## Math Education, elementary

### #1

Posted 2016-October-26, 16:42

Let's take a 12 year old. I have 12 year old twin grandchildren, so I may try this. Feel free to vary the age.

I will ask him, or her, a series of questions

1. The time is 9:35. What time will it be in an hour and a half?

2. Today is Wednesday. What day of the week will it be 37 days from now?

3. Today is Oct 26th. How many days until Christmas? Of course here the child needs to know how many days are in October and November.

Or, assuming every child knows how many days until Christmas ask them how many days until December 15th.

You get the idea. These questions require modest ability in arithmetic, and they require that a person be able to figure out what arithmetic calculations are relevant.

I am sure some 12 year olds can answer such questions, and I am sure some cannot. Take a guess at percentages? I am not really interested in knowing how many can do this if you give them a lesson in the morning and ask them in the afternoon. Rather I am interested in how many have enough of a grasp of the relationship between arithmetic and reality so that they could answer a broad array of questions such as these in, say, the middle of summer break.

I don't mind all that much if they need a calculator. Well, I do mind, but it isn't the main point. My question really is do they know what they need to calculate? No fair using Wolfram Alpha. [I checked Wolfram on question 3, it gives the answer]

And of course the political follow up question: Does Common Core seek to develop such understanding? Assuming the answer to that is yes, do you see it as successful?

### #2

Posted 2016-October-26, 17:07

kenberg, on 2016-October-26, 16:42, said:

Let's take a 12 year old. I have 12 year old twin grandchildren, so I may try this. Feel free to vary the age.

I will ask him, or her, a series of questions

1. The time is 9:35. What time will it be in an hour and a half?

2. Today is Wednesday. What day of the week will it be 37 days from now?

3. Today is Oct 26th. How many days until Christmas? Of course here the child needs to know how many days are in October and November.

Or, assuming every child knows how many days until Christmas ask them how many days until December 15th.

You get the idea. These questions require modest ability in arithmetic, and they require that a person be able to figure out what arithmetic calculations are relevant.

I am sure some 12 year olds can answer such questions, and I am sure some cannot. Take a guess at percentages? I am not really interested in knowing how many can do this if you give them a lesson in the morning and ask them in the afternoon. Rather I am interested in how many have enough of a grasp of the relationship between arithmetic and reality so that they could answer a broad array of questions such as these in, say, the middle of summer break.

I don't mind all that much if they need a calculator. Well, I do mind, but it isn't the main point. My question really is do they know what they need to calculate? No fair using Wolfram Alpha. [I checked Wolfram on question 3, it gives the answer]

And of course the political follow up question: Does Common Core seek to develop such understanding? Assuming the answer to that is yes, do you see it as successful?

I would not be against Common Core if I thought it would help answer these questions; I have read some sample questions from Common Core last year (I wish I still had them) and I could understand how they would teach anybody anything. (I assume the question about "Susie had 6 apples and she gave Johnny two, how does that make you feel?" was a joke, but I'm not certain.)

In my experience, most people under 30 can't make change without a calculator (and even then, it might be challenging without an app that tells the clerk that 32 cents is a quarter (picture included), a nickel, and two pennies.)

I would be surprised if more than 30% of 12 year olds or more than 30% of 18 year olds could answer any of the above questions. I wouldn't be surprised if it was less than 10%.

My big issue with Common Core is that a partisan government can shape education. You can guess my fears, but let me put it in prospective for the liberals. Let us say that Republicans were in control of everything and demanded that when we teach history, we teach only the failed effects of recent immigration policy, to leave out black history, and the only thing we teach about Muslim history is that they were constantly attacking warmongers who disrupted the advancement of civilization. I could list others, but you get the idea - alt-right wing brainwashing of our children.

I would think this would be deplorable if partisan politics came into what we were educating our children but I could see it happening. If there are safeguards against this happening, they could easily be overridden by any Congress or an executive order or perhaps by a Supreme Court ruling by a partisan high court.

Of course, I fear more that progressives will be the ones controlling the curriculum, but I would be just as unhappy if the alt-right got to teach our children racist ideas as fact.

### #3

Posted 2016-October-26, 17:20

Kaitlyn S, on 2016-October-26, 17:07, said:

No offense, but I don't consider the fact that you can understand something very telling...

Perhaps if you would care to provide an actual example of what has you so confused folks would be willing to help explain the value of the pedagogic method...

### #4

Posted 2016-October-26, 17:42

Kaitlyn S, on 2016-October-26, 17:07, said:

I would think this would be deplorable if partisan politics came into what we were educating our children but I could see it happening. If there are safeguards against this happening, they could easily be overridden by any Congress or an executive order or perhaps by a Supreme Court ruling by a partisan high court.

