http://mav.vic.edu.au/blog/index.php?blog=2&disp=comments

I can't get into the site to read the MAV response. However the NSW response is well-written, comprehensive and I have to agree with the majority of their arguments.

• There is nothing about assessment in the draft, nor whether assessment at Year 12 will be based on the two years (4 units) of each subject. At Year 12, assessment is a key part of the mix, without which, the document is incomplete.

• Assumptions about Year 10 background are not at all clear. While 10A is required for Specialist, Maths Methods refers to 10 / 10A which does not help to clarify what should be happening at Year 10. This uncertainty surrounding Year 10 must be addressed.

• The status of the CAS calculator is not clear. Some parts of the document refer to ‘technology’, some to ‘graphics calculator’ and some to ‘CAS technology’ – the reference needs to be more precise and consistent.

• The document should not make statements that ICT has been incorporated into all topic areas unless it is able to substantiate this. It would be preferable to read ICT has been incorporated into ‘most’ or ‘many’ or ‘where appropriate’.

• Cross curriculum dimensions are really pathetic and can only be considered tokenistic.

• The 4 unit nature of each separate subject is welcome and should help to overcome the confusion surrounding different implementations of the current VCE General Maths subject (GMS vs GMF etc.) and this should help with textbooks too.

• How viable is it for schools to offer 4 streams of Maths at both of Year 11 & 12?

• What pathways will be accepted, what will not? For example, can a student do three Year 12 Maths subjects?

• Although the document acknowledges the 4 courses are differentiated, there is nothing to suggest there will be recognition of this hierarchy in ENTER scores between the Maths subjects (possibly provenance of VTAC and equivalent?).

Comments and observations about the 4 courses

• Essentially three of the four subjects, with a little tweaking, could be viable. The fourth, Maths Methods, is of grave concern and if not drastically curtailed, could have disastrous consequences.

Essential Maths

• Content seems reasonable in that it is not demanding, although it does contain some algebra. There is repetition of some earlier year’s work and not sure if all the content is particularly meaningful or exciting even though it is accessible.

• Should some of the financial material from General Maths be attempted here because some knowledge of finance is a life skill?

• Don’t know how the Investigation will work in practice but sounds ok in theory.

• Should this have the status of a Year 12 subject? – perhaps it is a VET equivalent? Will many choose to do this subject? Will all schools be able to, or be expected to, offer it?

General Maths

• Year 11 content looks ok provided support material on price index numbers provided!

• Heavily financial in Year 12 – some newer material but a reasonable course. Time series back and a lot of recurrence material which may be found difficult although students will have CAS so probably this material will be able to be covered through formulae and ‘recipes’.

• Inconsistent with references to graphics, then CAS.

Specialist Maths

• The document says Specialist is designed to be taken in conjunction with Maths Methods but what does it mean by the statement “there has been consideration given to students who have studied units 1 and 2 Mathematical Methods to enter Specialist Maths at Unit 3”? Is this implying Specialist Units 1 and 2 may not be a pre-requisite?

• Options are totally ridiculous for a subject that attracts small numbers. Victoria knows this from when it tried to run 3, dropping to 2 modules, then giving up entirely and making the course fully prescribed. Do the same here – ditch statistical inference and prescribe either one of the other two options (difficult to choose between them) or preferably, prescribe a combination selected from the remaining two options. Another thought is to throw out Matrices so both of the non statistical options can be prescribed.

• I surprise myself by saying it but I have to applaud placing Graph Theory in Specialist Maths and I find ACARA’s argument for its inclusion very convincing. However, I hope there will be lots of good textbooks and support for teachers, such as myself, to learn this material at the depth required. How will the Graph theory treatment compare with its treatment in General Maths? Here would be a danger of there being fairly superficial treatment of the topic if the final assessment does not examine all 4 units of the subject.

• Some introductory work on vectors and polar co-ordinates is needed in Year11.

• It seems questionable that triple angle formulae need to be learnt.

• The more formal and precise language to be used in this subject is welcome

• Careful planning of the order of the syllabus to enable links with and to build on corresponding topics in Maths methods will be required.

