__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

Anwar Rifa’i

ReplyDeletePMAT C 2016 PPS

16709251061

Saya setuju dengan sekolah yang mengubah sistem tersebut menjadi kelas yang sesuai dengan level setiap siswa (seperti yang ditulis oleh Patty Langston). Lagipula pertanyaan disini adalah “flawlessly” dan yang dimaksudkan Victor sebagai penanya, bahwa flawlessly adalah siswa yang cepat dan benar menjawab pertanyaan mengenai tabel perkalian dan meskipun ditanya berulang kali siswa tersebut tetap bisa menjawab dengan cepat dan benar. Lalu bagaimana jika mereka benar menjawab, tetapi tidak cepat (menurut standar guru atau silabus). Anak kelas 4 SD yang masih berada pada tahap operasional konkret, anak pada usia ini masih belum konstan. Seperti masih ada anak yang mengulang materi karena proses belajar yang lambat, tetapi ketika anak memiliki rasa ingin tahu yang tinggi maka anak ingin mencari dengan antusias. Anak kelas 4 SD yang belum bisa mengetahui tabel perkalian dengan sempurna bisa jadi karena dia tidak mengetahui konsep dasar perkalian dan membuatnya sedikit lebih lambat untuk mengerti. Namun guru tidak boleh serta merta otoriter dengan keputusan untuk membiarkan anak kelas 4 SD tersebut tinggal kelas karena hal tersebut dapat membuatnya drop dan memiliki beban psikis.

Ardeniyansah

ReplyDelete16709251053

S2 Pend. Matematika Kelas C_2016

Assalamualaikum wr. . wb.

guru sebagai seorang pendidik diharapkan mampu melakukan suatu bentuk pendekatan kepada para siswa agar mereka tidak merasa malu dan sungkan untuk bertanya kepada guru. Hal ini akan menjadikan siswa menjadi lebih aktif dan berperan penting dalam pembelajaran. Guru sebagai seorang pendidik diharapkan mampu melakukan suatu bentuk pendekatan kepada para siswa agar mereka tidak merasa malu dan sungkan untuk bertanya kepada guru. Hal ini akan menjadikan siswa menjadi lebih aktif dan berperan penting dalam pembelajaran. Guru sebagai seorang pendidik sebisa mungkin mempertimbangkan media apa yang sekiranya cocok dan pas untuk diterapkan pada kegiatan pembelajaran. Tujuan dari pengaplikasian media itu sendiri adalah agar para siswa bisa menyerap materi pelajaran yang diajarkan oleh gurunya tanpa merasa jenuh dan tentunya menjadikan mereka ikut terlibat aktif pada proses pembelajaran.

Annisa Hasanah

ReplyDelete16709251051

PPs Pendidikan Matematika C 2016

Diperlukan komunikasi yang baik antara siswa dengan guru, guru dengan orangtua, dan guru dengan pihak-pihak yang berkepentingan dengan siswa itu sendiri sehingga tidak ada miss antara guru dan siswa dan juga ketercapaian tujuan pendidikan dapat terlaksana. Guru harus mampu merangkul siswa yang mengalami kesulitan dengan berbagai metode pembelajarn, karena siswa memiliki gaya belajar yang berbeda-beda. Anak yang biasanya “bermasalah” dalam belajar adalah anak kinestetik. Anak visual dan auditori bisa duduk nyaman mendengar guru mengajar. Oeh karena itu guru diharapkan bisa memilih pembelajaran yang membantu anak seperti ini agar bisa focus pada pembelajaran.

Syahlan Romadon

ReplyDeletePM C 2016 / 16709251047

Menurut saya, ketika siswa berada di kelas 4, siswa sebaiknya sudah mengetahui perkalian dengan mahir. Namun, ketika siswa tidak mahir perkalian kita tidak dapat serta merta menentukan apakah dia harus naik kelas atau tidak. Kita harus mencari tahu terlebih dahulu seberapa besar pemahaman siswa tersebut terhadap perkalian. Boleh jadi siswa terlihat tidak mahir perkalian hanya dikarenakan dia tidak teliti saat menghitung. Ketika siswa sudah memahami penjumlahan serta memahami perkalian sebagai penjumlahan berulang maka menurut saya siswa tersebut layak untuk naik kelas. Sebaiknya pada awal pembelajaran pada setiap tahun ajaran baru, guru mengingatkan siswa mengenai konsep perkalian dan pembagian sekaligus untuk mengetahui siswa mana saja yang membutuhkan perhatian lebih.

