Post by corastack1 on May 24, 2012 2:17:17 GMT -5
Problem Solving.
Hi,
In a lot of the studies of international curricula I have looked at Singapore seems to be regarded very highly.
Internation Bac almost universally very highly regarded. In NewZealand a number of schools offer this
Scottish advanced highers very good and Korean calculus excellent. Malaysia's additional mathematics is very technical but Singapore HC has more advanced calculus. IB very balanced but has no geometry.
In some currricula there is a move towards putting more geometry in. I would not have an issue with the inclusion of some geometry ( would favour it) but not to the extent that it would require the exclusion of introduction of fundamentals in integration, series and sequences , matrices and vectors.
I am not so convinced about PM and problem solving- this is now the latest buzz word -all mathematics curriculums must focus on problem solving as if the previous ones didn't focus on any- didn't do any problem solving!
Problem solving must mean doing very hard problems whose solution requires more than one or two steps in most cases. Another definition is doing any level of problem provided you hadn't come across this before- so called nonroutine problems. How will spending so much time on applied statistics or financial mathematics at this level provide and develop problem solving capabilites. Is not clear what is exactly requried but one thing that is required is deep mathematical knowledge.
You need to understand very well and know mathematics, ideas etc underlying a particular topic to be able to solve hard probems generally speaking in this area/topic. You can't solve mathematical problems unless you have the know how the key skills and capabilities to solve them. These skills usually involve mathematical techniques or skills etc i,e mathematical knowledge!
As Tony Dorlas argues you need to know some fundamental mathematics before you can solve hard problems requiring the use of these mathematical skills. How many HC student are capable solving really hard problems.
Surely it is only the top brass that are. So that if we want more and more to get C we will have to do the exact opposite ask simpler and simpler questions and make them look like they are hard problems when in fact they are quite the opposite!
Pretending something teaches problem solving when it does nothing of the sort is being profoundly dishonest about aims of the curriculum. Some of my investigations point to the fact that RME curriculumss when you look at them carefully are not teaching problem solving in non routine settings - something the curriculum designers boast it actually does! Papers all around the world claiming these types of curricula produce great problem solvers!!!
In fact it appears to be quite difficult to find curriculums that do effectivvely teach problem solving capability in non routine settings. Most of it is problem solving in routine settings- what is so wrong with this??
At least one guaranteed outcome is that students will have learned mathematics and approaches to certain types of problem solving difficult or otherwise. Perhaps it is arguable that you have to be very well versed in doing mathemaitics in routine settings before you can move on to doing problems in non routine settings properly or in a meaningful way- another buzz word!! Perhaps we weren't doing enough of this in the old LC moving from the routine to the non routine i.e the extrememly challenging problems- how many students would we keep with us if were to spend all our time focussing on these very difficult and challenging problems?? Why didn't the SEC ask more of these type of hard non routine type of quesion on the old curriculum. Some key person behing PM NCCA team said NCCA has simply run out of questions!!! Why didn't they go to Singapore and find a few there!!!
The result of PM could end up with students having neither the required problem solving skills nor the mathematical foundation - technical skills necessary for easy transition from school to University etc. In New Zealand this is now an issue for educators. Third level arguing that students not sufficiently technically capable etc! Huge amount of statistics on NZ curriculum and this is a source of debate amoung mathematics educators at third level.
Anyone else got views to share on all of this??
Hi,
In a lot of the studies of international curricula I have looked at Singapore seems to be regarded very highly.
Internation Bac almost universally very highly regarded. In NewZealand a number of schools offer this
Scottish advanced highers very good and Korean calculus excellent. Malaysia's additional mathematics is very technical but Singapore HC has more advanced calculus. IB very balanced but has no geometry.
In some currricula there is a move towards putting more geometry in. I would not have an issue with the inclusion of some geometry ( would favour it) but not to the extent that it would require the exclusion of introduction of fundamentals in integration, series and sequences , matrices and vectors.
I am not so convinced about PM and problem solving- this is now the latest buzz word -all mathematics curriculums must focus on problem solving as if the previous ones didn't focus on any- didn't do any problem solving!
Problem solving must mean doing very hard problems whose solution requires more than one or two steps in most cases. Another definition is doing any level of problem provided you hadn't come across this before- so called nonroutine problems. How will spending so much time on applied statistics or financial mathematics at this level provide and develop problem solving capabilites. Is not clear what is exactly requried but one thing that is required is deep mathematical knowledge.
You need to understand very well and know mathematics, ideas etc underlying a particular topic to be able to solve hard probems generally speaking in this area/topic. You can't solve mathematical problems unless you have the know how the key skills and capabilities to solve them. These skills usually involve mathematical techniques or skills etc i,e mathematical knowledge!
As Tony Dorlas argues you need to know some fundamental mathematics before you can solve hard problems requiring the use of these mathematical skills. How many HC student are capable solving really hard problems.
Surely it is only the top brass that are. So that if we want more and more to get C we will have to do the exact opposite ask simpler and simpler questions and make them look like they are hard problems when in fact they are quite the opposite!
Pretending something teaches problem solving when it does nothing of the sort is being profoundly dishonest about aims of the curriculum. Some of my investigations point to the fact that RME curriculumss when you look at them carefully are not teaching problem solving in non routine settings - something the curriculum designers boast it actually does! Papers all around the world claiming these types of curricula produce great problem solvers!!!
In fact it appears to be quite difficult to find curriculums that do effectivvely teach problem solving capability in non routine settings. Most of it is problem solving in routine settings- what is so wrong with this??
At least one guaranteed outcome is that students will have learned mathematics and approaches to certain types of problem solving difficult or otherwise. Perhaps it is arguable that you have to be very well versed in doing mathemaitics in routine settings before you can move on to doing problems in non routine settings properly or in a meaningful way- another buzz word!! Perhaps we weren't doing enough of this in the old LC moving from the routine to the non routine i.e the extrememly challenging problems- how many students would we keep with us if were to spend all our time focussing on these very difficult and challenging problems?? Why didn't the SEC ask more of these type of hard non routine type of quesion on the old curriculum. Some key person behing PM NCCA team said NCCA has simply run out of questions!!! Why didn't they go to Singapore and find a few there!!!
The result of PM could end up with students having neither the required problem solving skills nor the mathematical foundation - technical skills necessary for easy transition from school to University etc. In New Zealand this is now an issue for educators. Third level arguing that students not sufficiently technically capable etc! Huge amount of statistics on NZ curriculum and this is a source of debate amoung mathematics educators at third level.
Anyone else got views to share on all of this??