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I think you have to factor in the school leaving age in 1869, as far as I can tell, in a 2 minute search, it was 10 or 11. Therefore the very basics of algebra would have been all that was taught to most kids, if any.
When students in the USA would learn the (very) basic algebra needed to do well on the exam changed in the early 1960 because of the space race. Prior to 1960, most high school students would learn about this in their first or second year. After 1960, there was a push for more rigorous math and science education in the US. For math, this came about with the some what infamous School Mathematic Study Group (SMSG - some math, some garbage). With this, the techniques needed to solve the problems would have moved to the 7th or 8th grade.
Historically, you are correct that the timeline for teaching this shifted in the 1960s. But as a former math teacher myself, I'd say 7th grade would only happen for most of these topics for very advanced students. Typically, the first year of algebra is taught in 8th grade for better students, though some US students may not get it until 9th grade. And while most of the tools necessary to solve most of these problems are theoretically covered in algebra 1, frankly I doubt most average students would be able to score well on a test like this until their second year of algebra, which may not happen until 9th or 10th grade (or even later for some less talented students). In particular, the algebra of combining fractions as in #5 and factorizing a difference of squares involving multiple variables and higher powers as in #4 would likely be viewed as quite challenging for most first year algebra students in the US. #3 would likely trip up a lot more students even beyond algebra 2, in that they may not recognize that (a+b) needs to be a factor of one of the terms to be multiplied, which could lead to a lot of excess computation and confusion. To be perfectly frank, I recently taught (past few years) some beginning calculus students in the first year of college at a rather decent school, and I doubt that more than around half of them could have got a perfect score on this exam. Many would be stumped by problems involving algebra and fractions. Which was really distressing to me, but that's the state of math education in the US right now. But yes, in most cases students should theoretically be introduced to most concepts necessary to solve these problems by around 8th or 9th grade (ages 13-15). Many would not be fluent in these techniques until a year or two later.
@@BobJones-rs1sd Thank you for the feedback.I was in the 7th grade when the SMSG revolution occurred (along with similar changes to science curriculum). It was an exciting time for me as I went from hating Math which went from rote use of the standard algorithms for arduous computations to learning what math was really about. I went on to become a Mathematician (My interests are in model theory and the mathematical underpinnings of LLMs). While I have taught, it has mostly been upper division undergrad and grad students. So I can't speak to your experience with math as it is taught today in K-12 schools. I would point out that math and science education changed again with the "No Child Left Behind" update that led to common core. This, as I am sure you are aware occurred in 2001 and resulted in a changes in how most subjects are taught, including math. I believe that this changed the focus in many school districts from focusing on understanding to getting good schools on the assessment tests which I believe has ties to funding.. Having a daughter who went to school after the NCLB changes, I believe that where the child went to school would determine when a student would be able to solve the problems; which I believe is the point you are making.
I got 6 solutions for the first one. Ik were prolly going for the principle root (15) but still. Also here’s the solutions if any are wrong pls tell me cause im just 16 and don’t take any math classes: 15, -3, 21+2i✔️3, 21-2i✔️3, 27+2i✔️3, 27-2i✔️3
If i have your degree i make courses of math for different exams especially indian compt. Exams and sell . If your course price for math is assume 10k this should consume by 15000 indian you make 150000000 rs in 1 year hardworking to desine your course.
Do you regret going for maths major while you could've done something else? And what would it be? I'm currently in my first year in Mechanical engineering and I like maths so much!
I definitely don’t regret studying mathematics but there are things I’d have definitely done differently during that time! I’ll make a video on this! I also found a way to do my other passions alongside my degree :)
At that time, if you said that atoms existed, it would be an enormous blasphemy to reduce divine creation to small balls or very small blocks. And you, with your extraordinary intelligence, should be careful not to be mistaken for a witch!! 😁😁😆❤
Leucippus of Miletus (5th century bce) is thought to have originated the atomic philosophy. His famous disciple, Democritus of Abdera, named the building blocks of matter atomos, meaning literally “indivisible,” about 430 bce.
@@davidnewell3232 Yes, but the idea of the atom was only established in the scientific community, and in fact unquestionably accepted in society with Einstein's publications on Brownian movement, until then everything was not about ideas.
@@davidnewell3232 By the way, this publication by Einstein came after this examination of our dear Ellie Video, that is, at the time of this examination the idea of atoms was not openly accepted as it is today.
