That's something I've noticed many people aren't aware of, division (fractions) simply asks how many denominators do I have to add to itself in order to get to the numerator? The fact that Singapore combines pure notation and geometric interpretation is great, no wonder they are the #1 country in terms of education.
GZA I think you are talking about a division sum which looks like 18/3 and this would involve asking how many denominators are in the numerator. The presentation dealt with a fraction being divided by another fraction which has a completely different process. Most pupils in dividing a fraction by another fraction will explain that the procedure is to change the division sign to a multiplication sign and turn the second fraction upside down. This is procedural understanding without actually being able to justify why this process is mathematically sound.
Lots of appreciation to making understand / visualizing the concept of division by a fraction. Where most people just learn to multiply by the reciprocal fraction. Still, I need to say the maths-lessons are ambivalent. And the visualization is more of a trick than adding to understanding. As I understand mathemathics, subtraction (-) is the opposite action of addition (+). And dividing (:) is the opposite of multiplication (x). So, if I do 4 times 3 then the result is 3 + 3 + 3 + 3 = 4 x 3 = 12 The opposite action of that is 12 : 4 = 3 So, the actual question is: "How large is 1 group when I split 12 (again) into 4 groups". And the question is not: "In 12, how many groups of 4 are there" (as in 1:55 of the video). When I split 1 pizza in 2, I would be left with 1/2 pizza (per group = for example per person). There is not a child on earth that learns how many groups of 2 are in 1 pizza. (which would be 1/2 of 2 pizza's and a very illogical reasoning when I start the exercise with 1 pizza). We have all learnt that splitting 1 pizza in 2 simply gives 1/2 pizza (per piece). And this calculation is the opposite of 2 x 1/2 = 1 So, if I want to do a division by a fraction then I consider, for example, 1 : 1/2 = 2 (and which is logically the opposite of 1/2 x 2 = 1) Analogous to the above, I am actually asking myself how much is the total when a group of 1 was only 1/2 of the total ? The obvious answer is 2. So, the calculation 1/2 : 1/6, as in the video, should actually be seen as: how much is the total when 1/2 is only 1/6 of the total ? So, you have to multiply 1/2 times 6 to get the answer 3 (the same answer of course as in the video, but following another argumentation). I understand that this is a more difficult reasoning, but we need to admit that, also with this method, we are learning just tricks to get the job done, rather than really understanding what division by a fraction means. It is ambivalent because we learn, when we are very young, that 1 pizza divided by 2 would give 1/2 pizza, but schools use a different type of explanation, later on, that division by 1/2 means how much halves fit into 1 pizza, which is different than asking for the original amount of pizzas of which you took 1/2, which is simply 2 pizza's. I think that we lost that way of looking at the problem because we lost our view on what multiplication really means. Instead we get many exercises of a x b, with little or no visualization (where we could get used to seeing that 2 x 1/2 is something different than 1/2 x 2).
yes even in a Waldorf school here in the US (which has cutting-edge multi-sensory math ed in many ways), I was literally taught the horrible old rhyme "Yours is not the question why / just invert & multiply!" 😱😱😱😱😱😱😱😱
Why Singaporean mathematics. This was how I taught maths . The physical equipment were in every classroom I used and in constant use. Then came the National Curriculum in the UK. The equipment remained but was left unused in many schools. Hurrying kids through learning outcomes many failed to achieve and returning to the scary, paper and pencil, abstract work returned and the nine year olds coming to my class were often confused, just as I had been in my own Year four maths lessons.
Its good, but its not practical in the real world. What if I have 3/7 divided by 8/5, no one is gonna start cutting out circles, and split them into sectors. You just apply the rules of mathematics, to get the answer. But as an example its good, cause the question is 1/2 divided by 1/6 which means how many 1/6's in 1/2. We can see how this works visually to get 3, and then this confirms the mathematical technique that gives 3 as well.
+Colin Java that's right but at least they learn the basics through concrete materials more easily and efficiently before they get to those. Some smarter students can apply the basics and utilise that in their head to solve 3/7ths divided by 1 and 3/5th
+Colin Java As he explains, the idea is to introduce with concrete concepts, and then move on to pictorial and abstract methods once the mathematical idea is firmly grasped. This encourages successful students to eventually recognize the underlying concepts easily enough to function at the pictorial and abstract level. It's true, most adults will not stop to cut out circles. But this process begins in elementary school. Those who initially learned the concept in a concrete way will have a better understanding and memory of why the abstract process works. It is a method of encouraging creative mathematical thinking, rather than drilling traditional formulas that may not hold any conceptual understanding to the individual. And actually, I have seen many presentations that present bar charts and pie graphs to depict divided fractions. Even adults resort to concrete models when they want to be better understood.
We only use this method when we are first starting to learn this. When using bigger fractions, for example what you said, we will convert 3/7 ÷ 5/8 into 3/7 × 5/8 which is equal to 15/56. 15/56 is the answer for both of the number sentences I typed out. If you don't believe me then use a calculator.
That's something I've noticed many people aren't aware of, division (fractions) simply asks how many denominators do I have to add to itself in order to get to the numerator? The fact that Singapore combines pure notation and geometric interpretation is great, no wonder they are the #1 country in terms of education.
GZA
I think you are talking about a division sum which looks like 18/3 and this would involve asking how many denominators are in the numerator. The presentation dealt with a fraction being divided by another fraction which has a completely different process. Most pupils in dividing a fraction by another fraction will explain that the procedure is to change the division sign to a multiplication sign and turn the second fraction upside down. This is procedural understanding without actually being able to justify why this process is mathematically sound.
I love Singapore Mathematics. Now, I realize that math is more on understanding and analysis.
Hi
WOW. I just learned more of the concept of dividing fractions. Excellent video.
