for seventy five cents" when the other is saying "sure, they're yours for ninety six cents" - however you state it you need to be able to calculate one way or the other.
That's why stores now have to display their unit prices as well. Eg 7.5kg potatoes for 99p or 8.5kg for £1.15. Many shoppers might think that because they're buying more they're getting things cheaper, but this is frequently not the case. However, the first is 13.2p / kg. The latter is 13.6p / kg (rounded up). It's a common con trick used by the stores, but if people look at the units to actually compare like with like they get to see the real prices.

When I was at school, though, I couldn't handle maths (that's another thing - English includes the 's' in Maths, whereas American doesn't). My primary difficulty was understanding how it could be used in real life. I have still never had occasion where I've needed to solve a Quadratic Equation, and failed miserably in class. However, I later went on to go to College & qualify in Book Keeping & Accountancy, because I could see how that had a real life application. Similarly, I used to work for the British Trust for Conservation Volunteers on a project call Schools Environmental Education (B.T.C.V./S.E.Ed). Now, this wasn't just, as you might expect, just a matter of teaching kids about wildlife etc (although that did come into the curriculum quite a bit), but it would make use of the school's environment as a teaching aid. For instance, if you asked a kid approximately how many blades of grass on the football pitch all you'd be likely to get would be a pretty random response. However, you get them to chuck a quadrat (in this case a wire coat hanger) & count the blades of grass within that quadrat, and then to work out the area & multiply by the number of blades it not only increased their understanding of maths, but how it could be applied in the real world. And these were Primary School kids making quite complex calculations.

We woud also get them to write essays about their work (English). Make bird boxes (Woodwork). Take measurements of plant growth (Science / Botany) - all sorts of applications. Great fun.

Saint_ · Post by **Saint_** » Sun Jan 08, 2017 2:30 pm

Hey you guys, try this one. It's from a review I did on Wednesday for my brand new class...

Attached files

Post by **spot** » Sun Jan 08, 2017 2:31 pm

Ahso! · Post by **Ahso!** » Sun Jan 08, 2017 2:39 pm

One minute or less! Impressive!

Post by **LarsMac** » Sun Jan 08, 2017 9:01 pm

Ahso!;1505177 wrote: One minute or less! Impressive!

I bet he didn't use his calculator.

Post by **LarsMac** » Sun Jan 08, 2017 9:10 pm

As to the OP question, "Can Common Core save American Math"

From everything I have seen, so far, and from conversations with educators like _Saint, I fear not.

What started out as making a simple machine to perform a particular task, Improve and standardize Education across the several states and territories of the nation, has morphed into something that would give Rube Goldberg a migraine.

magentaflame · Post by **magentaflame** » Mon Jan 23, 2017 2:45 pm

Bryn Mawr;1505062 wrote: so one stallholder says "I've only got nine toms but you can have those for seventy five cents" when the other is saying "sure, they're yours for ninety six cents" - however you state it you need to be able to calculate one way or the other.

Are they of the same weight?