Mar 4, 2014

If a fourth grader does not know the times tables flawlessly, is it acceptable to transfer him/her to the next grade? (Victor Guscov-LinkedIn)

This re-posting discussion from LinkedIn is in the purpose of only to facilitate learning the aspect of mathematics education; and does not mean as business. (Marsigit) 

Docent vakdidactiek wiskunde at Hogeschool van Arnhem en Nijmegen
What do you mean with flawlessly. For me there is a difference between still making mistakes even when given enough time to think on the one hand and not being fast enough on the other hand.

If speed is the problem, then I would not worry too much. Especially if the child understands the math. 1 second loss in memorizing the tables is compensated by minutes of gain by knowing how to solve a problem.

If a child gives the wrong answers even when given enough time to think, that would be a good reason to check where this is coming from. Then there could be something that is a reason not to transfer him/her to the next grade. But then the time tables are not the main reason. In this situation there are probably a lot of other reasons.

Mehtamatics = mathematics with a difference
I agree with Geeke. I consider myself to be very good with my tables - to the 30 times table. But very occasionally I slip up with, say, the 23 times table. So I am not flawless. Maybe I should still be in grade 4 instead of having done a degree (and more) in mathematics.

Second, in the UK it is policy to transfer children up irrespective of their mastery of the earlier level. In my view that is flawed, but holding the pupil back is unacceptable.

teacher of mathematics
Geeke, under "flawlessly" I mean being able to quickly, correctly and repeatedly answer questions from any tables group in any sequence at any time. Also students should learn to use the memorized multiplication facts in practice. If a student finds it difficult to carry out any computations that include multiplication facts, then he/she has not mastered the times tables totally.
Anand, a very interesting standpoint. Thus it is necessary to define "flawlessly" more carefully. And are you totally sure that holding pupils back is unacceptable? .

Docent vakdidactiek wiskunde at Hogeschool van Arnhem en Nijmegen
I consider myself also good with my tables. I have a master degree in mathematics, but I know I still "calculate" 7 x 8 and 6 x7. I do think I know them by heart, but don't trust myself with the answer. I found that I am not the only one with a master degree in math. I also found, when I was practising with my daughter, that my speed is not constant.

I saw children that have the same: they check their answers even when doing a tables test. A main reason to not be fast enough. Another reason for being slower can be that your 'thoughts' do not transfer as fast to writing. So there is a problem in the speed of the output channel; i.e. reading, knowing the answer, and then writing it down

The big question is: how fast should you be?

Reasoning from cognitive load, you don't want them to have extra load by not knowing their tables, but that does not mean that you have to meet a strict time limit.

I agree with Anand that it is unacceptable to hold these pupils back.

I would even want to go further. Is it acceptable to hold gifted pupils (that are not fast enough on their tables) back from more conceptual mathematical work (for gifted students) until they do master the tables at the right speed?

Mehtamatics = mathematics with a difference
Holding pupils back presents a whole lot of issues and my responses to them are not the same.

In the UK it is government policy not to hold back. It is unacceptable in the sense that it is disallowed - whatever the merits or demerits! School year is strictly linked to chronological age. I know one set of parents who had to formally appeal for the due date of their severely premature child be used rather than the actual date of birth! But more generally, I do not see how a child can be working with processes and concepts at a higher level when they have not mastered the same subject at a more basic level.

Having said that, I have some comments on holding pupils back. What do you do with a child who is able in some subjects but not in others? Do they need to be held back in their grade for some subjects but move forward in others? If so, the school becomes a very complex organisation - with children in different grades for different subjects. Educationally this may be good but I would not like to try to timetable that school!

It is important to understand why the Grade 4 child has not mastered their tables. Will repeating the grade simply bore them to distraction? In that case they may not learn anything more and may be a disruptive influence on others in the classroom.

