Maths

[elam]

When I was in high school back in the late 1960s here in Oz four levels of Maths were taught 1st Level (theoretical maths), 2F (bit more practical), 2S (practical Maths) & 3rd level (vegie maths). At my school we didn't have a real choice at what level we could study.

Because my other subjects (Economics, History, Geography & English) were all at 1st level I only had a choice of 1st level or 2F Maths. I opted for 2F and was a dismal failure at it while at school (I must have been sick the day they explained all the cryptic symbolism). However, after completing my 12 years of captivity at school I entered the business world (finance) and suddenly found a use for Maths!

It is my contention that good Maths teachers who can communicate the predictive beauty of Maths are few on the ground. I often read in the press that there is a worldwide shortage of Maths & Science teachers, which isn't surprising given the old saying "those than can, do. Those that can't, teach" - and industry pays a lot better than a teaching job.

What is your opinion/experience?
___________________

This came to mind when recently I was asked "how hot is it?" We have been having an extended heat wave this Christmas.

Here in Oz we have been using the metric system (centigrade) for 40/50 or so years, so those of us brought up under the imperial system' (fahrenheit) have a hard time relating to the weather forcasts.

The person who asked me the question "how hot is it?" was having trouble with his mental arithmetic.

The official formula is: (C * 1.8) + 32 simplified as ((C * 9 ) / 5) + 32, which is hard to compartmentalise, especially for the older generation.

I use the metric formula which is much easier to compute mentally ((C * 2) / 10) * 9) + 32. Thus 42C = 107.6F = very hot.

An even easier formula is: A = C * 2 : B = A / 10 : F = 32 + A - B

Should school teachers simplify Maths for our kids rather than teach them complex formula?

[Sparko]

What is "vegie maths?" adding apples and oranges?

My experience growing up was mixed. I had algebra 1 in high school, and I was terrible at it. The teacher was horrible, never explained anything and just spouted off math technospeak without bothering to explain it. He sounded like an episode of star trek. I was completely lost. The next year I took geometry. when my teacher there saw I was lacking in basic algebra, he took the time to teach it to me in a way I could understand. Then I did well in geometry (I am visually oriented anyway so it was fairly easy) - I later took algebra 2, and did OK in it, passing with a B (A is highest, B is second..)

Even though I went into computers and electronics, I was never much of a "math guy" - geometry, angles, velocities and visual type math, I do well at. Formulas and equations, not so much.

[Boxing Pythagoras]

When I was in high school back in the late 1960s here in Oz four levels of Maths were taught 1st Level (theoretical maths), 2F (bit more practical), 2S (practical Maths) & 3rd level (vegie maths). At my school we didn't have a real choice at what level we'd study. Because my other subjects (Economics, History, Geography & English) were all at 1st level I only had a choice of 1st level or 2F. I opted for 2F and was a dismal failure at it while at school (I must have been sick the day they explained all the cryptic symbolism). However, after completing my 12 years of captivity at school I entered the business world (finance) and suddenly found a use for Maths. It is my contention that good Maths teachers who can communicate the predictive beauty of Maths are few on the ground. I often read in the press that there is a worldwide shortage of Maths & Science teachers, which isn't surprising given the old saying "those than can, do. Those that can't, teach" - and industry pay a lot better than a teaching job.

What is your opinion/experience?

It's definitely difficult to find good mathematics teachers with good mathematics curricula. On the one hand, I'm thankful for this, as it means that I'll never be lacking students to privately tutor. On the other hand, I love mathematics, and it drives me up a wall when I see it being taught poorly or incorrectly. After spending a decade in a profession which I came late to realizing I do not enjoy, I'm working towards becoming a teacher now, in order to do my little part in rectifying that aforementioned worldwide shortage.

Should school teachers simplify Maths for our kids rather than teach them complex formula?

Eh. The particular form of the formula is less important, in my eyes, than the reasoning behind the formula. I care less about whether a student can perform calculations in his head than I do about whether that student understands why he is performing those calculations.

