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View Full Version : No Need to Memorize Times Tables



GaryJ
08-18-2013, 04:42 PM
Maybe I am out of the education system too long but this makes absolutely no sense to me. If understand this correctly as long as one can justify how they got the wrong answer that is fine. With abstract items that render an opinion that its fine but with factual items? Give me a break! I can't imagine the education of kids coming out of high school in the future if we follow this logic.

http://news.yahoo.com/obama-math-under-common-core-3-x-4-151805230.html

Eric Johnson
08-18-2013, 08:19 PM
I had a roommate in college who completed a physics test problem with the answer in parens and a strange symbol showing next to it.

When the tests were handed back, he was called on it. "Brian! What was that strange symbol next to the answer in number 5.?"

To which he answered, "It's Von Gunten's factor. It's the number you multiply your answer by to get the right answer."

The professor chuckled and finished marking his paper and gave it back to him....an "A".

Two weeks later there was another test. A friend used the same funny squiggle and turned it in.

When the tests were handed back, he'd gotten -10 for that answer. "Wait a minute" he said. That's Von Guntens factor." The professor told him that he wasn't advanced enough in his understanding of physics to know when to apply that factor.

What Brian didn't reveal to anyone was that indeed he'd gotten the problem correct on the first test.

Terri
08-24-2013, 12:17 AM
I thought the speaker stated that the process was more important than the answer. So if the student showed the work and got all the steps right, except the step at the end, writing 11 instead of 12 he (student) would not be marked wrong for the equation. In math some teacher who do not understand the concepts give full credit or no credit, but a teacher who understands the concepts can give partial credit, but the main thing is to make sure the student understands the concept and has not just memorized a table. To me that is the better way to teach math.

Terri

huntinman
08-24-2013, 12:39 AM
If the kid can't get the answer to the simple equation... How the hell can you or anyone say they understand the "concept"? WTH? No wonder our kids are so screwed up.

Terri
08-25-2013, 06:13 PM
Bill, are you directing your question to me? If so then let me explain my point. The example from the video was a very simple problem, but in math as you move up into more complex problems there are many step before you get the answer to the problem. If the student had seven steps of the problem right(all work is shown), but for some reason wrote the wrong answer would you say the student does not understand the concept? The speaker explained that the student was able to show the work, explain the steps, but made an error. The teacher would show the student the correct final step, but would not discount the student's understanding of how to do the problem. All my kids were in the top math classes in high school and I have seen teachers that understand math concepts and ones that just know the answer in the back of the book. I think the reason so many people shy away from math has to do with poor math teachers. Teachers that can not think outside of the box. My oldest daughter who has her law degree is now in a doctorate program for economics, but she has dealings (her husband's best friends wife) with a woman who is a high school honors math teacher who can not divide a check from a restaurant between multiple couples. This woman made it through school, but she clearly can not apply the concepts to the real world. It is very common to have math errors, but do not discount the concept or an error.

Terri

GaryJ
08-25-2013, 08:18 PM
Bill, are you directing your question to me? If so then let me explain my point. The example from the video was a very simple problem, but in math as you move up into more complex problems there are many step before you get the answer to the problem. If the student had seven steps of the problem right(all work is shown), but for some reason wrote the wrong answer would you say the student does not understand the concept? The speaker explained that the student was able to show the work, explain the steps, but made an error. The teacher would show the student the correct final step, but would not discount the student's understanding of how to do the problem. All my kids were in the top math classes in high school and I have seen teachers that understand math concepts and ones that just know the answer in the back of the book. I think the reason so many people shy away from math has to do with poor math teachers. Teachers that can not think outside of the box. My oldest daughter who has her law degree is now in a doctorate program for economics, but she has dealings (her husband's best friends wife) with a woman who is a high school honors math teacher who can not divide a check from a restaurant between multiple couples. This woman made it through school, but she clearly can not apply the concepts to the real world. It is very common to have math errors, but do not discount the concept or an error.

