# Eliminating Geometry from High School?



## rochem

Cross-posted from the SML. I have my own opinions, but lets see what everyone else says. Does anyone staunchly support this?

What's the big idea?: Replace high-school geometry with entrepreneurship - The Washington Post


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## ScottT

Not at all. I personally use geometry on a daily basis and couldn't imagine someone starting a company in this business without knowing geometry.


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## zmb

Replace English instead of Geometry and now we're talking.


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## chausman

I say no, they shouldn't replace geometry with a business class. While that does apply to some people, and what they would like to do, but if you are going to be a doctor, or a elementary school teacher, do you need to have a class dedicated to running a business? 

And I don't just say this because I am currently in Geometry


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## Footer

ScottT said:


> Not at all. I personally use geometry on a daily basis and couldn't imagine someone starting a company in this business without knowing geometry.


 
Unless you want to become a promoter....

I have personally believed for awhile that there are several high school classes that should go away and be replaced with a more open concept. We are in a business that uses geometry and algebra, however, how often do we use biology and earth science? Those classes to me could have never happened and I would be fine today. As the pendulum swing back from the "Everyone must get a college degree to succeed in life", these questions are going to start coming up more and more.


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## shiben

Isnt that what the whole point of a business degree is for? Anyone who actually wants to start a business will take business classes at College and learn that way. I think the real problem is that students get taught geometry and then are given "you will need to know this because" examples that are absolutely moronic. Our textbook had "if you are a race car driver" as a "real world example". Anyone here a pro race car driver? And honestly, is a class in business really gonna help the kids who end up flipping burgers? I dont know, I get the impression that things were fine until people got lazy, but thats just me... No amount of classes in anything are gonna help that out.


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## shiben

Footer said:


> Unless you want to become a promoter....
> 
> I have personally believed for awhile that there are several high school classes that should go away and be replaced with a more open concept. We are in a business that uses geometry and algebra, however, how often do we use biology and earth science? Those classes to me could have never happened and I would be fine today. As the pendulum swing back from the "Everyone must get a college degree to succeed in life", these questions are going to start coming up more and more.


 
I liked biology tho. Where else do you get to dissect stuff?


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## len

The percentage of people in America who will retire from the same field that they started in 40 - 50 years earlier is shrinking and shrinking. Students need to be exposed to a lot of different disciplines in school. And they need to be able to explore more interests. Geometry isn't for everyone, but neither is running a business, or chemistry, or English.


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## MPowers

This is all IMHO. A course on entrepreneurship would be a very good thin in 21st century education. BUT, not at the expense of geometry OR English. English is far too overlooked by many people today. (can of worms here, now I'll probably make some terrible grammatical or spelling error in this post which all the grammar police will have to point out!) I'm often embarrassed for my boss, the Company Pres/owner, when I receive copies of correspondence he has sent out with multiple your-you're, There-their-they're, here-hear type of mistakes. I get stage hands on an install crew and I ask them to layout a center line square to the plaster line and they can't do it. I ask shop crew to figure the sq ft of carpet runner needed for a political rally and they can't do it. 

I wish there had been such a class as entrepreneurship when I was in school, it would have helped me a lot over the years. I feel everyone who has to run a home or a business would benefit from a course in entrepreneurship. 

All the above, IMHO.


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## techieman33

MPowers said:


> This is all IMHO. A course on entrepreneurship would be a very good thin in 21st century education. BUT, not at the expense of geometry OR English. English is far too overlooked by many people today. (can of worms here, now I'll probably make some terrible grammatical or spelling error in this post which all the grammar police will have to point out!) I'm often embarrassed for my boss, the Company Pres/owner, when I receive copies of correspondence he has sent out with multiple your-you're, There-their-they're, here-hear type of mistakes. I get stage hands on an install crew and I ask them to layout a center line square to the plaster line and they can't do it. I ask shop crew to figure the sq ft of carpet runner needed for a political rally and they can't do it.
> 
> I wish there had been such a class as entrepreneurship when I was in school, it would have helped me a lot over the years. I feel everyone who has to run a home or a business would benefit from a course in entrepreneurship.
> 
> All the above, IMHO.


 
I think if it covered home/personal finances for a semester, and business for a semester it would be much more valuable to everyone. My vote would be the class I proposed as required, and geometry as an elective math class that you could take if you want.


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## Footer

techieman33 said:


> I think if it covered home/personal finances for a semester, and business for a semester it would be much more valuable to everyone. My vote would be the class I proposed as required, and geometry as an elective math class that you could take if you want.


 
In Illinois you had to take "consumers ed" as a graduation requirement. It taught you how to balance a checkbook, how not to cheat on your taxes, and how to not get screwed by banks when you buy on credit. I tested out of it so I did not have to take it, but it was there.


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## derekleffew

I took a similar course, it might have been called "General Business," in eighth or ninth grade (along with Home Ec. and Industrial Arts). Not surprisingly, I didn't get along with the teacher (a football coach; he also taught Typing). He scolded me for using a hand-held calculator, at the time rare, during an exam.

I wouldn't trade my HS years of Honors Geometry or Honors Algebra II & Trig. for anything.


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## sk8rsdad




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## zmb

Footer said:


> In Illinois you had to take "consumers ed" as a graduation requirement. It taught you how to balance a checkbook, how not to cheat on your taxes, and how to not get screwed by banks when you buy on credit. I tested out of it so I did not have to take it, but it was there.


 
Sorta of got that in my 8th grade US History class in 2008, right when the economy took a nosedive. We watched documentaries about how Enron failed, the mortage crisis, and how Wall Street wasn't doing well. Probably more useful than the US history portion, which we cramed in and had our notes for last couple tests of the year.

Strangely enough, this teacher resigned and runs an outdoor education, Christian-based, program for home schooled kids.



*My view on the modern education system (as a junior in a high-performing public high school):*
We have too many extraneous items in the system that are getting in the way of what is really going to help us in the real world. Things like foreign languages and PE classes. I'm looking at going to school for engineering, undecided which type right now, when will I need three years of Spanish and 1.5 years of PE? The PE is required by the district just to graduate, but the language is for the universites. I am taking University of Washington (UW) Spanish 103 at my school, counts for one high school credit and five college credits and is thankfully enough that I have satisfied the language requirement for the UW's engineering program. And on the PE credits, yes, there is an obesity epidemic in America, but how does taking more gym classes fix that? I would like to have that out of the way for more important classes, but is ~$400 to take an online class were you record you're physical activity. I would consider my self a modernly fit individual but it isn't because of me taking racket sports for 2 semesters and body conditioning for 1 semester. On Footer's consumer ed class that he mentioned, my school offers finance as a third year math class in my school if you really need one more math credit. I am taking AP prep PreCalc right now and while that would be important for an engineering degree, a finance class would certainly be useful.


