"The teacher's aide in my first geometry class was Pythagoras."
Yesterday morning I attended a fund-raiser breakfast at the nearby American Legion. ?ÿThe fellow who sat down to my left is locally known as an electronics wizard who can fix all sorts of problems with a wide variety of devices. ?ÿVery few realize that his degree is in electrical engineering. ?ÿNext, another fellow took a chair across the table. ?ÿYoung people know him as the local pharmacy owner's husband who helps her with the business. ?ÿThe rest of us remember him as the only veterinarian working a large area around the town for two decades. ?ÿOnly a handful probably know his BS is in mechanical engineering. ?ÿNearly everyone knows I am a land surveyor, but relatively few are aware of my engineering degree.
We struck up a conversation about the role of arithmetic, algebra, geometry, trigonometry, calculus and differential equations in our careers. ?ÿThey laughed when I told them about Pythagoras. ?ÿThey could relate as they are both five years older than what I am. ?ÿThat introduction to geometry feels as though it happened a thousand years ago. ?ÿI mentioned that Pythagoras is cited by some sources as being one of the early proponents of complex and imaginary numbers. ?ÿWe would have none of our modern electronic gadgets without complex and imaginary numbers. ?ÿThe electrical engineer jumped on that like a chicken on a June bug and started talking about negative vectors and imaginary power versus real power. ?ÿThe mechanical engineer put his hand on his head and laughed as he told us he was getting a headache from thinking about such things for the first time in years.
As a member of the school board it is frustrating to see less and less emphasis placed on math and science by the high muckety mucks of education to be replaced by classes focused on being able to get and keep dead end jobs at the bottom of the pay scale that will require continual re-education to move to the next dead end job. ?ÿBut, there are big, shiny participation trophies for everyone.
I hear those same complaints all the time. Looking through the notes my kids took in High School tells a different story. This is recent stuff as my youngest is a freshman in College.
One of the notebooks has Analytic Geometry concepts that I would need three books and a computer to get through. Another is for a concurrent credit calculus class and still more are for AP Stats, pshych 2, and the list goes on. Most of it I did not see until I took a few college courses with some still beyond my knowledge base.
The problem here is NOT the quality of education, it's the lack of value placed on it. Vo-tech certificates used to be the foundation of the middle class. Now we demand a 4 year degree for everything and push an entire generation into useless student loan debt.
One of my kids graduated double major/double minor from the best private College in our area. She is teaching English and Debate to Korean kids in VietNam. Around here she was a $10/hour barrista.
My experiences do not bear out the complaints of my fellow grey hairs. They do demonstrate that a train wreck of useless debt and a severe shortage of technical and trade workers is on the horizon.
My .92 (adjusted for the coming inflation), Tom
My two kindergarteners are writing sentences (correct spelling is nonexistent of course), counting to 100, counting by 5s and 2s, and starting addition and subtraction up to 20. That's a heck of a lot more than I was doing in kindergarten 45 years ago. After coming home the first day, I supposedly announced I wasn't going back because they weren't going to teach me to read.
On the other hand, I hope a future math teacher won't waste time teaching them this topic that I had in 7th grade math--how to properly pronounce a number.?ÿ
124.56
"one hundred twenty four AND fifty-six hundredths"
Has that every been an issue in a later class or in my post-schooling life? Yeah, no.
I'll agree with the bionicman post above about the elevating of the curriculum in?ÿ high school courses in the present. Geometry I is not your grandpa's geometry of the 1960's. Same could be said of the sciences. Mostly all schools have some type of STEM courses offered or required. I'm not discussing AP courses either but regular and honors courses.?ÿ
There is no doubt standards have been raised and digital study is essential along with traditional note keeping of in class.?ÿ
Of course, not everyone can be A student's who become engineers etc. There will?ÿ be C & B students and that is fine.?ÿ
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Slight hijack - according to Charles Seife's (excellent) book "Zero - The Biography of a Dangerous Idea" the Greeks in general and Pythagoras in particular were vehemently opposed to the concepts of zero, infinity, and irrational numbers.
