Why was 5 + 5 + 5 = 15 marked wrong? America Common Core Math

[@PolygonSwan]

"600 x 3" hang on, be right back.

[@Bob94390]

Exactly! The pupil had understood the concept of repeated addition, and had also used the commutative law of multiplication: You can switch the order of the factors, e.g. to achieve more efficient evaluation as you show very well here.

[@hippophile]

@@Bob94390 😛😆

[@castirondude]

@polygonswan it's been 2 hours have you got the answer yet? :)

[@timeonly1401]

Great point. Worse yet, for the teacher or student to use repeated addition to find 100000000 X 1. 😅😂

[@bobli840]

Teacher, how do I solve 0x2 I only have a blank page

[@dazartingstall6680]

Yes it's repeated addition. But if you insist on the strict adherence to multiplier × multiplicant, good luck with ½ × 5 using this method.

[@WilliamLeeSims]

I was thinking the same, but with decimals. Like... how do I make 1.414 groups of 2.828?

[@dazartingstall6680]

@@WilliamLeeSims I think the additive method pretty much breaks down when applied to two non-integers, no matter what they are, to be fair. At some point we'd end up having to divert into a division side-project.

[@JohnDlugosz]

@@dazartingstall6680 Right; it's not even the same as repeated addition _in general_ . Look at matrices, for example. Or any definition of a field. It's just an odd thing about integers; multiplication is a thing of its own.

[@kristikule6768]

​@@dazartingstall6680 We can stay on Integers alone and say--- 100 × 3. Would you rather write 3 100s or 100 3s?

[@johnshaw6702]

Good example of why it makes no sense. LOL

[@ErikYoungren]

There's nothing wrong with teaching multiplication as repeated addition. However, I have a HUGE problem with potentially teaching people that 5x3 is not equal to 3x5.

[@Kernel15]

Presumably, the student lost one mark for their reasoning instead of losing all possible marks for both reasoning and answer. I mean, it's important to learn that working 8 hours for $20/hour is not quite the same as working 20 hours for $8/hour. They both add up to you earning $160, but you'd probably prefer one over the other.

[@JayTemple]

5% of 21 is equal to 21% of 5, but one represents an insultingly low tip on a $21 tab and the other represents a generous tip on a $5 tab.

[@faming1144]

​@@Kernel15Yes, it may be less preferable to work 20 hours for $8/hour, but it is still clever to calculate your total earnings by adding $20 8 times if you have to use addition. But actually this has nothing to do with the pure mathematical question at hand. As many others do in the comments you are giving (some arbitrary) context which is not there. This is not a life lesson, this is how to do multiplication by addition. Any interpretation wether it means 5 times of something 3, or something 5 3 times is irrelevant for the calculation. The easiest, most efficient way for 5 x 3 is 5+5+5 either way.

[@bait6652]

@@faming1144 yet as you say others put context/conditions ....u are doing the same. This question has nothing to do w the actual calculation but the semantics/syntax of method of " repeated addition"....it's a word/math-word problem not simple calculation.

[@ShapeKeyes]

@@Kernel15 You're example doesn't require multiplication to decide which you would prefer and therefore doesn't require repeated addition. What you are asking is would you prefer to be paid $20/hour or $8/hour? In other words, what is a bigger number 20 or 8?

[@ericbarlow6772]

I was taught it was repeated addition but was also taught that 5x3 is the same as 3x5, ergo, both 5+5+5 and 3+3+3+3+3 are both valid.

[@krzysztofmazurkiewicz5270]

Same thought here. That said sientific language must be precise. And the explanation states that the first numbers specifies the number of repetitions (groups) and the secone is the value of that group. So if we have to apply the definition the 3+3+3+3+3 seems to actually be correct

[@RilianSharp]

​@@krzysztofmazurkiewicz5270 the first number is the multiplicand and the second number is the multiplier. so 5 three times. 5+5+5.

[@matthewgraham2619]

So getting 5 apples from 3 friends is different from 3 friends each giving me 5 apples? Or how about $20/hour for 8 hours being different from 8 hours at a rate of $20/hour? I didn't realize the order mattered!

[@u.2b215]

Imagine the question was about 15x2 both 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2 and 15+15 would be valid to come to the solution of 30 but anyone who doesn't follow the latter to solve it is just being silly. There is no reason to be so devoid of common sense and insist on the former.

[@arturs7547]

@@matthewgraham2619 order mathers because i would rather work 8 hours for 20/h to earn 160 than 20 hours for 8/h to also earn 160.

[@jefffixesit60]

For me, this is an arbitrary assessment that has no place in 3rd grade mathematics. The commutative property of multiplication is far more important to learn than insisting on an arbitrary ordering of multiplier and multiplicand. ❤

[@otakurocklee]

yes, thank you.

[@RustyWalker]

It isn't arbitrary. "Arbitrary" doesn't mean "a method I don't like." They'll go on to learn commutative properties later. As the video showed, this has a history that's been documented all the way back to Euclid.

[@KeithAllen-pg8ep]

This has all the smell of "wokeness" about it and, as a famous person once said, "Everything woke turns to s***." Imagine insisting on this strategy with, say 0.2 x 3. Just teach that multiplication is successive addition, along with the commutative property!

[@bait6652]

@@KeithAllen-pg8ep imagine teaching grade1-3(7-9 year olds) 0.2 , 0.8. pi. E

[@five-toedslothbear4051]

These people are going to grow up to read a recipe and see “egg x 3“, and they will not be able to make a cake because they can’t figure out to make egg groups of the number three.

[@justinlloyd3]

This is how you make students disengage from math.

[@jamesday3591]

I would tend to believe that what makes students disengage from math is teaching them incorrectly, by allowing such answers that are "practically" correct, but technically incorrect, which then results in frustration and disillusion when they later learn that what they thought was correct actually isn't. The emotional difficulty that results from such deeply held contradiction can be quite traumatic, in fact.

[@sustrackpointus8613]

​@jamesday3591 the answer of 5 + 5 + 5 is as much correct as the "intended" one, because multiplication is COMMUTATIVE! 5*3 = 3*5 = 5 + 5 + 5. I'm 20 yo, second year of uni, have been competing in math competitions since i was 8, not once in my life the distinction of 3*5 and 5*3 has had any significance

[@jamesday3591]

@@sustrackpointus8613 It is correct in regard to the equation. It is incorrect in regard to the question, as the question is primarily about applying the specified method. As such, using a valid method that is inconsistent with the method intended by the question is not as much correct as the "intended" method, because applying the commutative principle is not the principle intended by the question. That seems inherently self-evident to me. Also, I'm glad that as a 20 year-old, second-year university student, having competed in math competitions since you were 8, and never having before learned this mathematical theory, you are now being introduced to the concept that has heretofore been a hole in your knowledge. As a retired computer programmer and financial advisor who has 40 years of experience in the professional application of this principle in both several programming languages and institutional investment applications, I can assure you that understanding this material significance can make or break your career. You should have learned this in elementary school. I'm glad that you're at least being exposed to it now.

[@matix676]

@@justinlloyd3 by making strict rules on what is expected from a student? Yeah, letting them do whatever they want and however they want surely has a lot to do with teaching and learning.

[@jfftck]

​@@sustrackpointus8613Does 5x = 15 equal 3y = 15? If it does, then your argument would hold true.

[@lugiagaurdien773]

the kid should have clearly done a rigorous proof that 5*3=3*5 using number theory and then said that 5+5+5 is 15

[@kamekaha52]

but still. its basic math

[@silverfeathered1]

Five baskets with three apples in each is not the same as three baskets with 5 apples in each. It's important to make that distinction early. The calculation is the same by a different principle, but understanding the actual principles is what they are learning. If reaching the total was the only thing that matters, then only teaching kids how to use a calculator would be superior.

[@nickincorvaiajr1255]

​@silverfeathered1 But it's still the same amount of apples, which is what you are adding. How you group them is irrelevant in this scenario. And yes, three groups of five is technically not the same as five groups of three in a real life scenario, but if they wanted it that way it should be explained in the question. I'll add that this is not representing a real life scenario, it's just multiplying two abstract numbers. The teacher is just wrong. Math should be taught to allow for creativity and going about problems in one's own way, as long as it's correct and rigorous. It is foolish to discourage that, especially over something so trivial and when the kid is correct. This teacher is not doing him any favors in setting him up for higher maths.

[@ShapeKeyes]

@@silverfeathered1 It's a good thing the problem talked about the units of apples x baskets then vs. having unitless numbers. A 3 in by 5 in piece of paper is equivalent to a 5 in by 3 in piece of paper. It's important for children to understand this as well. If no units are listed I assume the units are the same and you're likely calculating something akin to an area.

[@silverfeathered1]

@@ShapeKeyes What you're missing here is that these questions aren't out of the blue. They have a lesson plan that goes with it. The teacher has taught them this information, and this is their test to evaluate if they understand the concepts. It literally tells them before the equation what method the teacher requires to solve it. The parent might be blindsided because they weren't in the classroom, but the child certainly should know. If they don't know, this is how you gauge which students are on track with the current amount of education and who needs more. The older generations that failed to thrive in the public school system have no legs to stand on critiquing any "new" ways.

[@SirMerenos]

The question is why does math at a low level need to go into semantics? This is why so many people hate math these days Instead of teaching it as a puzzle to be solved, it is presented as trick questions where the end result doesn't matter so long as the process is as ordained. If this was college level, then sure it makes sense to go into the semantics, but at 2nd grade where this is supposedly taught, the focus should be on engaging children with math and teaching them to love numbers, not hate numbers. 5×3=3×5 So I argue it should have been allowed

[@deannal.newton9772]

There shouldn't have to be a discussion because it's pretty clear that it is allowed. The real discussion should be how that teacher got the job in the first place where they don't know that 5x3=3x5? Even in a college level, it's pretty straight forward for these teachers.

[@bait6652]

Cuz math at its fundamentals is semantics....akin to Grammar w numbers than words....or in relation how they use to make you translate a word problem to equation. Doesn't tell u tho what's being taught during that grade(ie how much later is commutation taught)

[@bait6652]

@@deannal.newton9772 the child deployed the commutative property so should have wrote 5*3=3*5=5+5+5... It's a question of Grammar not math. Teacher might not be afforded to mark ahead...even tho kids level might be accelerated by his parents(or media)

[@deannal.newton9772]

@@bait6652 Ok, but how was the child suppose to know unless the teacher told them in class how to properly express the equation. If the teacher didn't properly explain how it works in the class, can we really blame the student?

