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Post by katlady on Sept 6, 2022 23:36:56 GMT
I am not a theory person. I can do the math calculations, I can read music, I can play instruments, but don't ask me about theory. I can't explain a mathematical theorem, I can't tell you what key a song is in, I don't know how to play a piece in a different key without it being explicitly written out. Maybe math and music do go together because I understand both on the same level, the practical level.  |
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Post by busy on Sept 6, 2022 23:54:37 GMT
I loved math in high school and college. I took math for fun in college (Honors Calculus II, Linear Algebra, Multivariable Calculus) until I got to Advanced Linear Algebra second semester of sophomore year. That's when my brain hit a wall. No matter how hard I worked, I just couldn't master it. I eked out a B and literally that was the best I could do. I didn't take more math after that.
I've enjoyed learning math in a new way along with DS. I personally think they are taught it far better these days - there's a lot more transferable understanding than the way we learned most of math, which was a lot of memorization. Some of the processes haven't been immediately logical to me, but once he explained them, they made sense.
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Post by hopemax on Sept 7, 2022 0:26:45 GMT
As for the OP's confusion with the multiplication of negative numbers, the real world example I usually see is: debts and bank accounts. Let's say you have a $120 cable bill every month. Mathematically, that part is easy to represent (I hope)
-$120
A year has 12 months so if you wanted to know the effect of your cable bill on your bank account at the end of a year that should be fairly straightforward too (I hope)
12 x (-$120) = -$1440 A decrease of $1440.
Now, lets say *I* pay the $120 for 6 months, not you.
We still have a -$120 which represents the bill. It's not a zero, just because you aren't paying it. The bill still exists with your name on it. Real world, you might just not write the bill in your check ledger. However, that's a shortcut and doesn't mathematically represent your financial obligation as far as the cable company is concerned. So how do we represent "not you" for 6 months? A convention is sticking the negative in front of the number of months.
So -6 = "not you" for 6 months
-6 x -$120 = $720 This is a representation of the money your bank account didn't go down to cover the obligation of your cable bill. It should be positive. Me paying your bill doesn't cost you money, which is what the other possible option -$720 would represent.
What we're often trying to do is demonstrate a change in some condition (like who pays a debt, you or not you) and show that mathematically.
Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces".
So I don't know if these examples help visualize what is trying to be represented by negative numbers. If I ask you why is a cup a cup and a cat a cat what would you say? Like language, sometimes at the end of the day math is just about agreed upon conventions. The real answer to why is found in the algebraic distributive property, and remember multiplication is just repeated addition or subtraction. Just don't ask about imaginary numbers!
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Post by Merge on Sept 7, 2022 0:42:23 GMT
I am not a theory person. I can do the math calculations, I can read music, I can play instruments, but don't ask me about theory. I can't explain a mathematical theorem, I can't tell you what key a song is in, I don't know how to play a piece in a different key without it being explicitly written out. Maybe math and music do go together because I understand both on the same level, the practical level. Eh, transposing on the fly is a pretty advanced skill even for strong musicians. (Unless you play guitar and are reading a lead sheet and can just pop on a capo.) |
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Post by monklady123 on Sept 7, 2022 0:58:12 GMT
As for the OP's confusion with the multiplication of negative numbers, the real world example I usually see is: debts and bank accounts. Let's say you have a $120 cable bill every month. Mathematically, that part is easy to represent (I hope) -$120 A year has 12 months so if you wanted to know the effect of your cable bill on your bank account at the end of a year that should be fairly straightforward too (I hope) 12 x (-$120) = -$1440 A decrease of $1440. Now, lets say *I* pay the $120 for 6 months, not you. We still have a -$120 which represents the bill. It's not a zero, just because you aren't paying it. The bill still exists with your name on it. Real world, you might just not write the bill in your check ledger. However, that's a shortcut and doesn't mathematically represent your financial obligation as far as the cable company is concerned. So how do we represent "not you" for 6 months? A convention is sticking the negative in front of the number of months. So -6 = "not you" for 6 months -6 x -$120 = $720 This is a representation of the money your bank account didn't go down to cover the obligation of your cable bill. It should be positive. Me paying your bill doesn't cost you money, which is what the other possible option -$720 would represent. What we're often trying to do is demonstrate a change in some condition (like who pays a debt, you or not you) and show that mathematically. Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces". So I don't know if these examples help visualize what is trying to be represented by negative numbers. If I ask you why is a cup a cup and a cat a cat what would you say? Like language, sometimes at the end of the day math is just about agreed upon conventions. The real answer to why is found in the algebraic distributive property, and remember multiplication is just repeated addition or subtraction. Just don't ask about imaginary numbers!  |
