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Multiplication fluency?

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 Miccol71 Joined: Sep 2005 Posts: 436 Senior Member
Miccol71

Joined: Sep 2005
Posts: 436
Senior Member
Multiplication fluency?
06-06-2007, 03:46 AM
 #1

What do you consider fluent with multiplication and division facts?

Does your school or district have any benchmarks for this?

 SusanTeach Joined: Oct 2001 Posts: 15,415 Senior Member
SusanTeach

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Posts: 15,415
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fluency
06-06-2007, 10:34 AM
 #2

We consider them fluent when they can make 100% on 25 problems within 2 minutes.

I honestly don't think it's a benchmark, but they're told to be "proficient" in both areas so I guess it's our way of showing that.

 New Mex Teacher Joined: Aug 2005 Posts: 291 Full Member
New Mex Teacher

Joined: Aug 2005
Posts: 291
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fact fluency
06-07-2007, 04:50 PM
 #3

Our fourth grade team came up with 85% or higher on 100 facts in 5 minutes. When they reach 100%, they don't need to take it again.

Last edited by New Mex Teacher; 06-07-2007 at 04:51 PM.. Reason: addition

 Neil Dempsey Guest
Neil Dempsey

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Math Consultant
06-09-2007, 10:41 AM
 #4

I'd suggest two things: first, don't look for proficiency in a timed manner. Studies have shown again and again that the negative results of expecting kids to perform in a certain amount of time are too numerous to list (but I will list a couple)...it fosters math anxiety and doesn't necessarily result in learning. For me, the big one is that it serves to remove math from any real-world connections the kid might be forming. When you're an adult, it is very infrequent (if at all) that you are expected to multiply or divide a bunch of questions in a certain amount of time. Kids are pretty savvy. Doing this just becomes more evidence that "math is something we do in school".
Second, instead of focusing on facts per se, there are some wonderful constructivist activities through which students can construct their own meaning. In other words, they can get a solid picture of what multiplication and division really mean. Once they have that (and maybe their own personal algorithm they've developed), the facts are no longer a chore to learn. Generally, they have absorbed most of them and the rest follow suit shortly.
A lot of the stuff we do with kids is because that's the way it was done with us when we were in school. Learning facts is an example of this. We all did it. But was it worthwhile? In most cases, we were able to learn the facts. It didn't make a lot of sense to me or my friends and we sure weren't told why or how the operations worked. If anything, this is reflective of the procedural approach to math: here's how to do it, now go practice. We need to stop and ask ourselves a couple of things. Why am I doing this in my classroom? (Is it because I've always done it? Is it because everyone is mindlessly doing it? Is there research to support it?) Are kids truly learning? (Not just memorizing but really learning?)

 Miccol71 Joined: Sep 2005 Posts: 436 Senior Member
Miccol71

Joined: Sep 2005
Posts: 436
Senior Member

06-10-2007, 08:23 AM
 #5

Fluency is a grade level expectation..."demonstrates fluency with facts..."

Given that I have to evaluate students for the grade card, what is a suggestion?

 Neil Dempsey Guest
Neil Dempsey

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Math Consultant
06-10-2007, 11:24 AM
 #6

I would interpret fluency to be reflective of understanding. I'd consider a student fluent if he or she was able to answer something like "Can you show me, using a couple of different ways, why 5 times 6 is 30?" Or if the student is able to use arrays (for example) to demonstrate why 45 divided by 9 is 5, I would be delighted. In other words, I wouldn't focus on the acquisition of facts but rather understanding the deeper concepts. If understanding is there, the facts will come (more easily and sooner than you might expect).

 myoung Joined: Feb 2007 Posts: 819 Senior Member
myoung

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math fact fluency
06-10-2007, 07:23 PM
 #7

I definitely think a constructivist approach to introducing multiplication/division is worthwhile and necessary. However, I really think they need to have quick recall of math facts (at least multiplying 1-11). I teach 5th grade and their ability to do long division and work with fractions is seriously impaired if they're not fluent with their math facts. I think understanding the algorithm behind multiplication and knowing your math facts is two totally separate things. We work toward 100 math facts in 5 minutes--timing only eliminates counting on fingers and working the problems out manually. This year, I dedicated two class days a week to math fact practice (using games and timed speed drills) and saw dramatic growth--in some cases 86% growth in math fact proficiency from beginning of year assessments. I do think we need to make math as real-world as possible, but, from what I've seen, not providing adequate math fact practice just sets kids up for failure later on. Again, not because they don't understand the algorithm, but just because they haven't learned 8x6...

 Miccol71 Joined: Sep 2005 Posts: 436 Senior Member
Miccol71

Joined: Sep 2005
Posts: 436
Senior Member

06-10-2007, 07:46 PM
 #8

I teach 4th and I'm moving up to 5th this next school year. My students understand the idea of multiplication and division, however, they need to be able to quickly and accurately compute.

Math facts are to math what sight words are to reading.

 dolmansaxlil Joined: Jan 2007 Posts: 692 Senior Member
dolmansaxlil

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Agreed
06-11-2007, 02:47 AM
 #9

Our kids understand multiplication. They can show me WHY 6x7 is 42 in many different ways. But since I teach grade 7/8, I've noticed that a lot of kids are having problems with later concepts because basic math facts are not memorized. I think it's really important to make sure that students first learn multiplication through constructivist activities. But once they have a full understanding of how multiplication works, learning those basic facts until they are second nature makes later math easier.

 JRichard Joined: Jul 2006 Posts: 1,381 Senior Member
JRichard

Joined: Jul 2006
Posts: 1,381
Senior Member

06-11-2007, 03:45 AM
 #10

I totally understand and agree that understanding why something works in math helps them to see more value in it, use it in different ways, etc. HOWEVER, we can't give up on memorization entirely. I am currently teaching math summer school to 8th graders. I gave them an untimed multiplication test of 100 problems (0-9). It took them an average of over 20 minutes to complete. I asked them to evaluate themselves at the top and write "memorized" or "not memorized." Most of them put not memorized. I only had two or three out of twenty finish in what I would consider a reasonable amount of time with all of the problems correct.

When I got into working with each student, I discovered most of them did not have the upper numbers memorized. A few students only had 0, 1, and 2 memorized. I have one child who has memorized to 5, but has to count out on her fingers anything higher.

My point is this: my math coordinator vehemently told me that multiplication was not a grade-level standard and therefore I should not review this with them in summer school. I asked her, "OK, so how are they going to do four years of math in high school, get through algebra, trig, etc. if they don't know their multiplication?" She responded with, "It should have been taught in 3rd and 4th grade." I said, "I'm sure it was, but they have not memorized the material."

She basically kept coming back to "It's not your problem." If you cannot remediate something like multiplication in summer school, what is summer school for, I ask?

Constructivism is great, but it is necessary for the children to actually memorize their math facts after they understand the concepts of the operation. If they don't, they are seriously impaired when they get into algebra, trig, calculus, etc.

JMO
Jenny

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