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Post by corastack1 on May 27, 2012 13:12:05 GMT -5
This last message is confirming results of my internation findings exactly as discussed with key president in the university sector and key head of engineering. International evidence very strongly supports the facts that all top curriculums world wide put calculus way ahead of geometry. Calculus is at the very top of the top curriculums. So also are vectors and linear algebra and technical equations solving etc. PM has made a huge mistake here. Finland one of the only countries I could find that manages to do both! Has top extra course on top of advanved on on advanced calculuus same as New Zealand has scholarship calculus. PM = complelte disaster for technical educaiton unforunately. We the maths communities at second and third level must try to do something to ensure our maths education system at second level is not ruined by very poor curriculum design.
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Post by corastack1 on May 28, 2012 12:37:24 GMT -5
To summarise my conclusions from my investigations - key findings are that what PM had done to Irish mathematical education is to sigficantly position its top mathematics curriculum well below the best curricula world wide relative to where we were before and by now means were we at the top! This is a very serious mistake and will have major long term negative consequences unless something is done by the minsiter of education and the department. In emails to the dept it is clear to me that they simply do not understand this major point about education and curriculum positioning. People who have not studied the best curricula seriously may not understand this most important research finding.
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Post by corastack1 on May 28, 2012 15:47:59 GMT -5
When I saw the Ontoria mathematical tree I was able to map the old syllabus onto it and then the new one and it was crystal clear from this mapping of both syllabii that PM has repositioned our mathematical second level education downwards that means it has dumbed it down - another way of saying the same thing. I found the exact same pattern in all other top mathematical education systems but the Ontoria mathemaitcal tree said it all. Brillant depiction of levels of difficulties of all topics on mathematical curricula.
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Post by corastack1 on May 29, 2012 1:50:23 GMT -5
Any curriculum change at this level should be infomred by best practice internationally and PM clearly went well short of this. As is now quite clear- what PM did was to take the methodlogy of best countries, which UCC have come out and seriously questioned, but completely forgot to do the most important thing here, and that was to take their curriculums because all their top class curriculums put calculus and series and sequences, vectors and matrices and hard technical equation solving at the very top of thier curriculums! This was a major flaw with PM design and exposes complete hypocrisy of their aims which was to copy the best of what all these top countries to and taylor it to suit Irish scene etc. The truth is that this a complete falsehood and by not copying their curriculums did the completely wrong thing altogether and this has lead to signifiacnt repositioning of PM which puts our mathematics education system way below others internationally and way below were we were before. This will have major negative consequences for the quality of mathmatical education system unless minister does something here!
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Post by corastack1 on May 29, 2012 5:37:02 GMT -5
Geometry vs the rest- sent to top lecturer in geometry.
I think what I meant here is that because calculus is top of all these mathematical education trees in all the worlds top mathematical eduation systems is that these systems must consider calculus far more important than geometry. This has to be the conclusion. They perhaps percieve calculus far more useful for technical education than geometry. They must do if this is their educational priorty. I am completley in favour of introducing some geometry and introduction to proofs and logic and abstract thinking etc but not at the expense of calculus. Throw out all that applid statistics and some of financial mathematics and some of stuff on complex numbers - only need to know polar form here and put them into new applied mathematics course!! This is the best way to keep both in.
Sincerely, Cora.
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Post by corastack1 on May 29, 2012 5:54:06 GMT -5
Geometry vs the rest! Discussion with key group!! What I do know is that increasingly geometry is King in pure mathematics at research level in pure mathamtics algbraic geometry, differential geometry, geometric group theory etc etc.
However calculus is probably King in applied mathematics. Vast majority of top level education systems give far more priority to calculus than to euclidean geometry again which surprised me in view of PM's priotisiation of it!
This doesn't in any way diminish the huge importance of Geometrical ideas to pure mathematics of course!