[@DiavsArt]

@@deannal.newton9772It’s easy to zero in on the students that make mistakes like this, but everyone glosses over the students that do understand. Plus it overlooks the fact that mistakes are crucial to the learning process. Sometimes those mistakes can prove to be motivating. The path to my masters is paved over a foundation of screwups, each with its own lesson. At the end of the day math is little more than a bunch of instructions. Follow the instructions and the correct answer is inevitable.

[@elinope4745]

Sometimes schools are there to teach you to think inside a box and not to think for yourself. Critical thinkers are too demanding.

[@silverhammer7779]

Critical thinkers don't become teachers, which is a big part of the problem.

[@elinope4745]

@@silverhammer7779 Sal Khan begs to differ.

[@rosswalenciak3739]

@@elinope4745 *most

[@jamesday3591]

Other people are unable to comprehend the box itself, and so justify their irrationality by claiming that it's simply "outside the box" thinking. Critical thinking is too demanding for them.

[@pwmiles56]

You could just as well say "5x3 is 5 three times over, 5+5+5". It's a point of grammar, not of maths.

[@okaro6595]

You can't do math or you do not understand the problem.

[@pwmiles56]

@@okaro6595 I was pointing out that the grammar is commutative, like the operation itself.

[@okaro6595]

@@pwmiles56 You are putting your own reading on it.

[@pwmiles56]

@@okaro6595 So did the student.

[@Kernel15]

Would you prefer to work for 5 hours earning $3 per hour (5x3) or work for 3 hours earning $5 per hour (3x5)?

[@chaosgyro]

Hearing Presh defend terrible teachers and worse education standards was not on my bingo card today.

[@sans1331]

real

[@oleksandrkatrych9356]

he's got a trend to publish more viral stuff lately 😢

[@1st2nd2]

Please elaborate on the "worse education standards"

[@SpicyBee-p3j]

You dont know how the teacher taught the student, if the teacher taught the student as a x b = b + b...... then doing it as a x b = a + a...... shows that the student did not listen to the teacher, and exams are done to show application of what the student has learned. Besides we dont have all the evidence that the teacher did not say f2f "Everyone, make sure to do Part II as ......... " We dont have all the information and therefore we shouldn't keep assuming the teacher and/or the student was wrong.

[@KeithAllen-pg8ep]

@@SpicyBee-p3j The student was right (by the commutative property).

[@justinlloyd3]

There is no justification for this besides arbitrary bs rules that dont actually teach you anything

[@douginorlando6260]

Reminds me of “new math aka common core” bs … designed to equalize all students down to the least intuitive child

[@jamesday3591]

There is no justification for those who do not understand the justification. And those who view this as arbitrary, obviously do not understand the justification. Just like when my six-year old didn't understand the justification for cleaning his room, and just thought it was arbitrary. You can learn, just like he did. Or not. Some people never learn the value of cleaning their room. I know. I've seen their houses. :/ Likewise, you seem to have never learned the justification for this mathematical principle. I imagine that you also don't use math beyond simple multiplication in your profession. Why? You've never really understood it.

[@kristopherr8131]

@@jamesday3591 Maybe we should hire better teachers or require teachers to at least learn the commutative law of multiplication. Changing the order of numbers being multiplied does not change the product; in other words, "a × b = b × a" - meaning you can swap the positions of the numbers and still get the same result when multiplying them. Algebra involves understanding how equations can best be solved using different techniques to rearrange, reduce, and refactor equations.

[@JamesD2957]

why do you guys bother pretending you care go away

[@jamesday3591]

@@JamesD2957 Why do you bother pretending that you know anything?

[@thomasjefferson6225]

i cant watch the full video. the stupidity here makes me angry for the kid who might be turned off from math.,

[@user-matlee2477]

I can't either...

[@1st2nd2]

I was also infuriated by this. The full clip explains the reasoning. I am less upset about the grade now, but I still feel for the student. Willful ignorance is not flattering.

[@nieshamccoy9419]

It's really not that hard if you understand the concept of grouping and order. It's almost the same thing that is taught in high school algebra. My friend is a 3rd grade teacher and taught it to her students. They enjoyed it.

[@Blackspidy619]

Sounds like a typical educational gotcha that we all hate and has turned so many of us off from education. This isn't a problem with math, but rather how it's taught and how kids are smacked down and their natural curiosity slaughtered for not doing exactly UND EXACTLY what the syllabus asks of them.

[@1st2nd2]

@@Blackspidy619 The video makes it clear that this was not just testing if the student could multiply and add. This question was also testing the student's understanding of a method taught in class. The student's response displayed a lack of mastery of the method.

[@WombatDave]

Any argument that the teacher is correct is an argument that students should not be allowed to have more understanding of a subject than their peers. The student in this case appears to understand that the two things are the same, and is penalized because the teacher hasn't reached the point in the lesson plan where that is explained to the pupil. It is simply arguing that what matters is not actually understanding of the subject matter.

[@FireGamer99]

This might be exactly it. The student realized that multiplication was commutative before he was taught that. It's disappointing to see a kid penalized by his math teacher for learning math.

[@rosswalenciak3739]

When I was in high school geometry, I used a property of parallelograms to solve a problem when we had only learned triangles yet, and I got points off because "we haven't learned that yet"

[@KeithAllen-pg8ep]

Very few Elementary Teachers have mathematics degrees.

[@bait6652]

@@FireGamer99 or when students get docked marks for missing apostrophes hyphens comma colons and periods in English grammar at that age

[@WombatDave]

@@KeithAllen-pg8ep Which would be why I argue that the teacher is wrong from an education perspective.

The problem is that the question is not a math question, is a "follow the instructions" question that is in math format

[@beauthestdane]

I understand what they are doing, but, it's idiotic.

[@keithgoodnight3463]

Repeated addition is a fine strategy for understanding multiplication, and for performing the required calculation-- until the teacher somehow decides NOT to teach that multiplication is commutative. It's that omission, not the calculation method, that makes the teacher wrong. Commutativity is not an unimportant side detail that can be forgotten without compromising mathematical education.

[@cowdyayaad6378]

Then the student should have written 5*3=3*5 in the beginning.

[@RustyWalker]

The teacher was *NOT* wrong. The question explicitly demanded a particular method. The student got the method wrong. They lost a point. The argument, "If they'd done it the other way, the method would've been right," is also fallacious because the student got *THIS* method wrong. They weren't *TRYING* to commute the problem. They were trying to solve the problem using *THIS* method.

[@undercoveragent9889]

So, I have five bags and each bag contains three screws. Using the additive strategy, show how many screws there are in total. '5+5+5=15' is _not_ the correct answer.

[@travcollier]

​@@cowdyayaad6378Yep. Either the student didn't learn/understand that detail of the method, or they added an unnecessary step and failed to show it in their workings out. Docking a point is fair, especially if the question is worth more than just 1 point.

[@I3oozeAddict]

The student realized that 5+5+5 is both shorter to write and easier to calculate, while returning the same result, so props to him for critical thinking. Unnecessary rules that make no sense and don't affect anything shouldn't be a thing.

[@3dplanet100]

Or maybe he interpreted that 5×3 is FIVE three times, therefore 5+5+5.

[@I3oozeAddict]

@@jamesday3591 okay, please provide a single scenario where following this rule would make any sort of meaningful impact.

[@RustyWalker]

If you were instructed to build something according to how many rooms each floor has, with all floors being clones, you could get a very different building if you decided both methods were equivalent. The architect would be looking at you with a puzzled expression. "Why does my building only have 3 floors and have 5 very small rooms per floor when I specified 5 floors of 3 rooms each?"

[@jamesday3591]

@@I3oozeAddict 3X + 3Y = 3(X + Y) In more advanced forms of mathematical languages (perl, java, PHP, C+), syntax is *everything*. If you teach it correctly the first time, you don't have to re-teach it the correct way later. In other, more proverbial expression, an ounce of prevention is better than a pound of cure.

[@castirondude]

Critical thinking doesn't get you a degree. Only mindless repetition.

[@Petiscorei]

Math is based on fundamental logic not linguistics, you can't say something is wrong and the other is right when they are equal

[@KeithAllen-pg8ep]

If we read it as "5 multiplied by 3," then 3 is the multiplier and 5 is the multiplicand - so the student is correct. "Multiply" is a proper verb; "times" is not. You can multiply two numbers, but cannot times them.

[@jamesday3591]

They are equal, not identical. You can't say something is identical, if it isn't. A building front five feet long and three feet high may have the same surface area as a building front three feet long and five feet high, but are they identical? Uh, no.

[@John-ro2yk]

@@KeithAllen-pg8ep maybe he was using RPN (reverse polish notation) to solve the problem

[@JamesD2957]

you have no idea what your'e talking about with regards to math, logic, or linguistics. so why bother coming here to pretend you care?

[@jamesday3591]

@@JamesD2957 Those who cannot present facts, present emotion. The facts I presented speak for themselves. You may agree or disagree with me as you like and/or believe. Notice though, you didn't dispute anything that I said. You just whined about my saying it.

[@kvf8064]

If we're going into semantics here, the question doesn't ask to use only the repeated addition strategy. The student used commutativity and the repeated addition strategy. So even with that interpretation he was correct. Besides, in paragraph 27 of the very same chapter of Euler's book he writes: "It may be farther remarked here that the order in which the letters are joined together is indifferent; ... for 3 times 4 is the same as 4 times 3."

[@bursuc38]

I understand perfectly that the student did not correctly apply ‘the repeated addition strategy.’ My question is why children are taught such a strategy when there is clearly a superior strategy that everyone uses and that the child also applied. That strategy is to consider the expression 5 × 3 as both 5 elements taken 3 times and 3 elements taken 5 times. And then you can choose between the two variants to find the simpler one. This strategy seems superior. For example, if you have the expression a × 4, using ‘the repeated addition strategy,’ what would you write? 4 + 4 + 4 + … + 4 how many times? You couldn’t write anything meaningful. But using my strategy (which all people intuitively apply), a × 4 would be both "4 + 4 + 4 + … + 4" and "a + a + a + a". And from these two options, you would choose "a + a + a + a" because it is more useful and simpler. In a similar manner, if you have 100x2,using ‘the repeated addition strategy’ would take you a month to solve it. You’d have to write 2+2+2+2…+2. Madness! On the other hand, if we use the strategy I’m talking about, which is much more flexible and useful, you could simply write ‘100x2’ as ‘100+100’ and solve it very quickly. The repeated addition strategy seems rigid, profoundly inefficient, and devoid of sense. Why do we teach children such things when there are infinitely better strategies?

