The Art of Teaching Math and Science(quantamagazine.org)
quantamagazine.org
The Art of Teaching Math and Science
https://www.quantamagazine.org/math-and-science-teachers-pencils-down-20161011/
3 comments
England(+): 16 year olds take the GCSE Mathematics exams along with 9 other subjects. [1]
17/18 year olds take the GCE A/AS levels along with 3 or 4 other subjects. The layout of this qualification is changing with the cohort starting this year. [2]
What are the comparable exams in US? (and any other countries)? Just wondering where we are at...
[1] https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics...
[2] http://www.aqa.org.uk/subjects/mathematics/as-and-a-level/ma...
(+): Scotland has Standard and Higher grades, and NI and Wales have GCSEs with different syllabi.
17/18 year olds take the GCE A/AS levels along with 3 or 4 other subjects. The layout of this qualification is changing with the cohort starting this year. [2]
What are the comparable exams in US? (and any other countries)? Just wondering where we are at...
[1] https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics...
[2] http://www.aqa.org.uk/subjects/mathematics/as-and-a-level/ma...
(+): Scotland has Standard and Higher grades, and NI and Wales have GCSEs with different syllabi.
>What are the comparable exams in US? (and any other countries)? Just wondering where we are at...
I live in the US and my kids are in the middle of this right now, so I'll try to answer, but I'm not yet an expert: I came through the Scottish system and I'm reasonably familiar with England.
In the US there are exams called "AP" that are roughly analogous to A-levels. But, AP classes are not offered in all schools and they don't seem to cover all subjects (e.g. just Calculus and Statistics). The list is here: https://apstudent.collegeboard.org/apcourse
At the tier below AP afaik it is up to the state education dept, or even local schools to make up their own curriculum and although there are exams and the students are awarded grades, I get the impression they are less valued than for example an A-level result because the examinations are not set and graded by a 3rd party. These days the federal government tries to set some consistent standards across the country and most schools try to comply. These are available here : http://www.corestandards.org/Math/Practice/
fwiw when I have tried to compare US to UK school mathematics for the same student age I've always come to the conclusion that they are roughly the same, modulo the difference that there really aren't commonly valued exam results for the kids in the US. In general I find that there is much less emphasis on exam results in general in the US -- it is more like you either pass or fail, or pass with distinction. More like UK university grading I suppose.
There is not the O-level/A-level type split in the US at all. There is an order to the Mathematics classes (e.g. you can't take Calculus unless you're already passed Algebra 2) but otherwise things just seem to be done in whatever order the school allows (e.g. in our school you do Biology one year then Chemistry the next).
Hope some of that helps and doesn't offend the US education system experts here..
I live in the US and my kids are in the middle of this right now, so I'll try to answer, but I'm not yet an expert: I came through the Scottish system and I'm reasonably familiar with England.
In the US there are exams called "AP" that are roughly analogous to A-levels. But, AP classes are not offered in all schools and they don't seem to cover all subjects (e.g. just Calculus and Statistics). The list is here: https://apstudent.collegeboard.org/apcourse
At the tier below AP afaik it is up to the state education dept, or even local schools to make up their own curriculum and although there are exams and the students are awarded grades, I get the impression they are less valued than for example an A-level result because the examinations are not set and graded by a 3rd party. These days the federal government tries to set some consistent standards across the country and most schools try to comply. These are available here : http://www.corestandards.org/Math/Practice/
fwiw when I have tried to compare US to UK school mathematics for the same student age I've always come to the conclusion that they are roughly the same, modulo the difference that there really aren't commonly valued exam results for the kids in the US. In general I find that there is much less emphasis on exam results in general in the US -- it is more like you either pass or fail, or pass with distinction. More like UK university grading I suppose.
There is not the O-level/A-level type split in the US at all. There is an order to the Mathematics classes (e.g. you can't take Calculus unless you're already passed Algebra 2) but otherwise things just seem to be done in whatever order the school allows (e.g. in our school you do Biology one year then Chemistry the next).
Hope some of that helps and doesn't offend the US education system experts here..
Thanks for those links. I've always liked the look of the Scottish Standards and Highers but that could just be a case of the grass being greener over the border.