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## cpf

Don't diss PE, I know at least 3 electrical engineers who make (or have made) serious cash installing and maintaining heavy, cumbersome, expensive equipment  Obviously that just one case, but I firmly believe physical fitness is up there with home economics and cooking as a skill that will serve you well later in life, even if you don't take them as actual courses. 

And yes, studies have shown mandatory physed classes improve life-long fitness. That's enough ranting for me...


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## chausman

zmb said:


> We have too many extraneous items in the system that are getting in the way of what is really going to help us in the real world. Things like foreign languages and PE classes. I'm looking at going to school for engineering, undecided which type right now, when will I need three years of Spanish and 1.5 years of PE? The PE is required by the district just to graduate, but the language is for the universites. I am taking University of Washington (UW) Spanish 103 at my school, counts for one high school credit and five college credits and is thankfully enough that I have satisfied the language requirement for the UW's engineering program


 
I agree. I don't see the real advantage to forcing everyone to take two consecutive years of a foreign language just to graduate. I certainly see why school offer those as a class, but my school only offers Spanish, French, and German. None of which are even remotely interesting for me to learn. I don't like my PE class, but I can also see why it is required to graduate. 


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## Grog12

How are you going to know you're putting your business in a sound building without basic geometry? 

Also Chaus, you'll regret not taking and really embracing one of those 3 languages. To this day I rue having my girlfriend do all my homework because it "wasn't important" then.


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## chausman

Grog12 said:


> Also [-]Chaus[/-]*Chase*, you'll regret not taking and really embracing one of those 3 languages. To this day I rue having my girlfriend do all my homework because it "wasn't important" then.


 
I definitely am going to take a foreign language (don't know which) because I need to to graduate, but I don't like that it is required. At least offer something interesting...


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## MarshallPope

chausman said:


> I definitely am going to take a foreign language (don't know which) because I need to to graduate, but I don't like that it is required. At least offer something interesting...
> 
> 
> Sent from my iPad using Tapatalk


 

Would you rather learn something that you may actually be able to use some day, or Zulu or Icelandic that you will learn for nothing?

If nothing else, foreign languages are helpful in extracting more meaning from our English words when we can see their etymology. (I recommend German, by the way. It's a fun language, and English is also a Germanic language)


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## derekleffew

MarshallPope said:


> ...If nothing else, foreign languages are helpful in extracting more meaning from our English words when we can see their etymology. ...


Also, by taking a foreign language, I found I gained a better understanding of English. I had never been taught future perfect tense or past participles until I took Spanish. (Which may be the US's predominant language in a few short years.)


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## Footer

derekleffew said:


> Also, by taking a foreign language, I found I gained a better understanding of English. I had never been taught future perfect tense or past participles until I took Spanish. (Which may be the US's predominant language in a few short years.)


 
I wish I would have actually paid attention in spanish instead of dropping it after a year and 5 weeks. I can not tell you how many road shows we have in that are foriegn tours. We have a dance company that does a residency that most of them are either Italian or Spanish... a few don't speak english. Trying to tell the wardrobe chick to only used distilled water in the steamer took at least 10 minutes.


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## ruinexplorer

I do agree that our modern education system does a disservice to our students by not preparing them for the "real world". However, I disagree on many of the things that should be changed. No, I don't think that PE should be eliminated, however it probably should be altered by not focusing on sports but _physical education_. Also, in Arizona, some of the school districts have changed how to get your PE credits, including getting a half credit for marching band (since it can be quite exhausting).

I agree with the above that foreign languages are extremely helpful. Those of us who choose to only speak English are quite self centered, expecting the rest of the world to conform to us. We are one of the very few nations of the world who wait until high school to start offering a second language (when they know that learning a second language is more difficult). Many European countries are having their children know three languages. We have neighboring countries that speak different languages (even though Quebequoise is fairly regional). I agree that schools are falling behind in their language offerings. Chinese (Mandarin) should be a more regular offering.

The biggest failing of our educational system at this point is that it fails to teach students how to think. Studies on modern students who have grown up with the digital revolution have learned how to effectively use search engines, but they are lacking the skills in knowing how to disseminate between quality information and garbage (kind of like losing the ability to tell quality sounds as compared to highly compressed music files played back on crummy ear buds). It isn't the students' fault if they are never taught how to do it. After all, many school districts have to rely on test scores to evaluate learning, which means that they have to have empirical data driven from right and wrong answers (multiple choice questions). This is simple regurgitation, no thinking required. This may be why you would want to remove Geometry from your offering, since a portion of that is "proofs" where you actually have to _think _about how the answer is derived.


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## Tex

Why does geometry have to go away in order to offer entrepreneurship? 
The major problem with high schools is that we try to stuff all the pegs, no matter what shape they are into a round hole...


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## sk8rsdad

At the risk of gross generalization, I would posit that today's public education is a natural consequence of a century or two of institutional inbreeding. Think about it for a moment. The average teacher is a product of the education process, first as a kid in elementary school, then a teen in high school, then college or university, then teacher's college, finally returning to teach the next generation. At what point in the process did they experience entrepreneurship? At what point did the teachers learn that there is any other shape of hole than the round one? So when these teachers become administrators, or politicians, the whole thing becomes a closed loop feedback system. The whole concept of _adolescence_ can be argued to a product of compulsory education, and followed from child labour laws that produced a large number of no longer employable teenagers. We no longer even consider that it was ever any other way.


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## seanandkate

sk8rsdad said:


> The average teacher is a product of the education process, first as a kid in elementary school, then a teen in high school, then college or university, then teacher's college, finally returning to teach the next generation. At what point in the process did they experience entrepreneurship? At what point did the teachers learn that there is any other shape of hole than the round one? So when these teachers become administrators, or politicians, the whole thing becomes a closed loop feedback system.


 
Teaching today is a quite a different beast then when I was on the other side of the classroom, but certain structures DO make it seem like things haven't changed that much. Want shakeup? Let's group students in classes by level of proficiency, not age. But I digress... 

In answer to the original post: a resounding NO. From the article: "...great learning would accrue from dividing the class into two groups to see which group can create a more profitable business while retaining scrupulous ethics." The last thing I want my students to learn is that success is measured solely by profit, and that competition is better than cooperation. (I've also got concerns with how often "profitable business" and "scrupulous ethics" get on the same bus together, but that's a rant for another day.) 