[@Skyfighter64]

Three words: lowest common denominator. The Department of Education wants to protect the dim bulbs who are bad at math from feeling bad about it by removing the ability for good students to actually excel.

[@simonwahlen7150]

I don't really agree with teaching math as only the rigid application of formulae instead of actual reasoning but there is some reason in keeping the mental order in multiplication when you reach university level math. In matrix math your order of terms matters for multiplication and A*B =|= B*A for most matrixes A and B. Further in set theory where you define what opperations like multiplications are even supposed to mean for a particular set the order of terms probably matter. But still even if order matter in these specific high level math enviroments this really shouldn't affect fostering intuitive learning of the basics of math at gradeschool level.

[@davidjulitz7446]

The student applied it correctly. There are several ways to write multiplication as repeated addition.

[@tonyennis1787]

I think the child's answer is better than the alleged right answer because adding 5s is less error prone than adding 3s. That is, the child correctly deduced that 5+5+5 is easier to sum. My problem with the definition of repeated addition is that it makes a distinction where there is none. It implies that axb bxa. The definition is incomplete or imprecise. The best approach would be to show repeated addition (not a bad strategy) as an n x m rectangle, and show the repeated addition _both_ ways. Now there is a geometric representation as well as two equivalent solutions depending how one chooses to look at the problem.

[@matix676]

The answer is incorrect though. What if instead of "3" there would be "x"? Writing 3*x is easy: x+x+x. How would you do that the other way around? (x*3=?, how many threes?)

[@nieshamccoy9419]

This is like learning algebra concepts in elementary school. This is how some other countries do it. They teach some of these concepts in 3rd grade.

[@1st2nd2]

The student was asked to solve the problem using a specific method that was taught in class. The student solved the problem but did not use the specific method. If a problem states to find the volume of a sphere using rotation of a circle about the x-axis but solves it using roration about the y-axis, marks are removed despite the methods being equally analogous. This was not just seeing: can the student multiply 5x3 and add numbers together? This was also a question of whether or not the student fully understands the strategy. Their answer showed a lack of understanding of the strategy.

[@BrianHartman]

@@matix676 The answer is correct. The answer is 15. The problem is that the explanation of the answer is incorrect. I don't think the child should've been marked off, because they were asked to solve the problem, which they did correctly. If you wanted to test if they understood the concept of the difference between 3 x 5 and 5 x 3, the question should've been worded differently.

[@Eshtian]

​@@matix676Your example actually hurts you. If it was X(3), going by the intended method would be impossible, therefore teaching that order matters in multiplication like this hurts algebra. Also X(3)=15 is a completely different thing than to 5(3)=Y. It's just a completely different beast.

[@dbackscott]

This method is how we learned multiplication in my elementary school back in the early 1980s. However we learned that 5x3 represented three groups of five (read as “take five and add it three times”). Furthermore, we were taught the reverse interpretation was also acceptable and appropriate.

[@tonyennis1787]

That last point is what has me annoyed.

[@jamesfolken3163]

No, because "x" is an arithmetic operator, and in arithmetic operations the first number is the one that the second number operates on. Otherwise, how do you interpret 3+2, 3-2, 3/2, or 3**2?

[@Bagginsess]

⁠@@jamesfolken31635x3 = 5, 3 times 5x3 = 5 multiplied by 3 5+3 = 5 added by 3 5-3 = 5 subtracted by 3 5/3 = 5 divided by 3 English is read left to right as is our math otherwise division and subtraction wouldn't work. 5x3 is clearly read as 5 times 3 or 5 multiplied by 3. There is no reason the child should assume it is the other way around. Now 5(3) would make sense to write as 3+3+3+3+3 because anything inside the parenthesis is what we desire to multiply and the outside number is what we are multiplying by. But it was written 5x3 not 5(3).

[@rumpeldrump]

Ja ich multipliziere die 5 mit der 3 und nicht die drei mit der 5, ebenso teile die 5 durch die drei nicht dir 5 durch die drei durch die 5. 5 multipliziert mit 3 und nicht 5 mal die 3.

[@jamesfolken3163]

@@Bagginsess Exactly. Regardless of the language you speak, the first number is the one that the second number operates on.

[@ma9x795]

What is the point of limiting the ways to solve a problem? Kids find maths hard because they're not encouraged to make it easy. This is almost like saying "What is 4% of 75 (without using 75% of 4 )?"

[@yuribacon]

OMG, I NEVER KNEW PERCENTAGES WERE COMMUTATIVE LIKE THAT! THAT'S AWESOME!

[@carultch]

"What is 4% of 75 (without using 75% of 4 )?" Every 4% is 1/25th of the original number. I recognize this from playing Lemmings, since the levels with 25 lemmings, advance by 4% for each one of them. This means we want 1/25th of 75, which is 3.

[@KeithAllen-pg8ep]

@@yuribacon 1/2 of 8 = 4 1/2 x 8 = 4. 1/2 is 50%.

[@bruhseelas]

4/100 x 75

[@jbird4478]

The point of that in general is to teach kids a specific method. If a few years later this kid will use repeated addition to solve 123*4089, he will get the correct answer but it would rightfully be marked wrong. In this case however, the kid does use repeated addition, so there shouldn't be a problem.

[@AkilanNarayanaswamy]

What gets me with this is that as a math problem for grade school students, marking it wrong only serves to possibly confuse the student. The student clearly understands the repeated addition strategy and has internalized the commutative property of multiplication. Taking points off here is unnecessary as there is no reason to strictly enforce the order convention in a problem like this one, and it opens the possibility to confuse the student. Now if this was a word problem that clearly defined the groups in a certain way, then I can maybe understand this. But not in this case

[@benlap1977]

I fully agree about the importance of the situation! "There are 5 boys with 3 marbles each" and "I gave 5 marbles each to 3 boys" would intuitively both be written 5×3 since we would just write the numbers in the order they appear in the statement. But the first one is 3+3+3+3+3 marbles while the other one is 5+5+5 marbles!

[@KeithAllen-pg8ep]

Reading 3 x 5 as "3 multiplied by 5" and using "the strategy," the student's answer is absolutely correct!

[@jamesday3591]

@@KeithAllen-pg8ep The answer to the equation is correct. The answer to the question is wrong. You're confusing the question as being about solving the equation. It's not. It's using the equation to teach the principle of specifically ordered grouping. It's not about solving the equation. It's about understanding the grouping intended by "Repeated Addition".

[@dracmeister]

This is the problem though. While you can explain it away how historically it was interpreted. Questions like these that demand a VERY specific way of solving a problem really shouldn't exists for lower levels of education. I feel like fundamentals are better to teach than the one strategy the cirriculum suggests. Teach children of the properties of mathematical operations. And while in a practical situation 5 groups of 3 things is different from 3 groups of 5 things, that's already giving it context and therefore should be noted in test questions. Not just laid out as "here's numbers and an operand, solve it exactly as we taught you 4head."

[@patricksheldon5859]

This is by far the best criticism I’ve read here yet

[@geoninja8971]

How on earth did we learn multiplication in the 70's and 80's without these genius teachers?

[@EnriqueGonzalez-qo5hn]

Only the teachers below the age of 30 as of right now embraced Common Core. The older ones know better

[@shanehebert396]

@@EnriqueGonzalez-qo5hn most of the stuff that people wail about with Common Core is just teaching multiple ways to do certain things... much like the rest of the world does. In fact, many of us here in the USA who use math also use multiple ways of solving problems depending on whether we're doing them in our heads, on paper, or even based on the numbers. One of the most facepalm things is the meme that goes around with the label something like kids not being able to count back change because they're learning this stuff (showing a problem being worked in the image)... the sad thing is that what's in the image is *literally* teaching how to count back change. Most people have just been trained to think "Common Core hurr durr bad!!111oneone" because of politicians having a certain agenda.

[@EnriqueGonzalez-qo5hn]

@@shanehebert396 i totally get the purpose of common core and I think it's actually a great idea to learn multiple ways of doing certain things. I guess maybe my main frustration with it is the execution of it in the classroom. I have a feeling that, in this problem in particular, there was a concept that the teacher either glossed over or didn't really teach at all. If the concept was taught thoroughly at first, then there wouldn't have been this confusion

[@darreljones8645]

Schoolhouse Rock.

[@dbackscott]

This method is how we learned multiplication in 1981

[@저녘놀]

5 × 3 = there are five 3. (3 3 3 3 3) -> in America 5 × 3 = number of 5 is three. (5 5 5) -> in Korea

[@igorartemchuk311]

5 × 3 = number of 5 is three. (5 5 5) -> in Russia

[@Yooper_eh]

5 x 3 = 3 x 5 -> in every math book until Common Core. It's called the Commutative Property and it applies to both addition and multiplication of scalars.

[@KeithAllen-pg8ep]

It would seem that (at least) Koreans and Russians know that 5 x 3 means "5 multipled by 3."

[@torarne7796]

Let whoever came up with this strict interpretation solve 1000000 * 2 the same way. I would certainly allow a student to change the expression to 2 * 1000000 before adding up. In fact, I would encourage it.

[@cowdyayaad6378]

That question will not be given to a student to check if he knows what is repeated addition method. And there is no reason to change it to 2 × 1000000 if you want to make it simple. The simplest 1 step way is just to directly multiply it. And the simplest expression is 2 × 10^6, more simple then 2000000.

[@torarne7796]

@@cowdyayaad6378 that's irrelevant for my point. 2+2+2+.....+2 a million times is clearly the inferior approach to solving this question.

[@cowdyayaad6378]

@@torarne7796 Again the point is not to see how good he is at calculation. The point of that question is to see if he understands the meaning of the expression and what multiplication actually is. And as such your hypothetical question will never be given to a student if the question intends him to use repeated addition.