There has been some mumbling about whether we need GCSEs as we move to what is effectively education until 18, but no party wants to make the first move on what would be a huge change.
Good luck to the offspring.
There has been some mumbling about whether we need GCSEs as we move to what is effectively education until 18, but no party wants to make the first move on what would be a huge change.
Good luck to the offspring.
> Comer is also known for her dogged insistence that students solve their own problems. Too often, said Vice Principal Elizabeth Leebens, students “get the history of science rather than getting an opportunity to do it for themselves.”
I wholeheartedly agree!
It is amazing how long young students can spend in science classes before they do any science themselves. The class should serve two purposes: learning about how nature works and (perhaps more importantly!) learning to learn how nature works. The first is over emphasized in early education (which may include up to the end of highschool).
Most children at least go through a phase where they are fascinated with how things work and ask so many why questions. Science is the best technique to answer many of those questions. Kids can learn that it is possible to discover the answers to questions themselves and do not have to look up the answer in a book.
The process of discovering knowledge for one's self is so radically different from looking up a known answer. You make mistakes, you doubt your ability, you question if you have the right answer and even in the end you cannot be sure if you have come to the correct conclusion. This process is scary if you are not accustomed to it! Hell, it can be scary even when you are used to it. If you are not practiced at it, you will think that you are not smart enough. You may believe that the original people who discovered the fundamental facts of science were some kinds of gods; they were not, they instead went thought the same process of many many mistakes and errors and only after much failure did they arrive at the canonical result you see in textbooks today.
I wholeheartedly agree!
It is amazing how long young students can spend in science classes before they do any science themselves. The class should serve two purposes: learning about how nature works and (perhaps more importantly!) learning to learn how nature works. The first is over emphasized in early education (which may include up to the end of highschool).
Most children at least go through a phase where they are fascinated with how things work and ask so many why questions. Science is the best technique to answer many of those questions. Kids can learn that it is possible to discover the answers to questions themselves and do not have to look up the answer in a book.
The process of discovering knowledge for one's self is so radically different from looking up a known answer. You make mistakes, you doubt your ability, you question if you have the right answer and even in the end you cannot be sure if you have come to the correct conclusion. This process is scary if you are not accustomed to it! Hell, it can be scary even when you are used to it. If you are not practiced at it, you will think that you are not smart enough. You may believe that the original people who discovered the fundamental facts of science were some kinds of gods; they were not, they instead went thought the same process of many many mistakes and errors and only after much failure did they arrive at the canonical result you see in textbooks today.
"Comer is also known for her dogged insistence that students solve their own problems."
Setting up sensible accessible problems that are vaguely interesting to students, and that lead to the development of skills is the tricky bit. It is definitely a Csíkszentmihályi situation (too hard and students give up, too 'drill like' and their eyes glaze over, too abstract and its like fat off a non-stick frying pan, and to make it more fun each student in a class has a different set of thresholds).
Some examples from Maths in UK with sample student work and analysis...
http://www.bowlandmaths.org.uk/assessment/index.html
And some shorter tasks that the exam boards put out
http://www.greatmathsteachingideas.com/wp-content/uploads/20...
Setting up sensible accessible problems that are vaguely interesting to students, and that lead to the development of skills is the tricky bit. It is definitely a Csíkszentmihályi situation (too hard and students give up, too 'drill like' and their eyes glaze over, too abstract and its like fat off a non-stick frying pan, and to make it more fun each student in a class has a different set of thresholds).
Some examples from Maths in UK with sample student work and analysis...
http://www.bowlandmaths.org.uk/assessment/index.html
And some shorter tasks that the exam boards put out
http://www.greatmathsteachingideas.com/wp-content/uploads/20...
Try to teach special relativity as Michelson Morley and de Sitter to a student that you are tutoring. Present the paradox, if he is not one of the .1% gifted enough to come to the paradox themselves.
It's very rewarding to work in parallel to the historical version of events.
It's very rewarding to work in parallel to the historical version of events.
This is the textbook, and it's one of the few books that's actually changed my life. https://ocw.mit.edu/resources/res-6-011-the-art-of-insight-i...