[Sparko]

Eh. The particular form of the formula is less important, in my eyes, than the reasoning behind the formula. I care less about whether a student can perform calculations in his head than I do about whether that student understands why he is performing those calculations.

This!

That was what drove me crazy in Algebra. There was no "why" being taught. Or how the formulas related to the real world. I think that is why I did better in Geometry. I could see what I was working on and why. And the teacher there, used that to teach me algebra.

[Yttrium]

When I was in high school back in the late 1960s here in Oz four levels of Maths were taught 1st Level (theoretical maths), 2F (bit more practical), 2S (practical Maths) & 3rd level (vegie maths). At my school we didn't have a real choice at what level we could study.

Your old math program sounds very different than mine. I was in a private high school in the 70s. I had algebra in 7th grade, geometry in 8th, trigonometry in 9th, then two years of calculus. I ran out of math for 12th grade. Then again, I managed to get a couple years ahead of most other people in my class. Our 7th grade class was go at your own pace, and my math pace was very high.

I did have a good math teacher. He also taught physics, and was very science-oriented. I'd be interested in teaching math myself, but I'd have to go back to college to get a teaching degree, which would be a huge hassle at my age. I suspect that the teaching degree is more important to math teachers these days than actually being good at math.

[elam]

What is "vegie maths?" adding apples and oranges?

Almost! That is the term my kids applied to the level. In my day the subjects were color coded: Cerise, Blue1, Blue2 & Gold.

In the NSW educational system here in Oz, those that educators determine might have fewer prospects in the real world are given an education in absolute maths practicality. For instance: back when, how to balance a cheque book, I presume now that would be managing a credit card = minimising cost of debt repay ment, balancing the family budget. Then there is the usual spatial theory (distance, speed, height etc) and useful stuff one might use in a trade (eg: a plumber has to lay a line from x house to the main using various size pipes & connectors over a plot gradient of y with a 1 in 40 fall. How much pipe will he need? This sought of question is a practical introduction to trigonometry. Tell the kids "we are going to do trigonometry today." and they'll turn off. Give them a problem that might have relevance to them and they might turn on. Well that is the theory).

My experience growing up was mixed. I had algebra 1 in high school, and I was terrible at it. The teacher was horrible, never explained anything and just spouted off math technospeak without bothering to explain it. He sounded like an episode of star trek. I was completely lost. The next year I took geometry. when my teacher there saw I was lacking in basic algebra, he took the time to teach it to me in a way I could understand. Then I did well in geometry (I am visually oriented anyway so it was fairly easy) - I later took algebra 2, and did OK in it, passing with a B (A is highest, B is second..)

I struggled throughout high school with Maths 2F, barely passing the bi-annual exams, Failed the governments HSC which meant I couldn't go to Uni - had to have a pass in five subjects. So wasted a year doing 3rd level Maths just so I could get a pass in the 5th subject.

Even though I went into computers and electronics, I was never much of a "math guy" - geometry, angles, velocities and visual type math, I do well at. Formulas and equations, not so much.

Strangely enough, after a stint in finance I accidently ended up as a system designer (database & computer process), no need for maths in those fields. Formulae are usually embedded in the code, and formulae can be gleaned from the relevant text book.

I guess from an engineering viewpoint, building BIOS, encryption, comms etc advanced Maths knowledge is critical. I know in Civil Engineering they use computers a lot for determining things like wind sheer, load etc but in many cases they are reliant on humans to compute the impact of external variables that might challenge the veracity of inputs.

[elam]

Your old math program sounds very different than mine. I was in a private high school in the 70s. I had algebra in 7th grade, geometry in 8th, trigonometry in 9th, then two years of calculus. I ran out of math for 12th grade. Then again, I managed to get a couple years ahead of most other people in my class. Our 7th grade class was go at your own pace, and my math pace was very high.

I did have a good math teacher. He also taught physics, and was very science-oriented. I'd be interested in teaching math myself, but I'd have to go back to college to get a teaching degree, which would be a huge hassle at my age. I suspect that the teaching degree is more important to math teachers these days than actually being good at math.

