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

[@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. (Edited because apparently people like to have their say without checking to see if it's already been said)

[@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?

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

[@jamesday3591]

And for what reason is that a problem?

[@tabularasa0606]

@@jamesday3591 because if you want to do that you have to clearly state that as part of the question.

[@nooneatall5612]

@@jamesday3591 Because its worthless. It's a useless question that doesn't actually assess the students skills in math.

[@jamesday3591]

@@nooneatall5612 I may need for you to provide your comment with a little more context to be certain, but if my understanding of your comment at face value is correct, then I would suggest that your statement makes no rational sense. You wrote: "Because it's worthless." You also wrote: "It's a useless question that doesn't actually assess the students skills in math." I suspect that the context to which those comments apply is when I wrote: "And for what reason is that a problem?" to the original comment in this thread of: "The problem is that the question is not a math question, is a 'follow the instructions' question that is in math format" If I am, indeed, correct in my contextual representation, then my following response applies. If I am incorrect in my contextual representation, please clarify the proper context for me, and I shall be more than happy to provide a more relevant response. First, whether or not it is a useless question does not relate to the problem of marking a student's answer as incorrect when that student's answer is, in fact, incorrect. Regardless, allow me to also respond to your logical fallacy of red herring, despite the fact that such is, in fact, a logical fallacy. I would maintain that the question is neither a worthless nor a useless question. The purpose of the question is to ensure the proper understanding of a given principle relative to the discipline, very similar to an English teacher ensuring that students understood what is meant be terms such as "noun", "verb", "adjective", "subject", "predicate", etc. The purpose and value of such a question is to ensure proper understanding of terminology. Such is most definitely *not* a useless question, as conversantly accurate understanding of terms relevant to a given discipline are not only useful, but requisite to both academic progression and practical application of that discipline. I would further assert that "following directions" is also poignantly relevant to the applications of mathematics, as the applications for mathematics is rarely for the face value purpose of simply obtaining a numerical value isolated from any practical context. "Directions", as it were, are instrumental in establishing such requisite contexts of application, and a student *must* be able to understand the proper context provided by such directions in order to properly apply the raw, face, numerical values obtained by said mathematics. Otherwise, one ends up with simply a useless number. "4!" "Great. 4 what?" "Huh? Oh. I have no idea, but I really like this number 4. It's so cute, and all, you know. And I calculated it all on my own! Aren't you so proud of me?" "Uh, sure. Good job kid. Let me know if you ever figure out what to do with it, other than to simply sit there, look at it, and feel proud of yourself." And again, in even further disputation of your assertion, I would say that "assessing a student's skills in math" is not limited to purely mathematical calculation alone, but also in the student's ability to apply those calculations within the relative contexts of a given situation, again, stipulated, defined, and established by the "directions" of the assignment, whether that assignment be academic within a course of instruction, or pragmatic within the execution of a professional project received from either a client or employer. But again, if you meant your comment within some other context, please clarify, and I will be more than happy to respond.

[@nooneatall5612]

@@jamesday3591 brother are you ok? This seems like an AI response. To quickly clarify: The question is worthless because knowing the answer to the question doesn't make you better or worse at math. It's arbitrary whether 3x5 is 3+3+3+3+3 or 5+5+5 because they are mathematically equivalent. I know people that competed in math olympiads and their response would be 5+5+5. A students skill in math is determined by their ability to solve math problems and that's about it.

[@hdjong11]

I state that 5 x 5 is not the same as 5 x 5

[@idlesquadron7283]

lmao

[@Dakshgamehaksh]

I agree.

[@StopYFGA]

they're actually same

[@pd_heart]

@@StopYFGA 🤯

[@rodrigorebollos]

The worst I think is that it teaches kids it only goes one way. I'll be having kids asking What 1000 x 1 is And they'll be stuck in a room counting 1s for hours, when you can reverse it. Math and reason should be a tool to convenience your life

[@TheMattastic]

This feels like a system designed to make a generation of children innumerate.

[@noobandfriends2420]

Communist revolutionaries don't need to be literate for revolution. Math isn't required either.

[@TheMattastic]

@noobandfriends2420 That doesn't seem accurate. Who brought up communism?

[@GorrillaVision]

​@@TheMattastic its actually one of the sources of the issue schools care more about politics than education.

[@TheMattastic]

@@GorrillaVision Sorry, what?

[@СашаВолков-ф5н]

@@noobandfriends2420 As a certified communist, I can tell you with certainty that education of the working class is one of our main concerns. People who don't understand basic things, such as math, are a lot more likely to ignore all argumentation against the current system.

[@Hitarth_Rana]

"5 times 3" can be interpreted as both "5 times, 3" and "5, times 3". Accepting only one of them coz the book said so it's killing logical thinking required to do mathematics

[@karayura10]

Usually the former is the base number and the latter is the multiplication. This 5, 3 times

[@Leffrey]

@@karayura10what do you mean “usually”? It’s multiplication, both numbers mean the same and can be freely swapped. It’s only with subtraction and division (for basic operations) that each numbers order is actually critical, but completely irrelevant here. It’s just silly to take the standard at such face value as to exclude 5+5+5

[@karayura10]

@@Leffrey because that's usually that's how they presented the task. Back then they would present both 3x5 and 5x3, and they have different repeat addition solutions, like basic introductory of multiplication

[@etatauri]

agreed. i understand that it can be valuable to teach the method and not just the answer, especially in higher math where the method is more important than the answer. (for example, maybe the test was to demonstrate knowledge in trigonometry but the student used pythagorean theorem instead) but this example is far too rigid to have a point deduction. needing to memorize that its 5 times, 3, instead of 5, times 3 is just useless information.