[@torarne7796]

@@cowdyayaad6378 and that is also achieved if you add up 1000000+1000000, rather than 2+2+2... Are we really supposed to teach students to use the repeated addition method in the most awkward way possible? Or maybe we should encourage them to add up in a practical manner? The method, as it is phrased, makes an arbitrary decision which number to use for the addition. As rule I suppose that's fine, but there's no deeper purpose here, it might as well have been the other way around. A student might very well encounter a 1000000*2 problem, if not on a test (although that isn't entirely impossible either), and knowing you can add up either way is only an asset.

[@PugganBacklund]

Deducting point becouse the student used the Commutative to simplify the statement before applying the said strategy is hard, the student still used the strategy.

[@brothertaddeus]

The student didn't write anything to demonstrate they were using the commutative property, though. So they'd still lose a point for not showing that step. Gotta show all your work to get full points.

[@gruanger]

@@brothertaddeus Showing work is a waste of smart people's time!

[@dd-di3mz]

It is what it is. When I wrote my final exam (not in the USA), my teacher told me to not under any circumstance use l'hopitals rule (not even write it as a note to double-check my results). The reasoning was that we didn't officially learn it, meaning we didn't learn the "theorem"/proof, therefor we don't know how to apply it, thus it had to be marked as incorrect. I imagine it is the same reasoning for the commutative property of multiplication.

[@tonyennis1787]

That's proof that the teacher is an NPC.

[@patrickarmshaw]

It’s not the teachers. It’s the bureaucrats who design curricula and the politicians who tell the bureaucrats to do so that are doing this. You get people who don’t know math deciding how math should be taught and usually you get ‘i learned my times tables by rote, so should everyone else’ or ‘I heard of a new thing, let’s do it!’ Either way, the maths are over complicated and students are taught that maths are a chaotic, unpredictable, and arbitrary system of random crap to memorise.

[@vincemarenger7122]

This is why people hate school

[@silverhammer7779]

If you love education (that is, true education), stay away from modern schools.

[@ac0SE]

Yeah... In seventh grade I got 0 out of 40 in math because I copied the letters and answers, they recheck it and apparently I got a 38/40, but still my teacher told me that I didn't follow instructions so I got nothing, but dissapointment that they can be so petty over small things. I never took school seriously since then.

[@silverhammer7779]

@@ac0SE You weren't cheating, were you...?

[@ac0SE]

@@silverhammer7779 no

[@jamesday3591]

Personally, I hate schools that teach kids incorrectly, simply because it's easier to understand. Which reason did you mean?

[@harshgada4325]

Why does school teachers have a " Ur answer is correct, but u didnt use my method, so i will give it wrong " attitude.

[@Eshtian]

Tbf it was the point of the question.

[@otakurocklee]

@@Eshtian The question did not say using commutativity was not allowed.

[@jamesday3591]

@@otakurocklee But it did say to use the Repeated Addition method. It also didn't say to not use the Pythagorean Theorem or a number two pencil, or to write with your non-dominant hand. And guess what, the student wasn't graded on any of those things that the question didn't say. Coming up with things that the question *didn't* say in no way justifies ignoring what the question *did* say.

[@SomeGuy712x]

Regardless of all that history and whatnot, I think that using 5+5+5 is equally as valid as 3+3+3+3+3, as 5x3=3x5, and the student should've gotten full credit for the answer. There's no good reason why you should be restricted to adding them in any one particular way just based on which side of the "x" the numbers are on.

[@verkuilb]

In a way, though, the student DID use the repeated addition strategy, just not as the first/only step: 5x3 = 3x5 (commutative property) 3x5 = 5+5+5 (repeated addition strategy)

[@blueskull7898]

Now use the “repeated addition ‘strategy’” to multiply 1000x5.

[@461weavile]

​@@blueskull7898 why?

[@blueskull7898]

@@461weavile just try it and show me how efficient it is

[@12carbon]

I see 5×3 as 5+5+5 typically, since "5 three times".

[@stevegreen5552]

Yes, and prior to using the commutative property, credit should be given in recognising that 3 is less than 5 so that use of this property is justified - reducing potential errors using the repeated addition strategy.

[@verkuilb]

Repeated addition strategy: 1 teacher without common sense X 1 principal with common sense = 1 group of 1 fired teacher

[@matix676]

The answer is incorrect, even though they are both "15"

[@verkuilb]

@@matix676 It is not incorrect to anyone who has a basic comprehension of commutative property. And anyone who doesn’t have the ability to comprehend commutative property shouldn’t be teaching math.

[@Vienticus]

This is a good example of why common core is bunk. Multiplication is a shortcut for addition. That is why it was created thousands of years ago, even before Euler and Euclid. The problem is the teaching of instructions over understanding. If the question was about understanding, it would ask: Show the different ways this can be instead written as addition.

[@Zhiroc]

If you listened to the whole video, when multiplication was "created" in the past, "a x b" was defined precisely the way common core defines it. I still think it's a bit overly pedantic for this level of math though. On the other hand, at this level of learning, a lot of things, from word definitions to history questions, are expected to be regurgitated verbatim.

[@Vienticus]

@@Zhiroc I listened to the whole video. They didn't create it; the concept was around before they were even born. So their definitions are moot. And the expected to be regurgitated is just another part of the problem.

[@williamwells3026]

There weren't any teachers involve with the creation of common core didn't help it any either. And once teachers were asked their opinion of it, they were ignored.

[@Zhiroc]

@@Vienticus It was defined the "common core" way in 300 BC, so it's existed in that form for at least almost 2500 years. I can't say if there are historical sources that show the definition in reverse though. It seems overly pedantic, but I recall that the proof that 1 + 1 = 2 takes pages and pages in the Principia Mathematica (I think) so math can be intrinsically pedantic :) From a mathematical point of view, we know that because multiplication is commutative, we can rewrite it in reverse, but that it "technically" a reinterpretation of the original that has the same value. There are plenty of non-commutative functions where you can't just do this, and so I can appreciate a point of view where you are being asked to give a literal interpretation of the definition. It may seem a moot point once you are fluent with multiplication. But this is a first class (obviously) in multiplication, so sticking to the definition has at least some value.

[@Vienticus]

​@@Zhiroc That whole proof that 1+1=2 is a bunch of ridiculous, self-serving tripe. The idea of multiplication has been around since before anyone decided to define it, and just because someone defines something doesn't mean that definition is accurate, useful, or original.

[@nixxonnor]

According to "the repeated addition strategy" 5x3 is not equal to 3x5. What is the benefit of defining these expressions as different? In the example from the definition, they used the smaller number to equal the number of groups. What if the question was "Use the the repeated addition strategy to solve: 1000x2"?

[@richardokeefe7410]

Around the 2:50 mark, that's not a DEFINITION of the repeated addition method, it's an EXAMPLE. "interpret 5 x 7 as the total number of objects in 7 groups of 5 objects each" would ALSO be an example of the repeated addition method. We gave up trying to define mathematical procedures by giving examples about 2500 years ago.

[@user-ox4ii2bw6x]

The student used, applied, and understands one of the most important parts of algebraic systems, communicative properties (this doesnt go away)

[@theanitmeme]

Students at this level haven’t been taught commutative properties yet. They made a mistake that happened to get the right answer. If they “understood” anything, it’s just as likely that the order of numbers in math don’t matter. That’s not going to work when they get to division.

[@user-ox4ii2bw6x]

@@theanitmeme I remember being taught this exact communitive property in the case of multiplication. These same properties that addition has will hold for multiplication, and part of why it doesn't hold for subtraction or division as per THEIR defined operand rules.

[@MercuriusCh]

@@theanitmemeif in your school teachers at first lesson of multiplication didn't teach the commutativity of this operation, I would have a lot of questions to educational system in your country...

[@caetano239]

​@theanitmeme I was. Sure, we didn't call it "commutative property of multiplication", but I was taught that the order in which I wrote the numbers didn't matter in multiplication and addition.

[@theanitmeme]

@@user-ox4ii2bw6x First of all, this would be the commutative property of multiplication, not addition. I thought that was a typo in your original post, but apparently not. Second, concepts like the commutative properties are usually taught in Pre-Algebra or Algebra, which are Jr. High level classes. This is a second or third grade level assignment. I’m sure you leaned the commutative property, but if you learned it in third grade your school was outside the norm. That’s how most schools have taught math since long before Common Core was a thing.

[@MrValdesbg]

I agree that repeated addition gives structure and clarity and will help students learn the core mathematical principles better. What I don't agree with is marking an answer wrong when in fact it isn't. It is wrong solely because the question is asked in a way that the expected answer is only one. Since 5x3 = 3x5 then repeated addition can (and should) be applied in both scenarios. 5+5+5 is just as valid answer in this case. That's like saying 5% of 20 is not equal to 20% of 5 even though both sides are equal to 1.

[@Artaxo]

This could all be prevented if the kid demonstrated the commutative property of the real set.

[@silverhammer7779]

Apparently, commutativity is no longer politically correct. They want you to do everything the "official" way, and you will be penalized for daring to think. The future ain't what it used to be.

[@lightandtheheat]

The poor kid accidentally demonstrated a (slightly) advanced feature of multiplication relative to basic interpretation through repeated addition, and should not have been punished for it. This could have been an excellent teaching moment. "Hey, the order matters, here's the answer I was looking for and why, but here's why your result was still correct..." Write the expected answer, but explain why his still works. No points lost.

[@silverhammer7779]

@@lightandtheheat But that's just it - in addition, the order doesn't matter as long as the number line positions (+ or -) are accounted for. 3 - 2 is still commutative if you correctly account for the signs, that is, -2 + 3. In both cases, the answer is 1. That said, I agree - the student should have not lost points.

[@rosswalenciak3739]

@@lightandtheheat I got points off in high school geometry because I used a property of a parallelogram to solve a problem when we had only talked about triangles yet.

[@KeithAllen-pg8ep]

More preferable would be the teacher using common sense in interpreting common core.

[@manudude02]

Mathematics shouldn't ever be marked on a literal interpretation. As long as the student gives logical steps and comes to the right answer, give them full marks. It may even give rise to discovering more about the subject.

[@ceejay0137]

This is what happens when you have teachers who slavishly follow rules rather than understanding the mathematics involved. No further proof required that the American education system is seriously screwed!

[@bait6652]

They're not getting dinged for math but Grammar...yet apparently these mistakes turn kids away from math and not language and art??

