# Multiplication Facts help!

Discussion in 'Elementary Education' started by TeachCafe, Dec 10, 2019.

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Dec 10, 2019

How do you teach it? The district doesn't want us drilling them. We can't teach them in isolation (though we play silly videos as away of getting around this). Our math coach reiterates that drilling doesn't teach it.

Yet, THEY ARE NOT learning their facts above 5. I have some bright students and some very low students.

6x7....crickets for about 30 seconds to a minute. Let's not even talk about 2 digit by 1 digit.

How do you teach it? They need to know them. I feel like if they just knew the facts with somewhat automaticity then arrays, equal groups, etc would come much more easily.

A few are on the flip side and cannot understand why 4x6 and 6x4 are not the same in equal groups and arrays but that's a whole different ball game.

I need students even if they need to use their fingers to get 8x7 within 10-15 seconds at least. Maybe 20. I've tried the count up from what you know 8x5 is 40...plus 8 is 48...plus 8...crickets. Some need pencil/paper to add 48 + 8. They cannot mentally/visualize that 8 plus 8 is 16 so it's moving to the next number decade from the 40s to the 50s so it's 52.

Help!

3. ### RainStormPhenom

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Dec 10, 2019

TeachCafe,
This is a major problem in education today. Everyone says "they don't need to memorize it, they can use other strategies." But those other strategies take forever, and require perseverance that, if our students had it, they would easily memorize the facts.

Sorry -- if you want automaticity, you have to drill. If you don't want to drill, you aren't going to get automaticity.

I get so tired of hearing "don't use flash cards, don't drill, don't used time programs, don't make them memorize it" and then "why did they do so poorly on state testing?" Hello... part of being successful in math does require some memorization. Waiting for a 7th grade child to draw an 8 by 7 array and then count up the circles one by one is just not a reasonable strategy. The chances of them drawing it correctly, and then counting it correctly, and not giving up when it takes so long -- the strategy is just not appropriate to the occasion.

That's my story, and I'm sticking to it!

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Dec 10, 2019

First, they need to know all their doubles. 8+8, 7+7, 6+6 etc. If they don't, you are right that 48+8, they will be helpless.

Whatever way you choose to do multiplication they need to practice, practice, practice. I use a lot of games, stories, videos, and even flash cards. I do find that certain strategies work with different students, but nearly all of them need far more practice than any school would ever advocate. Multiplication facts are so helpful, and such a detriment to higher math if one doesn't know them.

5. ### a2zVirtuoso

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Dec 11, 2019

I am one against flashcards to teach. I am really against it. I am against timed tests to teach. I am not against either of those to improve speed once students have a solid foundation and knowledge of the facts and just need to improve speed, not accuracy.

What does the admin mean by drill. People have different ideas.

One good way to learn facts, in addition to teaching the concepts of multiplication, is oral and visual repetition. There are two ways to do this. The first is whole class repetition using displayed facts. The other is teaching and having students use the multiplication chart by using fingers or finger and pencil and saying the facts while they move down and to the right to find the facts. They must be saying it to themselves while they are tracing to find the fact. It brings it all together. It may be whisper voice, but they need all three senses. They can even have a fresh paper copy and the problem sheet can be designed so that when the kids color in the matching fact it creates a cool pattern. In fact, the chart is fabulous for teaching the patterns of numbers.

People don't do extra work longer than they need to, except when it is stated as mandatory and the rule follower will do it to follow the rule whether he or she needs it or not.

I know this goes against just about everything we do in school because of the fear of becoming dependent on the tool, but if you think about it, those kids who are dependent on it usually aren't the ones who know the facts anyway and will not learn them otherwise.

The best way to learn something that is rote is by accurate repetition of the information. The problem with flash cards and timed tests as a teaching tool is there is too much guessing involved. Above I did mention that you also have to teach the concept of multiplication also. Multiplication chart patterns support the conceptual goal of teaching facts.

There are strategies to fade out the chart as students know them.

Last edited: Dec 11, 2019

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Dec 11, 2019

I have some weird thoughts on memorizing multiplication.

Understanding and application are essential. Memorization without understanding only lessens the lessons because the purpose of the memorization is to use multiplication as a shortcut for adding or subtracting (as in division). On the other hand, understanding and application without memorization defeats the whole purpose of multiplication. If the facts aren't memorized, what's the use of multiplying in the first place?