[@stuffyouotterlistento1461]

When the order doesn't make a difference (5 × 3 = 5 × 3), the order doesn't matter. And ancient Greeks aside, I think people would tend to explain 5 × 3 as "5 groups of 3", because we encounter 5 first, reading left to right as we do, and saying "groups of 5 three times over" or some such thing is just clumsy. But 5 × 3 can be arrived at either way and thus either method is legitimate. 5 + 5 + 5 is repeated addition, and it gives you the correct answer. This reminds me of a quiz my brother took in middle school. They were asked something along the lines of what the most venomous animal was, and since my brother had recently read something in a science article that claimed to have made that discovery about a particular animal (it was decades ago, so I can't recall the specifics), he gave the answer from the magazine. He was marked wrong, which I understand, but when the teacher was shown the magazine, she dismissed it and said he should've known the answer he was expected to give (our mother was _not_ happy about this). This "5 groups of 3, not 3 groups of 5" nonsense strikes me the same way. It's about grading people for their obedience to pointless conventions/directions and not actually about learning useful information and mechanisms.

[@Ken-er9cq]

The student is correct. They have used repeated addition, just that they have chosen to reverse the order. What we want to do in maths is to reward students that find an easier way to answer the question. What the teacher is saying is there is a fixed rule to do this, and you must follow this rule. The main point of the question is to discover if students understand what multiplication is, and either answer does that.

[@gavindeane3670]

That's certainly what the point of the question SHOULD be.

[@willpina]

Nah, the student got the incorrect answer. But the main problem is that the question itself is something that shouldn't be asked as it is pointless.

[@gavindeane3670]

@@willpina The student only got the incorrect answer in the context of the arbitrary, unnecessary, and mathematically illiterate constraint the teacher has put on how the student is allowed to perceive 5×3.

[@willpina]

@@gavindeane3670 agreed, and that's my point. The "Repeated addition" method is a tool for learning multiplication, not a mathematical concept that needs to be memorized. I think we can all agree the student understands the concept even if he got the order wrong. So yes, the answer is technically wrong, but the question is not something that should be included in the test.

[@originalhgc]

I am shocked by how far off the mark Presh is on this one. It's not a question at all on whether one uses repeated addition. It's about whether the expression is symmetrical, which is most certainly is. I am pretty sure that Euler would have accepted 'a groups of 3' as equivalent to '3 groups of a.' Frankly, I can imagine no better way to introduce multiplication other than repeated addition. Neither could Euclid or Euler. Once a child memorizes the 10x10 multiplication table, then repeated addition can go bye-bye.

[@VladimirE.-is2ee]

And this is why kids end up hating math.

[@saftheartist6137]

🎯

[@jackdeniston6150]

And women

[@MaxTakeANap]

@jack Oddly specific

[@astrunkman6988]

@@jackdeniston6150 Uhhhhhh

[@InnerEagle]

@@jackdeniston6150 and women who does math

[@Haispawner]

The fact that people are DEFENDING this dictatorial self-defeating BS way of teaching here in the comments is so wild. I hope none of them apply to be teachers.

[@vfta7906]

One of the best comments here

[@Disgruntled_Grunt]

They're _all_ teachers. That's the only reason someone would even think to defend this.

[@Haispawner]

@@Disgruntled_Grunt Thank you Disturbed logo man

[@keep1t5imple5tupid]

Can't they just memorize the multiplication tables, and skip all these steps?

[@Boypogikami132]

@@keep1t5imple5tupidas if it’s soooo simple

[@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.

[@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

[@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

[@GabrielMartinFlores]

But what is the PRACTICAL VALUE of such a distinction in real life?!?

[@zde82]

The only practical value of such a distinction that I can think of is getting a higher grade for the math test...

[@GabrielMartinFlores]

@ 🤣

[@zoeherriot]

If you are asked to bake 3 batches of 4 cookies, it is different to 4 batches of 3 cookies. Same total amount, but the meaning is different. Or let's say we are talking about 3x4 matrices vs 4x3 matrices. Same number of elements different groupings of rows/columns. The point here is to show numeracy, it's not about the final result - it's about understanding how you READ the numbers.

[@fernandorochamedeiros5684]

​@@zoeherriotwhich is irrelevant in a math test.

[@Iron883Man]

Have you ever met a bureaucrat that cares about 'real life'? Neither have I 😂

[@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.

[@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.

[@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

[@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)

[@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.

[@jamesday3591]

@@bait6652 100% True!!!!!! Thank you. However, this concept is probably going to be lost on 75% of the population.

[@lucabonisoli]

I absolutely agree that focusing on applying a fixed procedure instead of building an understanding of the concept behind it is the wrong way to go. Want to use repeated addition? Fine. Take a bunch of square tiles and let the kids build a rectangle by putting together 5 groups of 3 tiles, then flip the rectangle and let them see that the same rectangle can be built using 3 groups of 5 tiles. In one fell swoop you can teach repeated addition, the commutative property, and the fact that any multiplication calculates the area of a rectangle.