One significant change is the introduction of more algebra and geometry in early grades. That's both good and bad. Many elementary and middle school teachers lack the background needed to teach these concepts other than by rote. But those students with math talent who have good teachers thrive with early math concepts. Parents really really need to monitor that process.
Several years ago, North Carolina essentially eliminated Geometry as a standalone subject in high school. That material was merged into three math courses creatively named Math 1, Math 2, and Math 3. Then lots of elementary geometry concepts concerning shapes and areas and angles were pushed down into lower grades. We'll have to wait and see what the result is; it literally could go either way. My main objection was the potential loss of formal logic principles taught in Geometry. I would judge that, for the bulk of our population, high school geometry is the only introduction to those principles and the best way for students to acquire reasoning skills.
Melita, I somewhat share your feelings about the emphasis on properly pronouncing numbers. However, I've seen so many students who had no concept of place value when they read a number that I have often prayed for more of that kind of detail in early grades. My area of frustration was with the time spent on Roman numerals. Given the plight of many of our college loan debtors, that time might have been better spent on Ramen Noodles.?ÿ
In the Asian countries, the problem seems to be the emphasis on rote learning and quick recall facts, with less emphasis on thinking and reasoning. Undoubtedly, there is opportunity and money to be made in solving these problems, but there's also a very steep slope to climb in the implementation.
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The current big move in education:
* social-emotional growth
*kindergarten readiness
*individual plan of study based on career interest
*graduation rate
*postsecondary success
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Postsecondary success is primarily based on what percentage of the graduates are still enrolled or who have completed at least a two-year course of study in formal education two years following their date of high school graduation. ?ÿAnyone who enters the military or who is in the work force does not count. ?ÿThey are failures.
Graduation rate is a joke. ?ÿThis encourages schools to find ways to give diplomas to those who do not follow the standard course of study. ?ÿIf you are still breathing, there's a way to get your diploma.
Individual plan of study is another way to let students avoid anything challenging or in which they might get a lower grade than an A. ?ÿFor exceptional students this can be great. ?ÿFor the masses, not so much. ?ÿOnce they enter the work world they will discover the folly of only taking the easiest courses.
Kindergarten readiness encourages the school to attempt to go directly into the homes of children from birth to Kindergarten age and tell the ignorant parents that they are ignorant and that the school needs to control that child's future. ?ÿI think Russia was famous for this type of thing.
Social-emotional growth involves the "everybody gets a trophy" mentality so as to boost the student's self-esteem at all times. ?ÿThe only bright spot is that this goal includes making students more aware of the needs of the community in which they live. ?ÿVolunteerism is promoted.
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Things run different here, but the focus on secondary education is similar.
How anyone can define being unemployable in your chosen field while drowning in student debt 'success' and serving your country while building a lifetime of benefits as 'failure' is beyond me....
I am on school board, and my wife teaches pre algebra and algebra in middle school. In my slice of rural America the disparity between pupils is huge.?ÿ It's a reaction to the disparity in parenting. Some parents push their kids, others expect the school to do it which never works.
I could not tell you who the truancy officer was when I attended our small town school decades ago, but for the last five years it's been a full time job at our school of about 700 pupils?ÿK-12.
The school?ÿneeds to stay financially viable and avoid constant parent conflicts. If a?ÿstudent?ÿdoesn't graduate we lose funding. If they get bad?ÿgrades most parents just want them 'magically' to get better. No follow through at home, it's always the teachers fault, there's too much homework, "I can't expect my kid to get up at 7am", man I have heard them all.?ÿ
The school's reaction with respect?ÿto math?ÿhas been to sort the students in 5/6th grade and funnel the them into more advanced classes if capable. The other students are placed in less aggressive course work.?ÿEssentially your math ceiling?ÿat high school is set?ÿas you enter 7th grade due to the way the pre-requisites?ÿand schedules work.
Other course work is flat our easier. Especially language arts.
The easy classes are?ÿextremely easy.?ÿ The?ÿadvanced classes are hard.?ÿAll the diplomas look the same, but they aren't equal.?ÿI guess that's?ÿwhy there are transcripts.
