Modern math
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- Start date
Whoah, whoah.....WOOOOOOAH now!
I believe the Terms of Use for this site specifically state "NO MATH"
I believe the Terms of Use for this site specifically state "NO MATH"
- Thread starter
- #3
2+2=5...for extremely large values of 2.
These days, as long as you try really hard, getting the correct answer is not really a measure of success.
Tell that to structural engineers, surgeons, men atop space vehicles, etc.
Tell that to structural engineers, surgeons, men atop space vehicles, etc.
I saw a math question that was phrased as per the following....
"Use the repeated addition strategy to solve: 5x3"
The student answered "5+5+5=15"
Smart kid, I thought....
But it's wrong? Apparently the correct answer is "3+3+3+3+3 =15".
I now understand why and how each answer is right/wrong (you're adding 3 five times, but I don't understand how this is a useful method of teaching math. I was always taught that the sum of a multiplication problem works the same both ways when multiplying two numbers. That's what stumps me.
"Use the repeated addition strategy to solve: 5x3"
The student answered "5+5+5=15"
Smart kid, I thought....
But it's wrong? Apparently the correct answer is "3+3+3+3+3 =15".
I now understand why and how each answer is right/wrong (you're adding 3 five times, but I don't understand how this is a useful method of teaching math. I was always taught that the sum of a multiplication problem works the same both ways when multiplying two numbers. That's what stumps me.
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The new process for teaching math, as well meaning as it may be, is summed up as thus: We'll teach you how to do math mentally, but first you must show your work visually, and your work must match my preferred method. Also, visual work should not use numbers. Apples, Animals, and Shapes are my preferred method.
Can someone explain why my son, who is in kindergarten, brought home geometry homework this week? And when I say geometry, I specifically mean concepts that I didn't formally learn until the 10th grade.
Actually, don't explain it... I don't want anyone to get banned.
Don't you love that?
In an effort to make this more glamorous or sexy, some education guru had to come up with the concept of "repeated addition strategy." What a load of Bravo Sierra.
Just memorize your multiplication tables and mystery solved.
For some things, rote learning is far and away the best solution, but it is not glamorous or trendy.
In an effort to make this more glamorous or sexy, some education guru had to come up with the concept of "repeated addition strategy." What a load of Bravo Sierra.
Just memorize your multiplication tables and mystery solved.
For some things, rote learning is far and away the best solution, but it is not glamorous or trendy.
Math Teacher: If I give you 6 cats, how many cats would you have?
Student: 7
Math Teacher: That's incorrect. You must be misunderstanding me. Let's say I have 4 apples and I hand them to you. How many apples do you have?
Student: 4
Math Teacher: Correct. Why do you think you would have 7 cats?
Student: I already own a cat.
Student: 7
Math Teacher: That's incorrect. You must be misunderstanding me. Let's say I have 4 apples and I hand them to you. How many apples do you have?
Student: 4
Math Teacher: Correct. Why do you think you would have 7 cats?
Student: I already own a cat.
You're both right, the teacher is just hard headed. This is a ridiculous way to teach math though. What does the kid's homework look like with several questions along the lines of, "Use the repeated strategy to solve: 100x500?" It'll be a bunch of pages of writing down a lot of repeating numbers. A young MicBaldy would've said screw it to that type of homework.
Too.....
Much..........
Math...................
Aaaaaaaaarrrgh!
Much..........
Math...................
Aaaaaaaaarrrgh!
And here is the picture of the 5x3 question the kid who got this wrong on his test...
Did you notice the kids answer to the array was also wrong!? Now it did not say the answer should be displayed vertically or horizontally so the kids answer is technically correct
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I agree, that teacher is a real delta bravo. What in the world has happened to math? Looking at that quiz, it seems that teachers just want kids to be able to count now. The kid had to actually draw 7 pans with 4 cupcakes in each pan...
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Yeah, I'm totally lost trying to help my kid with 4th grade math these days. I'm no math whiz but I did at least get through a couple Calculus classes. The teachers want them to use 3 or 4 different methods to solve the same problem. To me it makes sense that maybe different kids will do better in one way or another so fine, have them figure out which method works for them. But after they figure that out, why force them to use the method that doesn't work well for them? Weird.
Different strokes for different districts.
