Common Core Math

[Anonymous]

Anonymous wrote:

People keep saying that. But when I do math, I think in words.

Even if you are seriously challenged in math, I doubt this is true.

No, I'm not seriously challenged -- or maybe I am, but I nonetheless made it through various higher-level college math classes and work in a quantitative field.

Here's a word problem I did with my child last night. "Ann sold 188 apples at the market on Wednesday. She sold 64 more apples in the afternoon than in the morning. How many apples did she sell in the afternoon?"

Here's how we solved it: "OK, so Ann sold 64 more apples in the afternoon than in the morning. So in the afternoon, she sold the same amount of apples in the morning, plus 64. If I subtract 64 from 188, I get [do 188-64] 124 apples. Half of 124 is 62. So she sold 62 apples in the morning, and [do 62 + 64] 126 apples in the afternoon." (Or we could have, but didn't, say, "So she sold 62 apples in the morning, and [do 188-62] 126 apples in the afternoon."

Is this not the right way to solve it? How would you solve it?

[Anonymous]

How you solve it depends on the grade levels. You can solve it with algebra (2x+64=188) but before that you reason it through as you did. But I don't know how you teach a kid to reason it through.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

People keep saying that. But when I do math, I think in words.

Even if you are seriously challenged in math, I doubt this is true.

No, I'm not seriously challenged -- or maybe I am, but I nonetheless made it through various higher-level college math classes and work in a quantitative field.

Here's a word problem I did with my child last night. "Ann sold 188 apples at the market on Wednesday. She sold 64 more apples in the afternoon than in the morning. How many apples did she sell in the afternoon?"

Here's how we solved it: "OK, so Ann sold 64 more apples in the afternoon than in the morning. So in the afternoon, she sold the same amount of apples in the morning, plus 64. If I subtract 64 from 188, I get [do 188-64] 124 apples. Half of 124 is 62. So she sold 62 apples in the morning, and [do 62 + 64] 126 apples in the afternoon." (Or we could have, but didn't, say, "So she sold 62 apples in the morning, and [do 188-62] 126 apples in the afternoon."

Is this not the right way to solve it? How would you solve it?

Not sure what quantitative math field you are in.

Regardless, here is a generalization.
- Quantities that in a math problem can either be unknown or known regardless of apple/orange/fish/airplane.
- Processes are series of events/states regardless of Morning/Afternoon/at home/on buses/in school/with President/in a basket.

Mapping unknown/known quantities and processes to real life examples can be a subject within the field of applied math. However, most of time, mapping resides in other disciplines, i.e. physics, economics, etc.

Now, keeping apples/morning/afternoon in your solution is not quite a math way unless you want to confuse people particularly kids. Since if you switch apple to pear, morning/afternoon to at market a/b, kids will ask you for another "same" solution.

Keeping too much language aspects in earlier math material can potential slow down the development of the sense of math abstraction in kids' brain.

[Anonymous]

Anonymous wrote:

Not sure what quantitative math field you are in.

Regardless, here is a generalization.
- Quantities that in a math problem can either be unknown or known regardless of apple/orange/fish/airplane.
- Processes are series of events/states regardless of Morning/Afternoon/at home/on buses/in school/with President/in a basket.

Mapping unknown/known quantities and processes to real life examples can be a subject within the field of applied math. However, most of time, mapping resides in other disciplines, i.e. physics, economics, etc.

Now, keeping apples/morning/afternoon in your solution is not quite a math way unless you want to confuse people particularly kids. Since if you switch apple to pear, morning/afternoon to at market a/b, kids will ask you for another "same" solution.

Keeping too much language aspects in earlier math material can potential slow down the development of the sense of math abstraction in kids' brain.

This was a word problem from Singapore Math 5. Are you saying that Singapore Math is doing it wrong? Too much language? They don't understand math?

[Anonymous]

A physicist or engineer would look at the word problem and quickly throw up a table with a row for a (afternoon) , m(morning) and t (total) on a white board. The diagram would make it obvious to subtract 64 from 188 and then divide in 2. They would probably do this in their head and then off to the side throw up 64+62 and circle the answer. There would be no words used. Math has a purpose and relationships can be shown visually.