Children do not learn linearly. They go through learning spurts and then plateau while consolidating their newly acquired knowledge. During this period they may even regress a bit. Then the next spurt kicks in, and so on. A Grade 4 child could be at a point just prior to a spurt, in which case holding them back a year might not be appropriate.

I did my schooling in India where holding back was perfectly acceptable and I had a few classmates that were repeating - one even spent three years in one form! They did become bored, switched off and sometimes disruptive as a result. Targeted support may have helped but then that raises the question about money!

Sorry, no answers here - only more complications!

Lecturer at Yogyakarta State University
Victor, this idea seems that there is a powerful adult (you) to try to justify partially something about your belief (time tables) to work for a less powerful children. "Knowing the times tables" has many psychological aspects. We need also to clarify about the meaning of "knowing" and "times tables". For a certain context, this idea seems awkward; so I am striving to understand it.

teacher of mathematics
Marsigit, I can only repeat once more what I mean with "knowing flawlessly" - being able to quickly, correctly and repeatedly answer questions from any tables group in any sequence at any time. Also students should learn to use the memorized multiplication facts in practice. If a student finds it difficult to carry out any computations that include multiplication facts, then he/she has not mastered the times tables totally.

Classroom Teacher, University Tutor
Holding them back is both a stick and a stigma. While I totally agree with the need for accurate, rapid recall of number facts as a tool for enabling a student's performance in higher order tasks, the focus needs to be on the benefits of this recall as demonstrated through practice, rather than a gateway task for progression from one point to the next with peers.

Mehtamatics = mathematics with a difference
While I agree that holding pupils back is a stick and stigma, I think that a lot depends on the culture. I do not think that pupils that were held back at my school were stigmatised by their peers: it was usually good to have older kids on your sports teams! Also, anecdotally, a few years back, the son of a French friend of mine wanted to be held back because his best friend was being held back. Stigma? Their friendship seemed far more important!

teacher of mathematics
Scarce preliminary results of the first week (11 groups, 40 votes):
Yes - 24 (60%)
No - 16 (40%)
Why are there so few votes? Dear colleagues, what's the matter? Maybe, the question is not interesting or something else. I cannot understand.

I think we need to disaggregate several issues here.

The first one is the concept of 'holding back' because a child has not learned something which they should have. This is a complex issue -- for instance, should a child who has learned everything else, but has just barely failed the 'flawless' criterion -- be held back? Is the industrial assembly line batch-processing method the best, or the best-we-can-do-with-current-resources, model for education? I won't try to answer these questions, except to say that I think that technology is slowly preparing the ground for a much more individually-oriented method of education, which won't require the current proceed-in-a-group method.

The second issue is: how important is it that children know their times tables as flawlessly as Victor thinks they should? I personally think it is very important. But, of course, it is not impossible for exceptional individuals who are unable to learn them, still to do well in mathematics. But hard cases, as the lawyers say, make bad law. There are individuals who can climb to the top of Mount Everest, without additional oxygen, and still live. But most people who try this will die. And children who don't know their times tables are, for the most part, dead mathematically.

The third issue is, how hard is it for children to learn their times tables? Something might be important to do, but also very difficult. But in this case, happily, no such dilemma faces us. Learning your times tables by heart is easy, IF THE SCHOOL IS ORGANIZED TO MAKE THIS HAPPEN. The school leadership -- not the mathematics teacher -- must arrange it so that all children chant the times tables in unison for a few minutes every morning, and perhaps at other times during the day. There are other ways to keep the tables prominent -- 7 x 8 posters, 9 x 6 post-it notes in the loo, etc. The human brain is designed to make hundreds of thousands of such associations.

If children don't know their times tables, it's not their fault, it's the fault of the people who are supposed to be leading in their education.

