3rd Grade and Multiplication

[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.

This certainly seems to be the approach in DCPS, and now that I have a 4th grader working on multi-digit multiplication and long division, I understand why. He had a hard time memorizing his math facts (emphasized in 2nd and 3rd grade), and it definitely slows him down as he's trying to master the more complex concepts.

[Anonymous]

My third grader hasn't started learning multiplication yet this year, but was taught the concepts and some easy facts ( 2,5,10's) in second grade at school. I made him memorize his times tables in between first and second grade to get it over with. He then worked on division facts this summer which were really easy since he knows multiplication so well. Have your kid memorize them ASAP if your kid is in third grade.

[Anonymous]

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.

[Anonymous]

Here's the thing: for some kids, math is intuitive, easy. So, yes, they will understand multiplication concepts easier/faster, and it would be fine if they rote memorized the times table first.

For the kids that don't find math as intuitive, it helps to slow it down, and not learn math by rote memorization first, but by the concepts that the teacher PPs have stated.

So, really, it depends on your child. But, I have to say, judging by that article about how US adults' math skills suck compared to even some 2nd world countries, I think the majority of people are in the latter camp category - math is not a strong subject for most people.

[Anonymous]

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.

[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.

Yup. Memorizing facts is good. Understanding conceptual foundations is good. You need both if you're going to progress in math. BOTH.

[Anonymous]

Anonymous wrote:

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.

Yup. Memorizing facts is good. Understanding conceptual foundations is good. You need both if you're going to progress in math. BOTH.

First teacher here, and sequencing them is important. Kids who have been taught the multiplication is about memorizing facts, often don't do the heavy lifting they need to build conceptual foundations. On the other hand, kids with a strong conceptual understanding to at least a mid third grade level easily understand the point of memorization. If done, right memorization takes a few months. So, starting mid third instead of earlier still gives them plenty of time to get the facts down before they need to use the facts fluently in multidigit computations and fraction work in fourth and beyond.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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.

Yup. Memorizing facts is good. Understanding conceptual foundations is good. You need both if you're going to progress in math. BOTH.

First teacher here, and sequencing them is important. Kids who have been taught the multiplication is about memorizing facts, often don't do the heavy lifting they need to build conceptual foundations. On the other hand, kids with a strong conceptual understanding to at least a mid third grade level easily understand the point of memorization. If done, right memorization takes a few months. So, starting mid third instead of earlier still gives them plenty of time to get the facts down before they need to use the facts fluently in multidigit computations and fraction work in fourth and beyond.

I'm the "BOTH" PP, and I completely agree.

Anecdotally, as a Montessori student (and I see it's still done today with my two young kids), we spent a lot of time breaking down numbers and putting them back together in sets, arrays, and so on from the early years and on through 4th (when I stopped attending and moved to public school). Memorizing multiplication facts came in the middle of what would be considered 3rd grade. By then, memorizing them was easy-peasy. Division and fractions also came pretty easy.

[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.

Some people just suck at math--even some people who have managed to get themselves enrolled in "honors" math. That's the difference.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

Yup. Memorizing facts is good. Understanding conceptual foundations is good. You need both if you're going to progress in math. BOTH.

First teacher here, and sequencing them is important. Kids who have been taught the multiplication is about memorizing facts, often don't do the heavy lifting they need to build conceptual foundations. On the other hand, kids with a strong conceptual understanding to at least a mid third grade level easily understand the point of memorization. If done, right memorization takes a few months. So, starting mid third instead of earlier still gives them plenty of time to get the facts down before they need to use the facts fluently in multidigit computations and fraction work in fourth and beyond.

I'm the "BOTH" PP, and I completely agree.

Anecdotally, as a Montessori student (and I see it's still done today with my two young kids), we spent a lot of time breaking down numbers and putting them back together in sets, arrays, and so on from the early years and on through 4th (when I stopped attending and moved to public school). Memorizing multiplication facts came in the middle of what would be considered 3rd grade. By then, memorizing them was easy-peasy. Division and fractions also came pretty easy.

Teacher #2 again. I adore Montessori math. They get the concepts at the developmentally appropriate time (bead chains when they are in the concrete phase of development, then moving to the multiplication operation when they are in the abstract phase). Unfortunately a lot of that gets lost when parents storm in claiming their Kindergarteners are bored and need to be doing specific algorithms for multidigit addition so their brilliant 5 year old minds don't atrophy.

[Anonymous]

Anonymous wrote:

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.

Some people just suck at math--even some people who have managed to get themselves enrolled in "honors" math. That's the difference.

Well, that just goes against my philosophy as an educator. I'd rather all young students get the scaffolding they need to develop a strong sense of numeracy. I don't believe these students "suck at math." Rather, they are so reliant on memorized algorithms they freeze when they are required to problem solve.

[Anonymous]

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

We were told by our teachers, our principal, other parents, and by the teacher again - to work on having them memorize them.

[Anonymous]

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

[Anonymous]

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.

[Anonymous]

My third grader has done foundational work for multiplication already and understands the concept, but he hasn't done any memorization work yet. We just got this Kumon workbook to do as a supplement to homework, and he enjoys working through it: http://www.amazon.com/Grade-Multiplication-Kumon-Math-Workbooks/dp/1933241543/ref=sr_1_1?ie=UTF8&qid=1444916893&sr=8-1&keywords=kumon+multiplication I like the workbook because it starts off adding numbers (i.e.--7+7+7+7+7+7=) and then moves to drills. It's easier to understand, and he's excited to be doing something a little more advanced than what they're doing on class right now.