[@rosswalenciak3739]

@@bait6652 Yeah, it's because they see the pedantic side of grammar first in math class, when it isn't necessary yet.

[@danmerget]

Even if 5*3 was historically defined as 3+3+3+3+3, I think it makes more sense to redefine it as 5+5+5, in order to be consistent with modern higher-order operations. Exponentiation is repeated multiplication, just like multiplication is repeated addition. And 5^3 is defined as 5*5*5, not 3*3*3*3*3. We multiply 5 times itself 3 times. Going further, we have the Knuth up-arrow operations, in which 5^^3 is defined as 5^5^5. In general, if "op" is an operation and "OP" is the next-higher operation, then "a OP b" is defined as "a op a op a op a ... (b times)". IMHO, we should consider multiplication the same way.

[@OBrasilo]

Yes, but unlike addition and multiplication, these higher operations are not commutative. And this kind of exercise prepares children exactly for that - to pay attention at the order, so that when they get to non-commutative operations, they don't end up screwing up the order.

[@big_numbers]

@@OBrasilo Yeah but it does it in the exact opposite way that it's supposed to. doing a{c}b = a{c-1}a{c-1}...(b times) is correct for all hyperoperators. However, a{c}b = b{c-1}b{c-1}(a times) is ONLY correct when c is 1 or 2. The latter is what the teacher did.

[@holzmaurer1319]

Yes, of course, that's the standard way to do it! Multiplication is also not commutative for infinite ordinals. Georg Cantor defined it like you in the correct way: ω*3 = ω + ω + ω (and not 3 + 3 + 3 + ... = ω). Every serious modern math book I've seen follows this definition. US school math just has it plain wrong!

[@CM-dx6xu]

5×3 is more like 5(3), not 5^3. 5(3) means there are five threes.

[@davidjulitz7446]

"Even if 5*3 was historically defined as 3+3+3+3+3," It was not. Euler gives examples so it is easier to understand. It's not a definition.

[@ShadowWarrior277]

Why would any child know the exact definition of "The Repeated Addition Strategy"? I hope it's not just me assuming that children aren't looking at mathematical definitions. I think the question is poorly written, and the teacher is unreasonably stingy. It's a math class, not an English class, and at this level of mathematics children shouldn't be needing to know definitions of obscure terms that even you didn't know about. Now if the question was "Use groups of 3 to solve 5 x 3" then yes I would agree with you that the child should loose points. But that's not what the question was. What the question actually was is misleading.

[@jamesday3591]

Maybe because they were taught it? Just a guess. Why would any child know what multiplication was? Probably because they were taught what it meant. Again, just a guess. I mean, I know it's kind of absurd to think that a math teacher would explain words. What business does a math teacher even have *using* words? Doesn't math deal with numbers? I mean, really! What kind of child is even going to know what a square is? A square isn't a number! It's a shape!!! And why would any child even know what "the area of a circle" means? "Area" is a word, for crying out loud! That's not math! "Area" isn't a number! And Pi? That's not even English! That's a Greek letter! Teachers these days!!! SMH. Math is only numbers. It's not shapes or words or meanings or applications! Come on! Stop this confusing students with things that are more than just numbers!! My kid came home the other day and told me that his math teacher said that Pie Are Squared! The nerve! Everyone knows pie is round! Cornbread is square! That teacher should be fired!

[@mclley]

Interesting. In east Asia, we were taught M x N means N groups of M. I think it comes to grammars in different languages. People tend to say M times (of) N in English. While in other languages, it is the opposite.

[@michaelwarren2391]

Amazingly, we both got the correct answer!

[@Death-on1dq]

Because both answers are correct, so the teacher is wrong.

[@igorartemchuk311]

In Russia the same as in East Asia

[@bait6652]

@@mclley which is why east is better

[@KeithAllen-pg8ep]

I'm English, and I say "M multiplied by N."

[@Jerry_Fried]

The Common Core repeated addition strategy as you’ve presented it posits that “five times three” is qualitatively different from “five three times.” This imposes non-mathematical reasoning on an ostensible mathematical problem.

[@MosaicEcho]

As a non-certified mathematician myself, this aggravates me to no end. This video was hard to finish! I was taught over 12 years ago how to multiply, and was initially taught the method of repeated addition, BUT I was taught that it didn't matter which way I wrote it, but the preferred way is the shortest way. I really like this quote "We mathematicians always like to take shortcuts." Not only is it factual (just look at differentiation, we are first taught First Principles, than shortly after we do it the quick and easy way, bring the power to the front, multiply it with the co-efficient, and minus 1 from the power for all variables) but its something we all do subconsciously. So if they want 5x3 to equal 3+3+3+3+3, make students differentiate from First Principles. Also, the question can be rearranged to make it 'easier' to solve, if you still want to argue your point. Rearrange the equation, solve for 3x5 by 'repeated addition' and weep. This is outrageous, that poor student will now forever hold that to them, and think to themself that they aren't good at maths. I get it, history shows its past, but in circumstances like this, it really doesn't matter; it's the same darn question! I like a lot of these comments as well, using large numbers, fractions, or pretty much stating what I've said here. So here's one of my own: (43x7), not only does it use 2 numbers where students may struggle with adding with, without making a mistake, but now they have to write 7, 43 times! Not happening, they should be able to use whatever method they want to solve the question and get marked as correct, as long as they get the correct answer. I would suggest that the teacher should teach them the algorithm I was taught shortly after repeated addition and maybe give students the resources they need to learn multiplication without repeated addition. The algorithm is pretty simple as well, first 3x7 (easy, 21, if you want, repeated addition is now easier here, 7+7+7) then, place a zero in the units column, then 4x7 (28, they can just add 7 from their previous answer here) to get 280, then add the 2 answers together to get 301 (which is correct, fact checked by a calculator). There are many ways to get an answer, and they should all be marked correct, IF the answer to the question given is correct. This is absurd! I really hope that you agree with me here, because to say his wrong, is wrong itself. If you read this far, I hope you have an excellent day! Stay safe!

[@CKidder80]

I'm with you! I watched all the way to the end to see if he'd redeem himself but... nope. Don't bother. It's infuriating all the way to the end.

[@kimbaleon27]

How do you know the teacher _didn't_ teach them easier methods the next day? Or even the same day? There isn't enough information given about the situation to conclude the teacher is not a good teacher.

[@MosaicEcho]

@@kimbaleon27 Fair, but still, the method the student used was still correct, it doesn't matter if it was 5 3's or 3 5's. I do understand where you are coming from though, and I understand that it can be inferred that I said the teacher wasn't a good teacher, but that was not my intention. Teaching is a hard job, I know because I have tried it, given it was a class I had taken myself, but I never meant for it to sound like I was saying the teacher was a bad teacher. And maybe they did learn easier methods, but as I stated, the student should have been marked correct.

[@bait6652]

@@MosaicEcho the issue is are students at that grade level doing large(>100) or small(fractional) number arithmetic. Gotta match the grade level in numeracy and literacy....the question is a literacy/semantics equation rather than math/calc one. Or even allowing the student to use the phones calculator

[@MosaicEcho]

@@bait6652 As much as I want to believe students at that grade level are doing fractions, multiplication, and working with large numbers, I feel like, by your reply, that they aren't. I feel like they do, I learnt them simultaneously, but if these students aren't, no problem, they were just examples. Also my example is still valid by your rules, and I only used a calculator to fact check, because if I was wrong, I have no argument. Mathematics is still mathematics, even if you put literacy/semantics in the equation. It asked for an answer, they gave an answer, and for it to be marked wrong, is wrong by the teacher. Sure repeated addition was the way they needed to find an answer, they still correctly implemented repeated addition. The wording of mathematics questions are up for interpretation, 5x3, write 5, 3 times. It is still correct, so I am unsure what your argument was with literacy/semantics. At the end of the day, it was mathematics, it was still a calculation, and the student got it correct.

[@Ghork1]

I get repeated addition, that's fine, but since multiplication is commutative, and 5x3 = 3x5 both answers should be valid.

[@jamesday3591]

The solution to the equation (15) using both methods is valid. The student's demonstrated misunderstanding of the term "Repeated Addition" is what is not valid. Going south two blocks and west 10 blocks will not put you in the same place as going south 10 blocks and west two blocks. Both will move you 12 blocks, so they equal the same number, but in practical application, the number itself is not the only thing that matters.

[@Ghork1]

@@jamesday3591 tbh it's still repeated addition. It's commutative, you can do it both ways.

[@jamesday3591]

@@Ghork1 It *is*, technically, repeated addition, just like if I go 45 mph down a 45 mph street, I am going within the speed limit. However, if I'm driving on the wrong side of the street, I'm still incorrect. It's applying repeated addition in the wrong direction. That's *misapplying* repeated addition. The *mis* part of *misapplying* isn't saying that it's not repeated addition. It's saying that the repeated addition method is not being applied correctly.

[@Ghork1]

@@jamesday3591 man is exactly the same. As it's commutative. You guys are being needlessly pedantic

[@jamesday3591]

@@Ghork1 I'm not sure you understand the proper application of pedantic. Just because you don't like the rules, or just because you don't understand the rules, or just because you don't want to follow the rules ... none of those rationale require that the rules are too restrictive. The teacher was asking the student to demonstrate a specific method in order to evaluate the student's understanding of that specific method. The teacher was not evaluating the student's ability to effectively multiply numbers. Your argument of pedantry suggests that you believe that teachers should not test a student's understanding of either vocabulary or application, and that as long as a student can arrive at the correct numerical solution to the equation, then such is sufficient. I assert that teaching various methods of approach is core to understanding mathematical application, especially at higher levels. In any given instance, one method is usually better than another, and in order to select the most appropriate method, the mathematician will have to both know the theory behind each relevant method, and know how to apply each of them. Your argument would be like a basketball coach not teaching a player how dribble with their non-dominant hand, simply because it's easier to dribble with their dominant hand. Yes, both work at face value. No, dribbling with your dominant hand is not always the best choice. In dismissing the value of the assignment as "pedantic", you condone leaving holes of knowledge that limit later understanding of higher-level applications. Teacher: "Today, class, we're creating coal sketches in order to learn how shading can affect not only visual perspective, but also the emotional tone communicated through our art." Student: "Nah. You're being too pedantic, Teach! I'm using ChatGPT, and letting AI create the assignment in full color. The only value in the assignment is to produce a picture, and it doesn't matter how I do it."

