A common theme in blogs and twitter feeds is the need to teach 21st century skills. The point has been made over and over that we should not be requiring students to memorize facts that can easily be googled. Without getting deep into the argument of what these skills are or whether they are new, let me say that I agree this should be a primary focus of education. I believe in focusing on problem-solving using authentic, real world learning with collaboration both inside my classroom and globally.

But….this year I am teaching a 6th grade math class for the first time. One of the things that has amazed me in my 5 years of teaching a math-focused technology class is how many kids do not know the answer to simple math problems like 3 x 7. They want to use a calculator for basic math facts that I think they should know. So for my class I am thinking about starting the year off by requiring them to review and recite to me the times tables through 12 x 12. I believe that this foundation is necessary for most middle to advanced math concepts including fractions, multiples, factors, algebra, and calculus.

I think memorizing spelling words is another similar set of facts that should be memorized. Even when you have spellchecker you need to be able to spell close enough that it can recognize what you are trying to spell. You also need to be able to pick out the correct word from spellchecker’s choices. I have read many papers where students lacked those two skills.

So my question to readers is what do they think about rote memorization? Is it last century or still important. When is it useful or even necessary? Am I off-base or is it important to teach rote memorization of basic skills before students can perform many higher level tasks.

Thank you for writing this blog post and bringing up these valuable questions.

You are right to question if should we throw out basic skills taught for generations just because information is now available at a click. I teach 9th grade English, and it is imperative that students have basic knowledge related to our culture to understand difficult text, otherwise they do not understand allusions, and they misinterpret meanings. Have you read the Knowledge Deficit by E. D. Hirsch? He points out that teaching comprehension strategies in elementary school without including real knowledge is impeding our students’ ability to perform well in high school.

Another reason to continue to teach students to memorize is that they enjoy it. They want to carry around their “favorites” in their head. Just ask a student to give you his favorite line from a movie or to repeat the lines of the best commercial on tv, and that student will know every word. I think incorporating memorization into the classroom actually enhances engagement for this very reason. Every year my students memorize a soliloquy from Shakespeare. Not only does this give my students an appreciation for the language of that time period, but it also gives the students ownership of a piece of Shakespeare. I always smile when I see a student in the hall who tells me he can still recite his soliloquy. I am a proponent of teaching 21st Century Skills. I own as many tech gadgets as I can acquire, and I love to wear my Google t-shirt, but I also believe there is value in enhancing one’s brain by adding to the knowledge stored inside. Memorization is a valuable skill that every student should have.

The biggest problem with rote memorization is not that it can be replaced by Google, but that it isn’t suited to the human brain or to the modern classroom. Consider your two examples. Memorizing the multiplication tables makes sense — in third grade, after the kids have learned to multiply. It doesn’t make sense to have a whole class work on it beyond that, when many of them already know it and the rest never really understood multiplication. Comprehension has to precede memorization. Spelling words are a completely different animal. Research on spelling shows that some kids are natural spellers who can spell words correctly as soon as they learn the new words, and it’s a waste of their time to study spelling. Others are naturally bad spellers who will always have to rely on a dictionary (or Google) for correct spelling, and it’s a waste of their time to study spelling words, too — what they need is a good set of strategies, including but –as you point out — not limited to the correct use of a spellchecker. We know that people learn information best when they encounter it in a rich context, and we also know that our classes are filled with students whose backgrounds vary enormously. I agree that memorization of literature is a satisfying experience for kids, but memorization isn’t always the best way to approach the learning of information.

@Tara Thanks for another good example. I can not remember every line but I still have fond memories of “The Village Blacksmith” from elementary school. I also think that it is so true that students can remember items that are important to them.

Many students who can not remember “school facts” can tell me all kinds of details about their favorite sport, video game, or music. If they can remember the details about 50 Cent or Lebron James, than they can also remember things about George Washington. But I digress into a separate issue of motivation and making learning meaningful.

@Rebecca I would love to hear more of how memorization “is not suited to the human brain or modern classroom.” Without any research I would argue that memorization is a very natural human brain function.

As far as the “modern classroom” is concerned that was the purpose of this post to argue that today’s classrooms still need basic skills as a building block for problem-solving and higher level thinking skills. I do not see it as an either or but rather am asking when is the appropriate time to require memorization.

