3rd Grade and Multiplication

[Anonymous]

Research does not support the fact that students are hurt by memorizing basic math facts early. The teachers posting on this thread are not presenting the whole picture.

The whole picture is that children learn differently and at different speeds. Some of them are more left-brained than right-brained. Most would benefit from early memorization to bolster their critical thinking, without any injury to their deep understanding of math. Some with dyscalculia who *would have had problems anyway*, give the appearance of relying on their memory without understanding the concepts. Of course, because it's the only way they have of trying to keep up! Again, these are students without scintillating math ability who need extra support in math regardless of the teaching method chosen.

How do I know? I have both kinds of kid - and have seen the contrast in their intuitive grasp of math. For the child with a slower mathematical understanding, early memorization is even more important! It's not a crutch, it's a way to let them focus more energy on the underlying concepts.

[Anonymous]

Anonymous wrote:

Anonymous wrote:5-6 year olds learn multiplication in montessori. It is really taught in 3rd grade?

Yes, Montessori gives a great foundation for understanding multiplication. It is taught in third grade too, and is used throughout education, like multiplying fractions and decimals, etc. Your five-year-old has not learned all there is to know about multiplication in Montessori. Don't worry, they will not be bored in 3rd grade.

Yes they will. My child was

[Anonymous]

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

+1. The reason so many parents struggle to help their kids with math these days is because we weren't taught to truly understand it, just to memorize it. Don't let you kids fall into the same trap.

I'm 18:13 and I couldn't disagree more. There is a documented problem these days with kids lacking rapid recall of basic math facts. This is directly tied to the lack of encouragement they have at school to learn their facts quickly.
MCPS, and other school districts, slow down the math curriculum, not in itself a bad thing, but they make it a bad thing because their worksheets are unimaginative. They lose so many kids that way! If the teachers were offering them brainteasers and challenging ways to solve problems with basic operations, that would be wonderful. Except they don't, unless the kids are in the Highly Gifted Center.
First there is plenty of time in 3rd grade or before 3rd grade to work with manipulatives and other concrete displays for multiplication. My Kindergartner in Montessori is learning multiplication by manipulatives. These things can be taught at a very young age. There is no "developmental barrier".
Second even if there wasn't, there is actually virtue in memorizing and rote learning and copying. This has been pooh-poohed in the past, but research shows that memorization helps the brain to liberate more "solving power" for problems necessitating higher order thinking skills. So instead of getting bogged down by trying to recall basic operations, the student can focus on the actual problem, and organize of the logical steps to solve it.

You say there's a "documented problem." Show us the documents.

You are full of shit.

Why is it a problem if young ES kids lack the ability to instant recall basic math facts? Serious question.

[Anonymous]

Anonymous wrote:5-6 year olds learn multiplication in montessori. It is really taught in 3rd grade?

Yes, it is. Sorry your kids are in Montessori. That must be hard.

[asnmdirteha]

Anonymous wrote:
Research does not support the fact that students are hurt by memorizing basic math facts early. The teachers posting on this thread are not presenting the whole picture.

The whole picture is that children learn differently and at different speeds. Some of them are more left-brained than right-brained. Most would benefit from early memorization to bolster their critical thinking, without any injury to their deep understanding of math. Some with dyscalculia who *would have had problems anyway*, give the appearance of relying on their memory without understanding the concepts. Of course, because it's the only way they have of trying to keep up! Again, these are students without scintillating math ability who need extra support in math regardless of the teaching method chosen.

How do I know? I have both kinds of kid - and have seen the contrast in their intuitive grasp of math. For the child with a slower mathematical understanding, early memorization is even more important! It's not a crutch, it's a way to let them focus more energy on the underlying concepts.

I agree that each student learns different and at times it is up to educators and parents to understand the needs of the students. I typically use a variety of supplemental websites from memorizing basic numbers to actual learning of a concept. For me Beestar has been extremely helpful for my students. My students have really loved the website and I can pace each of them at a different speed which helps them in the long run. Beestar also has a gifted/talented section for students that can be placed in more challenging classes. In the end it is all about finding that balance and for my students Beestar does a great job between being challenging but keeping students motivated.