[@marcusscience23]

As a student from Hong Kong, China, I’ve always been taught that the multiplicand came before the multiplier, so 5 * 3 would be 3 groups of 5 rather than 5 groups of 3, as it was 5 added 3 times. It bewildered me to see that some people were doing it the other way round.

[@KangQingXu]

The insistence on strictly adhering to "multiplier × multiplicand" is impractical. By teaching students that a×b≠b×a, you’re effectively disregarding the commutative property of multiplication. Even if the intent is to simplify the "repeated addition strategy," teaching that "this is the way multiplication works" misguides students into a limited perspective. It prevents them from understanding multiplication's intrinsic properties in algebra. While it’s true that a×b isn’t always equal to b×a in certain non-standard numerical or algebraic systems, the commutative property holds in our standard system. For the vast majority of students-and even most people in mathematical fields-these exceptions are seldom encountered. Realistically, this rigid approach does more harm than good by narrowing students’ understanding of fundamental algebraic concepts.

[@stefanyalpoesy42]

My question is whether "the repeated addition strategy" was clearly taught by name, and that literal application of it was emphasized as the expected approach; if not then it's arbitrary and unfair to penalize a student who demonstrated a deeper understanding of how multiplication works and should have been given credit for that.

[@rosswalenciak3739]

It's arbitrary either way, but it is more unfair if it was emphasized.

[@DralaFiZero]

This whole thing sounds like a teacher just looking at the answer key and not thinking that there are actually two correct answers.

[@cowdyayaad6378]

No, the teacher is correct. The question didn't ask to solve it. It asked to solve it using repeated addition method. The intention of the question was to see if the students rember how that method works.

[@MadrugsPlays]

@@cowdyayaad6378 The title may have asked for it, but the space "3x5=____" wants the solution

[@cowdyayaad6378]

@@MadrugsPlays This is why he got partial mark. For not doing what the question says, he got 1 mark deducted.

[@MiccaPhone]

I would have argued: 1.) Due to commutativity of multiplication we have 5 x 3 = 3 x 5. 2.) Due to repetitive addition strategy we have 3 x 5 = 5+5+5=15. So with 1.) this means 5 x 3 = 5+5+5=15. I got the answer correct AND I used the repetitive addition strategy for my reasoning. So I should get full marks. The exercise does not say I should ONLY use the repetitive addition strategy, does it? How else would you explain the result of 1,000,000,000,000 x 3 within an hour or two and with limited amount of paper using the repetitive addition strategy?

[@bait6652]

@@MiccaPhone imagine telling a grade1-3 to do numbers past 1000 or use fractions

[@KeithAllen-pg8ep]

In recognition of your avatar, mike drop!

[@jbird4478]

That's what this kid does, he just doesn't explain it because, well, he's a kid. Clearly he understands that 3*5=5*3 though.

[@MiccaPhone]

​​​@@jbird4478Another possibility is that the kid has a different (and in my view even more natural) visualization: When it sees "5x3" it thinks: "Oh well, let's see: FIRST there is a 5, so I am dealing with 5 items of some kind here, lets say a group of 5 apples for example. Ok, got it: (🍎🍎🍎🍎🍎). Now what's next? 'x 3'. Oh I see! So I am supposed to take this group of apples three times, like this: (🍎🍎🍎🍎🍎) + (🍎🍎🍎🍎🍎) + (🍎🍎🍎🍎🍎), or in brief 5 + 5 + 5. Personally that's what I would have thought as a kid when writing 5 x 3 = 5 + 5 + 5. I consider this fully legit and not at all violating but fully conforming with the concept of the repetitive addition strategy. It's a shame that the educational system punishes this kind of free creative and fully correct way of thinking. Allowing only one of the two equally valid interpretations is fully arbitrary(!), demotivates the young students and turns them away from math! What is happening here is treating math like justice - horrible!

[@rennangandara7697]

5 x 3 = 3 + 3 + 3 + 3 +3 0.5 × 3 = 💀 (-5) x 3 = 💀💀💀 i x 3 = 💀💀💀💀💀💀💀💀

[@jamesday3591]

.5 x 3 = a lone group of 1.5 (-5) x 3 = a deficit of five groups containing three each i x 3 = a variable number of groups containing three each. Do you have any difficult questions, or just elementary pre-algebra?

[@cowdyayaad6378]

0.5 × 3 = half of 3 (-5) × 3 = what the guy above wrote i × 3 or 3 × i can't be corallated to real life if i = square root of -1

[@rennangandara7697]

@@jamesday3591 now use the repeated addition technique

[@jamesday3591]

@@cowdyayaad6378 Ah, yes! I mistook "i" to mean the common shorthand for "integer" in coding languages, as in: For i = 1 to 10 X = 5 * i Print X Next i As such, I think your application would be much more accurate than mine.

[@phiefer3]

My issue with this is that it's a pedantic reason for marking points off. I have no issue with teaching multiplication as repeated addition. I don't even have an issue with the purpose of a test question being specifically on the usage of a particular method instead of just being about the answer at the end. My issue is that the way that this method is being taught is pedantic and unhelpful. There is literally no value in teaching students that the repeated addition method is non-commutative. It should be taught that a x b can be done as EITHER adding a copies of b OR by adding b copies of a, because both are correct. The definition is needlessly restrictive in a way that provides no benefit and makes it less useful than it could be. Docking points because the student answered 3x5 instead of 5x3 is literally pedantic.

[@manuelbernal7807]

Not only did the kid follow instructions using the repeated addition strategy (repeating the addition of 5 three times), but he did it efficiently, cause 5+5+5 is shorter than 3+3+3+3+3.

[@silverhammer7779]

Agreed, except that he didn't do it the way the teacher wanted to see it. Apparently, the object of this was not to see if the student could calculate the correct answer, but if he knew to do it the way his commissar (err, teacher) wanted to see it done. We have seen the future of "education" and it sucks arse.

[@stevenfallinge7149]

Also makes more sense because any way of reading it should be 5 multiplied by three, meaning take 5 and combine it with itself three times. If they were taught the other way, that's the one that should've been wrong, if one of them has to be wrong.

[@silverhammer7779]

@@stevenfallinge7149 They're being taught WHAT to think, not HOW to think.

[@davidjulitz7446]

@@silverhammer7779 Yes, exactly the expectation of the teacher is the problem here. He should go back to school to get a proper math education without arbitrary expectations, which have nothing to do with underlying math.

[@beirirangu]

according to the Tetration article on wikipedia: 1. Addition: a+n=a+1+1+⋯+1 (n times) ; n copies of 1 added to a combined by succession. 2. Multiplication: a×n=a+a+⋯+a (n times) ; n copies of a combined by addition. 3. Exponentiation: aⁿ=a×a×⋯×a (n times) ; n copies of a combined by multiplication. 4. Tetration: ⁿa=a^(a^(⋅⋅⋅^a)⋅⋅⋅) (n times) ; n copies of a combined by exponentiation, right-to-left.

[@chasg5648]

No. Multiplication of simple objects like real numbers is commutative. 5x3=3x5. The order is immaterial. Teaching otherwise is crippling the students with useless and confusing pedantry, limiting their knowledge, and making another generation hate math. Of course repeated addition is a valid process but for gosh sake - TEACH IT RIGHT! The order of multiplication does not matter until you get to very different mathematical objects like matrices, quaternions... All that is years later in mathematics learning, and understanding the commutativity of more ordinary objects puts the non-commutative objects in a fuller context.

[@OBrasilo]

From my experience, non-pedantic teaching has produced people that pay no attention at details. This makes them very hard to debate with - I've personally ran into such people, and it then results in stuff like thinking two situations that in fact differ in details, are the same, because they've basically been trained to ignore the details.

[@chasg5648]

@@OBrasilo If you are arguing with someone who deploys erroneous math, then their teacher probably failed to get the underlying logic across. I'd argue that the teacher should insist on valid mathematical understanding - which would include the concept that 3 groups of 5 equals 5 groups of 3, and that order does not matter here. I would note that there are plenty of topics where a pedantic sounding approach is important. There are details in math that are vital, just not in this particular one. I believe this one gets in the way of understanding and fluency.

[@demonwolf570]

They're really justifying having your kids home-schooled more and more with foolishness like this.

[@nieshamccoy9419]

Really, this is like learning algebra concepts in elementary school. This is how some other countries do it. They teach some of these concepts in 3rd grade.

[@beniocabeleleiraleila5799]

The fact that you dont understand why the kid made a mistake just prove that home-schooling is ass

[@Eshtian]

​@@nieshamccoy9419can you please tell me what algebra concept this is related to and how subtraction and division, concepts where order does matter, can't be used in place?

[@Death-on1dq]

@beniocabeleleiraleila5799 the fact that you can't see how the teacher made a mistake is another reason showing that public school isn't good

[@beniocabeleleiraleila5799]

@@Death-on1dq the teacher didnt made any mistake, the only reason why the kid got the right answer is because multiplication is comutative, 5*3 is 3+3+3+3+3, period

[@luisrosado7050]

0:53 well thats blatantly enraging, 5 + 5 + 5 = 3 + 3 + 3 + 3 + 3, life has multiple answers and so does math.

[@s.p.a.3583]

As an Italian: here they teach that a*b is "a times b" that means a is repeated b times (for see it, look the Italian page of wikipedia about the multiplication)

[@jamesfolken3163]

That should be correct as "b" operates on "a". Exactly as a + b, a - b, a / b, a ** b, ...

