Course Counselling and Mathematics

The current Mathematics course is not my favourite of the past few editions.  

It has four main courses: 

- Foundations (for students that require basic numeracy)

- Essentials (for students to develop their basic numeracy to a TAFE level)

- Applications (for students to develop skills for higher learning)

- Methods (for students seeking maths skills for tertiary math/science courses)

and a fifth course Specialist that can be taken in addition to Methods (for those seeking to complete Engineering or Mathematics courses at University without additional courses to bridge to the level required)

Unfortunately WACE and University entrance is the main reason why the majority of students take Mathematics courses.  I would suggest that seeing Mathematics as only a pathway to higher learning or graduating high school is a very limited view as it does not consider the requirements after entry to a learning institution and for lifelong learning.  

The difficulty gap between Applications and Methods is large, much larger than in the previous iteration of ATAR courses (2AB/2CD 2CD/3AB 3AB/3D) as the option to do 2CD/3AB no longer exists.  The mean for Applications is 55, which results in half of the students sitting the course not having scores that is conducive to a university entrance score.   Given this is the case, half of these students end in TAFE or using other courses to build their ATAR score.  Getting a 1st or 2nd ATAR score with Applications is unlikely (and when done, tends to be students that drop in from Methods in Year 12.  Given this, as a counsellor, if I was unsure about whether a student should do Methods in Year 11, I would counsel them into Methods and parachute them into Applications if they were unsuccessful in Year 12).  This makes choosing Applications a problematic choice for many students (why do it if there are other subjects that I am more likely to gain a score with).

The mean for Methods is 65 with a SD of 12, with 3/4 of students getting a scaled score above 55, indicating that this is a course to build a reasonable ATAR score around. If students have the ability to do Methods, they should.  If they wish to do a Science based course, this is the only option to gain the thinking and capacity required for Science courses.  They may not use all of the Maths, but they will gain skills invaluable for learning new content beyond their current understanding.

The difficulty of Specialist has reduced its importance over time for maximising ATAR scores as the effort required is often better put to ATAR English, Chemistry, History or Physics and is only done by those with a passion for Mathematics.

My frustration with the current counselling thinking is that because many university courses do not have Mathematics pre-requisites, that it is better to do Applications (and pass) than Methods and potentially fail or that if students have C's or D's in Maths they should bypass Essentials or Applications and do other subjects instead.

To this I would simply say - Mathematics is about lifelong learning.  It is more than just entry to tertiary education.  There is no point gaining entry to higher learning, to only fail (or have to do bridging courses without the assistance available in school when you get there).

Doing Specialist puts you in an elite group of people able to do something that the majority of people cannot do.  Putting yourself in an elite is never a bad thing if you have the ability to do so.

Doing Methods takes effort, but is an opportunity to stretch yourself and truly learn how to learn. It will help a student get to university in the majority of cases if they have shown the aptitude in previous years.  If you complete Methods, you are likely to be a competent Mathematics student at university.

Doing Applications will develop your mathematical skills to a level that will mean in the majority of cases you will not need to learn more mathematics in later life but is unlikely (in at least half of all cases) to assist with University entry.

Doing Essentials will help you reach the next level in Mathematical understanding.  You will better understand the world in which you live from a basic numeracy, financial, measurement and statistical perspective.

Doing Foundations will raise your basic understanding of numeracy to allow you to function in society.

From a school point of view Mathematics provides opportunities in senior school to exploit 4 years of learning in lower school and has a course for any student - more so than any other subject (I'm looking at you English and HASS!!).  It is cheaper, more flexible and easier to run a full Mathematics course than 5 elective subjects trying to cater to various needs and ability levels under-subscribed.  A lesson learned by a few schools I dare to think.  Not making Mathematics compulsory results in significant bloat in school offerings.

To get students to choose Mathematics willingly requires many years of work.  Students must have an understanding that they will be supported, will pass and that there is an option tailored and available for them.  This is especially true for students with Ds and Es in lower school.  For the first time, in Senior school these students have courses that are designed for them (Foundations and Essentials) and there is a clear path to find success.