@@virais4605 The "reduc(tion of) divine creation to small balls or very small blocks" had been, at that point, understood for thousands of years of years. Avagadro was scaling up from molecular weights. In 1811, he published "Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons. Lavoisier and Proust had resoned the conservation of elements in chemical reactions decades earlier. Dalton had labeled them as indivisible and indestructible particles, each with unique characteristics. Science was much more familiar with the building blocks of matter than you suggest. The murder of 80,000 people believed to be witches took place between approximately 1500 and 1660 in Europe. Giordano Bruno was executed in 1600, by the Catholic Church, for advocating Copernican theory. The Salem witch trials took place between February 1692 and May 1693. Absolutely no one was worried about being mistaken for a witch in 1869. I tried searching the subject matter in several different ways. Einstein never comes up as a significant contributor to our understanding of the atom.
I've seen "entrance" exams from other ivy league schools from this time period which were very difficult especially with just understanding the English that was used at those times.
A few things. MIT was not as renowned during that time as it is now. I remember the likes of Feynman and Gellmann both being disappointed when they had to go to MIT for their undegrad and graduate studies, respectively. Also, this is just one section of the exam. I would gather that there was an analytic geometry section that was very difficult. Moreover, I believe during the 1800 is when mathematics, as we know today, in terms of notation, topics taught in school, etc., was properly "packaged."
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I'm getting admission to MIT this year 🎉❤ so like this comment 😊
Congratulations!!
Why?
@@Peter-q8v6v 😆😅🤣😂
In the US this is typically covered around ages 11 to 13 (grades 6 to 8), depending on the school.
In india also.
Can't believe it's this simple!!
I think you have to factor in the school leaving age in 1869, as far as I can tell, in a 2 minute search, it was 10 or 11. Therefore the very basics of algebra would have been all that was taught to most kids, if any.
It wasn't an engineering school back then and it wasn't more complicated elsewhere in the world
Thanks Ellie!
Keep 'em coming!
Will do! 🤩
IMMENSE THANKS and GRATITUDE for YOUR WORK)
I follow your channel from Malawi. Great work you’re doing ❤
Mathematicians are every where, and we all speak the same language. Greetings from Denmark 🙂
When students in the USA would learn the (very) basic algebra needed to do well on the exam changed in the early 1960 because of the space race. Prior to 1960, most high school students would learn about this in their first or second year. After 1960, there was a push for more rigorous math and science education in the US. For math, this came about with the some what infamous School Mathematic Study Group (SMSG - some math, some garbage). With this, the techniques needed to solve the problems would have moved to the 7th or 8th grade.
Historically, you are correct that the timeline for teaching this shifted in the 1960s. But as a former math teacher myself, I'd say 7th grade would only happen for most of these topics for very advanced students. Typically, the first year of algebra is taught in 8th grade for better students, though some US students may not get it until 9th grade. And while most of the tools necessary to solve most of these problems are theoretically covered in algebra 1, frankly I doubt most average students would be able to score well on a test like this until their second year of algebra, which may not happen until 9th or 10th grade (or even later for some less talented students).
In particular, the algebra of combining fractions as in #5 and factorizing a difference of squares involving multiple variables and higher powers as in #4 would likely be viewed as quite challenging for most first year algebra students in the US. #3 would likely trip up a lot more students even beyond algebra 2, in that they may not recognize that (a+b) needs to be a factor of one of the terms to be multiplied, which could lead to a lot of excess computation and confusion.
To be perfectly frank, I recently taught (past few years) some beginning calculus students in the first year of college at a rather decent school, and I doubt that more than around half of them could have got a perfect score on this exam. Many would be stumped by problems involving algebra and fractions. Which was really distressing to me, but that's the state of math education in the US right now. But yes, in most cases students should theoretically be introduced to most concepts necessary to solve these problems by around 8th or 9th grade (ages 13-15). Many would not be fluent in these techniques until a year or two later.
@@BobJones-rs1sd Thank you for the feedback.I was in the 7th grade when the SMSG revolution occurred (along with similar changes to science curriculum). It was an exciting time for me as I went from hating Math which went from rote use of the standard algorithms for arduous computations to learning what math was really about. I went on to become a Mathematician (My interests are in model theory and the mathematical underpinnings of LLMs). While I have taught, it has mostly been upper division undergrad and grad students. So I can't speak to your experience with math as it is taught today in K-12 schools.
I would point out that math and science education changed again with the "No Child Left Behind" update that led to common core. This, as I am sure you are aware occurred in 2001 and resulted in a changes in how most subjects are taught, including math. I believe that this changed the focus in many school districts from focusing on understanding to getting good schools on the assessment tests which I believe has ties to funding.. Having a daughter who went to school after the NCLB changes, I believe that where the child went to school would determine when a student would be able to solve the problems; which I believe is the point you are making.