This comment has been removed by the author.

ReplyDeleteHeni Lilia Dewi

ReplyDelete16709251054

PPs Pendidikan Matematika Kelas C 2016

Ini menjadi perhatian banyak pihak, tidak hanya guru tetapi dukungan orang tua, ketika seorang anak kelas empat belum mampu memahami tabel perkalian dengan mahir, padahal anak se level kelas empat sudah sepatutnya mahir dalam perkalian. Kasus semacam ini harus menjadi bahan perbaikan, bahwa penanaman konsep pada tahapan anak operasional kongkrit harus benar-benar ditekankan. Karena jika gagal disini, keberlanjutan materi berikutnya akan terbengkalai. Konsep harus diterapkan dalam pemahaman siswa dengan tepat, sehingga siswa mudah memahaminya.

Rahayu Pratiwi

ReplyDelete16709251077

PPS PM-D 2016

Soal yang banyak membutuhkan waktu yang banyak juga. Karena soal dalam matematika tidak dapat disamakan dengan soal untuk mata pelajaran lain. Diperlukan penggunaan waktu yang efisien. Selain untuk mengerjakan soal, disisihkan waktu untuk mengoreksi jawaban final.

Dessy Rasihen

ReplyDelete16709251063

S2 P.MAT D

Sebuah diskusi yang sangat menarik sekali terjadi disana, walaupun ada beberapa yang saya belum mengerti karena perbedaan bahasa, disini saya sudah mulai dapat melihat alur diskusinya sedikit demi sedikit. Sebagian berfikir bahwa murid yang belum mengerti tentang time tables -dimana pengertian "mengerti" itu dinilai berdasarkan, akurasi dan kecepatan- seharusnya tidak diperbolehkan untuk naik kelas, karena time tables itu sendiri merupakan esensi, dasar dari beberapa materi yang akan dipelajari di tingkat selanjutnya.

Dessy Rasihen

ReplyDelete16709251063

S2 P.MAT D

Sedangkan sebagiannya lagi berpendapat bahwa ketidak mengertian mereka pada satu materi tidaklah seharusnya menjadi penghambat mereka untuk terus melangkah ke jenjang yang lebih tinggi. Menurut pendapat saya sendiri, saya tidak setuju jika ketidak mengertian mereka mengenai satu hal harus menyebabkan mereka untuk tinggal kelas. memang pada akhirnya hal itu akan sedikit menghambat perkembangan mereka di jenjang selanjutnya, tetapi hal itu memang agak wajar karena pada akhirnya setiap siswa memiliki kemampuan dan kecepatan yang berbeda-beda dalam mengingat sesuatu.

Sylviyani Hardiarti

ReplyDelete16709251069

S2 Pendidikan Matematika Kelas D 2016

Siswa kelas 4 SD memang harusnya menguasai matematika dasar yaitu perkalian dasar. Antara satu materi dengan materi lain dalam matematika saling berkesinambungan, konsep perkalian merupakan konsep dasar matematika yang akan digunakan untuk pembelajaran matematika selanjutnya. Tapi jika siswa kelas 4 SD tidak menguasai perkalian dasar, maka guru tidak boleh serta merta otoriter membiarkan siswa tersebut tinggal kelas. Guru harusnya bisa menggali lebih jauh apa yang menyebabkan itu terjadi. Hal ini bisa saja terjadi karena dalam pembelajaran matematika, guru tidak memperhatikan tahap berpikir anak SD yaitu tahap operasional konkret, maka wajar saja jika mereka kesulitan untuk menguasai konsep perkalian. Guru tidak menggunakan benda konkret dalam mengajarkan perkalian, tapi langsung memberikan konsep matematika yang bersifat abstak dan menyuruh siswa menghafal tabel perkalian. Tentu tidak semua siswa bisa menguasainya, hal ini dikarenakan kemampuan setiap siswa berbeda-beda. Jadi, sebagai seorang guru, janganlah langsung memberikan definisi atau menyuruh siswa menghafal konsep matematika tanpa memfasilitasi mereka memahaminya terlebih dahulu, karena hal itu sama saja dengan membunuh intuisi siswa.