Why students are taking easy options in yr 12

Students are taking easy options in year 12. Schools are encouraging students not to take harder upper school subjects. Why?

Students have:

• little resilience - failure is an end product rather than a path to success
• do not experience exams in lower school and fear them
• have little work ethic - would rather coast than strive for excellence
• fear not making TEE score due to perceived issues with scaling and moderation
• have not been driven to complete lower school curriculum in lower school heterogeneous classes and have to make large leaps in year 11/12 to succeed (ongoing problem)
• have difficulty moving from developmental approach (going at own pace is ok) in lower school to graded syllabus approach (you're a C get used to it, we have to go at this pace to finish the course) in yr 11/12
• Core subject areas (Maths, English, S&E, Science) have lost actual teaching time to "equal" learning areas T&E, Health & PE and the Arts.
• VET courses are more readily available and provide an outlet after fatigue of 10 years education

Schools:

• Fear poor league table scores (and thus only attract weaker, behavioural issues students)
• Small academic classes creates timetabling issues
• Require more effort and experience by teachers to get students to pass a difficult subject
• Can only "suggest" that students take harder subjects
• "Good" students are being attracted to academic schools and G&T programs
• WACE issues; have to reach 100% graduation rate (therefore coach students out of difficult classes if at risk of failing)
• Specialist subjects are harder to staff (check the number of schools unable to run Lit, Economics and Maths Specialist or more than one class of each if they wanted to) - exacerbated by the half cohort
• Schools now cater to 'all students' rather than focus on academic students
• Correcting behavioural issues takes precedence to correcting academic issues (just check time allocated to both in any school) - schools can be seen as behaviour centres rather than learning centres.
• Lack of rigor and programming in lower school programmes
• No single point of responsibility within learning areas for performance with loss of level 3 HoD positions to behavioural/administrative roles
• Have a large number of 'refugee' or 'parents with work permits' students with little primary schooling when entering high school
• Students that traditionally left school in year 10 and now staying until year 12
• Students that may have found work in better years are finding it harder to do so in today's economic climate

This is a rather cynical comment and to be honest, this year we have the largest equivalent G&T, Calc course than we've had for a number of years (it raised some concern that we had been too lenient when coaching for subject selection) and next year's cohort for 3A MAS/MAT is an order of magnitude larger again. The issues listed are not true in all schools and when identified schools do look closely at them. I think many of them have occurred all at once due to the simultaneous introduction of the NCOS.

It's not rocket science. Just talk to a few teachers, they'll give you the remaining reasons.

Mathematics Pathways 2009

On paper the new courses next year look to be improvements on the existing 2008 MIPS/Foundations/Intro Calculus/G&T combinations. In 2008 MIPS was for weaker students, Foundations for mid tier students and Intro Calculus/G&T was for the capable students (think Maths 2/3 if you're from my era). In Year 12 MIPS lead to Modelling, Foundations lead to Discrete, Intro Calculus/G&T lead to Calculus/Applicable mathematics.

There were definite issues with the old structure. First MIPS was very language oriented which caused serious difficulties for low literacy students. The Foundations course was more difficult than the year 12 Discrete Mathematics course that it lead to. Many capable students opted to take the easier option (Foundations/Discrete) rather than Intro Calculus/G&T students as the scaling was never quite right for(although Intro Calculus/G&T students did get the benefit of satisfying many pre-requisites in university and avoided bridging courses)

The new courses for 2009 on paper better cater to a range of students. These courses are semesterised and labelled 1B-3D (eg. 2C in semester 1 and 2D in semester 2 year 11, and 3A in semester 1, 3B in semester 2 year 12). Each year 11 course (if necessary) can be sat again in year 12 (eg. if a student failed 2c/2D in year 11 and repeated 2C/2D in year 12). There are lower courses aimed at students with learning difficulties (PA/PB/1A).

Weaker students have a more traditional year 9/10 type course in 1B/1C/1D/1E or 1D/1E/2A/2B (replacing MIPS/Modelling)
Weak mid tier students now have 2A/2B/2C/2D (replacing Foundations/Discrete)
Strong mid tier type students now have 2C/2D/3A/3B (replacing Foundations/Discrete)
Capable students have 3A/3B/3C/3D & 3A/3B/3C/3D specialist (replacing IC/G&T/Calc/Applic)

The strong/capable students are typically university bound, weak mid tier students may use their score for low requirement university courses or TAFE. Level 1 courses are generally for vocational students.