[@artix548]

If my old Elementary School principal saw this marked wrong, someone would've been blacklisted from teaching in the entire State of Georgia.

[@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."

[@ambisinisterr5735]

Exactly. Repeated addition isn't an issue at all. The problem is the semantics in the education system that disregarded the cummutative property of multiplication. You shouldn't need a rule for or against allowing kids to use the cummutative property.

[@CLipka2373]

Brilliantly noted and researched - thanks @kvf8064.

[@nosajimiki5885]

Speaking of Semantics: The Common Core definition of Repeated Addition does NOT actually specify order. Everything after eg is not part of the rule, but only an example of the rule being applied. The entire actual definition of repeated addition is "Interpret products as whole numbers." Nothing more, nothing less. As for the historical context of doing it as Euler or Euclid did it is bad math because those conventions specifically predate the formalization of the commutative law of multiplication established by François Servois in 1814. In other words, by marking this answer wrong, the teacher is not teaching NEW math, she is actually teaching an invalidated form of OLD math that has specifically been incorrect for over 200 years.

[@halifur]

@@nosajimiki5885YES, THANK YOU. IT IS ABSURD

[@LumemDH]

Depends on how you read it. To me, he didn’t use the commutative property, he just read 5*3 as 5 multiplied by 3, thus 5+5+5 (5 repeated 3 times). Granted if this was my HS math teacher teaching Elementary Math, she’d just ask “why did you lose time by writing 3+3+3+3+3 instead of 5+5+5” regardless if it was 5*3 or 3*5.

[@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.

[@oliverfiedler8502]

because (most) teachers only know one Methode 😎

[@kevincaruthers5412]

Most math teachers are barely adequate to the title. This teacher used a solutions manual and used the solution provided for that problem. The teacher either refused to or was unable to evaluate the problem separate from the manual. . IE Those who can do. Those who can't teach.

[@beauthestdane]

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

[@twm1452]

Are you sure you understand? Frankly, I think I understand also, but if the teacher did not also cover more practical ways to arrive at a solution I’d have an issue with this strategy in isolation. I have to think that the additive addition method was followed by better, more practical methods. I was not in the class, so I’ll really never know. (Same for probably everyone with strong opinions on this comment section)

[@beauthestdane]

I have no issue with the general strategy, although it does fall apart pretty quickly as numbers get large, but with the lack of also teaching that you can calculate it both ways correctly, and should choose the easier of the two. 5+5+5 is just quicker and easier than 3+3+3+3+3.

[@wertigon]

I do believe the point is how to properly convey what differs in meaning from 3x5 and 5x3. I would give 1 point for correct answer, 1 point for correct method, 0 points for incorrect interpretation. Math is a language, so I see it no different than giving 2/3 on the sentence "I cookies eat." (spelling +1, a coherent sentence +1, grammar +0)

[@WuchtaArt]

​@@wertigon nothing differs between 3x5 and 5x3, thats the point of multiplication. You know there are synonyms in a language.

[@zedif1991]

This is why Algebra is easier

[@RichardCook-on3gf]

This is to discourage students from learning mathematics. Another way to help destroy education.

[@loganshaw4527]

AI asked you a question and you answered different same responses.

[@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.

[@johnt6806]

You are literally incorrect. Repeated addition has a well defined order.

[@zam023]

@@johnt6806 Says who?

[@VenetinOfficial]

@@johnt6806 Believe it or not, addition is commutative. Multiplication is also commutative by proxy. I am sick of people acting like they know math and then get the basics woefully incorrect. This is elementary.

[@johnt6806]

@@VenetinOfficial says the guy who doesn't have a masters degree in mathematics. The ignorance in this comment thread is out of control. We aren't debating the properties of "addition", we are debating the definition of "repeated addition". If you don't know what it is, stop pretending you do.

[@Coocoocrazy3]

@@johnt6806ok then, give me one multiplication question where one method wouldn’t work (other than with decimals and fractions and stuff) because in that case it will still work but you have to go on a little division side quest

[@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.

[@abigfavor]

No, still mad. 5+5+5 is valid. Imagine trying to teach 2xA as two groups of A but Ax2 as A groups of two. It's trying to confuse kids on purpose

[@reeshomer516]

Try replacing multiplication with addition in your examples. 2xA equal A+A, two groups of A. But Ax2 you cannot replace with addition.

[@whoeverest_the_whateverest]

​@@reeshomer516at the same time a×2 is equal to 2×a

[@boriscat1999]

Marking students off for not following directions has been standard practice in education for hundreds of years.

[@abigfavor]

@@boriscat1999 They did follow directions but let's not use an appeal to tradition in stem fields 😁

[@staryknight2452]

​@@boriscat1999the kid did follow instructions but its not what the teacher wanted. i have no problem with the strict accordance to the rules but, when is just for basic math and introduction to a concept it shouldn't matter. the problem is teachers are looking for a very specific way to show work and, when its not done the way the teacher wants it its wrong. lets take a different concept being taught. take 16+9, today its taught to do 10+6+5+4 or something along those lines. i would of done it as 16+4+5 but, thats wrong compared to what is taught.

