Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Memorization does not come at the expense of understanding. They are not mutually exclusive .

I don't think the teacher is saying that they are. But instead that the order of learning matters. A kid who learns to memorize early may not put the effort into learning the multiplication concepts thoroughly. And instead, s/he may just use the memorized algorithms to solve the problems. I can see my son doing that. He's working on three digit addition right now in third grade, and they are using the partial sums method of solving them, rather than carrying digits to the left. This method really instills place value for him, in a way just carrying a digit to a different column does not. He will learn that traditional algorithm, too, but if he had known it first, he probably wouldn't do the work involved with the partial sums method. Because this algorithm feels unwieldy, too lengthy, yet it teaches the concept very thoroughly.

The schools really don't give kids the opportunity to do that. Even if the facts are memorized, for years they are required to "show their strategies" in their work by skip counting, repeated addition, arrays, etc. Honestly the vast majority of students get these concepts pretty quickly, and having to do these long drawn-out processes for years after it's already understood it tortuous.

I have experiences from both sides. I went to business school here with someone who used a calculator to divide by ten. On the other hand, I often have business dinners with non-US people who are far more advanced than I in high level mathematics, and I am the one who instantly gets how to divide up the bill.

I use strategies like some of those described. I think it is because I use them often for everyday, for example, figuring out how much something costs if it is already marked down 30 percent when there is an extra 20 percent off, while they are immersed in their partial differential equations.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

I'd use the base 10.

10x17=170 and 2x17=34.

170+30=200 and 200+4=204

In Russia back in a day we'd would do:
10x17=170 and 2x17=34 and then add 170 and 34 by heart. That's it, keep it simple.
There is so much going on in your education system and I don't understand half the words used in math, but it hasn't helped your children learn to calculate.
I had a coworker(she has Bachelor's degree) who asked me if 20% tip on a $100 tab paid by 1 card is more than the same check paid by 4 credit cards plus 20% tip on each card based on their amounts.WTH!
The other girl had to divide cash into 5 piles equally. At the end she was left holding $5 bill. She had enough dollar bills in piles to make the change- put $5 into first pile and take 4 1-dollar bills out, then put one into each pile. Couldn't figure it out, went and got more change for the $5.
Even though I have worked with many more foreigners than Americans, it has always been an American who can't figure out how do calculate something. What gives?

This is why everyone is saying that these new methods are new, different from how we adults, including your coworker, learned it. The goal is to have our children grow up to be better at math than we are. Laudable goal, isn't it?

+1 I am an immigrant but educated here in the US. The way math used to be taught was mostly rote memorization. I can figure out the % problem because I am a math person, but the Russian PP is right, there are *a lot* of American adults who would have a problem with this kind of "simple" math because math education here didn't focus on the why's earlier on, or if they did, it was just cursory. I feel like most adults dislike math because they have a weak understanding of the basics, and I wonder if these same people would find math easier if they were taught math the way it is being taught today to little kids.

I like how math now in the early years focuses a lot more on playing around with numbers; some parents dislike that kids have to learn how to do simple math in different ways when math should be all about the fastest route. But, that's not the point of this type of teaching. It is to teach the kids at an early age how numbers work. In the later years, they do use the simplest and fastest method, and they don't have to always "explain their thinking" - my older DC is in 5th grade taking MCPS compacted math, and the way DC does math now is what most parents would recognize.

You can work with your DCs on rote memorization of the multiplication table, but I would not just rely on this method. You have to know your kid, and how your kid thinks/learns. For some kids, if they memorize first, they will rely on the rote memorization and not understand the whys.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

I'd use the base 10.

10x17=170 and 2x17=34.

170+30=200 and 200+4=204

In Russia back in a day we'd would do:
10x17=170 and 2x17=34 and then add 170 and 34 by heart. That's it, keep it simple.
There is so much going on in your education system and I don't understand half the words used in math, but it hasn't helped your children learn to calculate.
I had a coworker(she has Bachelor's degree) who asked me if 20% tip on a $100 tab paid by 1 card is more than the same check paid by 4 credit cards plus 20% tip on each card based on their amounts.WTH!
The other girl had to divide cash into 5 piles equally. At the end she was left holding $5 bill. She had enough dollar bills in piles to make the change- put $5 into first pile and take 4 1-dollar bills out, then put one into each pile. Couldn't figure it out, went and got more change for the $5.
Even though I have worked with many more foreigners than Americans, it has always been an American who can't figure out how do calculate something. What gives?