Lots of appreciation to making understand / visualizing the concept of division by a fraction.
Where most people just learn to multiply by the reciprocal fraction.
Still, I need to say the maths-lessons are ambivalent.
And the visualization is more of a trick than adding to understanding.
As I understand mathemathics, subtraction (-) is the opposite action of addition (+).
And dividing (:) is the opposite of multiplication (x).
So, if I do 4 times 3 then the result is 3 + 3 + 3 + 3 = 4 x 3 = 12
The opposite action of that is 12 : 4 = 3
So, the actual question is: "How large is 1 group when I split 12 (again) into 4 groups".
And the question is not: "In 12, how many groups of 4 are there" (as in 1:55 of the video).
When I split 1 pizza in 2, I would be left with 1/2 pizza (per group = for example per person).
There is not a child on earth that learns how many groups of 2 are in 1 pizza.
(which would be 1/2 of 2 pizza's and a very illogical reasoning when I start the exercise with 1 pizza).
We have all learnt that splitting 1 pizza in 2 simply gives 1/2 pizza (per piece).
And this calculation is the opposite of 2 x 1/2 = 1
So, if I want to do a division by a fraction then I consider, for example, 1 : 1/2 = 2
(and which is logically the opposite of 1/2 x 2 = 1)
Analogous to the above, I am actually asking myself how much is the total when a group of 1 was only 1/2 of the total ?
The obvious answer is 2.
So, the calculation 1/2 : 1/6, as in the video, should actually be seen as: how much is the total when 1/2 is only 1/6 of the total ?
So, you have to multiply 1/2 times 6 to get the answer 3 (the same answer of course as in the video, but following another argumentation).
I understand that this is a more difficult reasoning, but we need to admit that, also with this method, we are learning just tricks to get the job done,
rather than really understanding what division by a fraction means.
It is ambivalent because we learn, when we are very young, that 1 pizza divided by 2 would give 1/2 pizza, but schools use a different type of explanation, later on,
that division by 1/2 means how much halves fit into 1 pizza, which is different than asking for the original amount of pizzas of which you took 1/2, which is simply 2 pizza's.
I think that we lost that way of looking at the problem because we lost our view on what multiplication really means.
Instead we get many exercises of a x b, with little or no visualization (where we could get used to seeing that 2 x 1/2 is something different than 1/2 x 2).
yes even in a Waldorf school here in the US (which has cutting-edge multi-sensory math ed in many ways), I was literally taught the horrible old rhyme "Yours is not the question why / just invert & multiply!" 😱😱😱😱😱😱😱😱
Great work sir much love from Ghana
I love it I like to learn maths of fraction
гениально!!! спасибо большое! ну почему же в обычных школах так просто и наглядно не показывают!?
MINDBLOWING. Why didn't I learn math this way???
Because, most people only care about results and not the process/the why; and this is unfortunate 😢
Interesting.
good teaching
Why Singaporean mathematics. This was how I taught maths . The physical equipment were in every classroom I used and in constant use. Then came the National Curriculum in the UK. The equipment remained but was left unused in many schools. Hurrying kids through learning outcomes many failed to achieve and returning to the scary, paper and pencil, abstract work returned and the nine year olds coming to my class were often confused, just as I had been in my own Year four maths lessons.
Name: Aileen S. Repil
School: Azagra Elementary School
Thank you so much sir kasi nakita ko po channel nyo and I am learning so much.
O would like buy this material, It is amazing how i sim surprise by quality.
Este método ya mis bisabuelos paso a mi abuelo y a mi padres Y ahora a mi este método yo soy de PARAGUAY
Just asking but do you guys know SAKAMOTO
Its good, but its not practical in the real world.
What if I have 3/7 divided by 8/5, no one is gonna start cutting out circles, and split them into sectors.
You just apply the rules of mathematics, to get the answer.
But as an example its good, cause the question is 1/2 divided by 1/6 which means how many 1/6's in 1/2.
We can see how this works visually to get 3, and then this confirms the mathematical technique that gives 3 as well.
+Colin Java that's right but at least they learn the basics through concrete materials more easily and efficiently before they get to those. Some smarter students can apply the basics and utilise that in their head to solve 3/7ths divided by 1 and 3/5th
+Colin Java As he explains, the idea is to introduce with concrete concepts, and then move on to pictorial and abstract methods once the mathematical idea is firmly grasped. This encourages successful students to eventually recognize the underlying concepts easily enough to function at the pictorial and abstract level. It's true, most adults will not stop to cut out circles. But this process begins in elementary school. Those who initially learned the concept in a concrete way will have a better understanding and memory of why the abstract process works. It is a method of encouraging creative mathematical thinking, rather than drilling traditional formulas that may not hold any conceptual understanding to the individual. And actually, I have seen many presentations that present bar charts and pie graphs to depict divided fractions. Even adults resort to concrete models when they want to be better understood.
Kids Von Banking
Kids Von Bank zndjdj
We only use this method when we are first starting to learn this. When using bigger fractions, for example what you said, we will convert 3/7 ÷ 5/8 into 3/7 × 5/8 which is equal to 15/56. 15/56 is the answer for both of the number sentences I typed out. If you don't believe me then use a calculator.
على مدى قرون الدول العربية محرومة بسياسة ممنهجة من حكوماتها الفاسدة على عدم تطوير مناهج التعليم خوفا من وعي شعوبها والانقلاب عليها
هذا عكس ما اعتاد أسلافنا القيام به
что за книга у него в руках и как купить такую в России (Москва)? Может у кого есть?
сто вод m?,
I have difficulty in understanding singaporean math books :(
Hi I from Turkey. I want to buy this book. How can buy it?
Hi, did tou Buy the book? Do would you like to talk tô me?
maninisimio@yahoo.com.br
+5531986719857
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