Maths Methods

• This is awful. Far from lifting standards and encouraging more students to do Maths, this subject seems destined to have the reverse effect of steering even good students away from it and into General Maths and deterring all but the very few of the most mathematically able students from taking on Specialist Maths in conjunction with it.

• It tries too hard to cover too broad a range of topics. The subject needs to reassess what it stands for and devise a more reasonable course to service the needs of the student cohort it claims to identify with.

• Units 1 and 2 are really heavy – impossibly so, even if students remember perfectly the 10A material. Too much of the current Year 12 Maths Methods material has been placed in Year 11. It is quite unreasonable.

• Units 3 and 4 are fragmented and not put together well. There is no flow.

• Refers to assumed knowledge from10 / 10A so is 10A assumed to have been studied? This really needs to be clarified.

• Refers repeatedly to graphic calculators, but presumably CAS calculators will be used?

• There are hardly any pre-calculus concepts introduced, more a return to an earlier way of introducing calculus. Year 12 has second derivative as covered in Specialist. Why overlap?

• There is a huge chunk on Gaussian elimination - why, when students have CAS? This makes it even more tempting to throw out Matrices from Specialist and place the transformations from Specialist here to replace Gaussian elimination - or better still forget the lot because some things must be cut back to obtain a more reasonable course.

• There is also a huge chunk of statistical inference – didn’t go well last time round – Universities usually say they prefer to teach this themselves in context. Given all the statistics covered in previous years, there is sense in doing statistical inference but to fit this in so much current Year 12 material has been moved to Year 11 and something has to be deleted.

• It seems that the course is also prescribed in terms of order in which it is to be studied. Is that the case?

• Strangely, it appears to introduce surds from a very simple level.

• A number of topics that have appeared on syllabuses of various maths subjects at various times are assembled here: uniform and exponential random variables (can we expect to see Poisson and geometric before too long?), curve fitting using log-linear transformations, statistical inference… there is nothing ‘wrong’ with the topics, what is not right is there are too many topics trying to cover too broad a range. A depressing subject as presented.

Sue Michell

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I agree that some students lack facility in mental arithmetic and number sense as a result of their dependence on calculators. However, I am in favour of the many uses to which calculators can be put that actually help in the development of understanding of mathematical concepts. The important issue is to make sure that teachers have access to professional development that enables them to make sound pedagogical choices about their use of calculators and computer technologies.]]>

In his pamphlet “On education” John Milton sets out his views about education in England in the 17th century. One of his criticisms is the following. “…we do amiss to spend seven or eight years merely in scraping together so much miserable Latin and Greek as might be learned otherwise easily and delightfully in one year.” (Hughes (1957, p. 631))

A similar comment could be made about the strand on probability and statistics in the draft National Curriculum in Mathematics. Let me elaborate. I will refer to the draft National Curriculum in Mathematics simply as NC.

Data analysis is covered in the curriculum from kindergarten to Year 10. The aim is that students will be able to “recognise and analyse data and draw inferences” (NC, p. 2). Statistical inference is a well developed, formal branch of mathematics. To understand it properly one needs at least some calculus.

NC gives me the impression that statistical inference will not be addressed at all before the end of Year 10. In several places, NC mentions that, in data analysis, students will “make connections”, but a common error is for people to make connections without reference to statistical inference. It would be a mistake to teach students to draw conclusions by simply looking at data.

If formal statistical inference will not be addressed in K-Year 10 (and I would not suggest that it ought to be), then the data analysis section of NC consists of methods of elementary descriptive statistics. These methods could be taught easily and delightfully in a term.

I also object to the calculators that are so prominent in upper secondary schools. First they are very expensive and this only adds to the huge inequities in the school system. Second, the calculators are very clunky to use when compared to something like SPSS or Excel. A statistician would not use these calculators in practice; even students at university tend to use packages for statistical analysis. Spending time (and money) on these calculators to do statistics at school is a waste.

Reference

Hughes, M.Y. (1957) John Milton: Complete Poems and Major Prose. Indianapolis: Hackett Publishing Co.

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Thirdly - the draft does contain some stupid mistakes and errors - could someone clean up the MAV submission so that ACARA does not dismiss the MAV submission for containing some mistakes and typos.]]>