# Why are children first taught angles in degrees and not radians in math class?

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#1
The idea of the radian isn't a particularly hard concept.

Sure, pi is an irrational number. But if you know what pi is, which primary schoolchildren are supposed to have covered when they learnt how to calculate the area and circumference of a circle, learning radians shouldn't be tricky either. Yet students don't cover radians until well into secondary school (C2 to be precise). Why is this?

Plus I've heard that radians have significant advantages compared to degrees in mathematics and mathematics related fields.

Yes, I know. Only on TSR would you get these sorts of arguments.

I'm anticipating accusations of my trying to indoctrinate schoolchildren into STEM subjects.
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5 years ago
#2
(Original post by flibber)
The idea of the radian isn't a particularly hard concept.
Sure, pi is an irrational number. But if you know what pi is, which primary schoolchildren are supposed to have covered when they learnt how to calculate the area and circumference of a circle, learning radians shouldn't be tricky either. Yet students don't cover radians until well into secondary school (C2 to be precise). Why is this?
Plus I've heard that radians have significant advantages compared to degrees in mathematics and mathematics related fields.
Yes, I know. Only on TSR would you get these sorts of arguments.
I'm anticipating accusations of my trying to indoctrinate schoolchildren into STEM subjects.
Because in every day usage, the degree is the convention. That's because 360 has a huge number of factors which means that most common angles can be easily expressed as a whole number, rather than a fraction, and only uses numbers rather than symbols. Yes, there are lots of technical and scientific advantages of the radian but you've got to bear in mind that we don't exactly have a particularly mathematically literate public. For all of its disadvantages, the degree is simpler for many basic uses.

The big advantages of the radian only really become apparent with more technical applications and anybody going into a field where those applications are going to be used will probably be doing AS Mathematics (or equivalent) so it makes sense to introduce it there. I really don't see the benefit of introducing it at GCSE.
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#3
(Original post by Plagioclase)
Because in every day usage, the degree is the convention. That's because 360 has a huge number of factors which means that most common angles can be easily expressed as a whole number, rather than a fraction, and only uses numbers rather than symbols. Yes, there are lots of technical and scientific advantages of the radian but you've got to bear in mind that we don't exactly have a particularly mathematically literate public. For all of its disadvantages, the degree is simpler for many basic uses.
Harsh on the British public...

I can understand that degrees are much easier and common in everyday life, but while they should be covered well in maths class at primary school, why don't schoolchildren switch to using radians in math class as soon as they cover pi and the circumference and area of the circle, and not have to wait until A Level?
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5 years ago
#4
Degrees are more practical for most of the population as most will only use them for measuring angles where the 90 units to a right angle makes a lot more sense to use than the 1.57 units to a right angle that you get with radians. Radians only really become more useful when looking at ratios.
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#5
(Original post by Plagioclase)
The big advantages of the radian only really become apparent with more technical applications and anybody going into a field where those applications are going to be used will probably be doing AS Mathematics (or equivalent) so it makes sense to introduce it there. I really don't see the benefit of introducing it at GCSE.
It's still confusing to use radians when I finally learnt it, since everyone had been taught for so long using degrees. It's like an Englishman having to mentally convert Fahrenheit to Celsius each time he sees the temperature when he lives in the United States. Same goes for me having to convert radians to degrees to make sense of it each time I see something in radians.
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5 years ago
#6
(Original post by flibber)
It's still confusing to use radians when I finally learnt it, since everyone had been taught for so long using degrees. It's like an Englishman having to mentally convert Fahrenheit to Celsius each time he sees the temperature when he lives in the United States. Same goes for me having to convert radians to degrees to make sense of it each time I see something in radians.
You shouldn't be converting it in your head, you need to learn to just think in radians.
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#7
(Original post by StrangeBanana)
You shouldn't be converting it in your head, you need to learn to just think in radians.
It'd still be nice to have a topic on radians at primary school as an appendix to the circles topic in primary school. As for the argument that people aren't going to be using radians in everyday life, it's not as if people would be calculating the area of a circle or the number of lines of symmetry in everyday life either.
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5 years ago
#8
(Original post by flibber)
It'd still be nice to have a topic on radians at primary school as an appendix to the circles topic in primary school. As for the argument that people aren't going to be using radians in everyday life, it's not as if people would be calculating the area of a circle or the number of lines of symmetry in everyday life either.
Meh, it's not really needed. I'd be willing to be the majority of primary school teachers don't know how to use radians, anyway.
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#9
(Original post by StrangeBanana)
Meh, it's not really needed. I'd be willing to be the majority of primary school teachers don't know how to use radians, anyway.
If they can teach pi, then learning radians shouldn't take more than an hour even if they were unfamiliar to it.

On an interesting side note, my Year 6 maths teacher... well, she used to work at Marks and Spencer's before she became a primary school teacher.
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5 years ago
#10
(Original post by flibber)
It's still confusing to use radians when I finally learnt it, since everyone had been taught for so long using degrees. It's like an Englishman having to mentally convert Fahrenheit to Celsius each time he sees the temperature when he lives in the United States. Same goes for me having to convert radians to degrees to make sense of it each time I see something in radians.
That's true, but do you genuinely think it's sensible to change a system that works fine for most people just to make A Level Mathematics a bit easier? It's not at all like Fahrenheit/Celsius because the degree is genuinely the most simple way of measuring angles for most basic situations whereas the difference between Celsius and Fahrenheit in most basic situations is arbitrary. And let's be honest, as you point out, radians aren't exactly horrifically different. It's just about getting used to a new system and by the time you've finished AS Maths it should be just as easy as degrees.

