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

OP

Original post by cacra

The vast majority of common angles can be expressed in simplistic terms in radians also, 1/2pi, pi, 2pi... it isn't complex.

Also, the general consensus is that there are 360 degrees because the Persian calendar had 360 days in a year. The 'readily divisible' argument is widely seen as a myth.

A myth when describing the origins, but not a myth when describing why people have chosen to keep it for millenia.

Reply 23

Teaching the general population two different systems for measuring angles would cause confusion. After all, what benefit would teaching radians give to the average person? Those wishing to take maths studies far enough to need radians should be able to get to grips with radians, or at the very least the disadvantage in teaching them later than you might like is lesser than the disadvantage of trying to incorporate radians into the curriculum much earlier.

Of couse in an ideal world teachers would be able to introduce some pupils to radians earlier as part of extension tasks and differentiated learning - but that is far from easy to do with classes of 30+ with a range of support needs!

Reply 24

Original post by cacra

The vast majority of common angles can be expressed in simplistic terms in radians also, 1/2pi, pi, 2pi... it isn't complex.

Also, the general consensus is that there are 360 degrees because the Persian calendar had 360 days in a year. The 'readily divisible' argument is widely seen as a myth.

I would argue that using is radians is far more complex for the average person than you think. Certainly tricky enough for it to be unreasonable to ask them to learn it for no practical benefit. The crucial point for me is that it is much more difficult to teach the average person radians than it is to teach a maths student radians at a later stage.

Reply 25

OP

Original post by offhegoes

Teaching the general population two different systems for measuring angles would cause confusion. After all, what benefit would teaching radians give to the average person? Those wishing to take maths studies far enough to need radians should be able to get to grips with radians, or at the very least the disadvantage in teaching them later than you might like is lesser than the disadvantage of trying to incorporate radians into the curriculum much earlier.

Of couse in an ideal world teachers would be able to introduce some pupils to radians earlier as part of extension tasks and differentiated learning - but that is far from easy to do with classes of 30+ with a range of support needs!

There are many parts of mathematics which are taught for GCSEs, such as the sine and cosine rules, stem and leaf diagrams, and Pythagoras' theorem, which many people won't really need. Why are they taught, may I ask?

Reply 26

Original post by flibber

There are many parts of mathematics which are taught for GCSEs, such as the sine and cosine rules, stem and leaf diagrams, and Pythagoras' theorem, which many people won't really need. Why are they taught, may I ask?

Education is a balancing act between teaching young people the skills they will need in their lives and giving them opportunities and experiences that may affect their future pathways and hence the skills they will need...

If we decide at age 11 who will need anything beyond basic maths and English then we deny them the opportunity to access a range of careers. If we don't allow any specialisation or dropping of subjects then we aren't catering to the needs of the individual.

As I mentioned, Scotland has made efforts to create pathways that allow schools to cater different pupils when it comes to maths, but it's just an attempt and not a proven science.

For me the main difference between particularly trig and pythagoras and radians is that radians is a topic that can be approached at a later stage and easily learnt. Trig and pythagoras require more time to allow pupils to be prepared to attempt A-Level standard maths.

Reply 27

Joinedup

20

You want a system for everyday purposes that's usable by the maximum number of people.

everyday use of degrees means working with natural 'counting numbers'

everyday use of radians means working with fractions and irrational numbers

there's a lot of people out there who have trouble working out what 70% off £5.99 is or how many 3/4 m^2 rolls of turf will cover an 11x12 m garden or why you need 8 times as much John Innes to fill up a 1m cubic planter as you do to fill up a 50cm one... even if you give them a calculator

Reply 28

Plagioclase

21

Original post by cacra

The vast majority of common angles can be expressed in simplistic terms in radians also, 1/2pi, pi, 2pi... it isn't complex.

Also, the general consensus is that there are 360 degrees because the Persian calendar had 360 days in a year. The 'readily divisible' argument is widely seen as a myth.

It's not complex when you're competent at maths. You have to remember that most people aren't. We live in a country where most people feel panicked when they see a fraction so no, radians are not a good idea for general use.

And why do you think 360 was used by these older civilizations? Do you think they just picked a random number out of thin air?

Reply 29

OP

Original post by Joinedup

You want a system for everyday purposes that's usable by the maximum number of people.

everyday use of degrees means working with natural 'counting numbers'

everyday use of radians means working with fractions and irrational numbers

there's a lot of people out there who have trouble working out what 70% off £5.99 is or how many 3/4 m^2 rolls of turf will cover an 11x12 m garden or why you need 8 times as much John Innes to fill up a 1m cubic planter as you do to fill up a 50cm one... even if you give them a calculator

Are you saying that I'm overestimating the mathematical ability of the average Briton. I hope the government's efforts to make maths questions harder goes some way to drive up our educational standards so that people actually know how to solve a simple arithmetic problem, or at least know how to use a calculator in order to solve it.

I understand Plagioclase's argument when it comes to radians, but when it comes to those questions you've listed (70% off 5.99), it's a matter of basic skills.