[@MaybeFactor]

This is all good and well, except that 5*3 = 3*5 = 5+5+5 The student simply skipped writing down the absolutely trivial step of swapping the order of the numbers being multiplied. They DID demonstrate usage of the repeated addition strategy

[@zoeherriot]

No they didn't. They got the first step wrong. Using the repeated addition strategy, the student is supposed to read the equation as written. I.e. "Five threes" is not the same as "Three fives". Now - yes, it's the same if all you are interested in is the total. But if you are interested in the number of groups - then no - it's not the same. 4x3 batches of cookies, does not yield the same number of batches of cookies as 3x4. This problem isn't about the result of the multiplication. It's about understanding how the order of the equation affects how you read - i.e. numeracy.

[@YoshiGO71]

@@zoeherriot Math is abstract, don't confuse with the representation, if you want to say 3 cookies then say number 3 with variable cookies. For example 3x or 3 kilo, 3 mile. therefore 3 x 4 is the same as 4 x 3. Your example about comparison between number 3 and 3 objects does not equal in the first place. so the group logic does not apply to 3 x 4 .

[@zoeherriot]

@@YoshiGO71 it applies... if the context says it applies. This is from the 3rd grade common core curriculum, under the section for multiplication: "Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. " If this format of question has a predefined meaning in that class (i.e. the part about using addition to solve it) - then yeah. The kid got it wrong. Your example is correct - but there is always context with a test like this. The common core math books at this level usually teach multiplication as grouping - and to demonstrate understanding of how that works - they are asked to interpret equations like 5 x 7".

[@michealturner9498]

What good is a teacher if they punish a proper application of the communicative property?

[@gavindeane3670]

​@@zoeherriotNo. The problem is the teacher is dictating that a×b must be read as "number of batches × number of cookies per batch" and may not be read as "number of cookies per batch × number of batches". That's mathematically illiterate. A lot of people are trying to use real world examples like batches of cookies or bags of apples to try and justify the teacher here, but in fact examples like that show immediately and obviously why the teacher is wrong.

[@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.

[@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.

[@Skilletfan]

Which is the fundamental problem.

[@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.

[@NotHexaaaa]

I'm guessing it's because when you say something x3, it just means something tripled, or 3 of something. But you can also say 3x something which is just 3 of something. It's just how we use these notations today. Both are seen a lot in games or recipes or lists for example. (You got sticks x3, You got 3x stick) (3x 150ml milk, 150ml milk x3) (3 notebooks, notebook x3)

[@44Hd22]

0:22 I guess it’s obvious what the teacher wrote and how you can kinda disprove that there’s only one representation for a two number multiplication.

[@loganshaw4527]

And the whole video is trying to prove the teacher right. Did not watch it. Not going to.

[@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.

[@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.

[@Sleeping_Insomiac]

The point is that "strategy" shouldn't trump actual *laws* of mathematics. The commutative law prescribes that all factors of a multiplication can be freely exchanged with each other. The pupil in question showed not only that they understood that a multiplication is a repeated addition, but also the commutative law and used both to find an even more economic answer than the writer of the question expected. Insisting on children to deliver this "correct" answer is only turning them into automatons, punishing initiative and individual thought! This teacher, and whoever defends this decision, should be ashamed.

[@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?

[@mikemayuare]

A perfect way to make children hate math

[@Aaackermann]

I am a math teacher and I wanted to scream at Preshs "explanation"! All my students are glad I am not a prick and disengage them with nonsense like this. Utter bs.

[@arc-sd8sk]

actually the kids didn't care, only the parents were mad

[@Aaackermann]

@@arc-sd8sk Yeah, no.

[@arc-sd8sk]

@@Aaackermann actually yes nice try tho :)

[@Aaackermann]

@@arc-sd8sk Agree to disagree. And as I said, I am a teacher.

[@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.

[@jm7781]

Yes, as a math teacher, I am really glad we found a way to make math even more boring. It was really necessary to put more rules and regulations on this laid back subject. Please, read this in an ironic tone.

[@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.

[@briant7265]

The thing that is egregious here is, writing a week they will be taught the commutative rule, and that the order of the multiplication is inconsequential. Then none of the students will ever think about this again.

[@spoonwinnipeg2021]

@@davidjulitz7446 Actually there are only two ways, and one of them is wrong.

[@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.

[@Kollum]

@@cowdyayaad6378 yes. And by writing 5+5+5, the student proved that he remember how that method works

[@cowdyayaad6378]

@@Kollum It shows he forgot which one is the multiplier.

[@pnsdkrpndja12177]

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

[@Nikioko]

That's why you can simplify the problem by using commutative properties, once you have proven that commutativity always applies to multiplication. But before, you indeed habe to add 1 10000 times. By the way, exponentiation is not commutative, so 2³ is not the same as 3², and 2³ expressed by repeated multiplication is just 2 ⋅ 2 ⋅ 2, not 3 ⋅ 3.

[@aaronfleisher4694]

Or 10000 x 0.

[@rosynosyposy]

Or -2 times 10000

[@normanross3422]

@@zoeherriot Because they are pointing out the teacher's flawed reasoning. Negative numbers (and beyond) are very much a thing in real-life relationships between actual physical quantities.