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scrappinwithoutpeas
Pearl Clutcher
Posts: 3,004 
Location: Northern Virginia
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Post by scrappinwithoutpeas on Sept 7, 2022 1:28:47 GMT
hopemax, I love your explanation about multiplying negative numbers. Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces". The quoted portion is one reason why it's helpful for math students to learn how the numbers relate using a number line. If they learn to do things on a number line fairly early on in the math building blocks stages they'll have an easier time visualizing concepts like operations with negative numbers. Way back in the dark ages when my mom taught elementary school, she was a math specialist and was very big on the use of manipulatives and number lines (especially in K-3) - and this was in the early and mid-70s when their use was considered new and innovative, LOL. I was lucky enough to have had some excellent math teachers, and didn't struggle much with math until the latter stages of calc - I was initially an engineering major and ended up switching to computer science just before I would have had to take differential equations. (The switch was more about loving computer programming and hating physics; it really didn't have much to do with the math...although I was just as happy not to have to take Diff EQs.)
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seaexplore
Prolific Pea
Posts: 8,838
Apr 25, 2015 23:57:30 GMT
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Post by seaexplore on Sept 7, 2022 1:33:16 GMT
I have been a math teacher grades 6-8 since 2000.
This year I am a continuation high school integrated 1 math teacher,
I failed algebra 1 in 8th grade.
I greatly dislike geometry, trig, calculus, and statistics. Lol
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Post by monklady123 on Sept 7, 2022 1:40:09 GMT
Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces". Okay, so when I unglazed my eyes and read this again it does make sense. But my question still is "why?" Why not just say "move right 3 spaces"? Same with multiplying negative numbers... why ask someone what -5 x -3 is? why not just ask what 5x3 is? Also, the part of your post about the cable bill makes no sense to me. Too many words. But thank you for trying!  |
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Dalai Mama
Drama Llama
La Pea Boheme
Posts: 6,985
Jun 26, 2014 0:31:31 GMT
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Post by Dalai Mama on Sept 7, 2022 1:41:28 GMT
I love math like statistics and algebra and basic functions, but geometry makes about as much sense as chemistry to me.which is not at all. I do cross sums for fun on my iPad, but those are just basic math. I don’t know who said math and music go hand in hand, but I agree with the others they don’t. I know the names of the notes if I think about it (Every good boy does fine and FACE ) but I understand music at all. I like the way explained it your student today! The way they do math today is different, but it dies make a lot of sense and makes it easier to understand the further you go. I teach music theory - it's 100% math. Intervals, chord inversions, scale degrees, rhythm, meter, key signatures - all math. Invert a simple interval, the two intervals add to 9. Subtract 7 from a compound interval and you get the simple interval. And don't even get me started on frequencies and pitch. |
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Post by hopemax on Sept 7, 2022 1:52:43 GMT
hopemax , I love your explanation about multiplying negative numbers. Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces". The quoted portion is one reason why it's helpful for math students to learn how the numbers relate using a number line. If they learn to do things on a number line fairly early on in the math building blocks stages they'll have an easier time visualizing concepts like operations with negative numbers. Way back in the dark ages when my mom taught elementary school, she was a math specialist and was very big on the use of manipulatives and number lines (especially in K-3) - and this was in the early and mid-70s when their use was considered new and innovative, LOL. I was lucky enough to have had some excellent math teachers, and didn't struggle much with math until the latter stages of calc - I was initially an engineering major and ended up switching to computer science just before I would have had to take differential equations. (The switch was more about loving computer programming and hating physics; it really didn't have much to do with the math...although I was just as happy not to have to take Diff EQs.) Thank you. Sometimes with these threads I wonder if I should stick my neck out, because I'm not a teacher, and as I mentioned previously, it's been a long time since I've had to even think about advanced math concepts. So are my memories But I think our lack of understanding math concepts is hurting our ability as a society to make well-informed decisions. We saw that with infectious diseases and exponential functions. "I don't understand, so let's do nothing at all" is going to kill us. However, apparently, it didn't help OP. It's funny reading where other people reached their limits. I was in the honors track for college math. Multi-variable calculus was my most shaky. Although, I could solve homework problems and explain them for my roommates who were in the non-honors multi-variable class. Linear Algebra was better, but Differential Equations just clicked. I had a friend in these classes who just understood everything all the time, but it was Diffy Q's that I could match him, and even scored higher on one test than he did! |
