__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.

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.

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?

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!

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.

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?

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?"

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?

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.

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%)

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!

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!”

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?

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 read-about-it.blogspot.com

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.

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”.

Thank's

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”.

Thank's

Nurrita Sabrina

ReplyDelete14301244010

S1 Penddikan Matematika I 2014

Diskusi yang sangat menarik menurut saya. Saya jadi teringat permasalahan yang dikemukan dosen perencanaan saya pada semester 5 kemaren. Beliau mengatakan bahwa anaknya tidak hapal mengenai tabel perkalian akan tetapi ia paham konsep dari perkalian tersebut sehingga ketika ada permasalahan mengeai perkalian ia menghitung dengan manual. Dari permasalahan tersebut dosen saya mengatakan bahwa itu tidak masalah karena pada dasarnya ia paham mengenai konsep tersebut.

Nurrita Sabrina

ReplyDelete14301244010

S1 Pendidikan Matematika I 2014

Saya setuju dengan apa yang di kemukakan oleh J S Shipman bahwa ketika kita menemukan anak yang kesulitan dalam tabel perkalian dapat didekati dengan games. Pertama-tama kita dapat mengenalkan konsep dari perkalian itu sendiri kemudian dimulai dari angka yang sederhana lalu setelah itu terus bergeser ke agka yang lebih besar dan baiknya hal tersebut didekati dengan game dan kegiatan yang menyenangkan.

Suci Renita Sari

ReplyDelete14301241052

S1 Pendidikan Matematika I 2014

Menurut saya, jika siswa kelas 4 SD belum mengetahui tabel perkalian maka siswa tersebut tidak seharusnya dinaikan ke jenjang yang lebih tinggi. Hal ini dikarenakan tabel perkalian adalah hal dasar yang harus dikuasai siswa dan sangat diperlukan dalam pembelajaran di jenjang berikutnya. Jika siswa tersebut belum mengenal tabel perkalian maka siswa tersebut tidak dapat mengikuti pembelajaran yang diajarkan guru dikelas. Siswa tersebut akan kesulitan beradaptasi dengan teman-temannya yang telah mengenal, memahami bahkan menghafal tabel perkalian.

Muh Ferry Irwansyah

ReplyDelete15709251062

Pendidikan Matematika PPS UNY

Kelas D

Setiap siswa pasti memiliki kemampuan yang berbeda-beda. Sehingga dalam guru menjelaskan materi, akan ada siswa yang paham memahami maupun agak kurang dalam memahaminya. Dalam pelajaran matematika, objeknya bersifat abstrak dan konsep-konsep dalam matematika pada umumnya disusun dari konsep-konsep sebelumnya dan saling berkesinambungan.

Muh Ferry Irwansyah

ReplyDelete15709251062

Pendidikan Matematika PPS UNY

Kelas D

Dalam kasus ini, jika siswa kelas 4 belum bisa melakukan operasi perkalian secara baik dan cepat, apakah mereka layak naik kelas atau tidak naik kelas? menurut saya tidak, karena konsep matematika yang saling berkesinambungan dimungkinkan nanti pada materi selanjutnya (kelas 5) siswa akan merasa kesulitan.

Elli Susilawati

ReplyDelete16709251073

Pmat D pps16

Kita lihat dari perkembangannya dalam masalah yang dihadapinya. Disinilah guru berperan penting dalam memotivasi dan mengejar ketertinggalannya. Ketetapan untuk menaikkan atau meninggalakan kelas anak tersebut tergantung kebijakan dari guru dan kepala sekolah. Jika terlalu jauh ketertinggalannya maka menurut saya lebih baik ditinggalkan. Karena jika dipaksakan juga, anak tersebut malah semakin berat dalam melaksanakan pembelajaran.

Angga Kristiyajati

ReplyDelete17709251001

Pps UNY P.Mat A 2017

Thank you very much, Mr. Marsigit.

This is a good script of disscussion. This is a complex problem for me. If we transfer him to the next level, it will be hard for him/her to follow the lesson the next topics that need fast counting skills, even though using calculator is still prohibited in our education. But if using calculator or similar tools is allowed, I think it is no problem if we let him/her pass to the next level, as long as he/she understand how to count and how to use the counting concepts and principles.

Auliaul Fitrah Samsuddin

ReplyDelete17709251013

PPs P.Mat A 2017

Thank you for sharing this, sir. I personally can relate on this problem since i experienced teaching Mathematics to 4th graders. I think 'knowing/memorizing time table or not' is not the correct indicator. I said this because even aadults who already memorize time table perfectly can make mistake when answering 7 x 8, for example, in real-life context. Moreover i often find kids who are not expert at memorizing time table but they can answer word problems related to multiplication correctly because they 'understand how to multiply' not 'memorize the time table. So I believe understanding the concept is more important than just memorizing, though it would be better if they can memorize too.