[Anonymous]

IDK. My 4th grader did a ton of "jump counting" during preschool - so yes, it was "rote" memorizing, but it seemed to instill a great sense of number ordering. Maybe he would have had an intuitive grasp of math anyway, but he started memorizing the multiplication table in 1st grade (because it was fun), and has no problem with the "higher order math concepts" in 4th grade.

[Anonymous]

For all the upset about the current system of teaching children (and I am worried about quite a bit of it) I will say that the focus on UNDERSTANDING numeracy, and really GETTING math at it's fundamental level, is very different from when I was in being educated.

I was never taught to be "flexible" with numbers, that I could get the answer to 29+14 by doing 30+14 (which is easy) then taking away 1. I picture 29+14, start carrying the one in my head... it's a riot to see me! And takes me forever. My husband does that stuff in his head.

We were just talking about fractions the other day (we're in late 40s) and I realized that I have never stopped to really THINK ABOUT what multiplying fractions is - I learned the "rule" of how to figure it out and boy, do I follow rules well. But if I don't remember the rule (and I didn't 2 days ago) then I'm flumoxed. Since he knows the intention of multiplying fractions, he understands what he is doing.

I'm just a trained monkey. A well-trained one who got all A's in math classes, but a trained monkey.

I would rather my kids not be just trained monkeys.

And, yes, I also think children need to have their "addition tables" and "times tables" memorized at some point, but it seems to make more intuitive sense to wait until they understood what adding and multiplying mean before they just memorize stuff. Memorizing is important - you can't stop in geometry to use your fingers to figure out what 8+5 or 8x5 is - you gotta have that memorized. Just not before they understand what the concept is.

Of course, all children can "say their ABCs" and can count to 10 by walking up stairs and saying the numbers in the correct order way before they understand what each letter sounds like, how to combine it to make a word, etc. But that feels different than memorizing multiplication tables.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5-6 year olds learn multiplication in montessori. It is really taught in 3rd grade?

Yes, Montessori gives a great foundation for understanding multiplication. It is taught in third grade too, and is used throughout education, like multiplying fractions and decimals, etc. Your five-year-old has not learned all there is to know about multiplication in Montessori. Don't worry, they will not be bored in 3rd grade.

Yes they will. My child was

[Anonymous]

My child is in 3rd grade in MCPS (not a W cluster). They just finished up with multiplication (for now I assume) and are moving on to fractions and numerator and denominator stuff.

[Anonymous]

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

+1. The reason so many parents struggle to help their kids with math these days is because we weren't taught to truly understand it, just to memorize it. Don't let you kids fall into the same trap.

I don't see anything wrong with memorizing for faster recall, if you already understand the concept. My child figured out for himself that multiplication and division are just variants of the skip counting concept that he learned in K. But he has memorized some multiplication to get faster recall. He adores math, we don't force him to do memorize or do anything.

[Anonymous]

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.

[Anonymous]

Anonymous wrote:Has your 3rd grader started learning multiplication in school yet? If not do they already know their multiplication facts?

DS started around Oct-Nov in second grade - he's in Fairfax County. They worked on addition (up to one thousand) and then multiplication and division from the prospective of addition. After that it was memorization.

[Anonymous]

Anonymous wrote:For all the upset about the current system of teaching children (and I am worried about quite a bit of it) I will say that the focus on UNDERSTANDING numeracy, and really GETTING math at it's fundamental level, is very different from when I was in being educated.

I was never taught to be "flexible" with numbers, that I could get the answer to 29+14 by doing 30+14 (which is easy) then taking away 1. I picture 29+14, start carrying the one in my head... it's a riot to see me! And takes me forever. My husband does that stuff in his head.