There are a couple of dozen other 'know-by-heart' reflexive strings of words that children should know, in order to flourish in pure and applied mathematics. (The definition of a ratio, the definition of pi, how to recognize a perfect quadratic square ["rooty-toot-toot, twice the square roots"], how to deduce sin, cos and tan for a 30-60-90 triangle ["hee, hee, hee, one, two and the square root of three"] and they're easy to learn, if done right, and so helpful. These can be combined with certain basic visualisations [e.g. the "Magic Triangle" for products/quotients, applicable to so many formulae in physics] and small changes in notation (consistently using the 'raise to a fractional power' notation instead of the obsolete root sign), to make mathematics so much easier. The routine becomes easy so our brains can concentrate on the real difficulties.

I don't understand why the educational leaders have abandoned these useful techniques. I whole-heartedly approve of learning for understanding (as opposed to meaningless rote learning), and of learning how to solve problems, not just do 'fill in the blanks' routine problems. But having a few dozen associations of (meaningful) words off by heart is so very helpful in reducing 'cognitive load' as someone called it. Why don't we do it?

Associate Director of RSM-MetroWest
The question seems to miss an important point. Some students memorize times tables, but do not understand what they are doing. It is the same as memorizing the words to a favorite song. Others may conceptually understand the math, and take longer to complete a test, but still are fundamentally more advanced than their memorizing peers. I teach 5 and 6 year old kids whose parents have"taught" them that 100 x 10 = 1000. That doesn't mean they are ready for 5th grade. They still cannot understand much simpler multiplication, although they have memorized impressive sounding facts.

Memorizing, and understanding, must not be counterposed to each other. They are (at least somewhat) complementary. Just memorizing a string of sounds is pointless. For instance, the multiplication tables must be learned at the same time as visualizations of multiplication (six rows of seven things each, etc), and applications of them involving not just simple multiplications, but factoring and division, to help children become fluent with numbers: Twenty boxes with ten candies each in them, were opened and all the candies put into a bowl, and the candies then shared out equally among fifty children... how many did each child get?

A child who cannot quickly work out that twenty times ten is two hundred, and that two hundred divided by fifty is four, will be dead in the water on a problem like this. It's possible in theory that they could work out in principle how to solve it ... say, using the Singapore Model Method, in which you draw the appropriate bars ... but in practice I'll bet they won't.

And I'm always suspicious when I am told that children can solve a problem "in principle", because it invariably reminds me of an old Soviet joke, which Victor will no doubt know, whose punch-line is, "Where is this wonderful shop, 'Principle', which has everything you are out of here?"

teacher of mathematics
Doug, thanks for making me smile :)

Math department chair at Seabuy Hall
I was just informed that the DOE in HI no longer teaches the multiplication facts, nor long division. We are just starting to see these students in high school. They are lost, and the simplest of equations becomes monumental to solve.
Now what?

Mehtamatics = mathematics with a difference
Sean, it makes me so mad when politicians and bureaucrats make such decisions. Do they not realise that they are blighting the lives of a whole generation of children? I admit that, as a private tutor, I benefit from such incompetent decisions but I would rather that today's youngsters and tomorrow's adults were able mathematicians than to make money from their misfortune.

Classroom Teacher, University Tutor
We are teaching these basic skills in junior secondary because so many students have come to us not knowing basic facts or operations. My perception is that it has become worse so our orientation includes teaching formal setting out of algorithms and we have implemented a 2 year plan to improve speed and breadth of recall of number facts.

It appears that some people have set their focus as understanding, a concept that none of us would disagree with. Unfortunately the focus on achievement of standards and levels has been lost. Instead of students achieving levels and milestones through targeted mastery work, they are becoming consumed with elaborate, alternative algorithms designed to show understanding. These elaborations become far more complicated than traditional approaches and fail to utilise the inherent power of place value. They seem to have forgotten that students can have "fun with facts", and that increasing their skills and knowledge develops satisfaction with the subject and enhanced self-efficacy. When students feel like this they stop saying they hate Maths and feel confident to take on new challenges and topics.