The problem with learning multiplication tables only in 3rd grade is that we know that all kids will not get it as you state. The ideal would be individualized curriculum that would teach multiplication when they are ready. But in my public school situation, my best solution is to review them in 6th grade for all students because they are the basis for all the higher math coming.

My system would be to create some flashcards on the computer and/or on paper. Students would be required to practice them (mostly on their own time) until they were ready to “test” with me by reciting them at the beginning of class.

Students who know them and do not really need the practice could test out the first week and be done. This review would serve the purposes of identifying some of the best math students who could be peer tutors for others.

Students who “missed it” in 3rd grade would get a chance to catch up. At the same time we would do some mental math as a class showing authentic examples of how knowing your times tables makes life and math easier.

I just feel that a student that can not look at this equation 3x=21 and know that the answer is 7 without a calculator is at a huge disadvantage.

Great thought provoking stuff. As a high school math teacher, I feel that students should have the basics. For time purposes, knowing the basics is important. How would we feel if we walked into a construction site and the carpenters were measuring, then using a calculator. Would we feel comfortable?

I have a manual for how to use my remote on my tv. Should I need to use it every time?

What part of the topic are you wanting research on? Pro or con of rote memorization or something else? I can try to find some sources for you if I know more specifically what you would like to see.

That would be great. I am doing an Action Research Project on the pros and cons of using online flash cards as a way to learn math facts. Which incorporates a rote memorization tool with that of a 21st Century tool/skill. So anything you have would be great. Thanks

I am sorry I have not found any resources for you and I do not have time to look deeper right now. Good luck with your project.

Anonymous

I have students with learning disabilities who have difficulty retaining rote memorization facts, such as times tables. They really become disengaged if teachers keep making them spend time day after day trying to memorize these facts. I find it more important that they play with numbers and make their own connections that stick with them. This is done by showing side by side ways of obtaining answers to problems and pointing out patterns and sequences. Showing how multiplication is tied to addition is important. Manipulatives help and so does tying the info to real life experiences. For instance, students who get an allowance of 3 dollars a week can tell you exactly how much money they have in their piggy bank four weeks later!

yes, good points. I have found now that I am actually teaching the class that there is just no time to have them practice their times tables. Instead I talk about how multiplication facts are important and make the topics we are covering easier.

I also try to point students to multiplication games on the computer that are fun and self-motivating.

Marjorie Williams

Michael, I googled the question”.. should not third graders memorize multiplication tables?” I am a retired teacher, but have a small tutoring business. My students are not being required by their schools to learn the tables. My husband is a retired Phd organic chemist. We absolutely believe that students should memorize the multiplication tables. Minnesota state standards say children should know the tables, but when I talked to a math specialist in a local school district, the specialist balked at the idea of “rote memorization.” My husband, a retired scientist with 27 or so patents to his name, absolutely believes that it is an educational folly not to require that rote memorization. In some of the international conferences that he has attended he has met many college professors who say that American students just don’t seem to have the skill levels they once had. More and more freshman classes are remedial particularly in English and math.

Thanks for adding to the discussion. I agree that 3rd graders should memorize the times tables. If students have disabilities then we accomodate them, but gen. ed. students definitely should learn them

Anonymous

This is an interesting blog. My 11-year-old son was never required to learn his basic arithmetic facts. Some kids, like my daugher, memorized them practically without trying. Now that my son is in the 6th grade, he often does poorly on tests. Those that ask to show his work and give partial credit clearly show he can master complex processes like beginning algrebra, but he messes up on the basic arithmetic and gets the final answer wrong becuase he doesn’t have basic facts memorized. He always has to stop and think, sometimes using his fingers, often getting it wrong.

Interestingly, my 76-year-old mother who was never good at academics and was a highschool dropout, can still tell me her multiplication facts and never needs a calculator to help her with the basics. In the 1930s and 40s, they spent 10 or 15 mintues a day reciting the tables, and she never forgot them. They are like a song to her.

I would like to point out that constant repetition is very different from constant drilling. The school gave my son a year of drills, and all it accomplished was confirming that he didn’t know his facts. If they had taken that time to make him recite by reading, I think he’d would have had them down long ago.