And students need to know that just because they don't see the value in something right NOW, that it doesn't mean that it HAS no value. Sometimes it's only in retrospect that we realize the value of learning Spanish, or taking geometry. And when people like Prof. Nemko publish an article saying that a course entrepreneurship should replace anycourse, he is merely showing his own bias. People that say "Subject x is useless/irrelevant" are actually saying "Subject x is useless/irrelevant because *I* found it useless and irrelevant." It's the height of hubris.

And relevancy is is harder than ever to pin down today than it has in the past. In many cases, we are trying to prepare students for jobs that don't even exist yet. I filled out a thick stack of computer cards in data processing to add ten numbers together, and I programmed in BASIC in Computer Processing in high school. Haven't had the need to do THAT again, but the processing logic that I learned and practiced there I have probably used thousands of times since and not even known it....


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## museav

Personal views:

Get rid of foreign languages. The rest of the world will always learn English just for us and you gain nothing from learning about other cultures, thinking in other ways and so on.

Get rid of PE, with a lower life expectancy there will be a greater need for new people in the work force as the ones already in it die off sooner. A lower life expectancy may also mean less drain on Social Security, Medicaid, etc.

Dump geometry. Also get rid of parallel parking, traffic circles, square and line dancing, going off on tangents and the movie 'The Octagon'.

Instead offer Entrepreneurship classes so you identify unmet societal needs such as no one knowing foreign languages, physical education and geometry.


On a serious note, it is interesting how people often think that they don't need something until they do. Take the example of doctor's not needing to know business as a nearby college made their reputation by offering an MBA program specifically for those in the medical profession as changing laws, processes, documentation requirements, etc. led to virtually requiring any medical practice to have significant expertise in related business, law and tax aspects.


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## Nelson

museav said:


> Dump geometry. Also get rid of parallel parking, traffic circles, square and line dancing, going off on tangents and the movie 'The Octagon'.


 
 

I wish that Geometry classes related more to real-life scenarios. Instead of spending so much time with theory, I would rather learn hands-on, practical skills that I will use on the job and later in life. That's a class I'd enjoy!


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## mstaylor

I thought geometry was my favorite class in school. I use it daily for a varity of reasons. For years I operated a sucessful contracting business and used geometry, algerbra and trig in many areas of construction. In the theatre world I use it also. I agree that you have to change some of the things you are teaching but the basics still need to be there. 
The problem is great thinkers like the guy in the article saying idiotic things like competition turns us all into losers. You can't play dodgeball because it hurts a kid's self esteem. Zero tolerance rules put in place so administrators don't have to think. All these things make us lazy sloths that can't do things on their own. 
When I was contracting I was always amazed when I hired guys that could not read a rule. Sometimes I would ask for a measurement like 48 4/8 instead of 1/2 just to see if they could reduce the fraction. Most could not, they would count marks and then be shocked when it was half. They wouldn't know that 11/16 was just short of 3/4. Now they want to take out geometry. Amazing.


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## derekleffew

Nelson said:


> I wish that Geometry classes related more to real-life scenarios. Instead of spending so much time with theory, I would rather learn hands-on, practical skills that I will use on the job and later in life. That's a class I'd enjoy!


Ah but perhaps the more important lesson to be learned in geometry class is not circles, triangles, square footage, etc.; but rather *developing logical thinking*. Sort of the "give a man a fish..." paradigm. Which is more important: knowing that one calculates the area of a circle by using πr^2, or knowing that π = d/r ?


ruinexplorer said:


> ...After all, many school districts have to rely on test scores to evaluate learning, which means that they have to have empirical data driven from right and wrong answers (multiple choice questions). This is simple regurgitation, no thinking required. This may be why you would want to remove Geometry from your offering, since a portion of that is "proofs" where you actually have to _think _about how the answer is derived.


Exactly! Successfully performing a proof in Euclidean geometry extends far beyond mathematics.

_Q. E. D._


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## chausman

derekleffew said:


> Ah but perhaps the more important lesson to be learned in geometry class is not circles, triangles, square footage, etc.; but rather *developing logical thinking*. Sort of the "give a man a fish..." paradigm. Which is more important: knowing that one calculates the area of a circle by using &pi;r^2, or knowing that &pi; = d/r ?


 
Syllogism and Detachment, that sort of thing. 

It does seem a little sad that logic has to be taught to a person, to me.

And proofs...what would you say the general purpose of teaching proofs is? I'm just curious, how many of you use proofs...ever.


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## derekleffew

chausman said:


> ...And proofs...what would you say the general purpose of teaching proofs is? I'm just curious, how many of you use proofs...ever.


Ever ask your boss for a raise? Want the school board to buy you some new equipment? Have to defend/argue the validity of a statement you've made in a post on Control Booth?



> You teach yourselves the law. I train your minds. You come in here with a skull full of mush, and if you survive, you'll leave thinking like a lawyer.


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## chausman

derekleffew said:


> Ever ask your boss for a raise? Want the school board to buy you some new equipment? Have to defend/argue the validity of a statement you've made in a post on Control Booth?


 
But a proof like:

> Given:
> Segment AD bisects segment BC.
> Segment BC bisects segment AD.
> Prove:
> Triangles ABM and DCM are congruent.
> 
> 
> 
> Notice that when the SAS postulate was used, the numbers in parentheses correspond to the numbers of the statements in which each side and angle was shown to be congruent. Anytime it is helpful to refer to certain parts of a proof, you can include the numbers of the appropriate statements in parentheses after the reason.



I do see people's point as far as the foreign languages. (I just wish they had more choices)

There seems to be a reason that we have certain classes, and we sort of need to have all of them. How do they decide "Math isn't as important as...". "Entrepreneurship is really more useful then...". And asking a teacher can *sometimes* just adds to the confusion. Don't most teachers say their class is better or more useful then another class?


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## mstaylor

Proofs are there so you can apply the rules in more than one direction or plane. Without understanding complimentery and supplementery angles you could never use a speed square. Any trade, welding, carpentry, plumbing all require geometry. I had a HVAC mechanic tearing his hair trying to figure an offset in his duct. I told him to multiply the offset by 1.414 and he looked at me like I was nuts. I told him he was finding the hypotenuse of an isosceles right triangle so you have to multiply by the square root of 2. He was amazed when it worked. 
If you don't want to learn geometry don't rig.


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## viking33

Why not just make the school days longer and add another class like they have in Japan.


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## mstaylor

chausman said:


> But a proof like:
> 
> 
> I do see people's point as far as the foreign languages. (I just wish they had more choices)
> 
> There seems to be a reason that we have certain classes, and we sort of need to have all of them. How do they decide "Math isn't as important as...". "Entrepreneurship is really more useful then...". And asking a teacher can *sometimes* just adds to the confusion. Don't most teachers say their class is better or more useful then another class?