Steve
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I wonder if the requirement of a college degree for many jobs comes from a lack of faith in what earning a high school diploma requires. And I wonder if the requirement of an advanced degree reflects a lack of faith in the knowledge gained in earning an undergraduate degree.
Can you believe that I taught Pre-calculus students who came to the subject without knowing the difference between clockwise and counter-clockwise? They learned to tell time on digital clocks and never saw the need for analogue time-telling or the terms associated with it.
So the way they learned to tell time impeded their learning of angle values on a unit circle. Should we change the terminology or should analog time-telling be taught somewhere other than Pre-calculus? That's just one of the many stumbling blocks that teachers and students have to overcome every year.
@mathteacher, I attended a really small school (47 in my graduating class).?ÿ Our course work (or at least its organization) was simpler.?ÿ As a freshman you took Algebra I, as a sophomore you took Geometry, as a Junior you took Algebra II, as a senior you took College Algebra and Trigonometry.?ÿ All this assuming you plan to attend college.?ÿ Of course we didn't have semesters, you took a year of each subject.?ÿ Out of 47 I can think of 2 PEs, 1 land surveyor, 2 CPAs, 1 Navy Captain (retired) and at least 5 successful business owners.?ÿ No Calculus, no Psychology, no advanced arts just a good solid foundation in the basics.
Andy
My experience was similar, Andy. My graduating class numbered 32 and I had the basic 3 plus a worthless advanced math class. But I learned a great deal of math in chemistry and physics. In the 14 years that I taught, even good math students avoided physics like the plague. More took chemistry and I'm sure that they learned some math as I did.
When North Carolina dabbled in Common Core math, I studied a lot of the background research that the Common Core folks shared. One piece asked college math professors what they wanted their students to bring with them from high school. The professors wanted a background very similar to what you and I had. They wanted fewer topics covered in high school and deeper understanding of those topics.
Education gurus really need to conduct fewer studies and listen more to the people who get their graduates. Missing the mark on teaching essentials is hurting everybody.
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Cripes my grandson must have a gift for geometry; he is 6 years old and can recognize a dodecahedron in a book of geometric shapes. Me, I still can??t figure out why ??YIELD? signs are upside down. However, when I was in a Parochial prison early in life, I was "forced" to memorize "times tables" all the way to 15 squared in the 3rd grade. Damn glad I did too.?ÿ ??ÿ
Not math ?ÿbut a current deficiency in education. ?ÿThe young fellow who just aced the semester final in calculus had to admit last week that he could not decipher the hieroglyphics of the cursive writing on the survey we needed to use for our work.
Yup, cursive was completely?ÿremoved from the curriculum here three years ago.?ÿ It has probably been fifteen years since it was taught and graded with any real emphasis.
Steve
Maybe they just got tired of cursing, and, wanted something more intellectual.
Seriously, the fault I see in the education system is that no consideration is given to the students that know what they want to learn. It is always assumed that the "grown-ups" (and I put that in quotes, because most are merely physically grown up) are showing students a little of everything and allowing them to make up their mind on what to like.
This smorgasbord goes on through high school and college. I did not want to study any foreign languages in high school, and, I did not want to study electrical engineering in college. I did because it was the "curriculum"?ÿand that was the only explanation.
I knew in high school that what I wanted to study was mathematics and science. There was no chance of getting an education based on what I wanted. In college there were electives that allowed a little freedom. Not until graduate school was I allowed to break out and make a real choice on what I thought was important.
Too many people who consider themselves educators are simply interfering with the learning process. Their authority makes students lose confidence in what is really their own goal in becoming a thinking individual.
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I started out surveying with my dad.?ÿ After school I decided to try to "find myself" a bit and didn't survey.?ÿ Later I decided surveying was what I wanted to do, and I went to a survey school.?ÿ Some here are familiar with the Brinker school.