Dewi Thufaila

ReplyDelete17709251054

Pendidikan Matematika Pascasarjana C 2017

Assalamualaikum.wr.wb

Tabel perkalian memanglah salah satu pengetahuan basic yang hraus dietahui oleh siswa. tetapi jika siswa belum dapat mengerti tabel perkalian secara sempurna, belum tentu kita harus membiarkannya untuk tinggal kelas. karena tidak banyak manusia yang memiliki ingatan yang baik, begitu juga siswa. maka yang terpenting adalah bagi siswa untuk dapat memahami konsep dengan baik. karena, walaupun tabel perkalian adalah salah satu pengetahuan dasar yang penting, tetapi bukanlah satu-satunya pengetahuan dasar yang wajib diketahui oleh siswa. banyak pengetahuan-pengetahuan lainnya.

Wassalamualaikum.wr.wb

Dewi Thufaila

ReplyDelete17709251054

Pendidikan Matematika Pascasarjana C 2017

Assalamualaikum.wr.wb

Tidak dapat mengerti tabel perkalian bukanlah kesalahan siswa, bukan berarti siswa tersebut tidak belajar dengan baik di dalam kelas. guru dan sekolah pun menjadi salah satu faktor yang patut disalahkan atas kegagalan tersebut. karena guru bertanggung jawab dalam kesalahan tersebut, tidak sepatutnya guru melepas tanggung jawabnya dengan membiarkan anak tersebut tinggal kelas dan berjuang sendiri di kelas yang sama untuk tahun selanjutnya. sebagai guru seharusnya telah mengetahui bahwa siswa belum mengerti tentang suatu materi jauh sebelum waktu kenaikan kelas. guru yang baik dan bertanggung jawab seharusnya ikut berjuang, bukannya melepas siswa untuk berjuang sendiri dalam mempelajarai materi yang belum dikuasainya. jika guru langsung bertindak segera setelah guru mengetahui masalah tersebut, maka tidak akan terjadi perdebatan seperti ini di waktu kenaikan kelas.

Wassalamualaikum.wr.wb

Andi Gusmaulia Eka Putri

ReplyDelete17709251009

PPs PM A 2017

Tidak membiarkan siswa untuk naik kelas dengan pertimbangan hanya karena siswa tidak tau tabel perkalian dengan sempurna, menurut saya rasanya itu merupakan keputusan yang kurang adil bagi siswa. Ada banyak aspek lain yang bisa menjadi pertimbangan siswa untuk naik kelas. Dalam hal ini siswa hanya perlu terus berlatih untuk mengingat tabel perkalian dengan membiasakan diri dan mengulang-ulangnya, poin penting yang perlu dipahami siswa adalah konsep perkalian itu sendiri. Jika siswa memahami bahwa perkalian itu adalah penjumlahan yang berulang dan mengerti bagaimana prosedurnya. I think it’s okay to let her/him pass to the next grade.

Dimas Candra SAputra, S.Pd.

ReplyDelete17709251005

PPs PM A 2017

Assalamualaikum Prof,

Terdapat berbagai permasalahan di dalam pendidikan matematika. Salah satunya ialah seperti yang diungkapkan dalam diskusi tersebut. Bahkan hal ini masih sering terjadi di banyak siswa SMP. Menurut diskusi tersebut, kita perlu meninjau terlebih dahulu berbagai aspek psikologinya. Setiap anak memiliki perkembangan psikologi yang berbeda. Ini dipengaruhi oleh berbagai hal, bisa dari lingkungannya maupun dari proses pembelajaran di kelas. Namun, secara umum anak-anak berada di dalam ranah konkret. Sementara tabel perkalian merupakan konsep yang cukup abstrak. Maka alangkah baiknya bila guru tidak terlalu menuntut siswa untuk dapat melakukannya. Guru perlu membangun konsep pada anak melalui hal-hal yang bersifat konkret sehingga anak-anak dapat melakukan abstraksi sesuai dengan kemampuannya.

Wisniarti

ReplyDelete17709251037

PM B Pascasarjana

Diskusi yang dilakukan oleh para pakar sperti ini memberikan informasi dan pengetahuan kepada saya khususnya yang masih perlu bimbingan dan kesadaran mengenai hakikat anak-anak yang memiliki perbedaan baik dalam kemampuan berpikir, kemampuan bersosialisasi dan kemampuan spiritualnya. Pada diskusi ini menjelaskan dengan panjang lebar mengenai permasalahan yang terdapat pada siswa. Dengan menyadari kemampuan siswa itu berbeda-beda maka guru akan lebih bijak untuk memberikan pembelajaran yang sesuai dan berlaku untuk siswa secara keseluruhan. Selain itu dengan mengetahui batas kemampuan siswa sekolah dasar yaitu pemahanan kongkrit lebih dominan dari pada abstrak maka guru dianjurkan untuk memberikan berbagai contoh untuk membangun konsep.

This comment has been removed by the author.