Teacher of Chemistry at CARTERET PUBLIC SCHOOLS
Schoolhouse Rock was created in the early 1970's because the United States Government had made the decision that all students should be able to calculate up to the 12 Time Tables by the 4th grade. This was back when we called standardised test the "Iowa." I found it invaluable for myself. ABC would run the vignettes at the end of their Saturday Morning cartoon lineup because they knew that kids would be watching. When I had my own child, I bought the DVDs so that he would learn his times tables as well, plus a subscription to Brain Pop and the Encyclopaedia Britannica online [I had a set of them on my bookshelves when I was kid and did many a report using them]. Somewhere between the 1970s and Today, the public got it in their head that we don't need Schoolhouse Rock anymore or we have forgotten how to help our children find reliable reference sources on the Internet, much like we had to get help from our parents to get to the Public Library and find sources for reading and reports. Now, the United States is reaping what we have failed to sow and we are, hopefully, realising we need to actually have our children be competent in calculations and knowledge. My personal belief is that if we employ the our resources correctly, and that is a big "if" unfortunately, we can have a child held back not to stigmatise but to ensure they get more knowledge. Of course that requires work and support from school administrators and those of us teaching in the United States realise I have just written an oxymoron. Until that time, I have my own resources that I will utilise in my classroom, mostly because I see positive results that have very positive impacts on my students and the is truly our bottom line.

teacher of mathematics
The voting process perked up, and that's what we have for today (11 groups, 159 votes):

Yes - 103 (64.8%)

No - 56 (35.2%)

Education/Volunteer Coordinator at SciWorks
Having been a Math teacher in Elementary and in Middle Grades, I got to see first hand what happens when students do not know the multiplication table. However it does not stop there; the NCLB program forces promotion as schools are pressured to keep retention to a minimum.

Basic math skills (add, subtract, multiply, divide) are necessary skills for Science; Social Studies, Art and more. But let us not forget, if the child cannot read the problem and perform the task, we as educators have failed that child.

It is inexpensive to incorporate practice of basic math as well as basic language arts daily. It can be done with 3rd-7th graders as long as it is presented in the proper manner for their learning style.

I constantly reminded my student, regardless of the grade, they use math and science as well as reading daily. They just weren't aware of it. Personally I like the way a few schools are changing from graded classes (K-8) to go to the class for your level. That covers advanced learners, average who fall in the cracks, and more challenged learners. Data shows, which is how they were able to justify the change to the school board, this type of learning as well as utilizing a "Flipped Classroom" let the students work at a pace in which they can understand and actually learn-not memorize. Learning is stored in those filing cabinets in your long term memory. Memorizing is in the short term memory or equivalent to storing it in recycle bin.

Victor, great question!

Classroom Teacher, University Tutor
Memorising in the context of learning/understanding is meaningful and useful and this is why it stores so well.

Lecturer at Yogyakarta State University
The role of intuition can probably be considered and be examined in learning arithmetic including numbers operations. 
teacher of mathematics
The results of the poll at the point (11 groups, 205 votes):

Yes - 131 (63.9%)
No - 74 (36.1%)

And some interesting "yes" comments:

“I still don't know my times tables flawlessly, but I have advanced degrees and am successful at what I do.”

“Probably all but the single yes voter think it is a silly question. Can anyone think of a reason it might be inappropriate?”

“Too important of an impact to a child's life to have this one factor be the only consideration. Why would this even be a question?”

“Would you really hold a child back because she hasn't learned the basic multiplication facts? That's very disturbing. Here's a radical idea: how about teaching her instead of punishing her?”

“Are you kidding? This is the only skill lacking? Resounding, yes! No child should be retained solely because memorization of multiplication facts are lacking. If that were the case, most children would be retained.”

“Of course! How many adults don't know their "tables"? That's what tech is for. We are not all good memorizers! Many of these learners are really gifted and creative. Let's get with the 21st century!”

