What were your worst subjects in high school? For me, it was math and chemistry.
31-35, F
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ArishMell · 70-79, M
@jackson55 @helenS
It's notable that Mathematics seems here the least popular subject, and Algebra the least popular of its manifold fields. I battled with maths and did not like it much at school but in later years found ways to clarify at least some of it, by hooking it to real things.
One of the most common themes is that of perceived need. It is worth pondering what would happen if we did not have it. I don't know if my experience is shared by many others but as I recall we were not really taught
- What Algebra is,
- That among its definitions, its major one is that it is the language of virtually all Mathematics (as numbers are the language of Arithmetic)
- And how it all links to the real world. Without Maths we would not be able to talk about it like this - we would not even have the electricity to heat and light what would be our cold, draughty shacks with no mains services, etc.
True, the text-book exercises sometimes tried. Yet while some questions were credibly real-world, it was hard to see why for example, you'd want to calculate where between two towns, two cyclists pass each other. (Equivalent problems using trains were far more realistic, but we were not told that such calculations would be routine in transport management.)
'
I think the second barrier is of abstraction. Not all of us can grasp abstract concepts even when their manipulations are logical in their own ways. And of these apparently abstract ideas, Algebra reigns supreme due merely to its using letters. Yet learn what Algebra is, and what it is for, and much of that mystique evaporates; leaving you to concentrate on learning its manoeuvres - essentially the Laws of Arithmetic.
I left school with decidedly mediocre results, and it was to be another 30 years before I studied Mathematics again. I did though, have to be reasonably numerate in my work - and using simple arithmetic on real measurements of physical things.
For work reasons, in my 40s I took an adult-education evening-class course of the standard Middle School level Maths syllabus, complete with the formal examination at the end. (I was probably the oldest in the exam hall!) Though most of it was merely a refresher for me, it included a topic entirely new to me: Matrices. At basic level these are boxes of simple numbers and "sums" with fancy but non-intuitive names, yet so abstract and so devoid of any purpose that might help me, I failed to understand them beyond rote-learning their simplest manipulations. I know 2+3=5... but what does this grid of such sums really mean?
On the other hand my work and hobbies between them have meant understanding the principles of logarithms, various real formulae, simple mensuration, geometry and trigonometry, graphs and co-ordinates; and enough Algebra to use all those, for real. They even led to my understanding at last what [i]dy/dx[/i] actually [i]means[/i]!
''
So why was Maths the weak point for so many of us?
Obviously personal taste and interest play their parts; but I think too, that teachers and text-books failed to see many of us are not abstract-thinkers, so need the subject rooted in as much reality as possible to help us both understand it, and to appreciate its everyday importance.
''''
There is a further point, and if I am right it may be pertinent to ask if it has any bearing on the matter. In the UK we were all taught Mathematics as a single curriculum subject of many fields (Trig., Plane Geometry, Graphs, etc.) within its syllabus. The exam papers too, offer spreads of questions over several different fields in each paper. I have often thought though that the American system makes Maths' fields, separate curriculum subjects. If so, would either system have any advantages over the other?
It's notable that Mathematics seems here the least popular subject, and Algebra the least popular of its manifold fields. I battled with maths and did not like it much at school but in later years found ways to clarify at least some of it, by hooking it to real things.
One of the most common themes is that of perceived need. It is worth pondering what would happen if we did not have it. I don't know if my experience is shared by many others but as I recall we were not really taught
- What Algebra is,
- That among its definitions, its major one is that it is the language of virtually all Mathematics (as numbers are the language of Arithmetic)
- And how it all links to the real world. Without Maths we would not be able to talk about it like this - we would not even have the electricity to heat and light what would be our cold, draughty shacks with no mains services, etc.
True, the text-book exercises sometimes tried. Yet while some questions were credibly real-world, it was hard to see why for example, you'd want to calculate where between two towns, two cyclists pass each other. (Equivalent problems using trains were far more realistic, but we were not told that such calculations would be routine in transport management.)
'
I think the second barrier is of abstraction. Not all of us can grasp abstract concepts even when their manipulations are logical in their own ways. And of these apparently abstract ideas, Algebra reigns supreme due merely to its using letters. Yet learn what Algebra is, and what it is for, and much of that mystique evaporates; leaving you to concentrate on learning its manoeuvres - essentially the Laws of Arithmetic.
I left school with decidedly mediocre results, and it was to be another 30 years before I studied Mathematics again. I did though, have to be reasonably numerate in my work - and using simple arithmetic on real measurements of physical things.
For work reasons, in my 40s I took an adult-education evening-class course of the standard Middle School level Maths syllabus, complete with the formal examination at the end. (I was probably the oldest in the exam hall!) Though most of it was merely a refresher for me, it included a topic entirely new to me: Matrices. At basic level these are boxes of simple numbers and "sums" with fancy but non-intuitive names, yet so abstract and so devoid of any purpose that might help me, I failed to understand them beyond rote-learning their simplest manipulations. I know 2+3=5... but what does this grid of such sums really mean?
On the other hand my work and hobbies between them have meant understanding the principles of logarithms, various real formulae, simple mensuration, geometry and trigonometry, graphs and co-ordinates; and enough Algebra to use all those, for real. They even led to my understanding at last what [i]dy/dx[/i] actually [i]means[/i]!
''
So why was Maths the weak point for so many of us?
Obviously personal taste and interest play their parts; but I think too, that teachers and text-books failed to see many of us are not abstract-thinkers, so need the subject rooted in as much reality as possible to help us both understand it, and to appreciate its everyday importance.
''''
There is a further point, and if I am right it may be pertinent to ask if it has any bearing on the matter. In the UK we were all taught Mathematics as a single curriculum subject of many fields (Trig., Plane Geometry, Graphs, etc.) within its syllabus. The exam papers too, offer spreads of questions over several different fields in each paper. I have often thought though that the American system makes Maths' fields, separate curriculum subjects. If so, would either system have any advantages over the other?