[@heraldreichel1971]

@@zoeherriot Additive reasoning was stated as a goal. This goal was achieved. 5+5+5 is additive reasoning. If maintaining the order of operands in the question asked disregarding the rules of mathematics, it should have been stated clearly. A succinct definition of the expected procedure would have been, "Don't give us a correct solution, give us the solution we might have implicitly expected, given we are social studies majors incapable of grasping the most simple concepts of primary school math". Or maybe: "We want you to do the chore in the most onerous way you think we can think of, not proficiently".

[@christianbolt5761]

As someone who taught mathematics at a university, it makes me mad when definitional games get in the way of actually solving a problem.

[@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.

[@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.

[@joshuasweetman4903]

I member times tables

[@noyb7920]

I think you had the same curriculum I did, heh heh.

[@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).

[@Tronnyverse]

Kay, but human brains usually take the easiest path to the answer and it feels pretty twisted of asking a question like what's 169 x 2, and giving -1 because student "broke the mold" and wrote 169+169 instead of adding 2 169 times. 😶

[@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.

[@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?

[@MeemahSN]

@@bait6652 Those things can and do deter children, but because many kids already consider math to be more boring than their other subjects, docking marks like this will deter them faster than in English or Art, as those subjects are arguably more engaging. Kids are more willing to improve if they enjoy what they are learning.

[@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.

[@Jason9ll]

This is called conditioning. They are teaching kids to do exactly what the teacher tells them to rather than have them learn how to figure out problems on their own.

[@Jason9ll]

This is how you make an obedient society that won't question their leaders

[@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.

[@godsakezz]

I get the frustration. But we have to understand it may be the syllabus for them to follow. What you mentioned is based and for an adult mind, and also most of the comments I see here is typed by an adult mind. What is in play here is actually a student less than 10years old. Likewise as we adults learn how to drive or surf, we have to slowly learn the tedious theory, the syllabus, before getting on the road. So in their school, maybe for their age, their syllabus(key word) may be to teach them that whenever their test question asks for 5 x 3, the first digit represents the Group, and the latter represents the number of something. Don't you worry that they wouldn't understand 5x3 is the same as 3x5 when they grow up lol, no biggie there. So maybe we should just let the teacher do his/her job instead of us being quite immature bashing them simply just based on how we see and like it.

[@januszj444]

@@godsakezz At the end of my 1st grade I had a math task to calculate some substraction example. One of them was something like "2-3" and I answered "-1", what of course teacher marked as wrong, with correct answer being "substracion not possible". I still find her one of the worst teacher I had. The funny part was that when I tried to discuss the mark with her she admitted "your answer will be correct next year". Same approach as here. Fortunately I had many good and great teacher later.

[@godsakezz]

@@januszj444 Yeah no choice as students are expected to apply what they were taught for that particular test perhaps, probably meant to target that specific concept that may look tedious.

[@KangQingXu]

@godsakezz I understand your answer, and I’m sure it’s not the teacher's fault but the system’s (specifically, the syllabus). In school, I was taught from the start that A × B = B × A, and we never used the repeated addition strategy. I’m not sure if it’s related, but my math teacher was very strict-but in a good way-, and I always liked math. I’m actually pretty good at it-I even taught math and physics to teens at one point-and am currently halfway through my Electrical and Systems Engineering degree, with all my math subjects passed with high grades. With that said, I believe a fundamental part of learning math-and learning in general-is being able to see the big picture, not just the narrow view presented by your teachers. Penalizing a correct answer just because it wasn’t achieved using the 'expected' method stifles creativity and penalizes thinking outside the box. When this kid grows up, they may fear doing anything they weren’t explicitly told to do (like so many people do), which is a real shame. (Honestly, I bet this will also make them dislike math, which is sad but kind of predictable).

[@KangQingXu]

@januszj444 I had a similar situation at school with negative numbers, but instead, the teacher praised me and even marked my work as correct. I think this is how a good teacher should be-supporting different ways of thinking and encouraging students to explore beyond just the ‘standard’ method.

[@seektruth5119]

Your videos often show how to solve a problem in different ways. The process of learning to solve problems in multiple ways is important for advanced math and for real world applications. This teacher is teaching that there is only one way to solve the problem, and that following the convention defined by the herd is more important than critical thinking. This attitude will mentally cripple children.

[@zoeherriot]

No.. they aren't. You are looking at ONE problem and assuming that. They are testing one specific way, in this specific question, on this specific test. But they are also taught OTHER ways to do it. How would the teacher know if the student had learned that lesson without teaching it? Let's say this young lad gets his first job at a bakery... and he's asked to make 3x4 batches of cookies. He uses his critical thinking skills - and knows he has to make 12 cookies - but because he is unsure of how to read 3x4 - ends up making 4x3 batches of cookies. It's the same right? I mean great - he used his critical thinking skills, but he'll look like a complete muppet.

[@fernandorochamedeiros5684]

​@@zoeherriotblah blah blah

[@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

[@ZenoDovahkiin]

>multiplier/multiplicant In my German maths class, we used such terms for non commutative operations, for multiplication we just used factor.

[@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.

[@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.