I can't read your proof but isn't knowing that the def. of vertical angles a very important concept? I still remember the SAS, LL, HL and other postulates, corrolaries and theroms. You are very knowledgable for your age but you are still young and dumb in other areas. That isn't a slam, just a fact of life. 
I helped start a math tutoring club in HS and I heard the same excuses from kids I was teaching, "I'm no good at math"" I'll never use it"and "My teacher is stupid." I never had a kid that I couldn't help get better. 
I told my son about this discussion, he's a welder, 18 and hated school. His reply was," Are they stupid? That is probably the one class you will use regularly. "
While you will never have to do a formal proof in the wild, you will do them in practical application. Do you need a 26 degree or a 50 from a certain location? Sorry. I can't find that answer because they took geometry out of my HS.


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## chausman

mstaylor said:


> I can't read your proof but isn't knowing that the def. of vertical angles a very important concept? I still remember the SAS, LL, HL and other postulates, corrolaries and theroms. You are very knowledgable for your age but you are still young and dumb in other areas. That isn't a slam, just a fact of life.
> I helped start a math tutoring club in HS and I heard the same excuses from kids I was teaching, "I'm no good at math"" I'll never use it"and "My teacher is stupid." I never had a kid that I couldn't help get better.


 
Thank you. I was thinking through some things, but rigging hadn't crossed my mind during class earlier this week. Yes some of it is important. 

I think adding hours to a school day (at least in my school) would only add to frustration of many students. There is really only so much that a lot of students can do in a day, before they completely stop paying attention. I could be wrong, and it does depend on the school and students, but that's just my opinion.


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## mstaylor

chausman said:


> Thank you. I was thinking through some things, but rigging hadn't crossed my mind during class earlier this week. Yes some of it is important.
> 
> I think adding hours to a school day (at least in my school) would only add to frustration of many students. There is really only so much that a lot of students can do in a day, before they completely stop paying attention. I could be wrong, and it does depend on the school and students, but that's just my opinion.


I agree that making days longer is not the answer, at a certain point the kids just shutdown. They need time for extracuricular activities, jobs and simple down time. They need fewer stupid rules and worry more about just teaching. They need to spend less time testing and more time teaching.


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## blackisthenewblack

I know tomorrow I will be struggling with angles in the shop for hours (label your technical drawings properly!), so I will be using my maths all day.


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## Footer

mstaylor said:


> I agree that making days longer is not the answer, at a certain point the kids just shutdown. They need time for extracuricular activities, jobs and simple down time. They need fewer stupid rules and worry more about just teaching. They need to spend less time testing and more time teaching.


 
Yup. When I taught that was my thought as well. However, my kids minds nearly exploded when I started teaching algebra in a theatre class.....


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## mstaylor

Not to mention my math skills helped me get my wife of 25 yrs. She called me to tutor her in college calc which I had never taken. I taught it to myself so I could teach it to her. We started dating and finally married. If it wasn't for my background in HS math I wouldn't have been able to do that.


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## Nelson

Footer said:


> Yup. When I taught that was my thought as well. However, my kids minds nearly exploded when I started teaching algebra in a theatre class.....


 
I've always been concerned about the negative stigma that math in general seems to have. The "What, you mean we gotta do math?" attitude always concerns me. I'd rather hear them say "I've never done that before, but I'm willing to learn". What is so bad about learning and applying math? Why does it seem to have a negative stigma?


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## mstaylor

Nelson said:


> I've always been concerned about the negative stigma that math in general seems to have. The "What, you mean we gotta do math?" attitude always concerns me. I'd rather hear them say "I've never done that before, but I'm willing to learn". What is so bad about learning and applying math? Why does it seem to have a negative stigma?


Because it requires some work and logical thought process. I love it when kids say they hate word problems, what do they think the world is about. Your boss isn't going to up equations for you, you have to take random information, sift through it and decide how to find the answer. Algrebra and Geometry are essentials tools in that toolbox.


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## chausman

mstaylor said:


> Because it requires some work and logical thought process. I love it when kids say they hate word problems, what do they think the world is about. Your boss isn't going to up equations for you, you have to take random information, sift through it and decide how to find the answer. Algrebra and Geometry are essentials tools in that toolbox.


 
Not to mention common sense. I've heard people complaining that the word problem wasn't right, and they chose the wrong numbers to figure it out. Instead of trying different numbers they just start asking people around them. Or they automatically assume they chose the wrong numbers or formula, and then get completely confused. 

sadly I've done both of those things...but figured it out eventually


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## mstaylor

chausman said:


> Not to mention common sense. I've heard people complaining that the word problem wasn't right, and they chose the wrong numbers to figure it out. Instead of trying different numbers they just start asking people around them. Or they automatically assume they chose the wrong numbers or formula, and then get completely confused.
> 
> sadly I've done both of those things...but figured it out eventually[/dimgrey]



And that is called learning. Taking the information, trying to find the answer, knowing whether it is correct and then how to fix it. These are critical skills for the real world and knuckleheads like the guy in the article is trying to stifle that. 
When my son was in 4th grade they came up with a new state test. In the examples they gave three fractions that were to be put in order smallest to largest. Then as the second part of the question you were to write a brief constructed response, a term that makes my skin crawl, explaining how you did it. I went to the principal to complain. I did the problem, got it right but my method was different than their's. My question was would my explanation be marked wrong. She said she would hope not. I lost it, first there is no reason to explain how you do something in math if you get the right answer. She said they needed to make sure you understood the concept. I answered if you got the right answer then obviously you know how to do it. Second, if she can't tell me definitively whether my answer would be correct then it is a flawed test. Education has become so screwed up the kids are being exposed to tons of information and learning very little.


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## museav

mstaylor said:


> When my son was in 4th grade they came up with a new state test. In the examples they gave three fractions that were to be put in order smallest to largest. Then as the second part of the question you were to write a brief constructed response, a term that makes my skin crawl, explaining how you did it. I went to the principal to complain. I did the problem, got it right but my method was different than their's. My question was would my explanation be marked wrong. She said she would hope not. I lost it, first there is no reason to explain how you do something in math if you get the right answer. She said they needed to make sure you understood the concept. I answered if you got the right answer then obviously you know how to do it. Second, if she can't tell me definitively whether my answer would be correct then it is a flawed test.


It was so memorable that I still recall a college calculus test where several of us had the exact same answer for one question but had all been marked as having the wrong answer. A couple of us went to our TA and asked them to explain what was wrong with our answer and logic. Their response was that our answer was actually more correct than the 'correct' answer but it wasn't the answer the professor wanted so even though we were right, we were wrong. That was 30 years ago so some of the issues aren't exactly new.