Mehtamatics = mathematics with a difference
OK. I am going to play Devil's advocate:

Hold the child back and transfer the child's teachers (Grade 4 and earlier) to other profession. Are they blameless? What evidence is there to validate their blamelessness?

Biologist/Botanist/Writer/Consultant/Founding Editor at Science Literacy & Education focused
NCLB for me: "No child left behind, every child left behind." I have seen what happens when students get pushed through without getting to learn what they need. They get into college with A grades, thinking they are smart, then fail out of college the first semester. Then, they really feel like failures...Better to get the basics as children. I have taught kindergarten through university. I have seen the result of NCLB at many levels.

I was a child of the, "New Math" era so I learned to multiply and divide in base 2, 8, and 16 faster than in base 10. When I took chemistry at the university level, I learned that I'd better learn the times tables by rote if I wanted a chance to do chemistry. I did and passed chemistry and loved it. If I didn't learn the times tables, I could not have done that.

I encourage students to learn the times tables to 20 and squares and cubes as well. Many have come back to me and said what a help that was.

In some cities, where children and their families change schools often because of economic reasons, math is taught so the same math item is being taught on the same day in all the city schools. The result of that practice is that many students don't have time enough to learn the material before they move on to the next topic. A student might be taking calculus who can't multiply 2 x 2 without a calculator and not understand the calculator's answer.

I am a science teacher who realized I'd better learn to teach math (reading, and writing) within the science class if I wanted people to be able to pass the basic biology class. You can't understand pH without an understanding of exponents, for example. Understanding surface area in biochemical reactions in the body is impossible unless you can calculate area and volume. These calculations require comprehending multiplication and division. Without great math skills people die. A slipped decimal can result in a medicine a factor of 10 too strong. Try that with a heart medicine and you are dead.

Want another field than medicine? Look at engineering and building collapses.

It is not that hard to learn the times tables. Parents can teach their children these as a game, for example. Teachers are not to blame. I thought they were, so, I left university teaching to go back to high school teaching and then junior high teaching. I learned the teachers do teach. Children come to school hungry. Children come to school after working all night to support their families. Children come to school with no homework done because of home factors. Children come to school after dodging drunk parents all night. Teachers' hands are tied....they can't visit families, or give after school penalties in many places because of laws. It is wrong to blame the teachers, many of whom spend their own money to get things to help students learn. Another factor affecting students' learning is the number of deaths they face in their communities. Or, the number of parents abandoning them. Or, the number of parents going to jail. Or, the lack of hope. Or, the trip through the drug lands to get to school. Or, an infinite number of reasons they don't learn that have nothing to do with the teacher.

Students need hope. They need to believe in themselves. They need a safe place to learn and a caring home. Oh, and heat...It is hard to study when you are cold. We need to believe in them. We need to convey that we believe in them. A safe environment... If we build it, they will learn (the times tables and much more!).

The children at the Boys' and Girls' Club where I volunteer learned the times tables, squares, and cubes in less than a week when they realized it was fun and they could do homework faster and thus play sooner... Notice their parents, though working, had the children in a safe, warm environment after school.

A thought from my father: No one graduated from one room school house without knowing the times tables.

Lecturer at Yogyakarta State University
From Victor Guskov: "Know the Times Tables flawlessly: being able to quickly, correctly and repeatedly answer questions from any tables group in any sequence at any time"

I am just interested with and then try to collected the emerging related notions with Times Tables in this discussion as follows:

“still making mistakes with times tables, understands times tables, loss in memorizing the tables, memorizing the tables, wrong answers , enough time to think times tables, where this times tables coming from, very good with my times tables, slip up with times tables, carry out any computations that include multiplication facts, mastered the times tables totally, good with times tables, think times tables by heart, doing a times tables test, transfer as fast to writing, not fast enough on their tables, do master the tables at the right speed, visualizations of multiplication, fluent with numbers, work out that twenty times, long term memory, learn the times tables by rote, times tables as a game”.



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