I've often wondered why people see some mystery in Calculus. I understand it to be universal that infants are taught basic arithmetic using symbolism for addition, subtraction, division & fractions. By year 1 they have assimilated multiplication via the 12 times tables (though in the early 1970s the bleeding hearts discouraged making kids learn the tables, but by the mid 1970s they were back in vogue). I don't remember primary school very much other than I was totally bored. High school was a bit more interesting. Anyway, what occurs to me is that we start off educating kids well, then complicate their education with a lot of useless exercises. For instance: my Maths teacher in year 6 would make us enumerate a problem to its full extent, which could take a couple of exercise book pages when most of us kids could solve the problem in three or four lines.

An amusement: one of my uncles is a Civil Engineer and using standardised Math step computation he can demonstrate that 1 + 1 = 0.

Another amusement: My wife would brag to our friends that my youngest son (he was about 3 at the time) was a Maths genius but only if his father (me) gave him the problem to be solved. I'd give him a complex list of addition, subtraction, multiplication & division, the adults would have pen and paper following the equation, and in the end my son would give the correct answer. Was my son a genius? No! I taught him to repeat the last number I'd said when I asked "What is the answer?"

[Cow Poke]

When I was in high school back in the late 1960s here in Oz four levels of Maths were taught 1st Level (theoretical maths), 2F (bit more practical), 2S (practical Maths) & 3rd level (vegie maths). At my school we didn't have a real choice at what level we could study.

Because my other subjects (Economics, History, Geography & English) were all at 1st level I only had a choice of 1st level or 2F Maths. I opted for 2F and was a dismal failure at it while at school (I must have been sick the day they explained all the cryptic symbolism). However, after completing my 12 years of captivity at school I entered the business world (finance) and suddenly found a use for Maths!

It is my contention that good Maths teachers who can communicate the predictive beauty of Maths are few on the ground. I often read in the press that there is a worldwide shortage of Maths & Science teachers, which isn't surprising given the old saying "those than can, do. Those that can't, teach" - and industry pays a lot better than a teaching job.

What is your opinion/experience?
___________________

This came to mind when recently I was asked "how hot is it?" We have been having an extended heat wave this Christmas.

Here in Oz we have been using the metric system (centigrade) for 40/50 or so years, so those of us brought up under the imperial system' (fahrenheit) have a hard time relating to the weather forcasts.

The person who asked me the question "how hot is it?" was having trouble with his mental arithmetic.

The official formula is: (C * 1.8) + 32 simplified as ((C * 9 ) / 5) + 32, which is hard to compartmentalise, especially for the older generation.

I use the metric formula which is much easier to compute mentally ((C * 2) / 10) * 9) + 32. Thus 42C = 107.6F = very hot.

An even easier formula is: A = C * 2 : B = A / 10 : F = 32 + A - B

Should school teachers simplify Maths for our kids rather than teach them complex formula?

I think teachers should focus with MOST KIDS on things like being able to keep a checkbook, plan and implement a household budget, and things that they're actually going to experience in real life.

[rogue06]

Maths are of da debil.

As St. Augustine warned in his De Genesi ad Litteram ("The Literal Meaning of Genesis"):

"The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of hell."

The Dominican Father Tommaso Caccini (d. 1648) preached a sermon at the Santa Maria Novella in Florence on the subject of Joshua 10 a few days before Christmas of 1614 that ended with a quote from Acts 1:11, "Ye men of Galilee, why stand ye gazing up into heaven?" (in this context obviously a pun on Galileo Galilei), which insisted that "geometry is of the devil," and that "mathematics should be banished as the authors of all heresies." He would be promoted to the Master and Bachelor of the Santa Maria sopra Minerva convent in Rome and later prior of the famous monastery of San Marco.

[elam]

Your old math program sounds very different than mine. I was in a private high school in the 70s. I had algebra in 7th grade, geometry in 8th, trigonometry in 9th, then two years of calculus. I ran out of math for 12th grade. Then again, I managed to get a couple years ahead of most other people in my class. Our 7th grade class was go at your own pace, and my math pace was very high.