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Post by katlady on Sept 7, 2022 1:59:51 GMT
Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces". Okay, so when I unglazed my eyes and read this again it does make sense. But my question still is "why?" Why not just say "move right 3 spaces"? Same with multiplying negative numbers... why ask someone what -5 x -3 is? why not just ask what 5x3 is? Also, the part of your post about the cable bill makes no sense to me. Too many words. But thank you for trying! Let me try! You have a bucket that today has 300 gallons in it. Everyday for the past 3 days (-3) you took out 10 gallons (-10). So, that is -3 days x -10 gallons = 30 gallons taken out. So, three days ago there was 300+30=330 gallons of water in the bucket. Or: If you have a debt and someone relieves you of the debt, you've gained since you no longer have a debt. A grammar example: "not uncommon" = "common" The "not" cancelled the "un" and the statement became positive. |
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Post by katlady on Sept 7, 2022 2:00:52 GMT
I love math like statistics and algebra and basic functions, but geometry makes about as much sense as chemistry to me.which is not at all. I do cross sums for fun on my iPad, but those are just basic math. I don’t know who said math and music go hand in hand, but I agree with the others they don’t. I know the names of the notes if I think about it (Every good boy does fine and FACE ) but I understand music at all. I like the way explained it your student today! The way they do math today is different, but it dies make a lot of sense and makes it easier to understand the further you go. I teach music theory - it's 100% math. Intervals, chord inversions, scale degrees, rhythm, meter, key signatures - all math. Invert a simple interval, the two intervals add to 9. Subtract 7 from a compound interval and you get the simple interval. And don't even get me started on frequencies and pitch. OMG! Yes! Intervals, inversions, circle of fifths - they all make my head spin! |
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Post by worrywart on Sept 7, 2022 2:12:47 GMT
Proof using multiply and division fact family
2 (-3) = -6 two groups of -3 is -6 and multiplication works both ways so
(-3) 2= -6
therefore
-6 / 2 = -3 and so
-6 / -3 = 2 proof that a negative divided by a negative is positive
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Post by amp on Sept 7, 2022 2:30:03 GMT
I am a total math nerd and can easily make more money tutoring than at my real job 😂 I started college as a psychology major and ended up with a BS in mathematics when I realized I was taking math classes to keep my GPA up. Oops! I come from a long line of engineers though, numbers (even imaginary ones and Greek letters!) just made sense to me. DS graduated with a degree in Computer Engineering from a top school this past spring; it was the math-heaviest engineering degree they had. DH also has 2 degrees in Finance so that probably helps too. The nerdy genes carry on! Let me know if you get stuck solving any equations or word problems! Same! I'm glad I'm not alone. I <3 Math...but I'm an engineer, so it works for me.  Seriously. I think what I love about math is that it is so logical and structured and makes sense. The key to doing well at Math is to have one or more good teachers, and to do lots of problems. I remember the first time I saw a word problem, I about died and prayed this unit would be over quickly. I think it was around 4th grade. Obviously, word problems never went away, but I did enough of them they got easy. I hope this helps. |
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scrappinwithoutpeas
Pearl Clutcher
Posts: 3,004
Location: Northern Virginia
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Post by scrappinwithoutpeas on Sept 7, 2022 2:32:54 GMT
It's funny reading where other people reached their limits. I was in the honors track for college math. Multi-variable calculus was my most shaky. Although, I could solve homework problems and explain them for my roommates who were in the non-honors multi-variable class. Linear Algebra was better, but Differential Equations just clicked. I had a friend in these classes who just understood everything all the time, but it was Diffy Q's that I could match him, and even scored higher on one test than he did! I had a lot of people tell me that Diff EQs was simpler than MV calc so I may well have had an easier time with it. (The world will never know, LOL.) I do know that for me, it was Linear Algebra that just clicked and I helped a lot of my classmates with that. |
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Post by 950nancy on Sept 7, 2022 2:39:44 GMT