Back to understanding, often curricula begin with the "easy" facts, 0 or 1 as a multiplier, or perhaps even 10. These are, in reality, the most difficult to actually learn. Why? Because the next step is to double. Think of it from a kid's point of view. Suddenly, they can't just write 0 or the same multiplicand as an answer, or they can't just tag on a 0. Suddenly, they have different products. And then, lo and behold, we're at the 3's. The products are becoming stranger by the minute.

Times up. I'll write some more thoughts later. I have some strategies for memorization that I'd like to share....

Last edited: Dec 12, 2019

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Dec 11, 2019

All the conceptual training is great, but at the end of the day, 10 year olds needing to mentally add to think through 3 x 4 before recognizing common denominators is driving me crazy. We need both conceptual and memorization. Memorization has a bad rep, but it's really helpful in life - phone numbers, SSNs, anniversary dates.....and multiplication facts.

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Dec 12, 2019

A few more thoughts.

Often curricula presents the "facts" for a certain number by using that number as the multiplier only. This presents a problem later on. The students might not realize that not only does a*b=c, but b*a=c. I found it easier to bank on their current understanding of the commutative property and (in kid-language) recommend that they memorize the facts forwards, backwards, and inside out. By inside out, I'm referring to c=a*b and c=b*a. This prepares them for the next step in memorization--the division facts. I still recall how I learned the commutative property from the old black and white Dennis the Menace TV show.

Dennis was memorizing his multiplication facts and reviewing them with his father. He suddenly discovered that he could save time memorizing, because if he learned a*b, then he already knew b*a.

Except for my personal set of cards, I do not like store bought flashcards. The students learn so much more by creating their own cards on blank index cards. I also encourage them to be creative in decorating their cards. While they are busy decorating, their mind is associating and reviewing the specific fact on that card. I find cooperative practice in small groups with the handmade cards to be more effective than whole group practice, but on the other hand, kids seem to enjoy a "multiplication bee" game.

Another problem I find in the current memorization methods, sometimes parents or curricula tend to push too much memorization at one setting. It's important to memorize a few "bits" at a time. Personally, I hesitate to memorize the facts randomly. The succession of products is, in my opinion, part of the learning, but at the same time, randomized practice should be included. Time is needed to review and review again, and again, the first learned set of facts. Time is needed for false memorizations. This is not a fault of the students' brains: this is an advantage of the human brain over a computer. The student will be certain that the teacher taught 4x7=22 and s/he needs to adjust those neuron pathways accordingly. This results in a stronger usage of memory than any any any current computer can replicate.

Most educational psychology studies indicate that rote memory is not as rote as it might seem. All memorization is associated with previous and further learning if it will be recalled from permanent memory. This is a major purpose for including understanding and application within the "rote" learning. Along with that, some students' brains have no problem finding their own personalized association. It seems to the student (and teacher) that no association was made, it's kind of like a hidden association, but it's there, nonetheless. For me, and I still experience this, especially now that I know what to look for, my associations were connected with my own personal experience of my senses perceptually being mixed. This is probably due to my early heavy exposure to music, and many musicians experience this. I'll try to describe it. 3x6=18. When I think that, I also think specific physical feelings, colors, and shapes. For those who do not think this way, I know that probably sounds weird. (Actually, when I first learned about this in my psychology readings, I was surprised to learn that not everyone thinks like I do. I also found out that my mom experiences learning the same way, and she is also very musical). Anyway, there will be some kind of internal association, but...some students have difficulty finding an association. They are not slow learners or low students; their brain just coordinates facts differently. (I want to be cautious not to be misunderstood at this point, too. Not every association will depend on senses being mixed together such as mine, but every memorization will have some kind of associative experience). I find that creating some (I forget the new name for this) locale experiences in learning can assist these students. Placing the facts to be memorized on a special object or location in the room or building can jump start that student's memorization. For example, it's winter, bring in some old gloves to hang on the wall with the facts to be memorized written on the gloves--and have these students write the facts on the gloves for an extra boost.