Terri

i agree when it is "higher" math however unless something has changed, which is possible, the earlier years of education were based on absolutes or facts and starting around 6th grade the education of abstract came into play. 4*3 =12 is not "higher" math.

caryalsobrook
08-25-2013, 08:57 PM
Bill, are you directing your question to me? If so then let me explain my point. The example from the video was a very simple problem, but in math as you move up into more complex problems there are many step before you get the answer to the problem. If the student had seven steps of the problem right(all work is shown), but for some reason wrote the wrong answer would you say the student does not understand the concept? The speaker explained that the student was able to show the work, explain the steps, but made an error. The teacher would show the student the correct final step, but would not discount the student's understanding of how to do the problem. All my kids were in the top math classes in high school and I have seen teachers that understand math concepts and ones that just know the answer in the back of the book. I think the reason so many people shy away from math has to do with poor math teachers. Teachers that can not think outside of the box. My oldest daughter who has her law degree is now in a doctorate program for economics, but she has dealings (her husband's best friends wife) with a woman who is a high school honors math teacher who can not divide a check from a restaurant between multiple couples. This woman made it through school, but she clearly can not apply the concepts to the real world. It is very common to have math errors, but do not discount the concept or an error.

Terri

Terrie, I think you present the opinion of many teachers. To be sure, it is important to understand the concept but it is also just as important that you get the right answer. Let me give you an example. I am retired but when I practiced dentistry I can imagine if I explained to that a root canal that I performed for you failed because I wrote down the wrong lenth for the root. I understood the concept and technique of performing a root canal and did them perfectly and had I not written down the incorrect length of the root, it would have been a success. Well, in the real world, understanding the concept IS NOT ENOUGH. You also have to get the right answer. In the real world if you get the wrong answer, many times you are fired. It may be ok in the world of academia to only understand the concept and you may keep your job as long as you choose, but that is not the real world.

Take the example of the honors teacher of whom you speak. Do you really think anyone would keep her employed as a statistian, accountant, acutary or even a bookeeper? I think not. If one teaches the belief that understanding the concept is so important and that getting the right answer is only secondary, then they are doing the student just as much disservice as the teacher that can only come up with the correct answer by looking in the back of the book. I am not trying to put words in Huntinman's mouth but I think that is what he is driving at.

Terri
08-25-2013, 09:08 PM
i agree when it is "higher" math however unless something has changed, which is possible, the earlier years of education were based on absolutes or facts and starting around 6th grade the education of abstract came into play. 4*3 =12 is not "higher" math.

I think the speaker was using an overly simplistic example, but even when it comes to multiplication some teachers teach it as a concept, requiring the student to show all the steps needed to get the answer, not just memorize the times table. For example: the student would have to show 4*3=12 in a word problem with pictures for each step. Explaining the steps with the examples is always harder for students than just memorizing a function. If your child comes home with 30 math problems each requiring steps and examples, all of which need to be different you will soon realize how much harder this is than memorizing a times table.
I have had many friends that spent many hours each night working through these types of problems. My nephew is in 6 grade this year and my sister over the years has called to brain storm math examples with each of my kids more times than I care to remember. Remember besides the math homework there are several other subjects that require homework each night. Algebra is no longer a junior high school subject, but can be seen in 3rd and 4th grade. Teacher's do not get to come up with what subjects will be covered over the school year, there are state standards, which are always changing and tests that much be passed at a stated level to insure funding. I have seen the list and all I can say is I'm glad I'm not a teacher and all three of my kids ranked high among their peers on standardized test and on daily work requiring only minimal parental involvement.

Terri


Terri

luvmylabs23139
08-27-2013, 08:59 AM
I thought the speaker stated that the process was more important than the answer. So if the student showed the work and got all the steps right, except the step at the end, writing 11 instead of 12 he (student) would not be marked wrong for the equation. In math some teacher who do not understand the concepts give full credit or no credit, but a teacher who understands the concepts can give partial credit, but the main thing is to make sure the student understands the concept and has not just memorized a table. To me that is the better way to teach math.

Terri
OK dating myself but until we got into advanced math and science classes there was no partial credit for a basic math question. This would have been about 3rd or 4th grade times tables.
3X4 is something you should know off the top of your head not something that requires a long complex calculation. How many times of any of us gone to the store and if a kid is running the register and they enter the wrong amount of cash you give them, they have no idea what the correct amount of change is?

luvmylabs23139
08-27-2013, 09:11 AM
Terrie, I think you present the opinion of many teachers. To be sure, it is important to understand the concept but it is also just as important that you get the right answer. Let me give you an example. I am retired but when I practiced dentistry I can imagine if I explained to that a root canal that I performed for you failed because I wrote down the wrong lenth for the root. I understood the concept and technique of performing a root canal and did them perfectly and had I not written down the incorrect length of the root, it would have been a success. Well, in the real world, understanding the concept IS NOT ENOUGH. You also have to get the right answer. In the real world if you get the wrong answer, many times you are fired. It may be ok in the world of academia to only understand the concept and you may keep your job as long as you choose, but that is not the real world.