(Original post by flibber)
Harsh on the British public...
I can understand that degrees are much easier and common in everyday life, but while they should be covered well in maths class at primary school, why don't schoolchildren switch to using radians in math class as soon as they cover pi and the circumference and area of the circle, and not have to wait until A Level?
Think about the ordinary person who does not have a career where any technical knowledge of Mathematics is needed. Why would understanding radians help them? There are plenty of other genuinely useful pieces of Maths that will help the average person in their day-to-day lives but I fail to understand how understanding radians will help. I mean, how many times is the ordinary person going to need to work out the area of a sector of a circle or find the area under a trigonometric function? In comparison, they're much more likely to refer to angles for things like navigation and in that context, using degrees is much more convenient.
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5 years ago
#11
(Original post by flibber)
If they can teach pi, then learning radians shouldn't take more than an hour even if they were unfamiliar to it.

On an interesting side note, my Year 6 maths teacher... well, she used to work at Marks and Spencer's before she became a primary school teacher.
Well, I'm not sure it would be that simple. Even if it were, it's still just not really that big of a deal.
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#12
(Original post by Plagioclase)
That's true, but do you genuinely think it's sensible to change a system that works fine for most people just to make A Level Mathematics a bit easier? It's not at all like Fahrenheit/Celsius because the degree is genuinely the most simple way of measuring angles for most basic situations whereas the difference between Celsius and Fahrenheit in most basic situations is arbitrary. And let's be honest, as you point out, radians aren't exactly horrifically different. It's just about getting used to a new system and by the time you've finished AS Maths it should be just as easy as degrees.

Think about the ordinary person who does not have a career where any technical knowledge of Mathematics is needed. Why would understanding radians help them? There are plenty of other genuinely useful pieces of Maths that will help the average person in their day-to-day lives but I fail to understand how understanding radians will help. I mean, how many times is the ordinary person going to need to work out the area of a sector of a circle or find the area under a trigonometric function? In comparison, they're much more likely to refer to angles for things like navigation and in that context, using degrees is much more convenient.
Would you therefore scrap the sine rule and the cosine rule from GCSE as it's not required in everyday life and it features in C2 for those wanting to do it at A Level?
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5 years ago
#13
(Original post by flibber)
Would you therefore scrap the sine rule and the cosine rule from GCSE as it's not required in everyday life and it features in C2 for those wanting to do it at A Level?
Conceptually, that's a lot more basic because it's basically just two formulae you've got to memorise rather than understanding a new angle system. But sure, I don't think the sine and cosine rules are essential for everyone to know.
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#14
(Original post by Plagioclase)
Conceptually, that's a lot more basic because it's basically just two formulae you've got to memorise rather than understanding a new angle system. But sure, I don't think the sine and cosine rules are essential for everyone to know.
While the government is making GCSE maths tougher, would you make it simpler?

By the way, I now understand your point about debates given that my Breivik thread went downhill.
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5 years ago
#15
In Scotland the National Qualifications, equivent(ish) to GCSEs, feature two strands of maths - Maths and Lifeskills Maths.

The first is much as usual, with pythagoras and trigonometry etc, whilst the second bypasses that stuff and focuses on (dramatic pause) "life skills".

This is a great option to be have, although of course the problem is at what stage is it appropriate to split pupils down either path.
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5 years ago
#16
(Original post by Plagioclase)
Because in every day usage, the degree is the convention. That's because 360 has a huge number of factors which means that most common angles can be easily expressed as a whole number, rather than a fraction, and only uses numbers rather than symbols. Yes, there are lots of technical and scientific advantages of the radian but you've got to bear in mind that we don't exactly have a particularly mathematically literate public. For all of its disadvantages, the degree is simpler for many basic uses.

The big advantages of the radian only really become apparent with more technical applications and anybody going into a field where those applications are going to be used will probably be doing AS Mathematics (or equivalent) so it makes sense to introduce it there. I really don't see the benefit of introducing it at GCSE.
Couldn't it be argued that degrees are only in every day usage because they are taught first in school?

Besides, I don't see why pi is any more complicated than 180.
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5 years ago
#17
(Original post by cacra)
Couldn't it be argued that degrees are only in every day usage because they are taught first in school?

Besides, I don't see why pi is any more complicated than 180.
The most commonly used angles and rotations used in everyday life (90, 180...) and most easily expressed in degrees. Yes 360 degrees to a revolution is arbitrary and radians makes more sense in some mathematical applications, but the advantages of being able to express those common angles simply are huge.

Plus, as mentioned before, it isn't that difficult to learn to use radians for those who need to, and in fact it helps provoke discussions like this that examine the nature of our systems.
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5 years ago
#18
(Original post by offhegoes)
The most commonly used angles and rotations used in everyday life (90, 180...) and most easily expressed in degrees. Yes 360 degrees to a revolution is arbitrary and radians makes more sense in some mathematical applications, but the advantages of being able to express those common angles simply are huge.
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5 years ago
#19
Relatively speaking, the ability to express the most commonly used angles in easily expressed numbers, as opposed to a system that involves using a greek letter to represent a non-natural number to express the same fractions. How far is a quarter turn again? Oh yes, half-Pi, of course.... How do I know if this angle is more or less than perpendicular? Well, just look at the scale and compare your answer to Pi/2...
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#20
(Original post by offhegoes)
Relatively speaking, the ability to express the most commonly used angles in easily expressed numbers, as opposed to a system that involves using a greek letter to represent a non-natural number to express the same fractions. How far is a quarter turn again? Oh yes, half-Pi, of course.... How do I know if this angle is more or less than perpendicular? Well, just look at the scale and compare your answer to Pi/2...
I wasn't saying that degrees shouldn't be taught at all- they should for everyday applications. I just thought radians would be better for maths class.
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