[@gavindeane3670]

​@@cowdyayaad6378No, you do not need to state 5×3 = 3×5 in order for 5+5+5 to be correct here.

[@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.

[@PringoOrSomething]

I have no problem with repeated addition because that’s effectively what multiplication is, but making a fuss about 3x5 vs 5x3 is a pedantic technicality. You’re no longer grading a student based on their understanding of a mathematic concept, but rather their understanding of an arbitrary rule that is ultimately unhelpful and confusing.

[@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."

[@luisrosado7050]

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

[@jamesday3591]

And if the question was focused on the result, you would be correct. Unfortunately, the result of the equation was not the focus of the question.

[@ArturCzajka]

@@jamesday3591 and yet, when you ask someone to multiply these two numbers, both approaches are correct. And saying otherwise is incorrect 😂

[@jamesday3591]

@@ArturCzajka No one is saying that the solution to the equation was incorrect. This is your error. You fail to recognize that the purpose of the question was to evaluate the student's understanding of the method, not the student's ability to arrive at a correct numerical conclusion. If you focus on the wrong part of the question, you will *miss* the actual purpose of the question. Driving Instructor: "Please drive us through the obstacle course, so that I may evaluate your ability to drive a car." Student: Gets out of the car, and walks to the finish line. Driving Instructor: "You failed to demonstrate your ability to drive." You: "No they didn't. They arrived at the correct destination, and that's all that matters."

[@ArturCzajka]

In your example the student should’ve gone around the course in the car, instead of through, and not on foot. Or better - drive through the course on reverse. In both cases the student demonstrates they can drive instead of walk. But the math is correct by the virtue of multiplication being commutative. There is nothing in the exercise telling the student they can’t use that property. And we’re saying, that the exercise has to be read very carefully.

[@jamesday3591]

@@ArturCzajka You're ignoring the purpose of the question. You're treating the purpose of the question as evaluating the student's ability to multiply correctly, and that's *not* the purpose of the question. The purpose of the question is to determine the student's understanding of the Repeated Addition Strategy. They are given the expression in order to demonstrate the proper grouping, and then use *that proper grouping* to solve the expression. Therefore, anything that the student does that, at best, obfuscates the student's demonstration of the correct understanding of the proper grouping, or at worst, directly demonstrates a student's *incorrect* understanding of the proper grouping is a failure of the student to demonstrate correct understanding of the proper grouping according to the Repeated Addition Strategy. No one is saying that the student's *math* was incorrect, and you don't seem to either realize or acknowledge that facet. Until you're willing to allow that the purpose of the question was *not* to achieve a numerical solution, but rather to demonstrate the proper grouping of the two numbers according to the Repeated Addition Strategy, you will continue to miss the entire point of the question. You wrote: "the math is correct by the virtue of multiplication being commutative. There is nothing in the exercise telling the student they can’t use that attribute." Yes, there most certainly *is* something in the exercise saying that they cannot use the commutative property. The exercise directly states "Use the Repeated Addition Strategy". Applying the Commutative Property (if such, was indeed, what they were doing, which, in all likely was *not* what a second grader was doing in regards to the Repeated Addition Strategy, since the Repeated Addition Strategy is taught *before* the Commutative Property of Multiplication), ... but applying the Commutative Property (as irrational as that would be in this situation, given the order of instruction), ... applying the commutative property would defeat the purpose of demonstrating the proper grouping, expressly required by the question. Your argument, in this context, makes no rational sense whatsoever. If we're talking about a student who *has* learned the Commutative Property, then the wording of the question requires them to *show that application* in their work. Otherwise, it is assumed that they are applying the Repeated Addition Strategy to the expression as it stands, without first changing it. Since the student does not first change the expression, it cannot be asserted that such was what the student did, unless the student directly states that such is what they did. Did the student directly state this either directly to you or in their work? No. (I'm almost certain that you have not spoken directly to the student, but that is an assumption on my part.) The question specifically states what the student is required to use. Did the student apply the commutative property? Not in their work. Only in your own assumption. And it doesn't even make sense that a student who's being asked to demonstrate the Repeated Addition Strategy would even *know* the Commutative Property of Multiplication yet (much less *apply* it to a test question about the Repeated Addition Strategy), because the Commutative Property is taught *after* learning the Repeated Addition Strategy. That sequence of learning and stated requirement within the question itself aside, If you're going to make the claim that the student applied the Commutative Property ... as an additional step that makes the answer more complicated than it needs to be (at the second grade level, before the commutative property is even introduced, no less), then at least have some evidence for it, not just your own presumption. Can you point to any actual evidence that the student intentionally applied the commutative property, and then properly applied the Repeated Addition Strategy, rather than simply applying the Repeated Addition Strategy incorrectly? Can you? No, you can't. Why? Because there is no evidence for it in the student's answer whatsoever. The only "evidence" you have is you own presumption and projection and the student did so, which doesn't even make rational sense for a second grader to know before such is taught. You wrote: "And we’re saying, that the exercise has to be read very carefully." Uh, yeah. Of course? Duh? You somehow think that such should ever *not* be the case??? I would think that the requirement to carefully read the instructions should be fairly obvious, and inherently self-evident for *any* test. The sentiment that you seem to be somehow objecting to something so central life, itself, not to mention academic instruction and evaluation is ... perplexing, to say the least. When and where has it *ever* been acceptable to not read instructions carefully? "Oh! You mean I actually have to *know* what I'm supposed to do? Huh. Who would've thunk?" Besides, there are only seven words in the sentence, and the first five of them directly tell the student to "Use the Repeated Addition Strategy." Okay. I'll admit it. Hiding those five words as the first five words of the instructions, and then burying them with the only other two words in the sentence does make it very difficult for someone to understand what they're supposed to do. It should have been written *much* more clearly. Very deeply hidden they were, and no reasonable person would understand at first glance that "use the Repeated Addition Strategy to solve" would actually mean to "use the Repeated Addition Strategy". The average person is much more likely to interpret "Use the Repeated Addition Strategy" to mean, "in whatever method you want, including changing the following expression by the Commutative Property of Multiplication first, if you prefer to". You make a good point there.