Windi Agustiar Basuki

ReplyDelete16709251055

S2 Pend. Mat Kelas C – 2016

Ketika siswa kelas 4 SD masih belum bisa memahami tabel perkalian, ini merupakan refleksi bagi guru dan siswa. Sebagai guru, haruslah bisa memberi inovasi dalam pengajaran. jika strategi 1 gagal, maka bersiaplah untuk strategi atau metode yang lainnya. Mungkin jika sasarannya anak kelas 4 SD, maka strategi pembelajaran mengenai tabel perkalian bisa dimodifikasi dalam bentuk permainan misalnya.

Ratih Eka Safitri

ReplyDelete16709251059

PPs Pendidikan Matematika C 2016

Menurut saya saat ada anak kelas 4 tidak dapat menguasai tabel perkalian maka kita sebagai guru tidak bisa begitu saja memutuskan apakah anak tersebut akan tinggal kelas atau tetap naik kelas. Hal ini menjadi tugas tambahan kita untuk melihat letak kesalahan dalam mengajar, tentu dengan analisis kesulitan tersebut kita dapat memperbaiki kesalahan siswa. Kesalahan bisa saja terletak di metode guru mengajar, karena tidak semua siswa dapat belajar dengan metode tertentu, gaya belajar siswa bermcam-macam sehingga hal tersebut perlu dikaji ulang oleh guru.

Dessy Rasihen

ReplyDelete16709251063

S2 P.MAT D

Dalam hal ini diperlukan kebijaksanaan guru untuk melihat bahwa kemampuan kognitif tiap siswa berbeda-beda. Diperlukan pemahaman lebih lanjut bagi para guru untuk menganalisa penyebab kesulitan siswa. Guru kembali harus memahami bahwa setiap siswa memiliki kemampuan matematis yang berbeda. Kembali, peran guru sangat diperlukan untuk membuat siswa tersebut mengenali faktor penyebab keterlambatannya.

Listia Palupi Wisnu Aji

ReplyDelete14301241007

S1 Pendidikan Matematika I 2014

Di dalam dunia pendidikan ini, banyak ditemui anak-anak kelas 4 SD belum begitu mengerti tentang tabel perkalian dengan sempurna, tetapi banyak diantara mereka tetap naik kelas. Menurut saya, hal ini disebabkan mereka belum banyak berlatih tentang perkalian. Padahal dengan berlatih, anak-anak dapat menghafal tabel perkalian tanpa menyadarinya. Kurangnya berlatih ini bisa dipengaruhi dari dalam diri anak tersebut karena kurangnya motivasi dan kecintaannya terhadap matematika. Selain itu, bisa dipengaruhi dari luar, seperti guru yang tidak memperhatikan siswanya ataupun orang tua yang tidak memberikan kasih sayang dan dukungannya.

Muhammad Nur Fariza

ReplyDelete14301241024

S1 Pendidikan Matematika A 2014

Memang menjadi masalah bila anak kelas 4 belum paham tabel perkalian. Saya ingin berpendapat tentang materi perkalian ini. Sebenarnya bila anak tersebut tak bisa perkalian karena dia hanya 'dipaksa' menghafal tabel perkalian, ketakbisaannya bisa diwajarkan. Maksudnya ketika tabel perkalian menjadi satu-satunya media pembelajaran perkalian tentunya tidak cukup bagi pembelajaran. Hal yang perlu dipelajari adalah menalar perkalian lebih dari menghafal tabel sehingga dibutuhkan media yang menunjang.

Wahyu Berti Rahmantiwi

ReplyDeletePPs Pendidikan Matematika Kelas C 2016

16709251045

Dalam artikel ini membahas pentingnya teman sebaya. Kepentingan teman atau persahabatan seorang siswa akan mengalahkan segalanya. Ini terbukti ketika siswa memilih sekolah yang akan ditujunya jika ia berada di kelas ujung dia akan mengalami dilema hebat ketika ia memilih mengikuti pilihan sahabatnya daripada orang tuanya. Dengan demikian, peran orang tua dalam pendidikan anak sangatlah penting. Orang tua harus selalu ada disetiap saat siswa membutuhkan, orang tuapun harus rela kehilangan waktunya bekerja demi masa depan anaknya yang lebih baik. Tetapi jika diambil sisi positif siswa yang yang mempunyai sahabat ia akan selalu termotivasi ketika sahabatnya lebih pintar darinya.