(edited 8 years ago)

Reply 30

cacra

15

Original post by Plagioclase

It's not complex when you're competent at maths. You have to remember that most people aren't. We live in a country where most people feel panicked when they see a fraction so no, radians are not a good idea for general use.

And why do you think 360 was used by these older civilizations? Do you think they just picked a random number out of thin air?

There were 360 days in a year according to the Persian calendar.(Which is remarkably close when you think about it) - it certainly wasn't plucked out of thin air.

You can clearly see the link between a year and a circle, it is hardily a giant leap to link the two.

Reply 31

Original post by flibber

Are you saying that I'm overestimating the mathematical ability of the average Briton. I hope the government's efforts to make maths questions harder goes some way to drive up our educational standards so that people actually know how to solve a simple arithmetic problem, or at least know how to use a calculator in order to solve it.

I understand Plagioclase's argument when it comes to radians, but when it comes to those questions you've listed (70% off 5.99), it's not a matter of STEM vs non STEM. It's a matter of basic skills.

I think there's a little more to improving mathematical ability than just getting 'the government' to make maths questions harder...

Reply 32

OP

Original post by offhegoes

I think there's a little more to improving mathematical ability than just getting 'the government' to make maths questions harder...

I think it's certainly part of the solution. Perhaps utilising online resources such as Khan Academy can also be part of the solution- it made maths learning much more fun for me, and it's generally much easier to progress in something if you enjoy it.

Reply 33

Plagioclase

21

Original post by cacra

There were 360 days in a year according to the Persian calendar.(Which is remarkably close when you think about it) - it certainly wasn't plucked out of thin air.

You can clearly see the link between a year and a circle, it is hardily a giant leap to link the two.

But why do you think they used 360? Why do you think a large number of ancient civilizations used Base 60, with 360 being a very important number? Because 60 and 360 have a huge number of divisors, there we go.

Reply 34

And therein lies a large part of the solution... making maths more fun and engaging. Are 'harder' questions the answer? In the vast majority of cases, no. I have enough confidence in my own intelligence and enough freedom from peer pressure to enjoy being challenged. I have the time, opportunity and motivation to learn at home whenever I wish to. But neither I nor you represent the majority of pupils, not by a long shot.

Many pupils will fear being giving challenging questions, and will lose confidence and withdraw. Many pupils aren't able to access support at home. Many don't want to either.

It's is the responsiblity of class teachers to try to engage pupils, through learning styles, different contexts, a range of resources and differentiation. Under difficult circumstances.

The government shoud be focusing on giving teachers sufficient resources and support to allow these things to happen, not determining how hard the questions are...

Reply 35

OP

Original post by offhegoes

And therein lies a large part of the solution... making maths more fun and engaging. Are 'harder' questions the answer? In the vast majority of cases, no.

I think the government wants to make questions harder to bring our mathematical standards in line with the likes of 'developed Asia', that is, Singapore, South Korea, Taiwan, Hong Kong, and Japan, in order to compete with them in a world where technological advancements is becoming the face of innovation.

I have enough confidence in my own intelligence and enough freedom from peer pressure to enjoy being challenged. I have the time, opportunity and motivation to learn at home whenever I wish to. But neither I nor you represent the majority of pupils, not by a long shot.

You're right. In your honest opinion, do I sound elitist in the eyes of the majority of pupils?

Many pupils will fear being giving challenging questions, and will lose confidence and withdraw. Many pupils aren't able to access support at home. Many don't want to either.

I can understand why many pupils can't access support at home, but is there a reason why many people don't want to get support, even if they can access it? In my school, maths teachers are willing to help a student with something if they don't understand a question.

It's is the responsiblity of class teachers to try to engage pupils, through learning styles, different contexts, a range of resources and differentiation (dy/dx) :wink:

. Under difficult circumstances.

Agreed.

The government shoud be focusing on giving teachers sufficient resources and support to allow these things to happen, not determining how hard the questions are...

I can't disagree much on that.

Reply 36

Original post by flibber

I think the government wants to make questions harder to bring our mathematical standards in line with the likes of 'developed Asia', that is, Singapore, South Korea, Taiwan, Hong Kong, and Japan, in order to compete with them in a world where technological advancements is becoming the face of innovation.

I agree with a drive to improve standards of Maths, but there are two different elements here that I think you are blending together. One is improving standards in general which as I've mentioned is a far cry from making questions more difficult. The other is the standards of qualifications and the demands higher and further education place on students. These pupils are more lkely to respond to challenge, but they are a long way from the debate on teaching the average pupil about radians.

You're right. In your honest opinion, do I sound elitist in the eyes of the majority of pupils?

No, but I think you haven't had much experience working with the average pupils in the average class in the average school. Many people who end up at university will manage to get through school without ever seeing these classes.

I can understand why many pupils can't access support at home, but is there a reason why many people don't want to get support, even if they can access it? In my school, maths teachers are willing to help a student with something if they don't understand a question.

If all pupils were keen, or even willing, to work then a teacher's job would be very different!

Reply 37

OP