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## shiben

mstaylor said:


> And that is called learning. Taking the information, trying to find the answer, knowing whether it is correct and then how to fix it. These are critical skills for the real world and knuckleheads like the guy in the article is trying to stifle that.


 
And that is what is being lost with all this standardized testing BS. When I was working in a scene shop on the side of my ME gig, I was one of the few people who could read a plan, use a square, understood that using a plumb line meant that something was vertical, got how the level worked, etc. Its amazing to me how many people came in "what are these two sides we dont know? on a sheet of 4x8 plywood... And its not because Im brilliant. In Geometry and other math classes, you learn a lot about how to look at a problem and figure out how to solve it. Thats what worries me. I was helping my brother with his geometry class (college level) and the questions were asking you to use a specific rule or theorum to solve a problem. Apparently students had not figured out that you need to look at the problem and figure out which one applies. Thats a little worrysome to me...


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## ruinexplorer

mstaylor said:


> And that is called learning. Taking the information, trying to find the answer, knowing whether it is correct and then how to fix it. These are critical skills for the real world and knuckleheads like the guy in the article is trying to stifle that. <snip>
> I did the problem, got it right but my method was different than their's. My question was would my explanation be marked wrong. She said she would hope not. I lost it, first there is no reason to explain how you do something in math if you get the right answer. She said they needed to make sure you understood the concept. I answered if you got the right answer then obviously you know how to do it. Second, if she can't tell me definitively whether my answer would be correct then it is a flawed test. Education has become so screwed up the kids are being exposed to tons of information and learning very little.


See, I think that you start out right, but I disagree with the second part. Just having the right answer isn't enough. You can come up with the right answer incorrectly and thus not have repeatable results. While I don't think that anyone should ever be graded on their process, I do believe that it is important for the instructor to see how you come to your results. A good teacher may be able to better direct the student to more reliable results if need be. This is especially important in tests where the school district may be able to spot trends that many students are having difficulty in a certain area. 
With most standardized tests, they offer a few select answers to any given problem. A bright student can often surmize the answer without having to do the work, but that doesn't let the instructor know if they actually know how to do the problem correctly. Also, do we have to have an exact number? If I were to have a problem like 2+2, would 3.999 be accurate enough? As you get into machining tolerances, we probably wouldn't have any problems with a student not coming up with 4. However, if we know how the student arrived at their answer, it may help the teacher guide the student to a more precise answer.


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## mstaylor

ruinexplorer said:


> See, I think that you start out right, but I disagree with the second part. Just having the right answer isn't enough. You can come up with the right answer incorrectly and thus not have repeatable results. While I don't think that anyone should ever be graded on their process, I do believe that it is important for the instructor to see how you come to your results. A good teacher may be able to better direct the student to more reliable results if need be. This is especially important in tests where the school district may be able to spot trends that many students are having difficulty in a certain area.
> With most standardized tests, they offer a few select answers to any given problem. A bright student can often surmize the answer without having to do the work, but that doesn't let the instructor know if they actually know how to do the problem correctly. Also, do we have to have an exact number? If I were to have a problem like 2+2, would 3.999 be accurate enough? As you get into machining tolerances, we probably wouldn't have any problems with a student not coming up with 4. However, if we know how the student arrived at their answer, it may help the teacher guide the student to a more precise answer.


I agree as you move up in math you need to show the process, that's what equations and proofs do. However, in simple math getting the right answer is enough. In algebra it is very easy to miss a negative or even double negatives which leads to the wrong answer. This is why you are taught to insert the answer back in the equation to see if you are indeed correct. Under no circumstances should you have to write an explanation of process.


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## derekleffew

RE: "show your work"

mstaylor said:


> ...Under no circumstances should you have to write an explanation of process.


If you just write down an answer and it's wrong, you lose. Zero. F.
If you write down your answer and it's wrong, AND you've shown how you arrived at that answer, many/most teachers will give partial credit. They feel you shouldn't lose everything just because you made one minor error (like missing a minus sign in the third step of a ten step process).

Some see this as the downfall of civilization--no competitiveness, everyone's a winner, all receive a participation trophy.
Others see it as effective teaching, empathy, and encouraging.
Discuss.


And then there's these: 
"One learns more from his failures than he does from his successes."
"If at first you don't succeed, rigging is not for you!"


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## cpf

Partial marks for partial solutions fit how the real world works. Asked to design a system to optimize train traffic? Do a good job and get paid good cash. Do a great job and get paid great cash. Do a poor job that costs the company money? Still make a bit of money.


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## mstaylor

I don't disagree with partial credit for doing the procedure correctly and making a simple mistake, in higher math. In simple basic math, addition, substraction, multiplication, division and fractions, do the problem and get the right answer. I still agree to show your work, it is important to see what you are doing wrong but no partial credit during the basics.


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## ruinexplorer

And to that I also agree. We need to make sure that we teach the students the basics so that they have a firm foundation for the higher math. This is why I still think that the students need to memorize their times tables and learn how to estimate. These are the critical skills needed for the higher levels of math.


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## mstaylor

ruinexplorer said:


> And to that I also agree. We need to make sure that we teach the students the basics so that they have a firm foundation for the higher math. This is why I still think that the students need to memorize their times tables and learn how to estimate. These are the critical skills needed for the higher levels of math.


I almost put that in my post. In my area they teach times tables up through about the 6x and then leaves it to the kids to learn the rest. We made both our boys learn through 12x12. We also insisted they learn how to find combinations to make ten to increase adding in their head. My brother is incredible at estimating math. He is a VP of commercial lending and he can look at a project and figure debt service payments in his head.


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## DuckJordan

This where I disagree there is good and bad about memory such as times tables sure it makes you faster but I know several people who couldn't write out how to get to 8 x 9 

Sent from my ADR6300 using Tapatalk


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## mstaylor

DuckJordan said:


> This where I disagree there is good and bad about memory such as times tables sure it makes you faster but I know several people who couldn't write out how to get to 8 x 9
> 
> Sent from my ADR6300 using Tapatalk


Then they weren't taught the basics. They should have taught that multiplication is a short form for addition. 8+8+8+8+8+8+8+8+8=72. Then you memorized the table from 1x1 to 12x12. I showed a woman the other day how to mulitply by 11 quickly. She was 57 and never shown where 11x12=121 by taking the first and last then adding them. 12 becomes 1_2, to be the first and last digit, then add them for the third digit. 1+2=3, plug it into 1_2 and get 132. Put that on a standardized test and watch their head blow up. Or when factoring a large number add the digits to see if it breaks down to 9. If it does then it divisible by nine. Knowing that anything ending in 5 or 0 is divisible by 5. Knowing tricks doesn't mean that I don't understand the basics. 
Sitting in rigging class and showing teacher why his match didn't check is satisfying and possible because of my HS math.


