Eliminating Geometry from High School?

Speaking of showing one's work...
...no abuquities at all.
Exactly what word were we going for here? Ubiquities? (I didn't even know that was a real word, but it must be, as spellcheck didn't flag it.) In any case, I don't think it's what you intended. Ubiquity | Define Ubiquity at Dictionary.com

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Responding to a previous statement,
times table.jpg
Why bother with the memorization of times table(s) when one has Excel?:twisted: [For some reason, I always had/have trouble with 6*9 (and, due to the Commutative Property, 9x6); just too similar to 7x8 I guess.]
 
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By doing it "your way", you essentially just multiplied $17.50 by 6. Doubling the number and then tripling that answer yields the exact same result. A standardized test has multiple choice answers, thus if you mark the correct answer, your method of arrival cannot be invalid as long as it produces the correct answer. I see no reason as to why this could be marked "incorrect".

If you would have to show that as a written answer, you could do 2*17.5 then multiply that by 3. Not simplest route having two operations but it has the easiest numbers to work with.
 
If you would have to show that as a written answer, you could do 2*17.5 then multiply that by 3. Not simplest route having two operations but it has the easiest numbers to work with.

I still believe that the answer would be marked "correct". Even if the grader was not expecting your method, he/she would at the very least learn a new way to solve a problem. And if you were really worried about it, write a quick note with exactly what you just said. "This way was more efficient and I realized 2*3=6, thus why my answer is correct."
 
... they ask you to figure the total for 6 tickets at $17.50 per ticket without a calculator. Many would just multiply it out, I prefer to make it an easy number to work with. I add 17.5 to itself to get 35 and triple it, $105.00. That is done in seconds in my head but I think it be wrong a state test.
This is exactly the scenario that got me into trouble with the General Business teacher/Football coach. We were doing currency conversions, and one of the exchange rates was 0.5 drachmas (or something) = 1 USD. The teacher explained to convert drachmas to dollars one multiplies dollars by exchange rate. He then asked if anyone was using a different method. Being the smartblank that I was at the time (*fifteen year-olds know everything), I said yes--I'm dividing by two and then moving the decimal point. He said, "What if you're doing yen (or something) to dollars and the rate is..." Superiorly knowing where he was going {see above*}, I interrupted him and said, "it won't come out even" before he could state the rate to be used was 0.1234 (or somesuch). Thus began his having it out for me and him demanding that I put my calculator away during the test. F- you, Mr. Plunkett, aka Mr. Lunkhead.:evil:

I'm sure there was a greater lesson ("teachable moment" in PC terms) to be learned from that encounter, but danged if I know what it was.:rolleyes:
 
The reason the thread took this turn was my example of an elementary school state test. There was no work to show, it asked to list three fractions in order, smallest to largest. Then they wanted the process to be explained. I did it one way and the test example did it another. Both were sound methods but when I asked if my answer would be marked wrong because I did it differently the answer was,"I would hope not." If the answer isn't yes or no then the test is flawed.

Did all of the fractions have a common denominator? I am guessing not. So, to ensure that the students did not just guess at the correct order, they asked for the method. Since I again guess that the method answer was not just a multiple answer, but the student had to write their work, a machine could not grade the answer. The teacher probably couldn't answer you directly since she wouldn't be grading the test, but if it were solid math then it would likely have been graded correct (say, not caring if the student found the lowest common denominator but realizing that the denominator was required to match and that whatever you multiplied the denominator by that you also multiplied the numerator).

Let me ask a question. You are taking a math test, and they do exist on job apps, they ask you to figure the total for 6 tickets at $17.50 per ticket without a calculator. Many would just multiply it out, I prefer to make it an easy number to work with. I add 17.5 to itself to get 35 and triple it, $105.00. That is done in seconds in my head but I think it be wrong a state test.

Again, doing math in a different way doesn't make it wrong. You in some way made it a more complex formula, even if it makes it easier to do in your head. Instead of 6*17.50 you did 3(17.50 + 17.50) which was (6/2)(2*17.50). Of course all yeild the same answer, this is the beauty of math. However, without showing your work, it would be difficult for someone to help you, should you have made an error along the way. It is simple math for you because you understand the algebraic concepts.

Like I stated, maybe a poor analogy by using music which is another mathmatecal language, showing work is essential practice to build a foundation on. If you had not had a grasp of manipulating numbers in multiple ways, you would not have discovered that you could find a shorter method for solving a problem. It is difficult to understand the need for showing work when it you have an aptitude for numbers (I did). I ended up losing quite a bit of credit for not showing my work (it was easier to do in my head). Even though I did my own work, the teacher was quick to point out that half of the answers were generally in the back of the book and how were they to know if I did the work or copied the answers?

Math is logical. Since very few schools teach logic anymore (which may be why we have so few good public speakers), it is one of the few outlets that our brain has the opportunity to use that skillset. Why would you want to deprive students of that? We should embrace it.
 