I am strongly in favour of bringing it in but again would agree with top professors of applied mathematics that it should certainly not have displaced calculus. I teach mainly in engineering and although trained as pure mathematician really see calculus is still King in most areas in engineering
C.
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Post by corastack1 on May 29, 2012 6:01:16 GMT -5
The worst of all of this reprioritsation of Geometry over Calculus etc is that according to point made on pg 3 by key teacher and book author PM only gives 25 ( our of 600??) for geometry skills etc. This is appalling balance in terms of ratio or work required to marks allocated for skills and knowledge in this very difficult area. No decent mathematics curriculum worth its salt would do this to most difficult and. challening area in the curriculum
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Post by corastack1 on May 29, 2012 12:17:42 GMT -5
I think I have now made enough postings. All PM wanted is to increase the numbers taking hons mathemaitcs without any consideration for the impact on the overal standard of the mathematics education system because, if they did this, they would realise, that by repositioning the curriculum downwards, to attract more students as they have done, the consequence is that the top level mathematics standard is not protected, and the way to deal with this is to do what they did in all other countries were RME ( realistic mathematics education) ( Holland Singapore Canada) courses were introduced, and this is introduce addtional courses which support top level technical mathematics education. ( These curriculums are known internationally as differentiated curricula as I found out). No amount of extra students taking PM will compensate for the serious mistake made here by the NCCA not providing these additional course for top level mathematics technical education as in all these other countries. Not providing this extra mathemaitcs curricum will have very negative consequences for overall standard of mathematics education system. The PM curriculum compares very unfavourably now with all these other top curriculums because its positioning is much further down relative to before. When you are given an extra 25 points for a D then you will inevitably get considerably more hanging on. These doesn't mean they have achieved a good standard of mathematical education.
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Post by corastack1 on May 29, 2012 12:31:35 GMT -5
Hi one final point as is that any design team worth their salt would have done their best to preserve the top standard. It is up the mathematical chain we should be going if we want to have any chance of competing with other countries with top level educational systems. A good team if they wanted to introduce PM (RME) as the solution to the mathematics education problem should not have ignored what these countries did to protect the top standard. Example if you check out mathemtics professors or even sceintists CV's in Holland it is always the technical maths syllabii B or D that are on their CV not the RME A or C. Again people that don't really understand curriculum design and the consequecces of a poor one for the standard of mathematical education system may not appreciate these points. You really have to study all the curriculums very well before you can speak intelligently about them.
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Post by corastack1 on May 29, 2012 14:21:39 GMT -5
From top teacher and book author.
The numbers sitting the papers in June will be less than 11000 according to my (seat of the pants) estimate. The media are totally hung up on the students "who change their mind at the last minute" The reality is the estimate is based on the Feb figures from the schools. 90% of the students who change their minds do so weeks and months before exam day Many students beat a retreat to ordinary level after the mocks. This is not reflected in the figure mentioned. Many capable students who prefer languages often "drop down" to ordinary level in March/April for stragic reasons The 25 points BRIBE definitely got candidates into higher who would not normally go there. In fact its safe to say the BRIBE motivated many less diligent candidates to try for the bonus. One of the most frequently asked questions I encountered was "if I get an E grade will I still get the 25 bonus points. Many teachers tearing their hair out with the influx of less capable students in their class as a result of the bribe.
PM causing massive problems all round This year exams will be a watershed for PM Voices will be raised and heard afterwards
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Post by corastack1 on May 30, 2012 1:04:44 GMT -5
Why has NCCA repositioned Ireland's top level mathematics curriculum well below all the world's top interantional currciula - because of what topics it decided to throw out. What my findings show cateegorically is that these are the very topics not that our treatement of many of them was top level eg treatment of vectors certainly wasn't- world's top class curriculum way ahead of us in this most important area as my investigations showed: Our main problem now is how to we get minister who is repsonbsible for the NCCA to do something to protect the top standard of our mathematical educational system. What we need to be doing all the time is finding ways to improve it. What have we in our wisdom done - exact opposite. If more maths syllabii are required to suit this ambition and provide appropriate maths education at more levels this should be done! When you examine the Canadian curriculum they are able to provide a vast amount of different matheamtics courses not just OL and HL. To compete with the top them we need more mathematics courses and as I have strongly argued at least one more on top of PM if PM is going to stay to protect the top standard and indeed offer opportunities to improve it and stay ahead! This is what proper mathematics educations systems on top mathematics currriculums are doing getting better and stronger all the time witness Singapore's new H3 syllabus- way ahead of anything we are doing" We are now as a result of PM way behind the best.