[@idontwantanusername]

In italian "a x b" can be read as: - a per b - a moltiplicato per b - a per moltiplicato per b volte - a per b volte each of those sentences (we use "a per b" most of the times, because it's shorter) has the multiplicand on the left side and the multiplier on the right side. We make no confusion in our language. The only exception to the rule may be "b volte a" ("volte" is italian for "times", in this specific context), but it's not how we usually read a formula. I'd say it's used in the spoken language when you're trying to explain something to someone and you really want to stress on "how many times" a certain quantity - usually something "tangible" like weight, length, amount of money or maybe even a percentage - must be multiplied. I wonder if in english "a times b" and "a multiplied by b" are used interchangeably to read the same "a x b" formula (I'm not a native speaker). That could explain the confusion (even if one of them should be used with the factors swapped). I would have failed that test in english, because I'm Italian and I've been taught since I was a child that "a" (left side) is the multiplicand and "b" (right side) is the multiplier. The sentence "5 times 3" in italian would be "5 volte 3" and it would be clear that the expected result is "3+3+3+3+3"; but the formula "5 x 3" would be read as "5 per 3 [volte]" and the expected result is "5+5+5". If someone read the formula "5 x 3" as "5 volte 3" instead of "5 per 3" in Italy, people would probably have a short moment of "confusion" wondering how that person is talking / what he's trying to say / what is he thinking (I would, at least!). Different cultures/languages, different ways of thinking! I think this is akin to how the way we represent numbers relates to the algorithms required to perform certain operations (Latin vs Arabic numerals for example).

[@s.p.a.3583]

@@idontwantanusername bro, I hope u are not trying to teach me about my country, and I'm also pretty sure that no one in Italian history had read axb as "a volte b", that because "volte" is a litteral translation that go against the context; for make it clear, "time" can be also translated "tempo" that can mean the passing time, or can also mean the weather.

[@jamesfolken3163]

@@idontwantanusername Correct. But mathematics is a universal code, regardless of the language one speaks. To me in arithmetic operations the first number is the one that the second number operates on.

[@idontwantanusername]

⁠@@s.p.a.3583 I wanted to remark that you were right and provide additional arguments (to the benefit of those who don’t speak italian); my goal wasn’t to teach you about our country of course! And I agree, nobody reads “a x b” as “a volte b”. Maybe sometimes while speaking I may say “b volte a” (with the factors swapped) when I’m explaing something and I need to stress on what I’m doing, but that’s not good italian in my book (and in those situations I’m not reading a formula, anyway).

[@flikersprigs5641]

Well lets look at the purpose of the repeated addition strategy: teaching kids multiplication using something they already know - addition. It is a stopgap, a bridge, it is temporary and transitory; why then is a teacher concerned with the semantic correctness of the student's understanding of an educational crutch and not their grasp of the concept that crutch is trying to convey? This is the equivalent of deducting points because a kid counted on their fingers wrong.

[@Obi1Classic]

I hate how objectivity is being overruled by people with an agenda. I love math and I wish people could see the joy of it as well. It's educators like this that destroy potential.

[@silverhammer7779]

Not educators...indoctrinators.

[@Eshtian]

What?

[@Eshtian]

​@@silverhammer7779Why is it that people who believe in stuff like this have a sense of drama to them?

[@bait6652]

@@Obi1Classic 1 docked mark will deter a child from learning math??? What about all the docked grammar marks in language class or even verb conjugation Or not showing progression in art class?

[@mr.mikeygaming3723]

I don’t like the way the common core education works. This is a prime example of making students think inside the box. They should allow both strategies so students learn to do both strategies and learn to think for themselves

[@OBrasilo]

No, this literally teaches the students to pay attention at seemingly insignificant details which eventually allows them to think better for themselves.

[@taragnor]

Who the hell adds repeated 3s to something in a base 10 system when you could be working in increments of 5.... To do so really shows a lack of intuition with numbers. Sounds like this teacher is still salty from when the government rejected their idea for a 3-dollar bill that they got from that acid trip.

[@Vertraic]

Seriously, the problem is not that they specified to rewrite it as repeated addition, the problem is that they UNREASONABLY decided that one direction of repeated addition was wrong, and the other was right. If the kid had been marked wrong for just saying 5x3=15 I would never have had an issue with it. Saying that you HAVE to decide which grouping it is in a certain way is just idiotic though, when multiplication IS commutative, and any sane person would say that if either grouping works, use the shorter and easier grouping. This was a power play, not just wanting someone to fully understand the concept.

[@Eshtian]

Yes. Another smart person. I was getting tired of people not actually watching the video.

[@otakurocklee]

Yes, basically the teacher expects the student to read his mind.

[@Eshtian]

@otakurocklee we're assuming that it wasn't taught that way, which we have no way of actually knowing. Let's not make assumptions.

[@alkemis]

As a former math, physics and chemistry teacher, it is this sort of rubbish which has eroded the concept of math in schools. Students become frustrated when the syllabus starts nitpicking at math. It does a great disservice to the instruction of math. Euler and Euclid were adults who spent their lives looking at proofs to mathematical theorem and concepts. This is what you do when you decide to pursue math as a career....ie at the university level. When you are a student struggling to understand math, all you need to know are the basics...ie the 10 basic axioms of math, the way operators work and then move on to slightly more complex areas of algebra, arithmetic and geometry. When you complicate the basics, you prevent students from progressing to other areas of STEM, thereby continuing the erosion of the western education system. You can pontificate all you want to about this being old math, but it is old irrelevant math for the modern era. Much like riding horses gave rise to the term horsepower, no one is trying to put horses in cars now, we have moved on past that. And to say that we should accept the absurdity of common core math is no different than saying that people should return to riding horses as the primary means of teansport.

[@matt-fitzpatrick]

The problem is teaching there's _one and only one_ way to transform 5 × 3 into addition. That's false. Even teaching there's _two and only two_ ways to transform multiplication into addition is a disservice. Consider decomposition: "55 × 3 = 50 + 50 + 50 + 5 + 5 + 5". Bonus, allowing decomposition keeps repeated addition relevant for decimals (5 + 0.5 ...), compound fractions (5 + 1/5 ...), variable expressions (5 + 5x ...), complex numbers (5 + 5i ...), and more. Meanwhile, the rigid one-and-only-one way of repeated addition says, "5 × 0.1 = 0.1 + 0.1 + 0.1 + 0.1 + 0.1, but 0.1 × 5 is unsolvable." Ridiculous.

[@jamesday3591]

That's not what was being taught. Nothing in the question said that the Repeated Addition method was the only way. Stop being ... well, I'll be polite, because I don't even know you, but seriously. Stop inserting things that aren't there, and then getting mad about it.

[@TranquilSeaOfMath]

I read _The Progessive Higher Arithmetic_ by Horatio N. Robinson (1874), to be the reverse of this. He says, "Multiply 346 by 8." Which he analyzes as, " required to take 346 eight times." Being self consistent he reverses the labels multiplicand and multiplier from the examples you have given. This debate is long standing. Furthermore, from a modern axiom perspective, we have separate axioms for the algebraic operations of addition and multiplication.

[@syzygycalalignment]

When I was in elementary school, we had to do seemingly endless, 1-page, 100-problem quizzes in which we had to add and multiply single-digit numbers in a timespan of 10 minutes. This made me realize that it was advantageous for me to memorize the entire 12x12 multiplication table, which contained all 144 ways of multiplying 2 numbers together from 1 to 12. (In retrospect, I think that was the teachers' goal, which they wanted us to accomplish without telling us to do so!) Even after all of that practice, some students still didn't have that table memorized, and struggled to finish those 100 multiplication problems in 10 minutes. While I'm not a fan of having to memorize 144 multiplication facts, I am glad that I developed the SKILL of basic multiplication long before I had to deal with translating mathematical statements from prose into equations in order to solve algebra problems.

[@jkoh93]

5³ = 5x5x5. 5↑↑3 = 5^5^5. in these cases the left side is repeated n times

[@Superskull85]

That's true, but not applicable here since those operators are not cumulative like multiplication is. Why the students' answer is also correct is because it can be done both ways.

[@WillySalami]

I'm pretty sure it's only an arrow there, don't two arrows represent tetration?

[@pengxu9244]

@@WillySalamiyea but they show tetration is repeated exponentiation in the equation

[@holzmaurer1319]

@@Superskull85 Multiplication is also only commutative for finite ordinal numbers. The correct official definition is with the second argument being the iteration counter also for multiplication, take any Set Theory textbook. US schools teach it just wrong. The student did correctly apply the official mathematical recursive definition of multiplication. The teacher did it wrong (but was saved by the commutative law for natural numbers).

[@stevenfallinge7149]

The "standard" way to define multiplication as repeated addition is as follows: a×0 = 0 (or a×1=a, take your pick), and a×S(b) = a×b + a, where S means "successor." Therefore, the student's way is actually correct, under this definition.

[@AlexHeisEngholm]

Math is a universal language therefore the direction of the phrase shouldn’t matter, people of this world are reading from left to right, but also from right to left. There should not be any hidden concepts in math that can be interpreted differently based on language other than the order of operations.

[@pnsdkrpndja12177]

Good luck in finding what 10000×1 is with this method.

[@rockessence]

I'm Italian, and here 5x3 is read as 5 (repetetly added) for 3 (times) = 5 + 5 + 5 But, anyway, at least only burn out teachers could mark this answer as wrong, because, for a student, knowing the multiplication's commutative property has an higher importance.

[@logicalsparrow2130]

It can easily be argued that the student did indeed use the strategy of repeated addition but skipped a step in showing that they applied the commutative property of multiplication first. The problem as stated did not prohibit this operation. I recall being taught that when applying this strategy, it's a good idea to optimize the order of the operands in order to lower the amount of operations needed to solve the problem. E.g. 2 * 100 is both 2 groups of 100 and 100 groups of 2, but one of those calculations using the repeated addition strategy will take many times longer. Why penalize a student for understanding this?

[@Qwertyrion]

Now I know that special English math exist. Because in my native language both 'a' and 'b' in a x b can be named multipliers. It's easier to explain the commutative property this way. And in my native language 5 x 3 is literally read as 5 multiply by 3. The math can't be natural language dependent. So from my point of view the student was graded wrong.

[@KeithAllen-pg8ep]

In English, 5 x 3 means "5 multiplied by 3" or "5 times 3" (the lazy version). As a teacher, I avoided the latter so as to encourage students to avoid using the awful (non)word "timesing." So the student was absolutely correct.

[@ingiford175]

Depends on how you were taught, 5 lots of 3 is 3+3+3+3+3 5, 3 times is 5+5+5

[@Death-on1dq]

Both answers are correct.

[@rrangana11]

No wonder why kids in USA hate math.

[@sr6424]

So if you had 5.2 x 3 would the answer be 3+3+3+3+3+0.6?

[@tonyennis1787]

Brutal.