We were just talking about fractions the other day (we're in late 40s) and I realized that I have never stopped to really THINK ABOUT what multiplying fractions is - I learned the "rule" of how to figure it out and boy, do I follow rules well. But if I don't remember the rule (and I didn't 2 days ago) then I'm flumoxed. Since he knows the intention of multiplying fractions, he understands what he is doing.

I'm just a trained monkey. A well-trained one who got all A's in math classes, but a trained monkey.

I would rather my kids not be just trained monkeys.

And, yes, I also think children need to have their "addition tables" and "times tables" memorized at some point, but it seems to make more intuitive sense to wait until they understood what adding and multiplying mean before they just memorize stuff. Memorizing is important - you can't stop in geometry to use your fingers to figure out what 8+5 or 8x5 is - you gotta have that memorized. Just not before they understand what the concept is.

Of course, all children can "say their ABCs" and can count to 10 by walking up stairs and saying the numbers in the correct order way before they understand what each letter sounds like, how to combine it to make a word, etc. But that feels different than memorizing multiplication tables.

+1

I'm embarassed to say this is the same with me and my DH.

We both got excellent grades, and we both aced our SATs etc. That's not the issue.

But when we went off to college, he had with a far deeper and more conceptual understanding of math than I ever did.

For him, math is intuitive and easy. For me, it's mostly rule-based and tedious. Also, I found higher math far more difficult in college. I just lacked that conceptual foundation for math, and it held me back.

The sad part is that I very much enjoy conceptual and abstract learning. I would have loved to learn elementary and middle school math the way it's taught now, and it would have given me a much better math foundation for the long run. But that's not the way it was taught at my schools, and my parents did not know or have an interest in helping me understand it conceptually.

[Anonymous]

Anonymous wrote:

Anonymous wrote:For all the upset about the current system of teaching children (and I am worried about quite a bit of it) I will say that the focus on UNDERSTANDING numeracy, and really GETTING math at it's fundamental level, is very different from when I was in being educated.

I was never taught to be "flexible" with numbers, that I could get the answer to 29+14 by doing 30+14 (which is easy) then taking away 1. I picture 29+14, start carrying the one in my head... it's a riot to see me! And takes me forever. My husband does that stuff in his head.

We were just talking about fractions the other day (we're in late 40s) and I realized that I have never stopped to really THINK ABOUT what multiplying fractions is - I learned the "rule" of how to figure it out and boy, do I follow rules well. But if I don't remember the rule (and I didn't 2 days ago) then I'm flumoxed. Since he knows the intention of multiplying fractions, he understands what he is doing.

I'm just a trained monkey. A well-trained one who got all A's in math classes, but a trained monkey.

I would rather my kids not be just trained monkeys.

And, yes, I also think children need to have their "addition tables" and "times tables" memorized at some point, but it seems to make more intuitive sense to wait until they understood what adding and multiplying mean before they just memorize stuff. Memorizing is important - you can't stop in geometry to use your fingers to figure out what 8+5 or 8x5 is - you gotta have that memorized. Just not before they understand what the concept is.

Of course, all children can "say their ABCs" and can count to 10 by walking up stairs and saying the numbers in the correct order way before they understand what each letter sounds like, how to combine it to make a word, etc. But that feels different than memorizing multiplication tables.

+1

I'm embarassed to say this is the same with me and my DH.

We both got excellent grades, and we both aced our SATs etc. That's not the issue.

But when we went off to college, he had with a far deeper and more conceptual understanding of math than I ever did.

For him, math is intuitive and easy. For me, it's mostly rule-based and tedious. Also, I found higher math far more difficult in college. I just lacked that conceptual foundation for math, and it held me back.

The sad part is that I very much enjoy conceptual and abstract learning. I would have loved to learn elementary and middle school math the way it's taught now, and it would have given me a much better math foundation for the long run. But that's not the way it was taught at my schools, and my parents did not know or have an interest in helping me understand it conceptually.

Ditto.

[Anonymous]

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.

Both understanding and memorization should be learned. Whether multiplication understanding needs to be taught before memorization, I don't think matters as much.