Speaking of special associations, a parent told me how he (unfortunately) became frustrated with his daughter not remembering a certain fact. He lost his temper and repeated the fact correctly (with a few extra words I won't print and that he regretted using). Funny thing was, she remembered that fact from then on, (extra words included). I'm not recommending losing our patience, as that causes other problems in learning, but novelty is a shortcut to the permanent memory.

I also recommend not just forcing memorization to math class only. Throughout the day, include a quick review, even if it's just one fact. Perhaps the students can created a special card on construction paper as their "pet" fact for the day, to take to lunch with them and recess, and talk to their pretend pet throughout the day. Putting some facts to music or drilling while music is playing is helpful. Something I did, I played Baroque music while the students quietly memorized facts on the whiteboard.

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9. ### futuremathsprofPhenom

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Dec 12, 2019

Once again, RainStorm nailed it! Have you thought about ever becoming a school superintendent?!

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A balance of conceptual understanding, drilling, and repeated exposure and practice is needed. When I was in third grade, I learned my facts with skip counting music. The more I listened to it, the more I memorized it. Then, with repeated exposure and practice, I memorized my facts. In my current school, we drill. I honestly don't find that it works any better than drilling sight words. Kids have to be exposed to the sight words and math facts in many useful situations before they are memorized. Random drilling out of any context doesn't work for most.

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11. ### RainStormPhenom

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bella84,
I agree with you that drill, just to drill, is ineffective. The kids who are good at memorizing, memorize it quickly. The others continue to struggle. I hate when I see an entire class drilled on facts that 25% of the kids already know.

Skip counting to music is great -- it isn't something that was not available when I was in school, but as a teacher, I know methods change, and what works for one child or one class may be totally different than for another child or class. I frequently use skip counting songs to help my students. I have country, rap, rock, and pop versions.

I remember back to third grade, having the multiplication problems written on the chalkboard and the teacher pointing with her wooden pointer to each number sentence as we chanted "three times three is nine, three times four is twelve, three times five is fifteen" over and over again. I'm certainly not suggesting that type of drill.

But when administrators take away options (like saying no drill, no timed tests, no timed computer programs, no flash cards, no multiplication war games, etc) they are sharply taking away so many strategies that do work in the right situation. I think teachers need as many options as possible -- not having most of their options taken away from them.

12. ### a2zVirtuoso

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We did a lot of skip counting. We also did recitation.

Our teacher told our class directly when people would complain about doing this as a group that unless you were consistently getting 100% on the tests (and timed tests when they were introduced which were only somewhat timed) you needed the practice. Eventually those who mastered the tests were able to choose other things, math related of course, during this group time.

Timed tests were interesting. When time was up, kids marked the problems that were complete. They then went on to complete the sheet. The other way was to bring up your paper as soon as you were done. It was corrected on the spot for accuracy. Timing was based on student ability not some clock.

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I agree, Rainstorm. However, in my current situation, it’s the opposite. None of that is taken away. It’s all forced on us. We are required to give weekly timed tests. Everyone in the school must use the same tests on the same continuum. We are required to use a specific practice program on the computer, we are required to give students a specific amount of time, and we are required to send home the same pass/not pass notes. And that’s no better than than being told that you cannot do those things. My own reading and research tells me that there are other and better ways (Jo Boaler), but I’m not allowed to act on my knowledge and, instead, must implement it as directed by administrators. I’m generally all for curriculum and teaching it as directed by a district, but it’s tough spot to be in when your realize that your district has not kept up with the research and that you are being micromanaged... which could be true whether you are told that you must do timed fact tests or that you cannot do them at all.

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15. ### futuremathsprofPhenom

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Food for thought: I have numerous students from my school who go on to West Point and they are expected to memorize everything from the following link in its entirety to successfully complete their program:

Also, plebes are routinely quizzed at all hours of the day and at random intervals on any of the aforementioned linked things.

In the words of the superior officers, “There comes a time when you just have to know facts.”

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Sure... but my thoughts are that these are high achieving private high school graduates who have made a choice to take on this challenge. In this thread, we are talking about public school elementary students who come from all walks of life and are all heading in a variety of directions.

it’s also easier to remember patterns of words than patterns of seemingly unrelated numbers... That’s why more frequent exposure is necessary with numbers.