Thanks for sharing, I would suggest that it is not too late for your son to learn the basic facts. Perhaps spend a few minutes a day at home reciting them and it could help him catch up. Here are two resources I have found related to multiplication, a game: http://www.bigbrainz.com and http://www.hunkinsexperiments.com/pages/multiplication/htm for a Russian method on your fingers

Anonymous

There is nothing wrong with having children make flashcards to help remember details and rules. As we discover more about how children learn and realize that we are global learners/thinkers, we know that students retain information through different means. An auditory learner may like to repeat something out loud to help remember it. A tactile learner can tap out the numbers while counting, or use manipulatives. Both tactile and visual learners benefit from making flashcards and using colors to tie data to different units in their books. Visual learners can use MS Excel to create spreadsheets to study from by printing off and folding sheet in half. Using Excel allows a student to a) become proficient in Excel, and b) combine spreadsheets from different chapters to create an exam study guide.

I used flashcards in college and they improved my GPA dramatically. My son uses Excel and it has prepared him for his exams. Rote memorization – depends on the individual. Flashcards – definitely see the benefits, first-hand.

I currently have my 6th grade math students practicing multiplication facts on the computer for 5 minutes at the beginning of class daily. Yet there are a few students who still struggle with them even with this practice. Maybe they need something else? A better way?

sylvino tupas

I too is not against rote memorization. The issue in here is the fact that many math teachers ends in memorizing number fact. As mentioned by Benjamin Bloom, recalling is the least, we need to bring the students into a certain higher level of learning after recalling. I don’t memorize formula, instead understands them. As per experience, people normally forget them when not used often. In solving problems that involves those formula, i simply look for it and use them.

Anonymous

Ok I will put my 2 cents in here. I have worked in special education for 17 years and in my classroom we teach the multiplication facts with a program called “Times Tables the Fun Way”. It is a very visual program that works for all kids whether they be visual learners, special ed. or not. The sixth and seventh grade teachers are always amazed that my special ed kids ( who advance enough to be in “regular” class)know their multiplication facts better than most of the rest of the class. My point is that the program is great and it is great for all the students to learn the facts to mastery. I am not sure why regular ed has not picked up on this. If my special education kids can do it then it seems it would be worth a try in regular ed. Just sayin’

TaraThank you for writing this blog post and bringing up these valuable questions.

You are right to question if should we throw out basic skills taught for generations just because information is now available at a click. I teach 9th grade English, and it is imperative that students have basic knowledge related to our culture to understand difficult text, otherwise they do not understand allusions, and they misinterpret meanings. Have you read the Knowledge Deficit by E. D. Hirsch? He points out that teaching comprehension strategies in elementary school without including real knowledge is impeding our students’ ability to perform well in high school.

Another reason to continue to teach students to memorize is that they enjoy it. They want to carry around their “favorites” in their head. Just ask a student to give you his favorite line from a movie or to repeat the lines of the best commercial on tv, and that student will know every word. I think incorporating memorization into the classroom actually enhances engagement for this very reason. Every year my students memorize a soliloquy from Shakespeare. Not only does this give my students an appreciation for the language of that time period, but it also gives the students ownership of a piece of Shakespeare. I always smile when I see a student in the hall who tells me he can still recite his soliloquy.

I am a proponent of teaching 21st Century Skills. I own as many tech gadgets as I can acquire, and I love to wear my Google t-shirt, but I also believe there is value in enhancing one’s brain by adding to the knowledge stored inside. Memorization is a valuable skill that every student should have.

Rebecca HadenThe biggest problem with rote memorization is not that it can be replaced by Google, but that it isn’t suited to the human brain or to the modern classroom.

Consider your two examples. Memorizing the multiplication tables makes sense — in third grade, after the kids have learned to multiply. It doesn’t make sense to have a whole class work on it beyond that, when many of them already know it and the rest never really understood multiplication. Comprehension has to precede memorization.