A mathematician or chemist would do 2X +64 =188. They would probably also do the rest of the calculation in their heads. Math is an abstraction and the simplest form necessary is always sought.

A business/finance person might try drawing a table similar to the physicist or engineer but would have far more labels, columns and rows and spend too much time playing around with the Excel formulas. It would look pretty in the end when the finance person applies color to their chart. Math shows a bottom line but you still have to sell it.

A lawyer, public policy, or history major would do the wandering talk it out approach that the poster who does math in words shared with everyone. Never really understood math but can reason and wander my way through it if required.

An education major would get the problem wrong. Enough said.

[Anonymous]

Ah, I see. Math is what grown-up physicists, engineers, or mathematicians do, and everybody else is doing it wrong.

[Anonymous]

^^^Actually this reminds me why almost all of the math classes I took in college and graduate school were taught so badly -- because the math professors assumed that everybody does, or should do, math the one way they think of it, and if you don't do it that way, you shouldn't be in the class.

It also reminds me that university math professors have not the faintest idea of a tiny clue about how to teach math to fifth graders.

[Anonymous]

What you are missing is that the approaches used in the example by physicists and mathematicians scale up to higher order, exceedingly more complex problems. You can talk and wander your way through an easy elementary school word problem but you can't do this for more advanced mathematics.

If you had been properly instructed at an earlier age, you would not have struggled so much in college level math classes. It is not the job of a university professor to re-teach you fifth grade math because you never developed a good working math memory, don't understand how to approach problems from an abstract or visual perspective, and can't solve more complex problems.

Its fundamentally unfair to not teach kids math under the guise of teaching an alternate more verbal way. It creates a situation where only kids with a very innate math aptitude or kids who receive outside instruction end up with the foundational skills to pursue a career requiring math. A fifth grade teacher can lead the rest of her life with only enough skills to get through fifth grade level problems. She can't assume that every kid in her class should lead a similar life.

[Anonymous]

Anonymous wrote:What you are missing is that the approaches used in the example by physicists and mathematicians scale up to higher order, exceedingly more complex problems. You can talk and wander your way through an easy elementary school word problem but you can't do this for more advanced mathematics.

If you had been properly instructed at an earlier age, you would not have struggled so much in college level math classes. It is not the job of a university professor to re-teach you fifth grade math because you never developed a good working math memory, don't understand how to approach problems from an abstract or visual perspective, and can't solve more complex problems.

Its fundamentally unfair to not teach kids math under the guise of teaching an alternate more verbal way. It creates a situation where only kids with a very innate math aptitude or kids who receive outside instruction end up with the foundational skills to pursue a career requiring math. A fifth grade teacher can lead the rest of her life with only enough skills to get through fifth grade level problems. She can't assume that every kid in her class should lead a similar life.

You sure know a lot about me -- or think you do.

How much personal experience do you have teaching math? At any level.

[Anonymous]

Anonymous wrote:A physicist or engineer would look at the word problem and quickly throw up a table with a row for a (afternoon) , m(morning) and t (total) on a white board. The diagram would make it obvious to subtract 64 from 188 and then divide in 2. They would probably do this in their head and then off to the side throw up 64+62 and circle the answer. There would be no words used. Math has a purpose and relationships can be shown visually.

A mathematician or chemist would do 2X +64 =188. They would probably also do the rest of the calculation in their heads. Math is an abstraction and the simplest form necessary is always sought.

A business/finance person might try drawing a table similar to the physicist or engineer but would have far more labels, columns and rows and spend too much time playing around with the Excel formulas. It would look pretty in the end when the finance person applies color to their chart. Math shows a bottom line but you still have to sell it.

A lawyer, public policy, or history major would do the wandering talk it out approach that the poster who does math in words shared with everyone. Never really understood math but can reason and wander my way through it if required.

An education major would get the problem wrong. Enough said.

+10000 !!!