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17. ### RainStormPhenom

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This is, indeed, very unfortunate. It speaks to the fact that while schools scream "differentiate!" they then force us to teach every student "the same" -- and as we all know, not every student learns the same way. You make an excellent point.

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18. ### futuremathsprofPhenom

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The familial background is irrelevant. I work with mostly public school students who transfer in, are on scholarship or reduced tuition, and they can memorize tremendous amounts of information. For example, I have a student who comes from a family that makes no more than \$25,000/year and he can recite just about any quote from any movie, verbatim, and memorizes lines for various plays, plus many other things. If he, and others, can memorize that, then they can certainly memorize their multiplication facts.

And most students who go to West Point are public school students.

The numbers are very much related.

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None of this changes the fact that it’s a choice to go to West Point, while it’s not a choice to go to school... Nor does it change the fact that you are comparing exceptional high school graduates to a random draw of elementary age students. Furthermore, everyone’s brain develops and functions a bit differently, with memorization being a stronger and more developed ability for some than others. Stating that everyone can memorize the same things without issue is a blanket statement and untrue. Some will have no difficulty memorizing math facts, while others will struggle immensely, regardless of intelligence, which is why we need to approach learning the facts from a variety of angles. The hope is that we teach them in all these ways while they are young so that, by the time they get to you in high school (or to West Point), they’ll have developed the automaticity necessary to be successful with higher levels of math.

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Oh, and, yes, the numbers are related. But to a young child, they are seemingly unrelated. That’s why more than just drilling is necessary to help them understand the patterns and relationships between them.

21. ### futuremathsprofPhenom

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Fair points, but elementary children have significantly higher brain plasticity and their brains are sponges at that age. Their potential to learn is highest then.

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I can't argue with that.

I mean only to say that drilling and/or timed test should be just one method of teaching math facts for young children, if they are used at all. I don't argue that they need to be learned, just that there are additional methods that should also be used in the elementary grades to help students developing understanding, number sense, and, yes, memorize facts.

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23. ### futuremathsprofPhenom

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Yes, ma’am. I can not argue with you there.

I just meant that students are able to remember huge swathes of information that doesn’t relate to their education and with a small amount of effort, or maybe a great amount of effort, they can memorize their multiplication tables.

For me, it is important for students to not only know that something works, but how and why that it does and so I absolutely agree a variety of methods should be employed. With that said, what I’ve noticed more and more is that students are NOT learning what they should be learning and now they don’t even know basic rules or arithmetic or multiplication facts. An eight grader, to demonstrate, should know what the product of 6 and 2 is without having to use a calculator. A 9th grader should not be using their fingers to add 1 and 6. Or better yet, they fail to realize that it’s easier to count up one from six to “get to” seven, but instead, they keeping counting up from one. This happens all too often at my school when we get students from schools that are forced to use methods that have been suggested here, by and large, and we’re sick of it.

For example, I’m tutoring students right now who are “taught” using the Socratic method for math and they aren’t taught any rules and the teachers are ONLY allowed to do investigative tasks. They are expected to derive everything on their own and it is clearly is not working. Almost no one in the class is learning anything and they are way behind by several units. This is common spread these days.

There comes a time when students should just memorize something and apply the facts they’ve memorized in a variety of different circumstances. They do not have the time to derive everything for every single problem situation.

In my case, I have tutored and taught students from all walks of life from elementary and up and certain methods rarely work for the vast majority of students. They just don’t and I can say as someone who tutored at least a thousand or more students over a 10-year period with varying degrees of learning disabilities or no. Manipulatives work great, yes. Visual and auditory cues work wonders, absolutely. Making problems relatable and relevant to students’ interests is also excellent. Shortcuts work great, sometimes, but students oftentimes don’t know why they work or when they don’t. But, requiring students to do something tedious or mundane or not allowing them to do something is the wrong way to teach. A teacher should be able to, without limitation, employ different methodologies so that ALL students can do their best learning in the class. Be that as it may, there are times when certain things should be memorized. When students are adults and have to budget, for instance, they should be able to adeptly use rules of arithmetic to balance their budget without having to resort to shortcuts and charts to recall the information. It should be automatic.