So elementary, I wish I had been there😅
love your videos about maths and coding i follow your channel from morocco
Thank you so much for following my channels all the way from Morocco 🥺
I think I was 13 or maybe 14 when I did this at school in the UK but it's hard to remember because I'm of retirement age now.
I wonder how much time was allocated to this paper? It would also be nice to know what other sections there were.
Lady Ellie, you shuld try solve Riemann Hypothesis😁
I got 6 solutions for the first one. Ik were prolly going for the principle root (15) but still. Also here’s the solutions if any are wrong pls tell me cause im just 16 and don’t take any math classes: 15, -3, 21+2i✔️3, 21-2i✔️3, 27+2i✔️3, 27-2i✔️3
High school algebra in 1961.
Math, Chico. It never lies.
If i have your degree i make courses of math for different exams especially indian compt. Exams and sell . If your course price for math is assume 10k this should consume by 15000 indian you make 150000000 rs in 1 year hardworking to desine your course.
Were the students allowed to use a calculator when taking the test?
Is there have no question from calculas?
Good work Eli, I follow your videos from Iraq
Thank you for supporting my channel ☺️
Could you please tell me the list of maths book that you study-abhihiro
My gosh, a minute and a half to explain over and over what it is and start the first question?
Can you teach calculas on your channel please.
Do you regret going for maths major while you could've done something else? And what would it be? I'm currently in my first year in Mechanical engineering and I like maths so much!
I definitely don’t regret studying mathematics but there are things I’d have definitely done differently during that time! I’ll make a video on this! I also found a way to do my other passions alongside my degree :)
@@EllieSleightholm Will be waiting for it!!
So you are telling me I could have been accepted at MIT back in 1869?
I’m currently in middle school and I am able to solve all these questions
At that time, if you said that atoms existed, it would be an enormous blasphemy to reduce divine creation to small balls or very small blocks. And you, with your extraordinary intelligence, should be careful not to be mistaken for a witch!! 😁😁😆❤
Leucippus of Miletus (5th century bce) is thought to have originated the atomic philosophy. His famous disciple, Democritus of Abdera, named the building blocks of matter atomos, meaning literally “indivisible,” about 430 bce.
@@davidnewell3232 Yes, but the idea of the atom was only established in the scientific community, and in fact unquestionably accepted in society with Einstein's publications on Brownian movement, until then everything was not about ideas.
@@davidnewell3232 By the way, this publication by Einstein came after this examination of our dear Ellie Video, that is, at the time of this examination the idea of atoms was not openly accepted as it is today.
@@virais4605 The "reduc(tion of) divine creation to small balls or very small blocks" had been, at that point, understood for thousands of years of years. Avagadro was scaling up from molecular weights. In 1811, he published "Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons. Lavoisier and Proust had resoned the conservation of elements in chemical reactions decades earlier. Dalton had labeled them as indivisible and indestructible particles, each with unique characteristics. Science was much more familiar with the building blocks of matter than you suggest. The murder of 80,000 people believed to be witches took place between approximately 1500 and 1660 in Europe. Giordano Bruno was executed in 1600, by the Catholic Church, for advocating Copernican theory. The Salem witch trials took place between February 1692 and May 1693. Absolutely no one was worried about being mistaken for a witch in 1869. I tried searching the subject matter in several different ways. Einstein never comes up as a significant contributor to our understanding of the atom.
That has to be a hoax...no university exam, even back then was that easy, surely (??!!)
I've seen "entrance" exams from other ivy league schools from this time period which were very difficult especially with just understanding the English that was used at those times.
MIT was not an engineering university back then
❤ love you
Love you Ellie from india
A few things. MIT was not as renowned during that time as it is now. I remember the likes of Feynman and Gellmann both being disappointed when they had to go to MIT for their undegrad and graduate studies, respectively. Also, this is just one section of the exam. I would gather that there was an analytic geometry section that was very difficult. Moreover, I believe during the 1800 is when mathematics, as we know today, in terms of notation, topics taught in school, etc., was properly "packaged."
I give this to my grade 7 students in pakistan what is this 😅
And what was taught in South Asian madrassas back in the 19th century ?
Given the state of Pakistan, you don't have brilliant engineers
love you ellie from israel
My brother I'm From Ethiopia ❤❤🇮🇱 ❤
Family of Queen sheba and King Solomon
Thank you for supporting my channel ☺️
i'm from israel too
Free Palestine 🇵🇸🇵🇸 Israel doesn't even exist 😂😂
@@leagueofstealth3747
He didn't even cause the war