[@alphoz123]

I think we shouldn't get hung up on the minor details of definitions in math problems. 5x3 can be defined as five groups of 3 or three groups of 5; either way works. This problem is testing the definition itself, which is arbitrary and pointless.

[@oliver_twistor]

Exactly! Unfortunately, a lot of questions in school that are supposed to be about maths are really about language, which makes people who struggle with language (e.g. immigrants) appear to have a lower than average understanding of maths. I have always been a quick learner when it comes to maths, and I've always loved it, but I struggled on tests because I tended to misinterpret the question. I maintain to this day that people who write maths tests aren't typically very proficient in language skills. They often write confusing questions. I had a much easier time learning maths in university, because it was less focus on Tina and how many pair of jeans she could buy and more focus on concepts. This reminds me of my intense disdain for timed maths tests, because they test speed over accuracy and correctness.

[@etrnl0]

3:29 But the question says you should use repeated addition strategy, it doesn't say "only use". So what's the problem with first using commutative law first and then using repeated addition strategy?

[@zobiah1]

Because they didn’t show that that’s what they did. They didn’t say “5 x3 is the same as 3 x 5”, which while extremely simple and intuitive to most people, is likely not a guaranteed skill at the level of someone taking a test in 5 x 3. So, based off the markings left by the student, the only conclusion the teacher can make is they applied it backwards. There’s a reason you have to supply your work in most math problems

[@etrnl0]

@zobiah1 yeah that's fair

[@nicolassepulveda4669]

​@@zobiah1 Completely agree but, c'mon, this kids are not making a proof. You shouldn't need to list every axiom / property you use, they should have taught them that it is valid both ways, and accept both anwers.

[@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".

[@KeithAllen-pg8ep]

@@jamesday3591 5 x 3 means "5 multiplied by 3" (which is 5 + 5 + 5 = 15), which means the student was correct.

[@phunkydroid]

It doesn't confuse the student as long as you tell them why it was marked wrong. It teaches them to follow directions more closely.

[@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.

[@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.

[@GodwynDi]

​@@bait6652Kids aren't exactly lining up for English classes either.

[@bait6652]

@GodwynDi yet no big fuss about reading/writing.

[@paulkolodner2445]

The purpose of this question was to assess whether the student understands the "repeated addition strategy", not whether s/he can do arithmetic. It's important to be able to do arithmetic. It is completely unimportant to remember the "repeated addition strategy". I'm a retired experimental physicist. I have decades of experience doing arithmetic, algebra, geometry, calculus, programming, and the like. I have the intuition to check that my answers are correct. And I don't remember the names of any of the strategies or theorems we were taught in middle school. They are utterly irrelevant, even to people who do quantitative work all day like I did.

[@Leffrey]

It’s not even checking if the student knows repeated addition multiplication, it’s checking if the student knows the exact legal definition and ordering of repeated addition strategy. (Well, it does check both if the student knows the method and order, but you get my point) They knew what the strategy was, they just didn’t know or care what the exact order the standard used was, which is entirely valid. As you said, doing the math right is more important in math class than following the exact letter of the law on how to do it.

[@cliveshore416]

Well said Paul. I used to be an engineer. Would never have got off elementary math using this system. I'm fairly sure a proper math teacher would have seen both solutions as correct. Free thinkers are loose cannons. It's a philosophical argument presented here. This kid is going to spend his life counting on his fingers

[@SuprousOxide]

And the student DID demonstrate that they understood the repeated addition strategy. Are you claiming that "Repeated addition with swapped numbers strategy" is a DIFFERENT strategy?

[@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!

[@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?

[@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.

[@pridecat]

the thing that really frustrates me (19yo) is i remember it being emphasized when i was taught in school that it doesn’t matter which way the numbers are - multiplying them gives the same result. i think there was a specific name for this rule which i can’t recall, but that’s not the point. the fact that we were told the order doesn’t matter, but now the order matters and is getting answers to questions marked wrong. EDIT: another comment mentioned the commutative property, and yes that’s what i had in mind!

[@zoeherriot]

But they teach that too. This isn't replacing the idea of the commutative property of multiplication. I mean you must inherently understand that there are situations when 5x3 and 3x5 are different right? If I asked you to give me 5x3 groups of oranges... how would you do that? Because that kid would have given me 3 groups of 5 oranges. And that would have been wrong.

[@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.

[@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 transport.