This is why everyone is saying that these new methods are new, different from how we adults, including your coworker, learned it. The goal is to have our children grow up to be better at math than we are. Laudable goal, isn't it?

Anonymous wrote:

The schools really don't give kids the opportunity to do that. Even if the facts are memorized, for years they are required to "show their strategies" in their work by skip counting, repeated addition, arrays, etc. Honestly the vast majority of students get these concepts pretty quickly, and having to do these long drawn-out processes for years after it's already understood it tortuous.

Evidently not, though.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

I'd use the base 10.

10x17=170 and 2x17=34.

170+30=200 and 200+4=204

In Russia back in a day we'd would do:
10x17=170 and 2x17=34 and then add 170 and 34 by heart. That's it, keep it simple.
There is so much going on in your education system and I don't understand half the words used in math, but it hasn't helped your children learn to calculate.
I had a coworker(she has Bachelor's degree) who asked me if 20% tip on a $100 tab paid by 1 card is more than the same check paid by 4 credit cards plus 20% tip on each card based on their amounts.WTH!
The other girl had to divide cash into 5 piles equally. At the end she was left holding $5 bill. She had enough dollar bills in piles to make the change- put $5 into first pile and take 4 1-dollar bills out, then put one into each pile. Couldn't figure it out, went and got more change for the $5.
Even though I have worked with many more foreigners than Americans, it has always been an American who can't figure out how do calculate something. What gives?

Anonymous wrote:

Anonymous wrote:Memorization does not come at the expense of understanding. They are not mutually exclusive .

I don't think the teacher is saying that they are. But instead that the order of learning matters. A kid who learns to memorize early may not put the effort into learning the multiplication concepts thoroughly. And instead, s/he may just use the memorized algorithms to solve the problems. I can see my son doing that. He's working on three digit addition right now in third grade, and they are using the partial sums method of solving them, rather than carrying digits to the left. This method really instills place value for him, in a way just carrying a digit to a different column does not. He will learn that traditional algorithm, too, but if he had known it first, he probably wouldn't do the work involved with the partial sums method. Because this algorithm feels unwieldy, too lengthy, yet it teaches the concept very thoroughly.

The schools really don't give kids the opportunity to do that. Even if the facts are memorized, for years they are required to "show their strategies" in their work by skip counting, repeated addition, arrays, etc. Honestly the vast majority of students get these concepts pretty quickly, and having to do these long drawn-out processes for years after it's already understood it tortuous.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:
MCPS starts multiplication in a slow way in 3rd grade (more towards the middle of the year). It is reviewed again in 4th grade, and the 5th grade teachers remind parents that students need to know their basic math facts with rapid recall.

I would strongly encourage you to start working on multiplication as soon as possible, in a regular way, so that your child knows it off by heart. It will make word problems and multi-step processes so much easier, by freeing up brain space for working out the rest of the question.

Please don't do this.

It's important that kids have opportunities to explore multiplication concepts, and work with manipulatives, arrays and repeated addition to figure out problems before they start to memorize their facts. Memorizing math facts is important, but there is plenty of time to do it if you start in the second half of 3rd grade and 4th grade after they've had those experiences.

Kids who learn memorization first, before they explore the whys of multiplication, can end up with brittle understandings of multiplication, which will trip them up when they get to higher level math in middle school.

-- a teacher

Oh please, multiplication concepts are pretty simple...my kids both understood the underlying concept when they were five. It's not like we're talking about calculus here.

A different teacher here, and there is so much to explore in multiplication. If your five year olds understood the distributive, commutative, and identity properties, arrays, factors, and multiplication as an inverse to division...well, more power to 'em. But I have honors high school math students who rely on memorization who can't figure out 7x12 in their heads, while my third grader can do it in about 3 seconds by adding 70+14.

Obviously I couldn't agree more with the previous teacher.