I loved math in university, but the Calculus my kid has been doing for her Engineering degree is on a whole other level 😳😳😳 The first time I looked through my son's Calculus textbook, I said I thought it looked like a coloring book. So many pretty designs that I had no idea what you would do with them. My kid was beyond me in math by freshman year in high school. Good thing was he was so far ahead in Calc by the time he went to college. |
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Post by Zee on Sept 7, 2022 3:09:30 GMT
hopemax , I love your explanation about multiplying negative numbers. The quoted portion is one reason why it's helpful for math students to learn how the numbers relate using a number line. If they learn to do things on a number line fairly early on in the math building blocks stages they'll have an easier time visualizing concepts like operations with negative numbers. Way back in the dark ages when my mom taught elementary school, she was a math specialist and was very big on the use of manipulatives and number lines (especially in K-3) - and this was in the early and mid-70s when their use was considered new and innovative, LOL. I was lucky enough to have had some excellent math teachers, and didn't struggle much with math until the latter stages of calc - I was initially an engineering major and ended up switching to computer science just before I would have had to take differential equations. (The switch was more about loving computer programming and hating physics; it really didn't have much to do with the math...although I was just as happy not to have to take Diff EQs.) Thank you. Sometimes with these threads I wonder if I should stick my neck out, because I'm not a teacher, and as I mentioned previously, it's been a long time since I've had to even think about advanced math concepts. So are my memories But I think our lack of understanding math concepts is hurting our ability as a society to make well-informed decisions. We saw that with infectious diseases and exponential functions. "I don't understand, so let's do nothing at all" is going to kill us. However, apparently, it didn't help OP. It's funny reading where other people reached their limits. I was in the honors track for college math. Multi-variable calculus was my most shaky. Although, I could solve homework problems and explain them for my roommates who were in the non-honors multi-variable class. Linear Algebra was better, but Differential Equations just clicked. I had a friend in these classes who just understood everything all the time, but it was Diffy Q's that I could match him, and even scored higher on one test than he did! I'm not good at math but I certainly understand infectious diseases and how they spread. You don't need to understand advanced math to grasp how disease spread works. And it was more often a case of "that inconveniences me" rather than "i don't understand so let's do nothing" that hindered Covid response. |
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Post by Zee on Sept 7, 2022 3:13:41 GMT
I am a total math nerd and can easily make more money tutoring than at my real job 😂 I started college as a psychology major and ended up with a BS in mathematics when I realized I was taking math classes to keep my GPA up. Oops! I come from a long line of engineers though, numbers (even imaginary ones and Greek letters!) just made sense to me. DS graduated with a degree in Computer Engineering from a top school this past spring; it was the math-heaviest engineering degree they had. DH also has 2 degrees in Finance so that probably helps too. The nerdy genes carry on! Let me know if you get stuck solving any equations or word problems! Same! I'm glad I'm not alone. I <3 Math...but I'm an engineer, so it works for me. Seriously. I think what I love about math is that it is so logical and structured and makes sense. The key to doing well at Math is to have one or more good teachers, and to do lots of problems. I remember the first time I saw a word problem, I about died and prayed this unit would be over quickly. I think it was around 4th grade. Obviously, word problems never went away, but I did enough of them they got easy. I hope this helps. No that does not help, because you truly don't understand what it's like to NOT UNDERSTAND how algebra works. Plus I don't care because it's not interesting or relevant to my daily activities (other than in whatever ways I'm benefited by sometime else getting it and using it to advance tech--I've never needed it directly in my career). You sound suspiciously like my DH, who is an engineer and likes math and thinks it's easy, but he's lightly snoring next to me so I guess you're not him 🤣 |
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Post by hopemax on Sept 7, 2022 5:42:33 GMT
Thank you. Sometimes with these threads I wonder if I should stick my neck out, because I'm not a teacher, and as I mentioned previously, it's been a long time since I've had to even think about advanced math concepts. So are my memories But I think our lack of understanding math concepts is hurting our ability as a society to make well-informed decisions. We saw that with infectious diseases and exponential functions. "I don't understand, so let's do nothing at all" is going to kill us. However, apparently, it didn't help OP. It's funny reading where other people reached their limits. I was in the honors track for college math. Multi-variable calculus was my most shaky. Although, I could solve homework problems and explain them for my roommates who were in the non-honors multi-variable class. Linear Algebra was better, but Differential Equations just clicked. I had a friend in these