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Post by Stephen Wills on May 4, 2012 6:36:11 GMT -5
Everyone's thoughts welcome...
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Post by Stephen OBrien on May 15, 2012 5:22:46 GMT -5
Can anyone explain the logic behind the change of syllabus in Project Maths? Much of calculus, linear algebra and vectors has been discarded in order to introduce a strand (20%) of geometry (and to beef up probability and statistics).
The majority of users of mathematics at third level are in engineering, science, business etc. The omitted topics are at the heart of engineering, science etc.
Why would we want to disadvantage all these students? Do we want our engineers etc to be weaker mathematically?
Students studying mathematics as a speciality at third level form a small minority; those studying pure mathematics an even smaller group and a tiny number (none?) will go on to study geometry to any depth.
So why all the geometry and especially, why at the expense of bread and butter engineering, science mathematics?
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Post by corastack1 on May 16, 2012 9:55:54 GMT -5
I completely agree with this perspective.
However what concerns me really is the lack of continuity in approach as well as content in the way mathematics is presented in school and then further on in college for those wishing to pursue mathematics and engineering etc at third level. It will be presented and taught in a completely different way. In my opinion curricula should be continuous and everythiing needed for understanding at point A should be tuaght properly up to this point and developed in a way that the majority can understand it.
From a curriculum development point of view I would have major reservations about PM
particularly for science engineering mathematics and applied mathematics students.
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Post by corastack1 on May 17, 2012 16:18:55 GMT -5
Does anyone know of any country worldwide (other than Ireland) were PM type syllabus, methology and assessement is used as mathematics syllabus for all leaving cert (or equivalent) students?
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Post by corastack1 on May 18, 2012 9:54:01 GMT -5
This was written by well know teacher and book author John Brennan on concerns about PM in March 2010. I only found it on the net today. It makes for interesting reading on account in view of comments expressed in the first post here and I am sure both views have been arrived at completely independenly and from different perspectives.
Reasons for postponing the introduction of Project Maths in 5th year classes in all schools in September 2010
•The Report of Engineers Ireland February 2010 states “There are aspects of Project Maths which appear ill-conceived and poorly thought out, and has led to concerns that Project maths is diluting or dumbing down Mathematics”.
•There are no text books, no sample papers, no marking schemes, and the syllabus is not finalised. Teachers have attended at most two in-service courses.
•The syllabus (still not finalised) as now proposed will not prepare students for maths in third level.
•The proposed methods for teaching Project Maths have been abandoned in other countries. The program discourages rote learning, an essential tool for teaching maths.
•The probable removal of Vectors/Integration/Matrices/Transformations/ from the Syllabus (essential for students going on to study Science/Engineering/Architecture at 3rd level) is a retrograde step.
•The removal of choice of questions (students must answer all questions) is also a retrograde step.
•The inclusion of compulsory Euclidian Geometry at Leaving Cert Higher level for the first time ever. This will send students in droves to ordinary level. Euclidian Geometry is not examined in any exam at 1st year in 3rd level. It was also the least attempted question on the Ordinary Level Leaving Cert maths. There is no valid reason to include so much geometry.
•The inclusion of four compulsory questions on Statistics and Probability (135 marks out of 300 = 45% on the Ordinary Level and 150 out of 300 = 50% on the Higher Level) is totally unjustified! In the regular Leaving Cert, at most 33% of the total marks are for these topics and students have a choice!
•Students who take Project Maths will be at a serious disadvantage at 3rd level when competing with students from UK and Northern Ireland.
•Project Maths Leaving Cert results may not be accepted by UK universities.
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Post by corastack1 on May 18, 2012 10:15:28 GMT -5
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Post by corastack1 on May 20, 2012 5:36:00 GMT -5
elib.mi.sanu.ac.rs/files/journals/tm/23/tm1221.pdfI checked out Finland's mathematics professor that is referred to by John Brennan. This was one article he wrote in English. Make some very interesting and informed comments in my opinion on the teaching of mathematics.
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Post by corastack1 on May 20, 2012 6:08:34 GMT -5
Example of citation record of this professor.
[CITATION] Nonlinear potential theory of degenerate elliptic equations
…, T Kilpeläinen, O Martio - 1993 - getcited.org
... Author: Heinonen, Juha. Author: Kilpelèainen, Tero. Author: Martio, O. PUBLISHER: Clarendon
Press (Oxford and New York and New York). SERIES TITLE: YEAR: 1993. PUB TYPE: Book
(ISBN 0198536690 ). VOLUME/EDITION: PAGES (INTRO/BODY): v, 363 p. ...