In two different schools four different teachers made my kids learn their multiplication tables.
If they're not doing this, organize your fellow parents and get your school policy changed.
In two different schools four different teachers made my kids learn their multiplication tables.
If they're not doing this, organize your fellow parents and get your school policy changed.
Most mathematicians are familiar with -- or have at least seen references in the literature to -- the equation 2 + 2 = 4. However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantitiy, this history has a real part and an imaginary part; we shall deal exclusively with the latter here.
Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results.
Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements," and nothing more was heard of 2 + 2 = 5 for several centuries.
Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname "Blockhead." By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one.
Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it does." However, others objected that his argument was somewhat less than totally rigorous. Apparently, Fermat had a more rigorous proof which was to appear as part of a book, but it and other material were cut by the editor so that the book could be printed with wider margins.
Between the fact that no definitive proof of 2 + 2 = 5 was available and the excitement of the development of calculus, by 1700 mathematicians had again lost interest in the equation. In fact, the only known 18th-century reference to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it in an old manuscript, wryly commented, "Well, now I know where all the departed quantities went to -- the right-hand side of this equation." That witticism so impressed California intellectuals that they named a university town after him.
But in the early to middle 1800's, 2 + 2 began to take on great significance. Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean 2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great confusion as to the actual value of 2 + 2. Because of changing opinions on this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years later to yield, instead, the 5-color theorem. Dedekind entered the debate with an article entitled "Was ist und was soll 2 + 2?"
Frege thought he had settled the question while preparing a condensed version of his "Begriffsschrift." This condensation, entitled "Die Kleine Begriffsschrift (The Short Schrift)," contained what he considered to be a definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned mathematics altogether and went into university administration.
Faced with this profound and bewildering foundational question of the value of 2 + 2, mathematicians followed the reasonable course of action: they just ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing being done with its rival equation during the 20th century. There had been rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first forty pages taken up by the symbolic expression for the number five), but those rumor remained unconfirmed. Recently, though, there have been reported computer-assisted proofs that 2 + 2 = 5, typically involving computers belonging to utility companies. Perhaps the 21st century will see yet another revival of this historic equation.
The above was written by Houston Euler.
Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results.
Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements," and nothing more was heard of 2 + 2 = 5 for several centuries.
Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname "Blockhead." By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one.
Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it does." However, others objected that his argument was somewhat less than totally rigorous. Apparently, Fermat had a more rigorous proof which was to appear as part of a book, but it and other material were cut by the editor so that the book could be printed with wider margins.
Between the fact that no definitive proof of 2 + 2 = 5 was available and the excitement of the development of calculus, by 1700 mathematicians had again lost interest in the equation. In fact, the only known 18th-century reference to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it in an old manuscript, wryly commented, "Well, now I know where all the departed quantities went to -- the right-hand side of this equation." That witticism so impressed California intellectuals that they named a university town after him.
But in the early to middle 1800's, 2 + 2 began to take on great significance. Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean 2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great confusion as to the actual value of 2 + 2. Because of changing opinions on this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years later to yield, instead, the 5-color theorem. Dedekind entered the debate with an article entitled "Was ist und was soll 2 + 2?"
Frege thought he had settled the question while preparing a condensed version of his "Begriffsschrift." This condensation, entitled "Die Kleine Begriffsschrift (The Short Schrift)," contained what he considered to be a definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned mathematics altogether and went into university administration.
Faced with this profound and bewildering foundational question of the value of 2 + 2, mathematicians followed the reasonable course of action: they just ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing being done with its rival equation during the 20th century. There had been rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first forty pages taken up by the symbolic expression for the number five), but those rumor remained unconfirmed. Recently, though, there have been reported computer-assisted proofs that 2 + 2 = 5, typically involving computers belonging to utility companies. Perhaps the 21st century will see yet another revival of this historic equation.
The above was written by Houston Euler.
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- #18
That there was brilliant.
My daughter is 7 she comes home and I help her with homework. Some of the math she comes home with I truly do not understand. The rest is the longest most tedious way to work a problem. No professional meaning engineer, physicist types could ever afford to draw out simple math like that. I love the op!
Georg:
That's a good one!
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People say I'm considered to be smart, but its better to be [/FONT][FONT=&]sharp as a tack and keen as mustard. CBJ[/FONT]Similar threads