The real benefits are for mid tier and capable students that now have real options in selecting 2A-3A as a starting point in year 11. Students that sit higher end mathematics are now promised a more equitable scaling factor than was in place under the old system. The general opinion is also that the new courses are easier (in general) than the courses they replace. Only time will tell.

2009 subject selection

Many graduate teachers and even experienced teachers feel some anxiety when it comes to subject selections. It's one of those times where your judgement can make or break the aspirations of a student.

Ultimately school should be a safe place where students feel comfortable to attempt what they previously thought of as impossible. Too safe subject selections will put students into classes that they will not be challenged in and surrounded by students with weak work ethic / too hard subjects will place students at risk as their self esteem takes a pounding.

Teachers feel this pressure. It is important that any conflict over what students should and shouldn't be doing be overcome before students are counselled into their subjects. The issue over 3A MAS/MAT (old Calculus/G&T stream) subject selection has caused much angst as this is a class in small schools typically with less than 14 students (the DET magic number for whether a class will run in 2009) yet also a draw card for top students entering year 8.

The plus side is that theoretically the new level 3 courses have a reduced difficulty level / the downside is that nobody really knows what the exams will look like and how the CAS calculators will alter treatment of certain topics. With very few true mathematics graduates entering teaching, it has been a concern for some time as to who will teach calculus courses in the mid term.

Cases where counsellors and administrators are counselling 'A' students out of level 3 courses due to misconceptions of course difficulty, available staffing levels, questions over quality of recommendations and issues with grades given to students need to be resolved well before the counselling process. Students being told to pursue higher maths by teachers and then convinced otherwise by counsellors is an avoidable situation that requires clear communication from administration what subjects can run and clear guidance on how to guide students forward.

I think schools need to consider whether the prime role of schools is to guide students into their first job (eg. narrow but job focused education) or into lifetime learning (eg. broad pursuit of highest possible education and widest vocational choice). Where schools assume a split role (eg schools with strong competing VET & TEE courses) close attention needs to be made over who is part of the counselling process and their mandate in giving subject advice and applying/overriding teaching or vocational recommendations.

Opening doors to the future

Now, we all get a bit proprietary about our best students. When subject selection comes around we all have a quiet chat with our students about what they intend to do and how they think they can get there.

Then we recommend courses for them.

These courses set up their higher education opportunities. In my case I sat Maths II/III exams many years ago - the new courses equivalent being combined Maths 3A/B/C/D MAT and 3A/B/C/D MAS.

I was not a high achiever in school - ending in the 50%'s or thereabouts. Achievers in high end maths tend to go into Engineering, vet science courses and the like.. obviously not a teacher like myself.

What these courses did for me though was open doors throughout my career. I was able to enter physics, chemistry, mathematics, psychology, biology, computing and ultimately teaching courses at university using mathematics prerequisites and skip bridging courses. As a programmer I could understand technical algebra and trigonometric requirements, I was able to assist my wife complete her business degree, we were able to better manage our finances to buy our first home, as company director I could understand statistical and financial requirements, calculus gave me the ability to challenge what I thought were my limits(bad maths pun) and go beyond them.

Sure I could have scored higher in Mathematics I (2A/B/C/D or 2C/D/3A/B equivalent) and probably gained a higher TEE score but thankfully my maths teacher took a punt and put me in the higher maths classes.

My point is that as a student I wanted to be a teacher at that time (..and a company director.. and married to a ballerina.. and a millionaire.. retire by 30.. pay off my home by 25 ..and be a writer..). Without higher maths I may have been locked into teaching and not do all the other stuff. My maths opened doors and raised people's expectation of my capabilities, giving me the dozens of occupations I have been involved with and the ten enjoyable years of courses at university.

Is it right to narrow a student education to maximise TEE scores for a current occupational whim rather than stretch them as far as they can go to enable future potential and enable unthought of occupations?

I emphatically think not.