Of course, I fear more that progressives will be the ones controlling the curriculum, but I would be just as unhappy if the alt-right got to teach our children racist ideas as fact.

You do know that the federal government had nothing to do with the development of common core, right? Right?

### #5

Posted 2016-October-26, 17:47

### #6

Posted 2016-October-26, 18:09

I was 12 in 1951. Would the percentages have been higher then? I think so, but I am not sure.

I know I have told this before, but I'll do it again. My father's best friend was Len. Len "worked in the shops". I don't know how much schooling he had, but my father finshed 8th grade and went to work, Len was probably about the same. When I bought my first car, Len explained to me how to figure out the gas mileage I was getting. In other words, he knew how to do arithmetic and he knew how it applied to reality. So I have some basis for thinking that ordinary guys knew this stuff. But I have no data, for then or for now.

I didn't come to bury Common Cause, nor did I come to praise it. I have no idea whether CC advocates think it is important to do the sort of thing my questions get at. My time and date questions are different from miles per gallon, but not really. It all goes to whether arithmetic and reality match in the eyes of the child. Is that seen as the goal? Are the strategies effective?

I was not feigning ignorance, I really do not know the answers. From what I have seen, education at the high level public schools is far better now than it was when I was a child. But for the rest? There is a steep drop off, that much I am sure of. But how many could answer the questions that I pose? I have no idea.

### #7

Posted 2016-October-26, 18:30

cherdano, on 2016-October-26, 17:42, said:

Moreover, it would appear to be an argument against ANY form of public education rather than just the Common Core

### #8

Posted 2016-October-26, 18:56

kenberg, on 2016-October-26, 16:42, said:

Let's take a 12 year old. I have 12 year old twin grandchildren, so I may try this. Feel free to vary the age.

1. The time is 9:35. What time will it be in an hour and a half?

2. Today is Wednesday. What day of the week will it be 37 days from now?

3. Today is Oct 26th. How many days until Christmas? Of course here the child needs to know how many days are in October and November.

Or, assuming every child knows how many days until Christmas ask them how many days until December 15th.

...

And of course the political follow up question: Does Common Core seek to develop such understanding? Assuming the answer to that is yes, do you see it as successful?

Assuming all neurotypical kids

1. 75% 2. 90% 3. 90% If you are willing to tell them how many days are in October and November, and give them paper to write on.

To answer your other question: Yes, I think that Common Core seeks to develop such an understanding. I don't know how successful it is, as the crop of students I have were not exposed to common core.

In fact, one of the big criticisms I have seen of common core math is that it stresses concepts of numeracy too much at the expense of procedures. For example, people complain that their kids' math classes teach students to subtract 523 - 476 by adding up 24+23 instead of doing column subtraction.

Many teachers are implementing things called "Number Talks" (see Jo Boaler) which encourages students to work on numeracy skills, including multiple ways to solve a problem. An example would be displaying a problem like 18x12 and asking students to solve this in their heads without the "typical" algorithm, and then come up with multiple ways and share them with each other.

Students complain about the amount of explaining I require them to do. In other words, it's not enough for them to be able to solve for x in 3x + 15 =75; They must be able to explain why each step is mathematically valid, and be able to critique other methods of solving (as in recognizing correctness/noncorrectness) and be able to explain to others faults in their reasoning. Further, they must demonstrate ability to use this in modeling. So for example, I might require them to create a word problem that this equation would solve (and of course the classical given situations, come up with equations to help solve them). (I actually don't teach this math, I just wanted to use an easily understood example.)

Kaitlyn S said:

Not only is it a complete joke, it's an old one too (I remember this type of thing said about either "New Math" or the Math curriculum that followed it) as a protest to the amount of writing students might do in a Math class, usually stated by people who haven't studied how children learn.

### #9

Posted 2016-October-26, 19:01

cherdano, on 2016-October-26, 17:42, said:

Perhaps the original common core wasn't developed by the federal government, but you can be sure that if the Federal Government can mandate the curriculum, that those in political positions will affect that curriculum to cater to their pet voting groups.

### #10

Posted 2016-October-26, 19:03

kenberg, on 2016-October-26, 18:09, said:

EDIT: sorry, I missed your post, Elianna. I would be totally shocked if your high percentages reflected reality. It would be interesting to see Jesse Waters go to a few college campuses and ask these questions. It would surprise me if a higher percentage of these students could answer these questions than could answer who our first president was.

Also, I don't think people can do these problems at age 12 and then all of a sudden lose that talent by college age.

