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ArishMell · 70-79, M
How can you have "Pre-algebra"? That's like asking a book shop to obtain a copy of a treatise on mathematics, then saying you have "pre-ordered" it - impossible, except to Doctor Who, perhaps.
One useful definition of Algebra is that it encodes in an abbreviated, general form arithmetical rules or sets of instructions to carry out certain arithmetical steps, but is not arithmetic in a numerical sense. Neither is arithmetic, algebra.
So you won't learn Algebra (and indeed most of Maths) unless you understand Arithmetic first.
To show what I mean:
[2+4] X [2+4] = 6 X 6 = 36; alternatively {2^2 + 2X2X4 + 4^2] = 4+16+16 = 36.
That is pure arithmetic. I would not call it "maths" at all unless I was being rather Pseuds' Corner about it. But..... let's look at it algebraically:
(a+b)(a+b) = [a^2 + 2ab + b^2]. Oh that SW's text-editor would allow superscripts!
That is Algebra. It encodes exactly what the above arithmetic "sum" is doing with the values 2 and 4; but gives you a rule applicable to any pairs of values.
Is Algebra harder than Arithmetic then? It should not be.
It has foxed many generations of schoolchildren by its apparently abstract nature and saying things like a=b+t. How can a=b+t? After all, you don't spell the games implement "aaa". That mystique is wrong, but may reflect how Maths text-books and teachers, teach Maths.
So Algebra may be a lot easier if you bear in mind that definition above. You can extend it to, to consider that a Formula is a just shorthand instructions to work out Something Useful - like how much emulsion you need to paint the kitchen walls, or what value capacitor to use in an electronic filter circuit.
Also as my worked example shows, you can demonstrate to yourself how it works and that you are on the right track by substituting simple numbers for the letters.
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Your question raises another point.
Algebra is not an academic subject on its own, any more than are trigonometry or matrices or geometry or logarithms. I've seen evidence suggesting that some people try to break Maths into hermetic, separate lines of academic study, but that seems a recipe for failure by losing the all-important connections between topics.
All these and more are topics within the academic subject or science that is Mathematics. Also, each can be studied to whatever level you like, but many are mutually dependent.
Algebra goes even further. It can be taken to its own extremes, but for all practical purposes it is the language of Mathematics generally, just as ordinary numbers and operators are the language of ordinary, value-manipulating Arithmetic.
One useful definition of Algebra is that it encodes in an abbreviated, general form arithmetical rules or sets of instructions to carry out certain arithmetical steps, but is not arithmetic in a numerical sense. Neither is arithmetic, algebra.
So you won't learn Algebra (and indeed most of Maths) unless you understand Arithmetic first.
To show what I mean:
[2+4] X [2+4] = 6 X 6 = 36; alternatively {2^2 + 2X2X4 + 4^2] = 4+16+16 = 36.
That is pure arithmetic. I would not call it "maths" at all unless I was being rather Pseuds' Corner about it. But..... let's look at it algebraically:
(a+b)(a+b) = [a^2 + 2ab + b^2]. Oh that SW's text-editor would allow superscripts!
That is Algebra. It encodes exactly what the above arithmetic "sum" is doing with the values 2 and 4; but gives you a rule applicable to any pairs of values.
Is Algebra harder than Arithmetic then? It should not be.
It has foxed many generations of schoolchildren by its apparently abstract nature and saying things like a=b+t. How can a=b+t? After all, you don't spell the games implement "aaa". That mystique is wrong, but may reflect how Maths text-books and teachers, teach Maths.
So Algebra may be a lot easier if you bear in mind that definition above. You can extend it to, to consider that a Formula is a just shorthand instructions to work out Something Useful - like how much emulsion you need to paint the kitchen walls, or what value capacitor to use in an electronic filter circuit.
Also as my worked example shows, you can demonstrate to yourself how it works and that you are on the right track by substituting simple numbers for the letters.
.
Your question raises another point.
Algebra is not an academic subject on its own, any more than are trigonometry or matrices or geometry or logarithms. I've seen evidence suggesting that some people try to break Maths into hermetic, separate lines of academic study, but that seems a recipe for failure by losing the all-important connections between topics.
All these and more are topics within the academic subject or science that is Mathematics. Also, each can be studied to whatever level you like, but many are mutually dependent.
Algebra goes even further. It can be taken to its own extremes, but for all practical purposes it is the language of Mathematics generally, just as ordinary numbers and operators are the language of ordinary, value-manipulating Arithmetic.
Math was my best subject, so I might not give the best answer for the average person, but to me, they were basically the same thing.
Yes it was harder, but that's because it's the next level and the next level is harder, hit at the same point, it was basically more of the same stuff.