Spelling words are a completely different animal. Research on spelling shows that some kids are natural spellers who can spell words correctly as soon as they learn the new words, and it’s a waste of their time to study spelling. Others are naturally bad spellers who will always have to rely on a dictionary (or Google) for correct spelling, and it’s a waste of their time to study spelling words, too — what they need is a good set of strategies, including but –as you point out — not limited to the correct use of a spellchecker.

We know that people learn information best when they encounter it in a rich context, and we also know that our classes are filled with students whose backgrounds vary enormously.

I agree that memorization of literature is a satisfying experience for kids, but memorization isn’t always the best way to approach the learning of information.

concretekax@Tara

Thanks for another good example. I can not remember every line but I still have fond memories of “The Village Blacksmith” from elementary school. I also think that it is so true that students can remember items that are important to them.

Many students who can not remember “school facts” can tell me all kinds of details about their favorite sport, video game, or music. If they can remember the details about 50 Cent or Lebron James, than they can also remember things about George Washington. But I digress into a separate issue of motivation and making learning meaningful.

@Rebecca

I would love to hear more of how memorization “is not suited to the human brain or modern classroom.” Without any research I would argue that memorization is a very natural human brain function.

As far as the “modern classroom” is concerned that was the purpose of this post to argue that today’s classrooms still need basic skills as a building block for problem-solving and higher level thinking skills. I do not see it as an either or but rather am asking when is the appropriate time to require memorization.

The problem with learning multiplication tables only in 3rd grade is that we know that all kids will not get it as you state. The ideal would be individualized curriculum that would teach multiplication when they are ready. But in my public school situation, my best solution is to review them in 6th grade for all students because they are the basis for all the higher math coming.

My system would be to create some flashcards on the computer and/or on paper. Students would be required to practice them (mostly on their own time) until they were ready to “test” with me by reciting them at the beginning of class.

Students who know them and do not really need the practice could test out the first week and be done. This review would serve the purposes of identifying some of the best math students who could be peer tutors for others.

Students who “missed it” in 3rd grade would get a chance to catch up. At the same time we would do some mental math as a class showing authentic examples of how knowing your times tables makes life and math easier.

I just feel that a student that can not look at this equation 3x=21 and know that the answer is 7 without a calculator is at a huge disadvantage.

SusanYes. And if they don’t know them when they get to college, do it there.

We all agree they should memorize the alphabet, right? Similar tool.

Eric TownsleyGreat thought provoking stuff. As a high school math teacher, I feel that students should have the basics. For time purposes, knowing the basics is important. How would we feel if we walked into a construction site and the carpenters were measuring, then using a calculator. Would we feel comfortable?

I have a manual for how to use my remote on my tv. Should I need to use it every time?

Kristin SteinThis is a great blog, I am wondering if anyone has any scholarly information to support this topic?

concretekaxThanks Kristin,

What part of the topic are you wanting research on? Pro or con of rote memorization or something else? I can try to find some sources for you if I know more specifically what you would like to see.

Kristin SteinThat would be great. I am doing an Action Research Project on the pros and cons of using online flash cards as a way to learn math facts. Which incorporates a rote memorization tool with that of a 21st Century tool/skill. So anything you have would be great. Thanks

concretekaxKristin,

I am sorry I have not found any resources for you and I do not have time to look deeper right now. Good luck with your project.

AnonymousI have students with learning disabilities who have difficulty retaining rote memorization facts, such as times tables. They really become disengaged if teachers keep making them spend time day after day trying to memorize these facts. I find it more important that they play with numbers and make their own connections that stick with them. This is done by showing side by side ways of obtaining answers to problems and pointing out patterns and sequences. Showing how multiplication is tied to addition is important. Manipulatives help and so does tying the info to real life experiences. For instance, students who get an allowance of 3 dollars a week can tell you exactly how much money they have in their piggy bank four weeks later!

concretekaxyes, good points. I have found now that I am actually teaching the class that there is just no time to have them practice their times tables. Instead I talk about how multiplication facts are important and make the topics we are covering easier.

I also try to point students to multiplication games on the computer that are fun and self-motivating.