[@vsm1456]

"but it is old irrelevant math for the modern era" - I don't think it's the case though, I have a hard time imagining Euclid or Euler marking this answer wrong simply because the pupil understands the commutative property of this operation.

[@kevincaruthers5412]

Exactly! The 'teachers' have forgotten they are teaching a practical skill to be used the rest of the student's life.

[@alkemis]

@@vsm1456 you didn't understand my point....commutative law is all that is required at this stage. The concept of e pending to get 5 groups of 3 vs 3 groups of 5 is just semantics and irrelevant at this stage of a student's learning.

[@vsm1456]

@@alkemis maybe we didn't understand each other? my point is: I suspect that neither Euclid nor Euler actually *enforced* which number you need to add up which many times, ignoring the commutative property. I feel like Presh just made this assumption out of nowhere, and with that threw a shade on those great mathematicians as if they supported the idiocy shown by the teacher in question

[@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.

[@coryg1109]

Here is what kills me: Everyone has a way of doing things. The process the child chose was different then the approved process. So what did the child learn? Doesn't matter if you are correct in the end if you didn't obey the process. It's like programming: Give a problem to five programmers and there will be five different coded answers that have some things in common but others not so much. Certainly you could say "Well, this program is much more efficient" but it doesn't mean any of the other processes are wrong.

[@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."

[@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.

[@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.

[@blatantexcuse]

As a maths teacher I will say this distinction is worthless and ultimately counter productive.

[@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

[@acmhfmggru]

This is about teaching conformity and obedience to authorities, not 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.

[@noyb7920]

"4. Tetration ..." Well, that escalated quickly.

[@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.

[@jamesday3591]

I would suspect that the "good reason" that you claim doesn't exist might be to ensure that the student fully understands what the Method, itself, teaches, so that the student is sufficiently conversant in the terminology for subsequent discussions in higher levels of both mathematical instruction and application. That's my guess. I could be wrong though. A lot of people tend to think language is arbitrary, and can mean anything you want with impunity. Who needs uniform terminology in STEM fields anyway? My pronouns are he/her. Or where they she/it? I can't recall. It's all arbitrary anyway, right? (Actually, I think I'll just identify as an LLC. It gets me a better tax rate.)

[@tezzerii]

7:42 - NO ! the latter number in Euclid's description isn't necessarily the last number ! He refers to the multiplier, then the multiplied, and the latter, i.e. the multiplied, is added. But which is the multiplier ? IT CAN BE EITHER, regardless of the order they are written. And to me, 5 times 3 means 5 repeated 3 times - or it could be 3, five times. Which is the easier ? Obviously the former. If it was 3x5, obviously the latter (5, three times). Either way the kid used good strategy, which is surely what this method is all about. Ridiculous.

[@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.

[@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.

[@tolulaiyemo81]

Yeah. In Spanish, it's read as 5 by 3.

[@zoeherriot]

@@KeithAllen-pg8ep er... not quite. In english - it's also known as 5 groups of 3. Or five threes. The reason this is important. If you go to a bakery and ask them to make you 5x3 bags of cookies, you better believe 3x5 bags is different. Even if the total is the same. The point here is - the math is not language dependent - because when we are discussing numbers, the order of multiplication is irrelevant. But when we are grouping objects by quantity - then it really helps to know that the left hand number is the multiplier and the right hand number is the multiplicand (i.e. the number in each group of whatever that object is).

[@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.

[@Knottypine79]

Telling a child in grade three that 5x3 =/= 5+5+5 is ridiculous.

[@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

[@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.

[@jamesday3591]

@@torarne7796 You wrote: "The method, as it is phrased, makes an arbitrary decision which number to use for the addition." Whether or not the method arbitrarily assigns which number to use for addition, such would make the "Method" arbitrary, not the question. The student still has to understand what the "Method" is, even if said method was designed arbitrarily, but that doesn't make the teacher wrong for ensuring that the student correctly understands what the Method *is*.

[@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.

[@palerider2143]

Let me fix this for you guys 5*3 = 5+5+5 OR 3+3+3+3+3 Useless ass debate

[@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.

[@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.

[@TheBunzinator]

So... multiplication is only commutative most of the time? The kid still used repeated addition, they just commuted first to simplify. (Fewer addends.) I hate this kind of pedantry for which there is no justification.

[@juancolon4503]

This is an a example of teachers/mathematicians being pedantic and condescending.

[@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).

[@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.

[@zenaku666]

Believe it or not applying non-mathematical reasoning to mathematical problems is actually more common than you think.

[@RHGM71]

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

[@emolasher]

It's fine... don't worry about it. Department of Education is getting gutted, and the curriculum is getting overhauled.

[@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.

[@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.

[@jamesday3591]

Did he? Or did he just make a mistake? You seem to be assuming the former without even allowing for the latter. What's your basis for assuming either way?

[@NeverMatter]

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

[@Platanov]

I've been pretty immersed in mathematics in my 40 years, and I have NEVER heard the word Multiplicand before. I would think the idea that there is a meaningful identifiable difference between two numbers being multiplied is deeply poisonous to an intuitive understanding of multiplication.

[@gavindeane3670]

There is a conceptual difference, but the mistake is to think that a multiplication can only be written as multiplier × multiplicand and cannot be written as multiplicand × multiplier.