Cited by 1091 - Related articles - Cached- Library Search - All 3 versions
[CITATION] Injectivity theorems in plane and space
O Martio… - Ann. Acad. Sci. Fenn. Ser. AI Math, 1978
Cited by 252 - Related articles - All 4 versions
[CITATION] Definitions for quasiregular mappings
O Martio, S Rickman… - 1969 - Suomalainen tiedeakatemia
Cited by 232 - Related articles- Library Search - All 3 versions
[CITATION] Lipschitz classes and quasiconformal mappings
…, O Martio - Ann. Acad. Sci. Fenn. Ser. AI Math, 1985
Cited by 125 - Related articles
The Sobolev capacity on metric spaces
[PDF] from acadsci.fi
…, O Martio - ANNALES-ACADEMIAE SCIENTIARUM …, 1996 - emis.ams.org
Abstract. We develop a capacity theory based on the de nition of Sobolev functions on metric
spaces with a Borel regular outer measure. Basic properties of capacity, including
monotonicity, countable subadditivity and several convergence results, are studied. As an ...
Cited by 95 - Related articles - BL Direct - All 41 versions
[CITATION] Topological and metric properties of quasiregular mappings
O Martio, S Rickman… - Ann. Acad. Sci. Fenn. Ser. AI, 1971 - getcited.org
... Topological and metric properties of quasiregular mappings. Post a Comment. CONTRIBUTORS:
Author: Martio, O. Author: Rickman, S. Author: Vèaisèalèa, J. PUBLISHER: Suomalainen
Tiedeakatemia (Helsinki). SERIES TITLE: YEAR: 1971. PUB TYPE: Book. VOLUME/EDITION ...
Cited by 96 - Related articles - Cached
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Post by corastack1 on May 20, 2012 11:15:19 GMT -5
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Post by corastack1 on May 21, 2012 4:42:00 GMT -5
www.seab.gov.sg/aLevel/2012Syllabus/9740_2012.pdfThis is example of one of the singapore's mathematics curriculum. They talk about a possible key factor in high performance in key tests is due to the existence of a differentiated curriculum- haven't been able to find out exactly what this means in the context of this mathematical education system. In Holland this means if you want to pursue studies in engineering, science etc you have to do syllabus B or D which are much more technical than syllabus A and C which are coures for humanities students. If anyone can find a copy exam associations with this H2 syllabus could then provide a link to it for us. C. Often the best way to evaluate a curriculum is to look at the final examinatons.
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Post by corastack1 on May 21, 2012 5:10:51 GMT -5
In case you haven't time to look at the H2 Singapore syllabus absolutely top class compared to PM!!
even if does have a lot of applied stats but important calculus and vectors has not been thrown out to accomodate this - this is the point.
The syllabus prepares students adequately for university courses including mathematics, physics and
engineering, where more mathematics content is required. The syllabus aims to develop
mathematical thinking and problem solving skills in students.
Everybody is saying if PM is to stay we need this kind of sylllabus for out best students of mathematics.
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Post by corastack1 on May 23, 2012 8:36:52 GMT -5
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Post by corastack1 on May 23, 2012 8:43:42 GMT -5
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Post by corastack1 on May 23, 2012 16:17:19 GMT -5
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Post by corastack1 on May 23, 2012 18:15:01 GMT -5
In most cases, statistics and data analysis topics have been integrated into the secondary mathematics curriculum by being divided up and spread through various mathematics courses. While the integration of data analysis into mathematics courses has advantages, including providing motivation and generating student interest in the associated mathematics content and showing the connections between statistics and areas of mathematics, there are also disadvantages. Many important concepts of statistics and data analysis are not mathematical in nature and are not easily integrated into existing mathematics courses. Examples include the concept of sampling variability, good data collection practices in sampling and experimental design, an understanding of the role that the method of data collection plays in determining the scope of conclusions that can be drawn, the distinction between association and causation, and the reasoning of statistical inference. As a consequence, most students complete their secondary education having seen a number of graphical and numerical statistical methods but having not encountered many key concepts required for mature statistical reasoning. Is it therefore worthwhile spending so much time on applied statistics and also on financial mathematics when when you examine carefully the mathematical development involved is very little. Is this what we should be asking top level hons mathematics students to be doing with their time. Will this material teach deep problem solving and deep mathematical skills?? I tell my studens that every maths question involves some kind of problem solving skills to answer it and some thinking is required to decided which steps are neccessary to solve any maths question. The first step is to do this and the next is to do this etc etc. All mathematics questions involve some kind of problem solving. Key teachers and book authors saying teachers are spending huge amounts of time on applied statistics and financial mathematics and solutions to problems require minimal number of steps yet students having difficulty understanding words in these questions- what question is actually asking?? Is this fair on students at this level. Is it more a type of bogus problem solving. What mathematics skills techniques and competencies are learnt from doing these type of questions?  Has anyone else any thoughts on project mathematics? |
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