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## shiben

Estimation is a useful skill when you start dealing with very large numbers. Science Olympiad taught me that, and I just love it when things get big enough that you can count Pi as 1 and its still close enough...


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## FACTplayers

I didn't read the entire thread, but I see questions like the image I'm posting below and can't fathom how people get the answer wrong.


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## DuckJordan

So what's the correct answer? 

Sent from my ADR6300 using Tapatalk


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## chausman

DuckJordan said:


> So what's the correct answer?
> 
> Sent from my ADR6300 using Tapatalk


 
What's the question? I can't see it for some reason.


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## FACTplayers

The correct answer is clearly 14. The questions is:

"What is the answer? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0 "


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## MarshallPope

Are we sure? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
PEMDAS
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
10-6
=4

At least that's what I get...


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## derekleffew

MarshallPope said:


> ...PEMDAS...


*P*lease *E*xcuse *M*y *D*ear *A*unt *S*ally. 

FACTplayers said:


> ... and can't fathom how people get the answer wrong.


As demonstrated by the responses here, it's actually rather easy to fathom a wrong answer. It's a bad question.


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## FACTplayers

MarshallPope said:


> Are we sure? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
> PEMDAS
> 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
> 10-6
> =4
> 
> At least that's what I get...


 
You have the first part right, the first set of 1's (until the - sign) equal 10. Then subtract 1 from that 10; equal 9. Then, add another 5 to that 9; equals 14. Then, multiply 1 by 0; yields 0. Add that 0 to the running summation; equals 14.


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## sk8rsdad

Adding brackets to highlight the order of operation may help:

(1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1x0)
= 9 + 0 + 5 + 0
= 9 + 5
= 14

Do they teach order of operations any more?


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## chausman

sk8rsdad said:


> Adding brackets to highlight the order of operation may help:
> 
> (1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1x0)
> = 9 + 0 + 5 + 0
> = 9 + 5
> = 14
> 
> Do they teach order of operations any more?


 
In Washington it is on the 7th grade WASL, now MSP. I was taught that in Sixth. 

Please Excuse My Dear Aunt Sally

And Multiplication/Division & Addition/Subtraction go in the order they come in the equation, not Multiplication, THEN division. Same for Add. & Sub.


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## FACTplayers

sk8rsdad said:


> Adding brackets to highlight the order of operation may help:
> 
> (1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1x0)
> = 9 + 0 + 5 + 0
> = 9 + 5
> = 14
> 
> Do they teach order of operations any more?


 
I didn't think this was difficult at all. Maybe it can be blamed on Texas Instruments since they are the downfall of RPN calculators?

Edit: Let me expand on my comment for those of you who don't know what RPN calculators are. RPN calculators require you to enter the equation in the way you go about solving it by hand. For for the above equation, you need to enter the 1x0 first, then start on the far left and go about adding it. The first question everyone says when they try to use an RPN calculators is "where is the equals/enter button?". TI calculators don't require any thought; they use an algebraic method to solve equations.


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## DuckJordan

FACTplayers said:


> The correct answer is clearly 14. The questions is:
> 
> "What is the answer? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0 "


 
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
is
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
2+1+1+1+1+1+1+1+1+1+1+1+1
3+1+1+1+1+1+1+1+1+1+1+1
4+1+1+1+1+1+1+1+1+1+1
5+1+1+1+1+1+1+1+1+1
6+1+1+1+1+1+1+1+1
7+1+1+1+1+1+1+1
8+1+1+1+1+1+1
9+1+1+1+1+1
10+1+1+1+1
11+1+1+1
12+1+1
13+1
14

Easiest way to show it on a forum. Red Denotes First in sequence and the -1 is done right after to avoid confusion.


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## mstaylor

I don't use RPN calculators, if they are the graphing calculators. I am well aware of order of operations but the calculators hurt my head. Of course, I'm not too swift with a ten key either. I can use a regular or even a scientific calculator but others baffle me.


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## chausman

mstaylor said:


> I don't use RPN calculators, if they are the graphing calculators. I am well aware of order of operations but the calculators hurt my head. Of course, I'm not too swift with a ten key either. I can use a regular or even a scientific calculator but others baffle me.


 
I've used RPN calculators, and I hated it. My mom (a former accountant) loves it. 

I've found another reason for geometry. I'm in Intro to Engineering Design and currently we are working on different shapes and measurements. (Triangles, Octagons, Rhombus, etc..) and during lunch, I need to go talk to my geometry teacher abut a few of the questions. Things that we work on later in the year in geometry.


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## shiben

FACTplayers said:


> The correct answer is clearly 14. The questions is:
> 
> "What is the answer? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0 "


 
I dont get how people get that wrong...


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## FACTplayers

chausman said:


> I've used RPN calculators, and I hated it. My mom (a former accountant) loves it.
> 
> I've found another reason for geometry. I'm in Intro to Engineering Design and currently we are working on different shapes and measurements. (Triangles, Octagons, Rhombus, etc..) and during lunch, I need to go talk to my geometry teacher abut a few of the questions. Things that we work on later in the year in geometry.


 
I'm a civil engineer so I see geometry as crucial to any education. Just about everything can be solved by similar triangles.


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## shiben

MarshallPope said:


> Are we sure? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
> PEMDAS
> 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
> 10-6
> =4
> 
> At least that's what I get...


 
Adding and Subtracting are the same thing, thus there is no implied first operation, basically you dont do all of one type first then the other.


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## chausman

shiben said:


> Adding and Subtracting are the same thing, thus there is no implied first operation, basically you dont do all of one type first then the other.


 
The order they appear in the problem is what we were told. 

This almost should get moved into its own thread in QotD!


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## museav

mstaylor said:


> Under no circumstances should you have to write an explanation of process.


Which is why when I took my PE exam you had to show all your work even if you already knew the answer or shortcuts. There were several times I actually had to go back and and fill in some of the steps from what I normally did.

As already stated, the point was showing that you could not just get the right answer but more importantly that you actually understood the underlying concepts, thus showing that you might be able to apply those same concepts to other problems.


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## zmb

museav said:


> Which is why when I took my PE exam you had to show all your work even if you already knew the answer or shortcuts. There were several times I actually had to go back and and fill in some of the steps from what I normally did.
> 
> As already stated, the point was showing that you could not just get the right answer but more importantly that you actually understood the underlying concepts, thus showing that you might be able to apply those same concepts to other problems.