Marjorie WilliamsMichael, I googled the question”.. should not third graders memorize multiplication tables?” I am a retired teacher, but have a small tutoring business. My students are not being required by their schools to learn the tables. My husband is a retired Phd organic chemist. We absolutely believe that students should memorize the multiplication tables. Minnesota state standards say children should know the tables, but when I talked to a math specialist in a local school district, the specialist balked at the idea of “rote memorization.” My husband, a retired scientist with 27 or so patents to his name, absolutely believes that it is an educational folly not to require that rote memorization. In some of the international conferences that he has attended he has met many college professors who say that American students just don’t seem to have the skill levels they once had. More and more freshman classes are remedial particularly in English and math.

concretekax@Majorie

Thanks for adding to the discussion. I agree that 3rd graders should memorize the times tables. If students have disabilities then we accomodate them, but gen. ed. students definitely should learn them

AnonymousThis is an interesting blog. My 11-year-old son was never required to learn his basic arithmetic facts. Some kids, like my daugher, memorized them practically without trying. Now that my son is in the 6th grade, he often does poorly on tests. Those that ask to show his work and give partial credit clearly show he can master complex processes like beginning algrebra, but he messes up on the basic arithmetic and gets the final answer wrong becuase he doesn’t have basic facts memorized. He always has to stop and think, sometimes using his fingers, often getting it wrong.

Interestingly, my 76-year-old mother who was never good at academics and was a highschool dropout, can still tell me her multiplication facts and never needs a calculator to help her with the basics. In the 1930s and 40s, they spent 10 or 15 mintues a day reciting the tables, and she never forgot them. They are like a song to her.

I would like to point out that constant repetition is very different from constant drilling. The school gave my son a year of drills, and all it accomplished was confirming that he didn’t know his facts. If they had taken that time to make him recite by reading, I think he’d would have had them down long ago.

You can’t test knowledge into someone.

concretekaxThanks for sharing,

I would suggest that it is not too late for your son to learn the basic facts. Perhaps spend a few minutes a day at home reciting them and it could help him catch up. Here are two resources I have found related to multiplication, a game: http://www.bigbrainz.com and http://www.hunkinsexperiments.com/pages/multiplication/htm for a Russian method on your fingers

AnonymousThere is nothing wrong with having children make flashcards to help remember details and rules. As we discover more about how children learn and realize that we are global learners/thinkers, we know that students retain information through different means. An auditory learner may like to repeat something out loud to help remember it. A tactile learner can tap out the numbers while counting, or use manipulatives. Both tactile and visual learners benefit from making flashcards and using colors to tie data to different units in their books. Visual learners can use MS Excel to create spreadsheets to study from by printing off and folding sheet in half. Using Excel allows a student to a) become proficient in Excel, and b) combine spreadsheets from different chapters to create an exam study guide.

I used flashcards in college and they improved my GPA dramatically. My son uses Excel and it has prepared him for his exams. Rote memorization – depends on the individual. Flashcards – definitely see the benefits, first-hand.

concretekaxI am not against the use of flashcards. Not sure I agree with the learning styles part as some have called them a myth. See http://www.youtube.com/watch?v=sIv9rz2NTUk

I currently have my 6th grade math students practicing multiplication facts on the computer for 5 minutes at the beginning of class daily. Yet there are a few students who still struggle with them even with this practice. Maybe they need something else? A better way?

sylvino tupasI too is not against rote memorization. The issue in here is the fact that many math teachers ends in memorizing number fact. As mentioned by Benjamin Bloom, recalling is the least, we need to bring the students into a certain higher level of learning after recalling. I don’t memorize formula, instead understands them. As per experience, people normally forget them when not used often. In solving problems that involves those formula, i simply look for it and use them.

AnonymousOk I will put my 2 cents in here. I have worked in special education for 17 years and in my classroom we teach the multiplication facts with a program called “Times Tables the Fun Way”. It is a very visual program that works for all kids whether they be visual learners, special ed. or not. The sixth and seventh grade teachers are always amazed that my special ed kids ( who advance enough to be in “regular” class)know their multiplication facts better than most of the rest of the class.

My point is that the program is great and it is great for all the students to learn the facts to mastery. I am not sure why regular ed has not picked up on this. If my special education kids can do it then it seems it would be worth a try in regular ed. Just sayin’

Mike Kaechele@Anonymous

Thanks for the heads up. May buy the book for my own children.