Last edited: Dec 16, 2019
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Again I find myself agreeing with you. By the time they get to you in high school, those facts should be automatic for the majority of students. My understanding is that the OP is asking for suggestions for fourth grade students in her class. In that case, I think it’s fair to say that it’s acceptable for them to still be developing that automaticity. Although rote drilling and timed tests may be used, I would encourage the OP to continue frequent exposure and conceptual development through the use of number talks/number strings as an additional strategy. And, again, learning through skip counting music also worked well for me personally growing up. It’s just not something I use often as a teacher now.

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25. ### futuremathsprofPhenom

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Dec 16, 2019

Beautiful response.

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I agree. On timed tests with an assigned time limit, some students are under too much pressure to perform. In this case, the test is no longer evaluating the brain's automatic recall of the facts: instead, the test is evaluating the careful consideration of the cerebrum. The cerebrum is step by step processing each problem but simultaneously pushing the pencil to break the speed limit. But this is double jeopardy because the section of the brain that works for punishment/reward "becomes overly excited, draining the juice from [the] conscious cerebrum." (Beck, Henning. Scatterbrain. 2019). Perhaps this student will still accurately succeed within the timed limit, but the test wasn't developing the automatic recall that we're hoping to lodge within permanent memory. Instead, the brain has become geared to study and answer for the test, and like the crock pot commercial, it sets it and forgets it. More than likely, however, this is the student who fails the timed test and this discouragement does not result in encouragement to achieve, but rather to give up. Instead, I've found that the above method, of the students being timed during the test and then trying to beat their own time, does encourage the automatic recall of facts. A good method for this is to place a time on the Smartboard (or overhead) and have the student record the time prior to turning in the paper.

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27. ### a2zVirtuoso

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All private school students are public school students who transferred in but many transfer in K.

I think the point is the students at your school chose to be there rather than are there because of where they rent or own.

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I'm sorry, but drilling DOES teach it. It probably taught most of us on this site! I'm sorry you have to deal with this, however. My Middle Schoolers don't know their multiplication tables, either, so we've been relying on putting the tables into rhyme schemes (the sillier the better!), and our awesome ELA teacher has even incorporated them into her poetry unit.

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Dec 17, 2019

I had an interesting thought this morning. How are multiplication facts taught in other countries?

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30. ### RainStormPhenom

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When I taught in Japan, they had drill sessions. They taught it, the way they taught many things, through "recitation" classes. The teacher says the information and the children chant it back until they have committed it to memory.

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31. ### futuremathsprofPhenom

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And the Japanese have much better primary schools than we have here in the States.

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"Better" meaning what exactly? Just curious...

33. ### futuremathsprofPhenom

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Dec 18, 2019

The Japanese model clearly works because the vast majority of students learn mathematics and do it well.

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Dec 18, 2019

I had another thought. In thinking about multiplication or even addition facts and how they are taught in other countries, I also wonder how cultural differences affect the learning.

1. Cultural differences such as attitudes toward learning, school, and mathematics in general. In the U.S., often kids feel they're "dumb at math," parents inform them that they were never good at math either, and parents decide that mathematical progress is genetic. (On a humorous note, one of my students said her parents were discussing how good she is at math. Her mother said, it must be in her genes. She asked, "What do my blue jeans have to do with learning math?")

2. Cultural differences such as math application outside of school. In the U.S., students often ask, "When are we ever going to use this?" This attitude is reinforced by their parents. Found in a library book by one of my students years ago, "Now I sit me down to study. I pray the Lord I won't go nutty. If I should fail to learn this junk, I pray the Lord that I won't flunk." Also, how many (U.S.) kids watch their parents exchanging money at the store rather than a credit card? Today, very few cashiers count out the change; they just dump the money into the customer's hand from what their screen tells them to give. How many kids today have piggy banks? (I received much practice from opening up the bank, counting my money, and putting it back inside when I was a kid). How many kids play games that involve arithmetic? How many kids today make forts outside or build other stuff that might involve measuring? How many kids today set up pretend carnivals or play stores and count out pretend money?

3. Cultural differences such as propaganda against (or promoting) education. Children pick up negative attitudes about their current classroom from their parents when their parents are adhering to various media reports without checking for factual information. Much of this is now spread through the Internet through sites that base their information not on research but on how many people click onto their site, often for the sake of gaining income from advertisements.

35. ### Toby ARookie

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Real world examples promote interest and understanding.

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