 
I have to show work on tests in my AP Chemistry class to receive credit. Even if you get the wrong answer, showing work will yield partial credit, including on the real AP test. While that doesn't happen in the real world, you or someone else can pick it apart to see where you went wrong.


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## mstaylor

I freely admit that in higher math or science you have to show what your are doing, however, in elementary school you need to be graded on what you do, right or wrong. Learning the basics of addition, subtraction, multiplication and division are right or wrong. There are no signs to worry about, no abuquities at all. Higher math is also right or wrong but getting there is much more complicated so work needs to be shown.


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## ruinexplorer

So, would you admit that the above example was not higher math, but elementary math? Even still, by showing work we were able to (through different means) show how to obtain the correct answer. Showing work, even on basic math, is an element of problem solving, to verify a correct answer. If there were no need for showing how to do the math, then how would a teacher be able to know if the student misunderstood the concept or made a clerical error? 

Showing your work for math problems and knowing your times tables should be taught as an exercise of good practice. By learning that discipline at an early age, students will have a solid foundation as they get older and into more advanced subjects. I would liken this to a musician learning their scales. There are many self taught musicians who do not practice their scales, or never learned them, but you will not find very many playing in a major symphony orchestra.


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## FACTplayers

Math teaches so much more than just math. It is (arguably) the only subject where someone must actually understand all of the concepts and why the numbers work they way they do. Tests aren't multiple choice (multiple guess) for a reason and partial credit is the key to passing most exams. Even more, every solution has a proof for the solution. 

With all of that being said, every situation in life has a solution that needs to be found. This solution needs to be understood and a (type of) proof can then be established. Even the simplest of situations can be interrupted incorrectly (as shown above in my picture). Math should be teaching students to think through a problem, whether it be a math problem, economic problem, theatre related issue, etc. What other subject teaches you to think?

There is an old saying that goes something like this... "When a client tells an engineer he/she needs a ladder, a good engineer will ask how long, but a great engineer will ask 'why a ladder?'"


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## mstaylor

ruinexplorer said:


> So, would you admit that the above example was not higher math, but elementary math? Even still, by showing work we were able to (through different means) show how to obtain the correct answer. Showing work, even on basic math, is an element of problem solving, to verify a correct answer. If there were no need for showing how to do the math, then how would a teacher be able to know if the student misunderstood the concept or made a clerical error?
> 
> Showing your work for math problems and knowing your times tables should be taught as an exercise of good practice. By learning that discipline at an early age, students will have a solid foundation as they get older and into more advanced subjects. I would liken this to a musician learning their scales. There are many self taught musicians who do not practice their scales, or never learned them, but you will not find very many playing in a major symphony orchestra.


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. 
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.


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## FACTplayers

mstaylor said:


> 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.


 
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".


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## derekleffew

Speaking of showing one's work...

mstaylor said:


> ...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

-----
Responding to a previous statement,

Why bother with the memorization of times table(s) when one has Excel? [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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## zmb

FACTplayers said:


> 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.


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## FACTplayers

zmb said:


> 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."


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## derekleffew

mstaylor said:


> ... 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.

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.


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## ruinexplorer

mstaylor said:


> 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.


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## Chris15

mstaylor said:


> ...no abuquities at all.


 

derekleffew said:


> 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


 
My guess is the intended word was ambiguities...


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## mstaylor

FACTplayers said:


> 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.


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## mstaylor

Chris15 said:


> My guess is the intended word was ambiguities...


You are correct, ambiguity was the intended word. I have good math, music and language skills but suck at spelling. Running neck and neck are my typing skills.


----------



## FACTplayers

derekleffew said:


> Why bother with the memorization of times table(s) when one has Excel? [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.]


 
7*8=56 because 5,6,7,8. I still remember it this way.


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## sk8rsdad

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 = ...


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## derekleffew

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?


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## mstaylor

> 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.


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## zmb

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)


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## shiben

zmb said:


> 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...


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## zmb

shiben said:


> 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.


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## ruinexplorer

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.


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## mstaylor

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.


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## sk8rsdad

mstaylor said:


> 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?


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## mstaylor

sk8rsdad said:


> 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?


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## zmb

mstaylor said:


> 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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## cpf

On the quality/quantity topic: period length. In my opinion from my canadian K-12 schooling, the work accomplished/time spent curve maxes at about 45 minutes for early grades, rising to 70 for later ones. Anything more and kids start to get antsy, anything less and it's impossible to fit a lesson's worth of material in. You can't just expect kids to go into class at 8whatever and learn for 7 hours straight, breaks are essential.


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## chausman

cpf said:


> On the quality/quantity topic: period length. In my opinion from my canadian K-12 schooling, the work accomplished/time spent curve maxes at about 45 minutes for early grades, rising to 70 for later ones. Anything more and kids start to get antsy, anything less and it's impossible to fit a lesson's worth of material in. You can't just expect kids to go into class at 8whatever and learn for 7 hours straight, breaks are essential.


 
In Spokane, almost all the high schools have class from 8:15/8:30 to about 2:30/2:45/3:00. Our periods are 52 minutes at my school, it's similar at other schools in the area. For me, 52 minutes often isn't enough time. We do have block days twice a week with access time and periods 1/3/5 or 2/4/6 (depending on the day) with 90 minute periods that are great. We get at least twice as much done, most days more. There are good for tests because we have so much more time, and block days give us time to work with teachers before hand. We did have to have "power blocks" that were 105, 110, and 115 minutes long, and everyone hated them. Those days we started at the normal time and then had insanely long classes where students had a very hard time concentrating and teachers ran out of things to do. The only teachers that liked it were the PE teachers who could do lots of things in one day, and the drama teacher who was working on building the set for our show.

One thing about the video discussion, my geometry teacher (one of my favorite teachers ever, btw) recorded all of his lessons for the past three years, and has them available on Blackboard for free for anyone. [In fact a teacher at the other district high school "happened" to plan lessons one day later then my teacher, and replay our videos the next day when my teacher put them online.] so, because I was visiting my grandparents out of town, I can just go watch his videos to get caught up and then meet with him for things I don't understand. It is a great resource. And, he talks very fast (comically so intact) so you can go play him back at half speed!

(If any words seem weird, it might be the iOS autocorrect)


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## mstaylor

I could see recording classes for anybody not there to use to catch up. I don't see it as a useful tool fulltime. We live in a very rural area and I believe school starts at 8:30. Some students are 30 to 45 minutes from the nearest HS.