While I can subtract 476 from 523 by adding 24 to 23, I'm pretty good at math (not a surprising trait for someone attracted to bridge) and I suspect that everybody on this thread can do that, but I don't see your average student with an IQ of 100 thinking that way.

### #11

Posted 2016-October-26, 19:06

Kaitlyn S, on 2016-October-26, 17:07, said:

### #13

Posted 2016-October-26, 19:18

Elianna, on 2016-October-26, 18:56, said:

I was taught with New Math, and it was a little strange. We started off with Venn diagrams, and covered union and intersection before plus and minus.

I assume that everyone is familiar with the Tom Lehrer song.

EDIT for non-Americans: the TV and print ads for Castro Convertible sofa beds notes that they were so easy to open that even a child could do it.

### #14

Posted 2016-October-26, 19:19

Elianna, on 2016-October-26, 18:56, said:

### #15

Posted 2016-October-26, 19:29

Kaitlyn S, on 2016-October-26, 19:03, said:

The student does not have to "think that way". The child can be taught. That is what teachers are there for.

### #16

Posted 2016-October-26, 19:34

Elianna, on 2016-October-26, 18:56, said:

1. 75% 2. 90% 3. 90% If you are willing to tell them how many days are in October and November, and give them paper to write on.

To answer your other question: Yes, I think that Common Core seeks to develop such an understanding. I don't know how successful it is, as the crop of students I have were not exposed to common core.

In fact, one of the big criticisms I have seen of common core math is that it stresses concepts of numeracy too much at the expense of procedures. For example, people complain that their kids' math classes teach students to subtract 523 - 476 by adding up 24+23 instead of doing column subtraction.

Many teachers are implementing things called "Number Talks" (see Jo Boaler) which encourages students to work on numeracy skills, including multiple ways to solve a problem. An example would be displaying a problem like 18x12 and asking students to solve this in their heads without the "typical" algorithm, and then come up with multiple ways and share them with each other.

Students complain about the amount of explaining I require them to do. In other words, it's not enough for them to be able to solve for x in 3x + 15 =75; They must be able to explain why each step is mathematically valid, and be able to critique other methods of solving (as in recognizing correctness/noncorrectness) and be able to explain to others faults in their reasoning. Further, they must demonstrate ability to use this in modeling. So for example, I might require them to create a word problem that this equation would solve (and of course the classical given situations, come up with equations to help solve them). (I actually don't teach this math, I just wanted to use an easily understood example.)

In other words, they want kids to

*understand*what they're doing and

*why*, not just follow rote procedures that they could easily get their smartphone to do for them. I consider this a great leap forward.

When everyone has a powerful computer in the palm of their hands, it's not as important for them to learn the mechanics of arithmetic. You need to know what numbers to plug in to solve a problem that involves math. It's similar to the idea that Google means you don't have to memorize every historical detail -- it's more important to learn

*why*World War II happened than to know the specific names and dates that were involved. If you need a specific, you can look it up, so long as you know the context to start from.

Old timers will bemoan this as "dumbing down", but it isn't. It's taking advantage of technology to handle the boring details, and concentrating on the important stuff that requires human intelligence. This has been the way humanity and culture has progressed since time immemorial. For instance, before printed books, people had to memorize everything. Which basically meant that most people couldn't have very broad knowledge, because they simply couldn't learn everything about everything.

### #17

Posted 2016-October-26, 19:43

Kaitlyn S, on 2016-October-26, 19:01, said:

For a while, there were special grants ("race to the top") from the federal government to states that were contingent on either adapting common core, or establishing similar standards by themselves (which two states did). In 2015, a law was passed to prohibit the federal government from continuing to do so.

At no point was the federal government directly involved in developing common core.

### #18

Posted 2016-October-26, 19:49

cherdano, on 2016-October-26, 19:43, said:

At no point was the federal government directly involved in developing common core.

Indeed. Common Core was an initiative of the National Governors Association and the Council of Chief State School Officers -- it comes from the states themselves, not the feds.

### #19

Posted 2016-October-26, 19:58

barmar, on 2016-October-26, 19:34, said:

*understand*what they're doing and

*why*, not just follow rote procedures that they could easily get their smartphone to do for them. I consider this a great leap forward.

When everyone has a powerful computer in the palm of their hands, it's not as important for them to learn the mechanics of arithmetic. You need to know what numbers to plug in to solve a problem that involves math. It's similar to the idea that Google means you don't have to memorize every historical detail -- it's more important to learn

*why*World War II happened than to know the specific names and dates that were involved. If you need a specific, you can look it up, so long as you know the context to start from.