Take the example of the honors teacher of whom you speak. Do you really think anyone would keep her employed as a statistian, accountant, acutary or even a bookeeper? I think not. If one teaches the belief that understanding the concept is so important and that getting the right answer is only secondary, then they are doing the student just as much disservice as the teacher that can only come up with the correct answer by looking in the back of the book. I am not trying to put words in Huntinman's mouth but I think that is what he is driving at.

Lets take this to a real life situation. Say it is a payroll clerk calculating someone's paycheck. How many wrong paychecks would be reasonable if they simply oops on the final answer but proved out their work thru 6 of 7 of the calculations? Yes a realize that a lot is automated these days but manual checks are still done for numerous reasons and the point is that the person would be fired unless of course they work for the gov't. Then they would just be sitting at home collecting a full paycheck.

Terri
08-29-2013, 10:11 PM
I was not trying to discredit the need for the right answer nor was the speaker. What I got from her speech was that teachers should not just give full credit or no credit on math problems, but partial credit for the work that was correct and then explain where the error occurred. This is the teaching part of math. Just like when we train our dogs, first teach the concepts. Reward the dog for the things it does right, but correct the mistakes. School is not the real world, but a training ground. As the trainer all you can do is teach at the best of your ability and to always be fair to the dog. I was told once by a very good trainer that people are always fast to make harsh corrections, but slow to give praise. Kids are not much different than dogs when it comes to praise and harsh treatment. If we want our dogs to make it to their full potential we need to keep that drive alive. Kids also need to be encouraged to keep up their drive for higher learning. Most kids start hating math very early in their education. Why? Teachers kill the drive. Just like not all dogs will be field champions, not all students will be doctors, that is just a fact. How many dogs could have been FC, but due to the fact that they had a poor trainer. I read that hear all the time. So how many kids could have been doctors, but because of a poor teacher never took advanced math and science classes, but majored in English instead?

Terri

charly_t
08-29-2013, 10:29 PM
I was not trying to discredit the need for the right answer nor was the speaker. What I got from her speech was that teachers should not just give full credit or no credit on math problems, but partial credit for the work that was credit and then explain where the error occurred. This is the teaching part of math. Just like when we train our dogs, first teach the concepts. Reward the dog for the things it does right, but correct the mistakes. School is not the real world, but a training ground. As the trainer all you can do is teach at the best of your ability and to always be fair to the dog. I was told once by a very good trainer that people are always fast to make harsh corrections, but slow to give praise. Kids are not much different than dogs when it comes to praise and harsh treatment. If we want our dogs to make it to their full potential we need to keep that drive alive. Kids also need to be encouraged to keep up their drive for higher learning. Most kids start hating math very early in their education. Why? Teachers kill the drive. Just like not all dogs will be field champions, not all students will be doctors, that is just a fact. How many dogs could have been FC, but due to the fact that they had a poor trainer. I read that hear all the time. So how many kids could have been doctors, but because of a poor teacher never took advanced math and science classes, but majored in English instead?

Terri

I always liked math a lot better than English. Seemed to me it made more sense at least. Teachers that I had may have made the math seem better.

Terri
08-30-2013, 02:23 AM
I always liked math a lot better than English. Seemed to me it made more sense at least. Teachers that I had may have made the math seem better.

Teachers can make or break it for students. Another thing I was thinking, high school and college students are closer to entering the real world than students in grade school. These upper level students almost always get partial credit in math classes. My husband will take off points if the student forgot to put the word units as part of the answer, but got the number right. He does this to remind the student how important that is in the real world to not forget that important piece of information. He realizes they understand the concept, made a careless error, but they are still students. By the end of the class he hopes he has explained the importance of being careful not to make careless errors. Under some people's reasoning that is okay because it is more complex problems, but since they are almost in the real world then maybe they should get a big fat zero. In grade school the student is not ready for the real world for many years. This is the time to teach the concepts, point out the errors, but not forget to praise the positive. Partial credit is a form of praise for students. I'm just a bit more tolerant of careless error in younger students than older students. Just like I'm more tolerant of puppies making errors than master hunters, but even the best dogs make mistakes. Takes a pretty big mistake to get a zero at a hunt test, but I have heard about a lot of dogs getting sevens and eights on test. Not perfect, they got partial credit from the judge and earned a Q for the weekend. Who are we taking hunting the puppy or that master hunter? I know the master hunter is the dog that will be hunting and that is the real world.