classes who just understood everything all the time, but it was Diffy Q's that I could match him, and even scored higher on one test than he did! I'm not good at math but I certainly understand infectious diseases and how they spread. You don't need to understand advanced math to grasp how disease spread works. And it was more often a case of "that inconveniences me" rather than "i don't understand so let's do nothing" that hindered Covid response. So if I told you that there is a new disease with an estimated incubation period of X and an estimated CFR of Y and that we needed a budget of Z in order to prepare a response, of a specified scale and ready at a specified date, you would be able to grasp whether the budget and timeline I gave you was inadequate, adequate or outrageous? If so, that's great but many people demonstrated a failure to do that. The number of times ID people had to explain that a less deadly disease did not automatically mean that fewer people would die over time, also demonstrates the difficulty other people have in visualizing the math of disease. But again, if you could, great! |
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Post by hopemax on Sept 7, 2022 5:50:35 GMT
Other examples I've seen are used to indicate changes in direction or rotation. Where right is represented as a (+) and left is (-). If I say move "not left 3 spots", in the real world, you would move right 3 spots, but I didn't tell you to move right three spots, so to mathematically represent what I specifically asked it wouldn't be to start and finish with +3 it would be -(-3) where the first - represents "not" and the -3 represents "left three" and then resolve it to +3 or "right 3 spaces". Okay, so when I unglazed my eyes and read this again it does make sense. But my question still is "why?" Why not just say "move right 3 spaces"? Same with multiplying negative numbers... why ask someone what -5 x -3 is? why not just ask what 5x3 is? Also, the part of your post about the cable bill makes no sense to me. Too many words. But thank you for trying! I'll take a last stab... I am going to WDW on Thursday and I have to pack, so no pea-ing for awhile. In a bank ledger, positive and negative numbers have specific meanings. Dropping the negative affects another person's ability to read the ledger and accurately calculate the current balance. If you write $5 but what you really meant was -$5, the person redoing the calculation is going to get an incorrect answer. The ability for the next person to understand and duplicate your work is critical. Not just accounting, but physics too. Up/down, right/left, debt/savings, positive/negative charge. We can't just drop negatives because they don't seem important, because in dropping them, you lose part of the meaning. -5 is not 5 and -3 is not 3, we shouldn't get in a habit of treating them as the same, because there will be situations when we can't. That's what I was trying to do with the cable bill. Demonstrate not just the total value of the cable bills over six months, but also who paid. Who pays the bill, has a real impact on the balance. When the account holder pays, it goes down. When another person pays the account balance doesn't change. Someone still might want to know or need to record how much money was saved by the account owner. So how would you mathematically represent all of this? No words, no explanation, only math. I represented it as the bill/month: -$120, as debts are always recorded as negative numbers in accounting, the number of months: 6, and the payer: (-) because it was not the account owner. If it was the account owner I would represent the payer as (+). -$120 x -6 = a savings of $720. You didn't answer my question why we call a cup a cup and not some other word  . In reality, someone just decided, and then it became an established convention. In this case, according to the internets... a Chinese mathematician was the first to write down rules regarding negative numbers, originating for the need of a way to resolve merchant accounts, and money transferring through multiple hands. An Indian mathematician expanded on those and wrote "The product or quotient of two debts is one fortune." An Arabic mathematicians adopted the negative x negative = positive, in the development of algebra to get the math to work. The Greeks thought the concept of negative numbers absurd, and those thoughts lingered in European circles into the 17th century. But with all the advancements in mathematics, negative x negative = positive, the math always works and has held up over time, while European attempts to avoid the use of negative numbers did not. In the move right or left example, if I say "move 3 right" that proves that you understand "move 3 right." Maybe the next person you talk to can't remember the English word for right. So they say "move not left 3 ." Do you still comprehend how you need to move? We sometimes need more than one way to represent the same thing depending on the type of equations we need to solve. Sometimes we need placeholders (which is why we have imaginary numbers) to find solutions in complex applications. For example, Electrical engineering is loaded with imaginary numbers to assist in circuit design. Translating between words and their mathematical representations... The ol' annoying "word problem." In these simple examples it's easy to ask "why not just say" but in more complex modeling and applications, it's not so easy. Specific concepts have to be represented fully so they can be accounted for properly from start to finish. |