Old timers will bemoan this as "dumbing down", but it isn't. It's taking advantage of technology to handle the boring details, and concentrating on the important stuff that requires human intelligence. This has been the way humanity and culture has progressed since time immemorial. For instance, before printed books, people had to memorize everything. Which basically meant that most people couldn't have very broad knowledge, because they simply couldn't learn everything about everything.

*think*. Thinking is work and is hard, so the lazy child is going to try to avoid it. I would be in favor of a program that can get children to think to the best of their ability. This is a necessity IMO because the way technology is changing the workplace, the exact skills needed cannot be predicted as jobs that are prevalent now may be automated by the time the child becomes an adult. A new entrant to the workforce may have to be able to use a skill set that didn't even exist when he was in school. Of course, understanding math concepts and reading comprehension as well as being able to express ideas so others understand them are always going to be necessary skills, but the ability to think through an unfamiliar situation seems like it will be a necessary skill as well for anybody that doesn't want to do menial work (if that even exists) in the not too distant future.

### #20

Posted 2016-October-26, 20:49

Elianna, on 2016-October-26, 18:56, said:

1. 75% 2. 90% 3. 90% If you are willing to tell them how many days are in October and November, and give them paper to write on.

To answer your other question: Yes, I think that Common Core seeks to develop such an understanding. I don't know how successful it is, as the crop of students I have were not exposed to common core.

In fact, one of the big criticisms I have seen of common core math is that it stresses concepts of numeracy too much at the expense of procedures. For example, people complain that their kids' math classes teach students to subtract 523 - 476 by adding up 24+23 instead of doing column subtraction.

Many teachers are implementing things called "Number Talks" (see Jo Boaler) which encourages students to work on numeracy skills, including multiple ways to solve a problem. An example would be displaying a problem like 18x12 and asking students to solve this in their heads without the "typical" algorithm, and then come up with multiple ways and share them with each other.

Students complain about the amount of explaining I require them to do. In other words, it's not enough for them to be able to solve for x in 3x + 15 =75; They must be able to explain why each step is mathematically valid, and be able to critique other methods of solving (as in recognizing correctness/noncorrectness) and be able to explain to others faults in their reasoning. Further, they must demonstrate ability to use this in modeling. So for example, I might require them to create a word problem that this equation would solve (and of course the classical given situations, come up with equations to help solve them). (I actually don't teach this math, I just wanted to use an easily understood example.)

Not only is it a complete joke, it's an old one too (I remember this type of thing said about either "New Math" or the Math curriculum that followed it) as a protest to the amount of writing students might do in a Math class, usually stated by people who haven't studied how children learn.

I was hoping that you would reply..Your estimates surprise me in two ways. I am skeptical that the numbers are that large. But also, problem 1 is first because I thought it would be the easiest. You can visualize a clock and see that in half an hour it will be 10:05 and then add an hour.

For the second one would it matter if I said 100 days instead of 37? I had in mind that they would realize the relevance of 37 being 2 more than a multiple of 7.

For the third, yes, I could tell them how many days. Here I can well imagine using pencil and paper. It could be tough to get it all organized in the head.

I see these questions as being different from finding alternative ways of multiplying 18 X 12. Asking them to do this multiplication is telling them what calculation to perform, even if the detailed method is not stipulated. It has no specific real world connection.

Another story. I have told this before also, but I swear it is true and it will explain why I am skeptical of the 90%

I was in a generic McD type of place. One line over the amount due, let's say $16.27, was announced. The customer gave the cashier some money and received change.

Customer, No, I gave you a $100 bill, not a $20.

Cashier, checking the drawer. Oh! I am sorry. Yes you did.

Total crisis. The cashier had rung it up as 20, the register said the customer was to get $3.73 in change. Nobody knew how to reset the cash register so that 100 could be entered. The cashier talked to an older cashier. No idea. They went over to talk to the guy doing the french fires. Nope.

I intervened. Everyone agreed that 100 was 80 more than 20. I explained that since the customer had given the cashier 80 more than the 20 she rang up, the cashier should give the customer 80 more in change than what the cash register said. Everyone agreed that this sounded fair, it was done, and they could go on to the next customer.

There were either three or four people behind the counter, and one customer, all trying to think of how to figure out how much change was right.

This seems pretty basic. I would love to believe 90%, or even 75%, with my questions but I am not so sure.

I thank you for your estimate, and I would like to hear from other teachers. Or from other parents, except that I have found that everyone's child is at the top of his/her class and very advanced.

I may do some experimenting with some random 12 year olds.

Added: I assume that if, with the clock problem, I asked what time it would be after five and a half hours the number of correct answers would go down?