ReplyDeleteMuhammad Sabri

ReplyDelete17701251034

S2 PEP B

Diskusi yang menarik, membahas hal yang sederhana (seringkali diabaikan) dengan sudut pandang yang kompleks, menghafal perkalian dengan tabel perkalian dapat memudahkan siswa untuk mempelajari matematika ditingkat selanjutnya, namun rasa-rasanya kurang bijak jika hal tersebut dijadikan indikator kenaikan kelas untuk siswa kelas 4, karena banyak indikato-indikator lain yang perlu dilihat dan di perhatikan untuk dijadikan pertimbangan dalam kenaikan kelas, siswa yang belum menghafal perkalian bukan berarti tidak bisa berhitung bisa jadi karena daya ingat atau daya hafal mereka lemah, namun tidak menutup kemungkinan kemampuan berhitung dan analisis mereka tinggi.

Hari Pratikno

ReplyDelete17709251032

Pendidikan Matematika S2 (Kelas B)

Menarik dari percakapan diatas yaitu apakah siswa yang belum bisa perkalian bisa naik kelas. Kalau menurut saya, psikologis siswa yang tidak naik kelas tentu terpengaruh, mungkin dia akan menjadi minder dan malu terutama untuk anak-anak. Mereka akan dianggap bodoh oleh teman-teman lainnya. Jadi saya setuju dengan kebijakan di Inggris bahwa semua anak harus tetap dinaikkan kelas. Tugas gurulah disini membuat siswa mengerti tentang perkalian misalnya.

Latifah Pertamawati

ReplyDeleteS2 PM B

17709251026

Bismillaah..

Well, in my opinion sir, this is such a classic problem in teaching and learning mathematics. There is always a student, two students or more students who don't excel at mathematics and we have to admit that some students are slow in learning mathematics. As a teacher, we have to be patient facing this problem.

As what we have known that there is a theory called multiple intelligence. Thus, I think that it is fine, fourth grader who doesn't know time tables flawlessly of course is acceptable to be transferred to the next grade. Why? Let us take a look at the word "who doesn't know times tables flawlessly". Those words indicate that students need to know the times tables flawlessly. Hmm, doesn't it then mean that they have to "memorize" the times tables? What is the purpose of learning then? Memorizing? Of course not. In my opinion, it doesn't matter. I my self, to be honest, sometimes still forgetting 6 x 9 while I was in high school.. but here I am now, being someone who is willing to teach mathematics and share what I have learned about this subject. I even graduated from mathematics major with specialization in applied maths, so it doesn't matter. Every students are special, every students have their own specialties and we must encourage them to do their best.

Gamarina Isti R

ReplyDelete17709251036

Pendidkan Matematika Kelas B (Pascasarjana)

Seorang anak belajar dan diajar sesuai tingkatannya, namun kecerdasan seorang anak berbeda-beda dan daya tangkap serta serapnya juga berbeda. Ada anak yang langsung paham ketika guru mengajar namun juga ada sisw yang memiliki proses belajar lambat. Siswa seperti inilah yang harus menjadi perhatian seorang guru apalagi siswa tersebut merupakan siswa kelas IV yang masih panjang perjalanannya dalam sekolah. Guru harus dengan sabar dalam menghadi seorang murid seperti ini bukan malah meninggalkannya karena tidak mau merasakan kesulitan dlaam mengajar.

Nama : Habibullah

ReplyDeleteNIM : 17709251030

Kelas : PM B (S2)

Assalamualaikum wr.wb

Konsep perkalian sangat penting untuk dikuasai siswa tidak hanya pada siswa kelas IV namun pada jenjang semua pendidikan. Karena menurut saya proses perkalian merupakan hal yang sangat krusial sebagai pendukung agar dapat menguasai proses perhitungan yang lainnya. Kebanyakan apabila siswa lemah dalam proses perkalian maka dia akan susah untuk mengerjakan soal matematika terutama di dalam proses manipulasi aljabar di jenjang sekolah yang lebih tinggi. Maka dari itu sebaiknya guru harus selalu memonitoring penguasaan proses perkalian yang dimiliki siswa.

ReplyDeleteNama: Hendrawansyah

NIM: 17701251030

S2 PEP 2017 Kelas B

Assalamualaikum wr wb

Saya sangat antusias dalam menyimak alur demi alur mengenai diskusi di dalam postingan ini meskipun dengan pemahaman bahasa inggris saya yang masih minim.Point penting yang saya dapat tangkap dari postingan tersebut bahwa kecakapakan seorang anak dalam memecahkan masalah yang duhubungkan dengan waktu.Megungkap tentang pengetahuan anak.Tidak semua anak-anak memiliki kecerdasan dan karakter yang sama di dalam pembelajaran.Terkadang ada yang membutuhkan waktu yang lama di dalam menangkap dan ada juga membutuhkan waktu yang cepat.Proses mingkin lebih baik di kedepankan mengingat tingkat kecerdasan mimiliki level yang berbeda.Seorang anak biasanya membutuhkan intuisi yang dihadirkan lewat pengalaman.Pengalaman tersebut membutuhkan waktu yang lama.Menyoalkan tentang anak kelas 4 yang tidak dapat membaca waktu dalam memecahkan masalah tidak dapat dinaikkan ke kelas berikutnya.Ini mungkin sesuatu yang tidak diingnkan baik oleh siswa itu sendiri maupun guru.Oleh karenanya, mungkin guru harus sedikit memahami kedaaan hingga hal tersebut tidak terjadi.