[@mvans-f7e]

Correct

[@FastKnight401]

once you get to rational numbers, and integers actually, multiplication can't be explained as repeated addition. What does it mean to add 1.3 by itself 2.7 times? At this point, I like to see multiplication as a scale transformation on the number line. You scale the number line so that the number 1 transforms into the first number, and then see where the second number ends up. This interpretation can also extend to matrix multiplication which is the reason I like this interpretation. Of course, I don't think multiplication should be taught like that from the beginning as it's a very confusing introduction. Repeated addition works as long as you're talking about the whole numbers and I see no reason to teach it differently and every reason not to.

[@将軍九八.彁]

3+3+3+3+3+3/5, may be more inline with the strategy.

[@jamesday3591]

I think you're starting to understand the principle.

[@notspm9157]

I disagree. While there might be a definition, it was always really taught back in the day to use the easier to add number. Adding 3 + 3 + 3 + 3 + 3 while it would be right back in my day if you did 5 + 5 + 5 you would still be marked as right as it's not penalizing utilizing the communitive nature of ab = ba to simplify the working. Also it is using it, it's just applying communitive property first. I think it's at heart making kids focus too hard on the exact definition and taking any leeway out of the question for actual problem solving skills

[@Chris-hf2sl]

The problem here is that the kid is clearly more advanced than the teacher because he understands the commutative property of multiplication, whereas the teacher doesn't seem to have reached that level yet. The kid's mistake is that he showed his working, which wasn't actually asked for in the question.

[@iambrianparks]

I got marked off when I was learning “estimation” because I would do the simple problems in my head and be “too accurate”. If you want students to use repeated addition a specific way, make it a harder problem to do the “wrong” way.

[@Chris-hf2sl]

@@iambrianparks Estimation is incredibly important and contrary to what many folk believe it's entirely different to guessing. Years ago, I knew someone, an engineer, who went to an exhibition where there was a bicycle with its back wheel driven by a motor. It also had a milometer on it. There was a competition: guess the number of miles that the milometer would record during the exhibition, and the nearest guess would win a prize. Instead of making a wild guess like everyone else, he stood there and timed how fast the wheel was spinning. He then estimated the diameter of the wheel and with a simple calculation, arrived at an answer. He won the prize. I'm also an engineer and non-engineers are amazed when I estimate things that turn out to be reasonably accurate. It's also very useful as a check that a proper calculation hasn't got some silly mistake in it.

[@otakurocklee]

@@iambrianparks yes, or at least make the question clear. Teachers shouldn't expect students to read their minds.

[@jamesday3591]

@@otakurocklee Yes, how is the student supposed to know to use the Repeated Addition method if the question doesn't even specifically say something like, "Use the Repeated Addition Method to solve: 5x3". The nerve! Really! How did *Presh* even know that this was what the teacher wanted??? Mind-reading. That's what this is. Pure mind-reading.

[@anthulett4286]

To be honest, I'm more bothered by the 'score' of -1 (assuming this is applied to the overall test result, and not just this question). This teaches the pupil that attempting to solve a problem carries the risk of being so wrong that previously correct answers can be wiped out. Safer to do nothing and get zero, rather than do the work and possibly get a negative score.

[@merosario731]

Basically "5 x 3" is read as the following: "You have a 3 and you need it 5 times", and that's the important part, '5 times', as in '5 times 3', ergo '5 x 3' is '3+3+3+3+3'. It's not like Goku going Kaioken times 3...hold up

[@glennjohnson4919]

Huh, so multiplication is no longer commutative in newthink.

[@glennjohnson4919]

And if you keep putting out apologies for poor teaching, you may no longer be “one of the most popular” math sites on KZbin.

[@BoringLoginName]

Thank you for being so thorough. Videos like these are why you are my favorite math channel. This question is pretty terrible, though. I'm sure the teacher meant well, and I think there would've been no controversy if this was a question posed in a more scholarly environment, since this nuance would've been the whole point of the question. However, as a question meant for a kid, this is a little baffling. It makes math look pedantic, and if I were the kid, it would've made me feel like math is just not for me and should just use a calculator app or whatever instead of trying by myself. This is not a math problem. It's a language one. Plus, it could be argued that the equation could've been read as "five, times three", and thus 5+5+5. Sorry for the harsh reaction. The answer just felt mean.

[@rosswalenciak3739]

Math is pedantic, just at a much higher level than the one the student is currently at. The student needs to get these basic things before he worries about being pedantic about what specific things are called specific ways.

[@KeithAllen-pg8ep]

Yet you still say: "Videos like these are why you are my favourite math channel."

[@BoringLoginName]

@@KeithAllen-pg8ep Fair. I didn't mean to be abrasive to Presh. His explanation is great (as usual), which is why I like the video and his channel. My issue is towards the question itself. Like I said, this kind of reasoning would've been completely fine if the question came from something more advanced, like a math olympiad or a college-level thing or whatever (not saying the question is difficult enough to be in such places). If it were so, the nuance that Presh explains would've been the whole point of the matter. But AFAIK the question was made for kids, who are just learning the basics. In this level, 5+5+5 should be perfectly acceptable, because the kid used the same line of thinking that would lead to 3+3+3+3+3. That's what doesn't sit right with me.

[@RHGM71]

while it would be an error if you interpret the question literally, it is a failure of math education

[@Jonas-h4w3q]

Such a negative feedback is discouraging students to restructure a mathematical problem to a form which is easier to solve. And it is easier to summarize three groups of five than five groups of 3, because there are fewer elements to add up. For instance, no one would ever come to the idea to form 1024 groups of two's when calculating 1024 * 2, even though Euclid or Euler used that method to teach the principle understanding what multiplication is about. They did not imply by any means that the sequence has any significance.

[@gavindeane3670]

Exactly that. Presh has lifted a couple of snippets from eminent historical mathematicians and taken them completely out of context to try and bolster his brain dead argument. He's projecting his own misconception onto their words. There's nothing in the video to suggest that Euler or Euclid would support the idea that 5×3 should be expressed as 5+5+5.

[@sramctc]

why people can accept 3a = a+a+a, but find it difficult to understand 5x3 = 3+3+3+3+3

[@MB-ny6is]

I see what you're doing Presh. Just admit it, you love shitstorms in the comments section, why else would you make such a video? 😂

[@tonyennis1787]

A man's gotta eat, and momma needs a new pair of shoes. I like the channel, so I try to feed the algorithm.

[@the.true.mjdavis]

Repeated addition technique is fine. It's easy to understand. Just teach the students about commutativity at the same time.

[@guyhoghton399]

Addition is a binary operation so a more rigorous layout of the working would be: ((((3 + 3) + 3) + 3) + 3) However, if the brackets can be missed out then the teacher accepts that the student intrinsically understands that addition is associative, so allows him/her to modify their working to a more convenient form (bracketless). Why not then allow another convenient modification courtesy of the commutative law?

[@bait6652]

@@guyhoghton399 cuz assoc ppt is probably taught first cuz we learn counting first. 1+1 2+1 = 1+1+1 or the other way 3+1 = 2+1+1 or the other way. Mult is taught further when students are counting past 10-20s or even higher. And they need to be taught multiplication first or in concurrency w commutative.

[@guyhoghton399]

@@bait6652 Clearly though in this example the student does know and understand the commutative law of multiplication. It's immaterial (to the point I was making) how and when they learnt it.

[@bait6652]

@@guyhoghton399 does he ...Mult on N -sys by default commutative.. If it was longdiv of 5longdiv/radic would the student have deployed it correctly. Or even in obelus or / division. Would he have swapped the numbers?? We don't know

[@pijanV2]

We never did this, we just memorised it for each one, in first grade

[@TheLobsterCopter5000]

The teacher has it backwards. in 5x3, the equation is saying " the number 5 multiplied by the number 3", therefore it should be 5+5+5, not 3+3+3+3+3. If it was 5/3, you wouldn't divide 3 by 5, you would divide 5 by 3. Same with 5x3, you multiply 5 by 3, not the other way around. Of course you get the same result due to how multiplication works, but it's important to understand that the second number is the one changing the first number, for when you do division and subtraction.

[@Eshtian]

2:06 it's not... I hate to be defending this, but hating something for the right reason is important.

[@NeverMatter]

Could make out how silly the video is when seeing the thumbnail!

[@davidg5898]

Repeated addition is how I was taught (though not as rigorously as common core teaches it), but when I later learned the geometric method and that makes higher multiplication much easier. Additionally, teaching repeated addition as strictly multiplier/multiplicand ignores most real world applications, which is rarely a matter of a unitless scalar imposed on a value with units, where the distinction between "multiplier" and "multiplicand" breaks down.

[@user-rcghjewqw]

Same problem has been seen in Russia. Some elementary school teacher insist that that there is fixed meaning for both terms in multiplication.

[@user-rcghjewqw]

The funny part is that it is exactly backwards

[@danielschegh9695]

I think you made a mistake in describing the argument for the "correct" answer. It's not the "repeated additional strategy" that is the issue here, but whether or not the "repeated addition strategy" has a hard-fixed ordering for multiplication. That is, 5x3 = 5 groups of 3 items OR 5 items in 3 groups. The issue here isn't whether teaching multiplication as repeated addition or not. That is, after all, where it came from. The child did write it out at a repeated addition. Rather, the objection is that the "repeated addition strategy" should not require you interpret the first number at the number of additions and the second number and the thing being added. It should allow for the reverse. If not, then why not. Why does "repeated addition strategy" create and artificial constraint that does not exist in the math?

[@OBrasilo]

He showed that the teacher's implementation is one that has been favored at least since the times of Euclid who used the same definition in 300 BC.

[@coctailrob]

There is no context to the numbers in the equation 5x3 which can be interpreted as 5 multiplied by 3 (5, three times over) or 5 times 3 (5 lots of 3). For example: I give you 5 pounds for 3 days in a row, or for the second one: There are 5 grocery bags, each containing 3 oranges.

[@user-pn4dp4br7n]

literally the example you gave can be 5 multiplied by 3. 5 pounds per day and 3 days, ie 3 groups of 5

[@michaeldeal1625]

But the student DID use the Repeated Addition Strategy. He just first switched the order around (using the communitive property) first and then applied the strategy to 3x5. What would you do for 850x2, with the instructions to use the repeated addition strategy?

[@OBrasilo]

Did the student know of the commutative property or was he (or she) just taught to read multiplication the other way by the parents? I somehow think it's the latter, so the children basically switched the order around without even understanding why that works.