Terri

firehouselabs
08-31-2013, 12:56 PM
Taught by a nun (and proud of it!) who made us do EVERYTHING long hand, as in show ALL the steps. A fairly straight forward division problem would take up one quarter of a page in a wide ruled notebook. If along the way, we screwed up by transposing numbers or miscalculating, we could at least show step by step how we got to the final answer. The fact that we were writing it all out and were NOT allowed the use of a calculator (until the 8th grade when we got into scientific notations anyway) was teaching us the concept. Could we get partial credit for a "wrong" answer? Yes, but we had to have the work written out to show how/why we screwed up. You can't do that verbally!
By the way, we were doing long division in the 2nd grade, the memorization of the times tables occurred in the 1st grade. We were reading in kindergarten and then only going to class for "half days". Remember those! :) Our nuns were NOT accredited teachers by the way, and Sr. Mary Michaeline (God rest her soul) would literally beat you for messing up. There was no ADHD, or other "syndrome". IF you had "ants in your pants" that got cured right away......she would swat them for you, while they were in your pants. She hated lefties, and by her and the good grace of God, I do NOT distort my wrist like a contortionist when I write or draw. Yes, the page smears sometimes, but not if you gently blow on the ink as you are writing.
And speaking of writing, she threw out all of those long alphabet guides that kept getting more and more like printing instead of cursive. Yep. I learned PENMENSHIP along with spelling.
I now work as the church secretary that the school is attached to- moved back home this last January. Here are some fun facts for our school:
Since it opened in 1955- we have had grades 1-8, with Kindergarten opening in 1984.
Of our 8th grade graduates which then go to our public high school, we have produced 98.5% of the Valedictorians and/or Salutatorians of the public high school graduates.
Our teachers teach two grades in the same room (1st-2nd, 3rd-4th, 5th-6th, 7th-8th) except for Kindergarten. This gives the underclassmen the chance to listen in on the advanced class so that they are further ahead, and gives gifted students a chance to learn without becoming bored.
Our class sizes are small- my son is currently in third grade, his grade has 4 kids, and the 4th grade-same room- has 4 kids, for a class size of just 8 kids.
Our tuition is HORRENDOUSLY low. Most private schools in the surrounding larger towns are on average- $1000-1500 a semester per child. Our tuition is $555 per child.....per year! Add a child, get a discount, have three and you get a deeper discount! Great for our Catholic families!!! This cost only covers the cost of books and supplies ordered each year by the teachers. And speaking of a supply list- when I lived in MO, it was a list that was a page long and included basic things such as sterile wipes, 3! Large boxes of kleenex, plus other mundane things in quantities that should have lasted for a couple of years, let alone the fact that every kid was bringing the same things! My list for St. Mary's....only had 10 items. Crayons, markers, pencils, paper, folders (2), erasers, glue, a small box of kleenex, brown paper bag to cover two text books (remember that!)and scissors. That's it. The only thing I had to actually buy were new markers. Every thing else I had left over from previous years of school shopping.

So if you want a great education, small town-quiet yet comfortable living, cheap yet great education, conservative values, great hunting and fishing area too! Move to Ord NE. !!! :) Or find a similar town or school near you. :)