What has been removed from PM is basically all the hard stuff that was on it!
CALCULUS Limits of functions, rules for sums, products and quotients. Differentiation from first principles of all but linear and quadratic functions. Derivatives of inverse tan and inverse sine. Application of derivative to finding tangents of curves. First derivatives of implicit and parametric functions. Curve sketching using points of inflection, turning points and asymptotes. Newton-Raphson. ALL integrals other than integrals of polynomials and exp(kx). Integration by substitution. Integration by parts. Taylor/Maclaurin Series. Volumes of revolution.
LINEAR ALGEBRA ALL material on matrices, including uses for solving equations and in coordinate geometry. ALL material on vectors.
DISCRETE MATHS ALL material on difference equations.
OTHER MATHS Ratio Test. Telescoping series. Sum of n^2. Sum n*x^n Parametric equations of line and circle. Transformation geometry. Derivations of some of the double angle formulae in trigonometry. ALL group theory. Ellipses (coordinate geometry).
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Post by corastack1 on May 31, 2012 7:29:50 GMT -5
In final conclusions and can others join to help move the situation forward.
Two major things wrong with curriculum design here. NCCA did two very bad things. 1 Took out the Wrong stuff 1 Took out the Top stuff.
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Post by corastack1 on May 31, 2012 19:13:49 GMT -5
Korean Mathemtics Curriculum. Very strong emphasis on teaching fundamental and advanced algebraic mathematics skills at beginning of middle school. www.cimt.plymouth.ac.uk/journal/hwang.pdfKorean syllabus page 21 or so is the middle school. This is a very strong feature of this world class curriculum. Next is very technical approach to the teaching of calculus with proper approach to understanding limits and continuity first all the best places do it this way- the right way. After middle school you go to high school 15-17 finishing at 18 -19. www.mathnet.or.kr/mathnet/kms_tex/115181.pdfMoving on to pg 16 here you will see the two high school syllabi 1 and 11. Ii places very strong emphasis on integration as you can see up to integration by parts etc. This curriculum places huge emphasis of developing the fundamentals in algebra in a very comprehensive fashion before it moves to anything else. Its treatment of calculus is very strong and highly technical. So it PM says it is copying the best of Korean syllabus it is clearly doing nothing of the sort.
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Post by corastack1 on Jun 1, 2012 1:00:46 GMT -5
The top proessor in mathematics education in Singapore got back to me - equivalent of Oli in Finland educationally, www.seab.gov.sg/aLevel/2013Syllabus/9824_2013.pdf www.seab.gov.sg/aLevel/2012Syllabus/9740_2012.pdf Student taking science and engineering have to take this H2 second syllabus. Same as Holland, Even if we had this syllabus we would be very happy. Very balanced etc. If you want to do engineering and science you have to take H3. Our old hons LC was not as good as this but with more development of content in certain areas it could have been. The content balance compares favourable to the one of the old Hons (LC) Much stronger focus on vector geometry and none on euclidean geometry as far as I can see. Finland does a lot on vector geometry as well.This stuff would be accessible for all engineeing and science students.
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Post by corastack1 on Jun 1, 2012 1:02:49 GMT -5
Sorry - you have to take H2 with very strong and technical emphasis on calculus and indepth treatment of vectors etc.
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