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Post by monklady123 on Sept 7, 2022 10:29:36 GMT
Proof using multiply and division fact family2 (-3) = -6 two groups of -3 is -6 and multiplication works both ways so (-3) 2= -6 therefore -6 / 2 = -3 and so -6 / -3 = 2 proof that a negative divided by a negative is positive Now that makes sense! We talk about fact families all the time when I sub in elementary school. I guess I just need to stop trying to figure out *why* something is the way it is, and just do the calculations. I mean, your explanation makes perfect sense on paper since I know the rules of a fact family... But my brain doesn't accept that two negatives can equal out to a positive. But -- at least when I take my unit test at Khan Academy I'm going to get all these questions correct! And in the end I don't really need to understand the "why", I just need to get the answer correct. |
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Post by monklady123 on Sept 7, 2022 10:32:37 GMT
You didn't answer my question why we call a cup a cup and not some other word . In reality, someone just decided, and then it became an established convention. Yes, someone just decided the meaning... but I've always thought numbers were more black and white than words. There are so many nuances to words, and many things aren't exactly as they might seem. But numbers are supposed to be logical! lol. And anyway, I love words, but don't love numbers.  |
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Post by monklady123 on Sept 7, 2022 10:44:01 GMT
Let me try! You have a bucket that today has 300 gallons in it. Everyday for the past 3 days (-3) you took out 10 gallons (-10). So, that is -3 days x -10 gallons = 30 gallons taken out. So, three days ago there was 300+30=330 gallons of water in the bucket. Or: If you have a debt and someone relieves you of the debt, you've gained since you no longer have a debt. A grammar example: "not uncommon" = "common" The "not" cancelled the "un" and the statement became positive. If I were editing someone's writing I would suggest they change "not uncommon" to say simply "common". But that's my preference for writing, although that would depend on what the context was. But it makes sense that the two negatives "not" and "un" cancel each other out to create a positive. Now for the water in a barrel -- if someone gave me a word problem that said "My water barrel has 300 gallons in it today. Every day we take out 10 gallons. How many gallons did I have three days ago?" I would think "10 gallons a day times 3 days equals 30 gallons, add 30 to my current 300 so three days ago I had 330 gallons." There isn't any need for negative numbers of any kind. I'm not trying to be difficult, but honestly I don't get it. Why is there a need for subtraction of any kind? I used multiplication (3x10) and addition (300+30). |
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Dalai Mama
Drama Llama
La Pea Boheme
Posts: 6,985
Jun 26, 2014 0:31:31 GMT
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Post by Dalai Mama on Sept 7, 2022 12:12:24 GMT
Okay, so when I unglazed my eyes and read this again it does make sense. But my question still is "why?" Why not just say "move right 3 spaces"? Same with multiplying negative numbers... why ask someone what -5 x -3 is? why not just ask what 5x3 is? Also, the part of your post about the cable bill makes no sense to me. Too many words. But thank you for trying! I'll take a last stab... I am going to WDW on Thursday and I have to pack, so no pea-ing for awhile. In a bank ledger, positive and negative numbers have specific meanings. Dropping the negative affects another person's ability to read the ledger and accurately calculate the current balance. If you write $5 but what you really meant was -$5, the person redoing the calculation is going to get an incorrect answer. The ability for the next person to understand and duplicate your work is critical. Not just accounting, but physics too. Up/down, right/left, debt/savings, positive/negative charge. We can't just drop negatives because they don't seem important, because in dropping them, you lose part of the meaning. -5 is not 5 and -3 is not 3, we shouldn't get in a habit of treating them as the same, because there will be situations when we can't. That's what I was trying to do with the cable bill. Demonstrate not just the total value of the cable bills over six months, but also who paid. Who pays the bill, has a real impact on the balance. When the account holder pays, it goes down. When another person pays the account balance doesn't change. Someone still might want to know or need to record how much money was saved by the account owner. So how would you mathematically represent all of this? No words, no explanation, only math. I represented it as the bill/month: -$120, as debts are always recorded as negative numbers in accounting, the number of months: 6, and the payer: (-) because it was not the account owner. If it was the account owner I would represent the payer as (+). -$120 x -6 = a savings of $720. You didn't answer my question why we call a cup a cup and not some other word . In reality, someone just decided, and then it became an established convention. In this case, according to the internets... a Chinese mathematician was the first to write down rules regarding negative numbers, originating for the need of a way to resolve merchant accounts, and money transferring through multiple hands. An Indian mathematician expanded on