Not like statistics, trigonometry, calculus, etc, which can be something entirely different.
Yes it was harder, but that's because it's the next level and the next level is harder, hit at the same point, it was basically more of the same stuff.
Not like statistics, trigonometry, calculus, etc, which can be something entirely different.
ArishMell · 70-79, M
@sstronaut It was about my weakest subject, but I have caught up in some topics in the years since; by using them and seeing them in new, real-world ways.
I know the various topics can be very different themselves - and Euclidean Geometry seems to exist in a world of its own - but most still need algebra to express them, and many are linked in all manner of other ways.
It is that inter-dependency that was my point about algebra; but I'm still puzzled by "pre-algebra" which your question implied is some sort of maths topic or even its own curriculum subject.
I've no idea who invented that term, nor why; but something is either algebra or it's not. If it's arithmetic, why not simply call it arithmetic?
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Incidentally I am not a parent so I don't know what they teach in arithmetic and maths in UK schools now. However, I do know the syllabus differs from the one I knew, and which is still valuable in real life.
Not only that, they baffled parents trying to help their children understand their homework, by introducing some very strange methods for ordinary arithmetic. My local adult-education college even offers courses to help parents understand these mystery new ways! I have not seen these fads, but my brother (who has a son and daughter) says it makes things like long-multiplication very awkward and long-winded.
I know the various topics can be very different themselves - and Euclidean Geometry seems to exist in a world of its own - but most still need algebra to express them, and many are linked in all manner of other ways.
It is that inter-dependency that was my point about algebra; but I'm still puzzled by "pre-algebra" which your question implied is some sort of maths topic or even its own curriculum subject.
I've no idea who invented that term, nor why; but something is either algebra or it's not. If it's arithmetic, why not simply call it arithmetic?
.
Incidentally I am not a parent so I don't know what they teach in arithmetic and maths in UK schools now. However, I do know the syllabus differs from the one I knew, and which is still valuable in real life.
Not only that, they baffled parents trying to help their children understand their homework, by introducing some very strange methods for ordinary arithmetic. My local adult-education college even offers courses to help parents understand these mystery new ways! I have not seen these fads, but my brother (who has a son and daughter) says it makes things like long-multiplication very awkward and long-winded.
@ArishMell Pre-algebra is basic algebra, to make sure you have your math fundamentals down first, and reinforce them, as if you're fundamental aren't down, you're basically screwed going forward.
Because it's about to get more complex, and apparently there were enough people that struggled with straight to algebra, that they decided there needed to be a basic algebra first.
So see it as Basic, Intermediate and Advance
Pre-algebra is Basic
Algebra is intermediate
And I don't know what is advanced, but unless you're in math, physics or engineering field you probably won't have to worry about it.
Because it's about to get more complex, and apparently there were enough people that struggled with straight to algebra, that they decided there needed to be a basic algebra first.
So see it as Basic, Intermediate and Advance
Pre-algebra is Basic
Algebra is intermediate
And I don't know what is advanced, but unless you're in math, physics or engineering field you probably won't have to worry about it.
ArishMell · 70-79, M
@sstronaut Ah, I see. Thankyou. I wonder why they didn't simply call it "Basic Algebra", so you do know what it's about.
A problem I found at school was that it seemed all taught as something so abstract. I could not belay it to real things to help me see what it's about.
Once, at work maybe ten years ago now, somebody asked to borrow my computer while I busy with something else. He wanted to refer to a technical paper without having to traipse all the way back to his office. He did that, but when I returned to it I found he'd been distracted into also looking at some paper about some alternative way to solve Someone's Equation. He'd left it open, perhaps as a little joke as he knew I was not a fellow mathematician.
"Advanced Algebra"? This stuff was Pure Algebra so pure I could not recognise most of the operators, and had to look hard to spot those nice friendly '+' and '=' signs! I had no idea what it was about, or what anyone might use it for; or if it was just an academic puzzle at the Highest Levels!
A problem I found at school was that it seemed all taught as something so abstract. I could not belay it to real things to help me see what it's about.
Once, at work maybe ten years ago now, somebody asked to borrow my computer while I busy with something else. He wanted to refer to a technical paper without having to traipse all the way back to his office. He did that, but when I returned to it I found he'd been distracted into also looking at some paper about some alternative way to solve Someone's Equation. He'd left it open, perhaps as a little joke as he knew I was not a fellow mathematician.
"Advanced Algebra"? This stuff was Pure Algebra so pure I could not recognise most of the operators, and had to look hard to spot those nice friendly '+' and '=' signs! I had no idea what it was about, or what anyone might use it for; or if it was just an academic puzzle at the Highest Levels!
Spoiledbrat · F
RedBaron · M
Math is all simple until you get to calculus.