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## gumboot

I didn't even know Geometry was an individual subject in America. Imagine that- having only five or so subject spaces to fill (as I have) and having to take up two or three of them with individual aspects of Mathematics. It doesn't make much sense to me. I prefer the one core Mathematics course that has a selection of papers which cover all the bases- Algebra, Geometry (+trig), Number, Statistics etc,. You can also choose to take subjects like accounting, economics and enterprise and the only compulsory thing in that regard is half a year of Financial Literacy in Year 11 (year I've just finished) in which you learn how to draw up a budget and understand financial terms and documents. The other half of the year is spent learning about safe sex.

For my second to last year of High School starting in February I've picked:
Mathematics with Calculus
Physics
Electronics
Programming
English 
Music


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## z2oo

gumboot said:


> I didn't even know Geometry was an individual subject in America. Imagine that- having only five or so subject spaces to fill (as I have) and having to take up two or three of them with individual aspects of Mathematics. It doesn't make much sense to me. I prefer the one core Mathematics course that has a selection of papers which cover all the bases- Algebra, Geometry (+trig), Number, Statistics etc,. You can also choose to take subjects like accounting, economics and enterprise and the only compulsory thing in that regard is half a year of Financial Literacy in Year 11 (year I've just finished) in which you learn how to draw up a budget and understand financial terms and documents. The other half of the year is spent learning about safe sex.
> 
> For my second to last year of High School starting in February I've picked:
> Mathematics with Calculus
> Physics
> Electronics
> Programming
> English
> Music


 
That's actually interesting - only having 5 class spots. I have up to 9 classes that I can choose each semester, granted one must be some sort of physical education. I'm a sophomore (10th grade) and I've already taken Algebra I + II, and am now taking Plane and Solid Geometry. Apparently the order my school uses for math classes is strange for American education... Anyway, I have to say that geometry is still alive and kicking. Oh, and class lengths are 50 min each period for me.

Currently though, I'm taking these classes -
English 2 Honors
Plane/Solid Geometry Advanced (woo!)
AP Modern European History (MEAP)
Advanced Percussion Ensemble (APE, two period class)
Chemistry 1 (took Biology last year as a requirement)
Spanish 3
Scout Experience (phys. ed. class)


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## gumboot

Our cirriculum isn't half as... varied. We use the NCEA system for HS qualifications. In year 11 (I just finished YAY!) you work towards your Level 1 certificate, Year 12 Level 2, and Year 13 (12th grade equivalent) Level 3. Each level offers standards across the different subject areas, passing them will earn you credits, 80 credits at a certain level will earn you the certificate for that level. Some standards are internally assessed, especially in Technology and Arts subjects, while others are externally assessed (Exam format). Some of the standards in my Y11 Math course were:

-Apply algebraic methods in solving problems
-Investigate relationships between tables, lines, graphs and equation
-Solve problems using geometric reasoning (this included trig)
-Demonstrate understanding of chance and data

Depending on the Levels of NCEA you achieve by the time you've left school you are eligible to enter various forms of tertiary education. Level 3 will get you into most undergraduate degree courses at Uni, but some may have special subject requirements. Level 2 will get you into trade apprenticeships, polytechnics, and Diploma level study.

I like NCEA because it means I could get credit for a Drama standard to do with lighting/technical roles without actually taking the whole subject.

Sorry for the novel. XD


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## mstaylor

In my area the order of math is Algebra I, Algebra II, Geometry, Trig, Calc and any AP math you qualify for. Geometry used to come between the two Algrbra classes but they found they were spending too much time getting the kids back up to speed on the algebra. By the time you have two years of it, then back it with geometry then you can go into trig and be fine. 
Math is a touching spot for me, they need to go back and just teach the **** subject and forget all this creative crap to make kids more successful. Math came very easy for me so I help found a math tutoring club to help other kids. We found many times we could take what the teachers were saying and put it in language they could understand. For the ones of us the excell at a subject we should do our part to help others along.
Because I worked so late every night I tended to sleep through trig class. I would sit center row, first seat, put my head on the desk and sleep. I did my homework and aced the class, drove my teacher nuts. 
My point is, if you are spending your evenings watching videos of your teacher's lecture, seems to still be sit and listen, how are you to ever do any extracurricular activities? How could you play sports, do shows, work, learn karate, join scouts and just sit around and be a kid? While I agree there should be a small amount of homework to assure you understand the subject, teaching needs to done at school. 
It is like saying you need to work at the office for eight hours, but we need to have meetings to plan the work and assign responsibilities so they will all be in the evening. Idiotic!


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## gumboot

Is that order of math subjects spread across one year? Or do you spend your first year or two of HS doing Algebra and Geometry and then move on the the others over a period of years?

Once you get to year 12 (11th grade) you have the option of dropping math altogether. The only compulsory subject is English. So if the university/polytech course you're applying for doesn't have a great math component you don't have to take the subject.


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## zmb

My choices for PE is take it at school or pay around $500 to quasi-private school to maintain an online log for physical activity. Why does it cost so much? That would probably be the easiest credit to get outside of school but I don't think that it should take so much money. For comparison, my Spanish class from the University of Washington at the high school is $299 and carries 5 easily transferrable credits.


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## derekleffew

Original premise of thread:

> Replace one high school course with a course in entrepreneurship.



From _Lighting&Sound America_, November 2011, article _The ETC Culture_, by Lee Baldock, page 66:

> "Had I gone to business school, there would have been times that I would have quit." [Fred] Foster says. "Had I known--back when I was starting out--that an eight-to-one debt-to-equity ratio was, essentially, insolvency, that probably would have been the end. There's an advantage in being too stupid--you just push through to make it happen." Business school graduates, he believes, will not make the best entrepreneurs--although they may prove very useful to an entrepreneur one day.


Good thing Fred took classes in geometry, as well as those in theatre.


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## mstaylor

gumboot said:


> Is that order of math subjects spread across one year? Or do you spend your first year or two of HS doing Algebra and Geometry and then move on the the others over a period of years?
> 
> Once you get to year 12 (11th grade) you have the option of dropping math altogether. The only compulsory subject is English. So if the university/polytech course you're applying for doesn't have a great math component you don't have to take the subject.


Yes, a year a subject, so from Algebra I to calc it is five years.


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## gumboot

mstaylor said:


> Yes, a year a subject, so from Algebra I to calc it is five years.


 
Ah, that makes more sense. Sometimes I wish I could only take Geometry for a whole year or whatever, but Math isn't my absolute strongest subject (falls behind English and Music) so I think revisiting Algebra, Geometry and Trig etc in smaller units that get progressively more complex each year has served me well. It means that if I wanted to, I could drop Mathematics altogether in my second to last year and still have a well rounded knowlege of Algebra, Trigonometry, Statistics, Probability etc (but not Calculus) before I turn 16. However I need the full five years for an Engineering degree so I'm sticking with it.


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