I did have a good math teacher. He also taught physics, and was very science-oriented. I'd be interested in teaching math myself, but I'd have to go back to college to get a teaching degree, which would be a huge hassle at my age. I suspect that the teaching degree is more important to math teachers these days than actually being good at math.

I don't know what or how they teach Maths these days - my youngest son turned 40 last year. In my day the different disciplines in Maths weren't differentiated. Arithmetic/Algebra & Geometry were taught in primary school. Trig & Calculus/Algebra in high school. One big book each year as the difficulty increased. Strange thing: at the start of the year., our first instruction was to get out our books and cut out the answers at the back of the book (we had been instructed to bring a Gem blade to class).

[Raphael]

I think teachers should focus with MOST KIDS on things like being able to keep a checkbook, plan and implement a household budget, and things that they're actually going to experience in real life.

Yeah, there should be more of that, but at the same time school is meant to prepare students for whichever possible career path they choose to go to. When my brother was lecturing Civil Engineering he expected his first year students to already have a high competency in maths (for little things like working out the tensile strength of this concrete beam etc. and understanding the maths, and reasoning behind those equations)

[Bisto]

I would like to teach at my university (of perhaps somewhere else, I don't know) later in life. Maybe when I'm fifty or something. But I'm not sure I'd do maths like BP, I think I may come to be of more use in other subjects depending on the experience I develop throughout my career. I like teaching, and I'm told I'm not bad at it by fellow students to whom I do assistantships and by teachers when I do presentations and things like that, so hopefully I'd help improve the system too :-)

[elam]

I think teachers should focus with MOST KIDS on things like being able to keep a checkbook, plan and implement a household budget, and things that they're actually going to experience in real life.

Imu, in the Oz (NSW) system that is the basis of 3rd level (Vegie maths) - give those who are viewed as having little prospects in the real world the basic skills to survive. Other kids need a challenge. For instance: my uncle was involved in Australia/Britian/USA's early aerospace development out in Womera and as a kid I had aspirations of developing and designing spaceware - pity I was lousy at advanced Maths.

Very strange thing here: we are an immigrant nation and because of our location have a high Asian representation. A lot of those guys, in my experience, just take to Maths & Music like ducks to water - year on year topping the state in the HSC.

[elam]

Maths are of da debil.

As St. Augustine warned in his De Genesi ad Litteram ("The Literal Meaning of Genesis"):

"The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of hell."

Thankyou.

I went to a Catholic school (Marist brothers) here in Sydney, NSW and that quote from nAugustine would have come in very handy back whenever...

I'll put it in my archives. Who knows it might benefit my grand-children, if I ever get any...

[elam]

I would like to teach at my university (of perhaps somewhere else, I don't know) later in life. Maybe when I'm fifty or something. But I'm not sure I'd do maths like BP, I think I may come to be of more use in other subjects depending on the experience I develop throughout my career. I like teaching, and I'm told I'm not bad at it by fellow students to whom I do assistantships and by teachers when I do presentations and things like that, so hopefully I'd help improve the system too :-)

Life can be surprising and in your career you might find yourself in a formal teaching role within your occupation.

In my case, in the early 1990s I occasioned a peculiar, high paying occupation called a "Systems Designer". This was a new position in the IT sector that came into vogue in the late 1980s. These days the occupation might be labelled "System Architect" or "System Specialist" or "Systems Consultant (Internal)" At one time or another I've held each of these titles.

Anyway, when I was dubbed "System Designer" my employer would annually do an intake of grads, and make me responsible for them. The irony: Though I had a track record in implementing and customising MIS & FIS systems, I'm self taught in computer languages, technology and systems. Though I have other qualifications in seemingly unrelated fields. The upshot: I had a good reputation in the IT industry, and consequently had professors consult me about what they should be teaching. As one of my grads once said to me "you know, I came out of Uni thinking I knew it all, and now I know I knew nothing! Thankyou."