charly_t
08-31-2013, 03:45 PM
Taught by a nun (and proud of it!) who made us do EVERYTHING long hand, as in show ALL the steps. A fairly straight forward division problem would take up one quarter of a page in a wide ruled notebook. If along the way, we screwed up by transposing numbers or miscalculating, we could at least show step by step how we got to the final answer. The fact that we were writing it all out and were NOT allowed the use of a calculator (until the 8th grade when we got into scientific notations anyway) was teaching us the concept. Could we get partial credit for a "wrong" answer? Yes, but we had to have the work written out to show how/why we screwed up. You can't do that verbally!
By the way, we were doing long division in the 2nd grade, the memorization of the times tables occurred in the 1st grade. We were reading in kindergarten and then only going to class for "half days". Remember those! :) Our nuns were NOT accredited teachers by the way, and Sr. Mary Michaeline (God rest her soul) would literally beat you for messing up. There was no ADHD, or other "syndrome". IF you had "ants in your pants" that got cured right away......she would swat them for you, while they were in your pants. She hated lefties, and by her and the good grace of God, I do NOT distort my wrist like a contortionist when I write or draw. Yes, the page smears sometimes, but not if you gently blow on the ink as you are writing.
And speaking of writing, she threw out all of those long alphabet guides that kept getting more and more like printing instead of cursive. Yep. I learned PENMENSHIP along with spelling.
I now work as the church secretary that the school is attached to- moved back home this last January. Here are some fun facts for our school:
Since it opened in 1955- we have had grades 1-8, with Kindergarten opening in 1984.
Of our 8th grade graduates which then go to our public high school, we have produced 98.5% of the Valedictorians and/or Salutatorians of the public high school graduates.
Our teachers teach two grades in the same room (1st-2nd, 3rd-4th, 5th-6th, 7th-8th) except for Kindergarten. This gives the underclassmen the chance to listen in on the advanced class so that they are further ahead, and gives gifted students a chance to learn without becoming bored.
Our class sizes are small- my son is currently in third grade, his grade has 4 kids, and the 4th grade-same room- has 4 kids, for a class size of just 8 kids.
Our tuition is HORRENDOUSLY low. Most private schools in the surrounding larger towns are on average- $1000-1500 a semester per child. Our tuition is $555 per child.....per year! Add a child, get a discount, have three and you get a deeper discount! Great for our Catholic families!!! This cost only covers the cost of books and supplies ordered each year by the teachers. And speaking of a supply list- when I lived in MO, it was a list that was a page long and included basic things such as sterile wipes, 3! Large boxes of kleenex, plus other mundane things in quantities that should have lasted for a couple of years, let alone the fact that every kid was bringing the same things! My list for St. Mary's....only had 10 items. Crayons, markers, pencils, paper, folders (2), erasers, glue, a small box of kleenex, brown paper bag to cover two text books (remember that!)and scissors. That's it. The only thing I had to actually buy were new markers. Every thing else I had left over from previous years of school shopping.

So if you want a great education, small town-quiet yet comfortable living, cheap yet great education, conservative values, great hunting and fishing area too! Move to Ord NE. !!! :) Or find a similar town or school near you. :)

LOL, Dad was present when a relative's child was throwing a hissy fit. Dad's sister said "oh, he is a nervous child ( can't help the way he acts etc. ). Dad said, "they had a cure for that when I was a child". Your church school sounds a lot like the good old country schools ......all 8 grades in one room school. Hubby said he knew the Gettysburg Address by heart before he got to the grade level where they required students to recite it without help from book, chalkboard or human. He said that he learned a lot of things by listening to the higher grades practice memorizing things. One of the things they learned was to he kind and helpful to younger children I believe.

1tulip
09-05-2013, 09:43 PM
I think this point was made by others here but let me put a spin on it. I am an RN (a professor of nursing). There is something called "death by decimal point." A person makes a "minor" error... does everything right, but just doesn't get the fact that milligrams to micrograms means the decimal moves to the right. But, they set the problem up and do everything right and end up killing the patient. 0.25 milligrams of digoxin might work... 250 milligrams instead of micrograms and you're dead.

It's very distressing. But to tell you the truth, we can usually get students past the math. What we have a LOT of trouble doing is getting them to read labels. That is even scarier. And it's a problem with which they arrive in nursing school. And we struggle and struggle to get them to understand what they are reading. (If they are reading it... "Store at room temperature"... not a lot of confusion there... if they read the label.)

caryalsobrook
09-05-2013, 10:01 PM
I think this point was made by others here but let me put a spin on it. I am an RN (a professor of nursing). There is something called "death by decimal point." A person makes a "minor" error... does everything right, but just doesn't get the fact that milligrams to micrograms means the decimal moves to the right. But, they set the problem up and do everything right and end up killing the patient. 0.25 milligrams of digoxin might work... 250 milligrams instead of micrograms and you're dead.

It's very distressing. But to tell you the truth, we can usually get students past the math. What we have a LOT of trouble doing is getting them to read labels. That is even scarier. And it's a problem with which they arrive in nursing school. And we struggle and struggle to get them to understand what they are reading. (If they are reading it... "Store at room temperature"... not a lot of confusion there... if they read the label.)

You only have to be on the front line to know when a MINOR mistake is not so minor.

Terri
09-09-2013, 07:09 PM
My daughter had to take a math test to be allowed to stay in the doctorate program. She is studying economics. This is her first year and all the students must pass this test. She answered all the math problems correctly, but she did not get a perfect score. Why? Because she failed to discuss the problems, even the ones that did not state that a discussion was needed. She could not believe how harsh he was with the negative points, but she is happy to have passed. I guess he thought she lacked an understanding of the concept. I was surprised she did not write a full discussion considering she has a law degree and was an editor for law review. I did tell her that I'm glad she didn't make any careless errors and she better be ready to discuss all problems in the future. You really need to know how you arrived at the answer, even if you show your work.

Terri