Anyway, we started out with not allowing calculators.?ÿ We had to go back to basics that we had all learned in Jr. High and High School.?ÿ We started out with addition and subtraction.?ÿ We got hundreds of problems to solve by hand.?ÿ You soon learned that just running through it once had room for errors.?ÿ Moving on to long division and multiplication, logs, log tables, trig tables, etc.?ÿ We learned to do the long math and double-check it.?ÿ As in field work back in the day, you had to get the answer correct when you were calculating a traverse closure by hand.?ÿ With calculators you soon loose the importance and emphasis of getting the answer right and double-checking your work.?ÿ More so with fancy computers.?ÿ You just run it through a program and apply the answers that are spit out.?ÿ Total loss of even knowing if an answer "looks correct".?ÿ For the most part the modern software can speed up your production a "million-fold" but the errors are much more sophisticated and hard to recognize.?ÿ (same is true with understanding statistics, imaginary numbers, calculus and higher-math concepts I am sure.)
(Same is true for learning to use the instrumentation we have these days, vs. reading angles off of verniers and distances off a tape measure).
I agree with learning modern equipment and techniques, but I disagree with (not) having a strong understanding in the fundamentals.?ÿ Learning the old stuff until you have a strong understanding is lost, often, in education.?ÿ Pushing yourself to higher math concepts without having strong fundamental math is a bit of a mistake.?ÿ I would also apply that to reading, writing, cursive writing, etc.?ÿ Talking to an audience of surveyors, I am sure we can all relate to trying to read difficult cursive notes.?ÿ I remember good ole Gene Kooper showing us some old solar observation notes, and pointing out that the math had an error in them that made for an incorrect bearing on the line.?ÿ How many of us would have spotted that error and been able to correct the bearing of the original line.
Sorry for the bit of rambling on this post.?ÿ I was kind of typing as I thought.?ÿ (Oh, yeah, and it's nice to have good typing skills so you can hammer out a sentence as you think it, and noticing typos that spell-checker won't necessarily catch - I'm sure someone here will catch some of my typos above, haha).?ÿ How many have typing class in Jr. High these days I wonder.
I was able to get a hold of a partial transcript of HC's conversation with his two Engineer friends.?ÿ Not sure if you want engineers talking theology but anyway it went something like this:
The Electrical Engineer said: ??God must be an electrical engineer. You only have to look at the complex nervous system powered by minute electrical impulses to see that.?
The Mechanical Engineer said: ??I??m sure God must be a mechanical engineer, how else could he have designed such advanced mechanical systems: the heart a pump, the veins pipes and the tendons and muscles an advanced pulley system.?
The Civil Engineer replied: ??You are both wrong. God is a civil engineer. Who else would run a sewer system through a recreational area??
I am glad you learned to type. Especially now that we all have keyboards.
When I wanted to take typing classes in high school the faculty frowned on the idea. They told me that after graduation I would most likely have a secretary who would type for me.
What a horribly ignorant and sexist point of view. Teachers should be qualified or be required to take mind-opening exercises.?ÿ ?ÿ
Would you rather a teacher be an inspiration or an authority?
I am glad you learned to type. Especially now that we all have keyboards.
When I wanted to take typing classes in high school the faculty frowned on the idea. They told me that after graduation I would most likely have a secretary who would type for me.
What a horribly ignorant and sexist point of view. Teachers should be qualified or be required to take mind-opening exercises.?ÿ ?ÿ
Would you rather a teacher be an inspiration or an authority?
Typing class teaches your hands to hit the letter you're thinking of.?ÿ I guess it's giving it that muscle memory???ÿ Anyway, I took the class back in 1969 or '70....maybe'70.?ÿ And virtually?ÿnever typed again until around 1990 when we were getting computers @ work.?ÿ It was surprising how quickly I picked it back up.?ÿ I was slow at first, but generally I knew where the keys were.?ÿ Sometimes I would stop and look for a Q or a Z or some other letter you don't hit often, until I got back into the hang of it.?ÿ In school, they had you work on several "pangrams" such as "The quick brown fox?ÿjumps over the lazy dog".?ÿ (The pangram is a sentence that include all of the letters of the alphabet.)
(sorry for the semi-hijack to everyone)