those and wrote "The product or quotient of two debts is one fortune." An Arabic mathematicians adopted the negative x negative = positive, in the development of algebra to get the math to work. The Greeks thought the concept of negative numbers absurd, and those thoughts lingered in European circles into the 17th century. But with all the advancements in mathematics, negative x negative = positive, the math always works and has held up over time, while European attempts to avoid the use of negative numbers did not. In the move right or left example, if I say "move 3 right" that proves that you understand "move 3 right." Maybe the next person you talk to can't remember the English word for right. So they say "move not left 3 ." Do you still comprehend how you need to move? We sometimes need more than one way to represent the same thing depending on the type of equations we need to solve. Sometimes we need placeholders (which is why we have imaginary numbers) to find solutions in complex applications. For example, Electrical engineering is loaded with imaginary numbers to assist in circuit design. Translating between words and their mathematical representations... The ol' annoying "word problem." In these simple examples it's easy to ask "why not just say" but in more complex modeling and applications, it's not so easy. Specific concepts have to be represented fully so they can be accounted for properly from start to finish. I have found my people.  |
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dlb
Shy Member
Posts: 14
Oct 2, 2018 14:54:25 GMT
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Post by dlb on Sept 7, 2022 13:00:40 GMT
I'll take a last stab... I am going to WDW on Thursday and I have to pack, so no pea-ing for awhile. In a bank ledger, positive and negative numbers have specific meanings. Dropping the negative affects another person's ability to read the ledger and accurately calculate the current balance. If you write $5 but what you really meant was -$5, the person redoing the calculation is going to get an incorrect answer. The ability for the next person to understand and duplicate your work is critical. Not just accounting, but physics too. Up/down, right/left, debt/savings, positive/negative charge. We can't just drop negatives because they don't seem important, because in dropping them, you lose part of the meaning. -5 is not 5 and -3 is not 3, we shouldn't get in a habit of treating them as the same, because there will be situations when we can't. That's what I was trying to do with the cable bill. Demonstrate not just the total value of the cable bills over six months, but also who paid. Who pays the bill, has a real impact on the balance. When the account holder pays, it goes down. When another person pays the account balance doesn't change. Someone still might want to know or need to record how much money was saved by the account owner. So how would you mathematically represent all of this? No words, no explanation, only math. I represented it as the bill/month: -$120, as debts are always recorded as negative numbers in accounting, the number of months: 6, and the payer: (-) because it was not the account owner. If it was the account owner I would represent the payer as (+). -$120 x -6 = a savings of $720. You didn't answer my question why we call a cup a cup and not some other word . In reality, someone just decided, and then it became an established convention. In this case, according to the internets... a Chinese mathematician was the first to write down rules regarding negative numbers, originating for the need of a way to resolve merchant accounts, and money transferring through multiple hands. An Indian mathematician expanded on those and wrote "The product or quotient of two debts is one fortune." An Arabic mathematicians adopted the negative x negative = positive, in the development of algebra to get the math to work. The Greeks thought the concept of negative numbers absurd, and those thoughts lingered in European circles into the 17th century. But with all the advancements in mathematics, negative x negative = positive, the math always works and has held up over time, while European attempts to avoid the use of negative numbers did not. In the move right or left example, if I say "move 3 right" that proves that you understand "move 3 right." Maybe the next person you talk to can't remember the English word for right. So they say "move not left 3 ." Do you still comprehend how you need to move? We sometimes need more than one way to represent the same thing depending on the type of equations we need to solve. Sometimes we need placeholders (which is why we have imaginary numbers) to find solutions in complex applications. For example, Electrical engineering is loaded with imaginary numbers to assist in circuit design. Translating between words and their mathematical representations... The ol' annoying "word problem." In these simple examples it's easy to ask "why not just say" but in more complex modeling and applications, it's not so easy. Specific concepts have to be represented fully so they can be accounted for properly from start to finish. I have found my people. This is my tribe too! |
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Post by candygurl on Sept 7, 2022 13:07:12 GMT
Haha feel the same way! I’ve googled the worksheets to find the answer key, helps a lot! I really don’t understand why they teach a different way because one time we raced to see who would get the answer first and the old way won. Oh well!