There's still no harm in memorizing them early. They will be learning the underlying concepts of multiplication ad nauseam for the next few years in school.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:
MCPS starts multiplication in a slow way in 3rd grade (more towards the middle of the year). It is reviewed again in 4th grade, and the 5th grade teachers remind parents that students need to know their basic math facts with rapid recall.

I would strongly encourage you to start working on multiplication as soon as possible, in a regular way, so that your child knows it off by heart. It will make word problems and multi-step processes so much easier, by freeing up brain space for working out the rest of the question.

Please don't do this.

It's important that kids have opportunities to explore multiplication concepts, and work with manipulatives, arrays and repeated addition to figure out problems before they start to memorize their facts. Memorizing math facts is important, but there is plenty of time to do it if you start in the second half of 3rd grade and 4th grade after they've had those experiences.

Kids who learn memorization first, before they explore the whys of multiplication, can end up with brittle understandings of multiplication, which will trip them up when they get to higher level math in middle school.

-- a teacher

Oh please, multiplication concepts are pretty simple...my kids both understood the underlying concept when they were five. It's not like we're talking about calculus here.

Agree.

Another teacher

My Montessori first grader knows multiplication pretty well. Not by memorization, but he can figure out the answer in his head most of the time for anything up to 10x10. And instead of saying "times" they think of it as "rows of." So the question is: what is 5 rows of 6? He will continue in this program through 8th grade (thank you PGCPS!), so I'll be interested to see how it progresses. Montessori seems to be on its own schedule.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

New poster but isn't it obviously 12 x 12 + 12 x 5 ?

Yes. And this is a easier method than base ten for anyone who has memorized through 12x12.

Cool. I'm the one who suggested base 10 above. For whatever reason that's what came to mind for me first. But your way is easy and intuitive, too.

I think that's the whole point, really. Numbers are great. There are so many different ways to get to the same answer, and different paths/strategies will resonate more with different kids.

So we want to do whatever we can to help them manipulate and play with numbers so they can learn many different ways to get to the same end point. In part so they have different tools in their arsenal, and in part so they go into higher math with confidence that they can break down complicated problems into familiar parts in order to solve them. Shortcuts and memorizing math facts are helpful but ultimately not nearly enough.

I find this fascinating, actually. I'm an engineer, so no stranger to math. But I was shocked when we started working on the multiplication tables with DS (rising 3rd grader) over the summer, at his school's request. After we got through the "easy" ones (2, 5, 10), we threw 6x8 at him, just to see what would happen. He thought for a few minutes, counted on his fingers, and announced 48. Huh?!?!?

We asked him to explain what he did. He told us that 5x8 = 40 (got that by counting by fives, using his fingers to keep track, until he got to 8 5s). Then another 8 would be 48.

He still uses that method, although he knows more of them by recall now just through repetition. But I love that he has this fallback method to figure things out, and really understands what is going on. I learned the old-school way of sitting down with a huge matrix and running flash cards until I was blue in the face, so I think this way is awesome!

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

New poster but isn't it obviously 12 x 12 + 12 x 5 ?

Yes. And this is a easier method than base ten for anyone who has memorized through 12x12.

Cool. I'm the one who suggested base 10 above. For whatever reason that's what came to mind for me first. But your way is easy and intuitive, too.

I think that's the whole point, really. Numbers are great. There are so many different ways to get to the same answer, and different paths/strategies will resonate more with different kids.

So we want to do whatever we can to help them manipulate and play with numbers so they can learn many different ways to get to the same end point. In part so they have different tools in their arsenal, and in part so they go into higher math with confidence that they can break down complicated problems into familiar parts in order to solve them. Shortcuts and memorizing math facts are helpful but ultimately not nearly enough.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

New poster but isn't it obviously 12 x 12 + 12 x 5 ?

Yes. And this is a easier method than base ten for anyone who has memorized through 12x12.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

New poster but isn't it obviously 12 x 12 + 12 x 5 ?

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.

I'd use the base 10.

10x17=170 and 2x17=34.

170+30=200 and 200+4=204

Anonymous wrote:

Anonymous wrote:What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level. Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means. it doesn't mean that they won't learn more and develop a deeper understanding. But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.

If your child memorizes the times tables up to 12x12, that's great. It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head. Quickly.


A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication." It's not just about the basic concept of repetitive addition. It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both. Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child. Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory. Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory. Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.