By doing it "your way", you essentially just multiplied $17.50 by 6. Doubling the number and then tripling that answer yields the exact same result. A standardized test has multiple choice answers, thus if you mark the correct answer, your method of arrival cannot be invalid as long as it produces the correct answer. I see no reason as to why this could be marked "incorrect".
Because the test I was complaining about wants a written explanation of operation. My methods many times are different than the approved method. The school said it shouldn't be wrong, my response is it shouldn't because it is correct. My problem is they answer definitively and makes it a bad test.
 
The other trick is to remember that if a number is evenly divisible by 3, then the sum of the digits of that number are also evenly divisible by 3.

54 -> 5+4 = 9 / 3 = 3
56 -> 5+6 = 11 / 3 = ...
 
In a similar vein, I just read about triplen harmonics causing over-current on the neutral. Article said it's the odd triplens (3rd, 9th, 15th,...) one must worry about; I guess the evens cancel? Elsewhere I see triplen defined as only the odds. So is "odd triplen harmonics" redundant/unnecessary?
 
Did all of the fractions have a common denominator? I am guessing not. So, to ensure that the students did not just guess at the correct order, they asked for the method. Since I again guess that the method answer was not just a multiple answer, but the student had to write their work, a machine could not grade the answer. The teacher probably couldn't answer you directly since she wouldn't be grading the test, but if it were solid math then it would likely have been graded correct (say, not caring if the student found the lowest common denominator but realizing that the denominator was required to match and that whatever you multiplied the denominator by that you also multiplied the numerator).
They did not have a common denominator plus one was a regular fraction, one was a mixed fraction and one was an inproper fraction. The person I was arguing with was not a teacher but the principal. Her husband is our state senator sitting on the committee overseeing education plus he is on our local Board of Education, or was at the time.
 
More food for thought about how the educational system is broken: http://graphjam.files.wordpress.com/2011/11/funny-graphs-flipped-classroom.png
(This is a long image and that's why I didn't embed it)

Interesting... Stinks if you dont have a computer, or are good at the tuv BS thing... It sounds to me like kids get lazy, dont keep doing things until they get them, and then fail when they stop getting it. Perhaps youtube, the solution, is also the problem? As one of those kids who had to fight every day to stay interested, engaged, and had to be fought to actually do things, I feel their pain. Doesnt change my perception that you have to be lazy to not finish High School...
 
Interesting... Stinks if you dont have a computer, or are good at the tuv BS thing... It sounds to me like kids get lazy, dont keep doing things until they get them, and then fail when they stop getting it. Perhaps youtube, the solution, is also the problem? As one of those kids who had to fight every day to stay interested, engaged, and had to be fought to actually do things, I feel their pain. Doesnt change my perception that you have to be lazy to not finish High School...
Maybe we could provide documentaries and other videos in a way that could be viewed from home and free up more class time for discussions and the like. Not sure about having a whole lecture.
 
I don't know if this Flipped model would work everywhere. It sounds more like a re-direction of homework and not maximizing the time in the classroom. I'd rather see our education take on the model of Finland. If our teachers were more able to instruct and not focus on crowd control, I think our students would come out ahead.
 
Internet classes are fine for college where a kid is more inclined to actually do the work. HS kids that would struggle with homework would tend to not watch the lecture either.
 
Internet classes are fine for college where a kid is more inclined to actually do the work. HS kids that would struggle with homework would tend to not watch the lecture either.

Assuming this is true, would it still be true if those kids were the product of a different form of elementary education? For instance, what would those kids be like if they arrived in high school feeling a sense of ownership for their education instead of 8 or 9 years of preconditioning toward a sit-and-listen model of teaching?
 
Assuming this is true, would it still be true if those kids were the product of a different form of elementary education? For instance, what would those kids be like if they arrived in high school feeling a sense of ownership for their education instead of 8 or 9 years of preconditioning toward a sit-and-listen model of teaching?
The problem with public education is there is no way to make an one size fits all method of teaching. Kids that actually are self motivated and want as good an education as possible will learn in most systems devised. When I went to HS it wuld have been terrible for me because I worked too much to survive in such a system. I worked three jobs, played in the band and did theatre, no way was I watching lectures at night.
My question is does having lectures at night mean the school day will be shorter. If not then when are the kids supposed to decompress?
 
My question is does having lectures at night mean the school day will be shorter. If not then when are the kids supposed to decompress?

I'm home no later than 2:20, my school gets out at 1:40 and starts at 7:10. Somedays it feels like I have too much time.

But the federal government is preaching that we need longer school days while the districts and state governments want to shorten it. What really bugs me is that no one seriously talks about quality, just quantity. Just because I'm spending more time in school doesn't mean that I'm necessarily going to learn more.

Surprised this hasn't be mentioned yet, but how early high school starts for most people. I know that I'm going to draw a whole storm of responses about this, but I'm up around 5:50 every school day and I can't stand it. Most of the year is spent arriving at school with the sun not visible over the horizon and during the worst of it not until after 1st period. Everyone, including administration and teachers, use it as an excuse for why somethings just don't go right. Just about all research says that starting school later improves test scores, but we're being held to the start and end times by the transportation union in my district. I'm just looking to start at more reasonable time to get more sleep and trying to go to bed earlier just doesn't work when having to get up in and start the day in the dark.
 

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