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Post by workingclassdog on Sept 7, 2022 13:12:06 GMT
I am slamming my head against the wall right now.
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bethany102399
Pearl Clutcher
Posts: 3,640
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Post by bethany102399 on Sept 7, 2022 13:39:30 GMT
I'm just about to run screaming out of this thread, but I did want to say I'm one of like 5 people who loves the way math is taught now. I sucked at memorization and basically got labeled "stupid" in elementary school because of it. Thank you late 70's early 80's. did all my math requirements at the community college level with a tutor over the summer just to get them done.
Flash forward to my own kids struggling and reading the worksheets it makes sense to me now! I also love Kahn as he walks you through the process of how to do whatever it is they want you to do. If I've got the process (and a calculator) I can get to the correct answer most of the time.
It's not about how fast, it's about understanding the why. If you can get kids to understand the why, then they can use that skill as math builds to bigger concepts. Even my artistic kid who dislikes math does ok in it as she gets the why, she just doesn't care for it.
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Post by amp on Sept 7, 2022 13:45:13 GMT
Same! I'm glad I'm not alone. I <3 Math...but I'm an engineer, so it works for me. Seriously. I think what I love about math is that it is so logical and structured and makes sense. The key to doing well at Math is to have one or more good teachers, and to do lots of problems. I remember the first time I saw a word problem, I about died and prayed this unit would be over quickly. I think it was around 4th grade. Obviously, word problems never went away, but I did enough of them they got easy. I hope this helps. No that does not help, because you truly don't understand what it's like to NOT UNDERSTAND how algebra works. Plus I don't care because it's not interesting or relevant to my daily activities (other than in whatever ways I'm benefited by sometime else getting it and using it to advance tech--I've never needed it directly in my career). You sound suspiciously like my DH, who is an engineer and likes math and thinks it's easy, but he's lightly snoring next to me so I guess you're not him 🤣Oh, that describes me...except I've been told I snore really loud. |
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Post by Zee on Sept 7, 2022 16:04:56 GMT
I'm not good at math but I certainly understand infectious diseases and how they spread. You don't need to understand advanced math to grasp how disease spread works. And it was more often a case of "that inconveniences me" rather than "i don't understand so let's do nothing" that hindered Covid response. So if I told you that there is a new disease with an estimated incubation period of X and an estimated CFR of Y and that we needed a budget of Z in order to prepare a response, of a specified scale and ready at a specified date, you would be able to grasp whether the budget and timeline I gave you was inadequate, adequate or outrageous? If so, that's great but many people demonstrated a failure to do that. The number of times ID people had to explain that a less deadly disease did not automatically mean that fewer people would die over time, also demonstrates the difficulty other people have in visualizing the math of disease. But again, if you could, great! If you broke those terms down for me in real numbers, sure. If you can't do that, you're not making your case very well. People don't need to be able to do the calculations themselves in order to understand what's needed, they just need the figures. That would be YOUR job. Acting as though people are too stupid to grasp the concepts without being able to do advanced calculations is pretty simplistic. |
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. In reality, someone just decided, and then it became an established convention. In this case, according to the internets... a Chinese mathematician was the first to write down rules regarding negative numbers, originating for the need of a way to resolve merchant accounts, and money transferring through multiple hands. An Indian mathematician expanded on those and wrote "The product or quotient of two debts is one fortune." An Arabic mathematicians adopted the negative x negative = positive, in the development of algebra to get the math to work. The Greeks thought the concept of negative numbers absurd, and those thoughts lingered in European circles into the 17th century. But with all the advancements in mathematics, negative x negative = positive, the math always works and has held up over time, while European attempts to avoid the use of negative numbers did not.
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