Subject selections

I had a call from my dad today who asked, "I've been told all along that your stepbrother is university bound by the school but I have his subject selections for year 11 and they are all level 1 subjects."

When I dug a bit further he had been counselled into 1C English, 2C Maths and some non NCOS subjects. He had been given not recommended for 3A MAT and 3A MAS and told that he would "struggle" in 2A English, 2A Physics and 2A Chemistry.

I think many parents may be getting suggestions like this soon where schools make cautious subject selections to ensure that only the best students seek university entrance and along the way maximise league table results.

This move from encouraging students to seek excellence and challenge themselves towards seeking subjects that they will definitely do well in is contrary to the human spirit (especially when many of the non NCOS subjects lead nowhere). When we seek the improbable, all too often we succeed as we have underestimated our own capabilities. So many students that develop late are currently thrown on the TEE scrap heap without being given an opportunity.

Worse still, many parents still do not understand that level 1 subjects (in general) condemn their child to TAFE and not university - with ECU now saying that level 2 subjects are minimum for entry to university. Schools are effectively moving the university entry point to year 10 rather than pushing students through the year 11/12 learning curve/ litmus test where they have a go. Many TEE students succeed/many fail but all learn about themselves from the experience.

Somewhere we gave up on our youth.. before they turn 16 we drown their dreams in politically correct statements about students finding success and designing courses suitable to their needs. Shoot, we can't even devise an assessment programme systemically that can measure their ability (yes, I am talking about the failed levelling experiment). How can we judge with 100% accuracy who will improve enough to reach university? We are failing the 5-10% of students (or maybe even more if we count those that benefit from the effort) by not making them try to extend to university levels - especially those without environmental or behavioural issues. We have an obligation to encourage them to try, extend themselves and seek excellence.

It always amazes me what kids can do when given opportunities and are taught to value them.

Another IOTY candidate

The next nomination for idiot of the year goes to Barry McGaw chairman of the National Curriculum Board for his statement "the new standards will clearly show what skills and knowledge a student should aim for at each year level, making it easier for teachers to identify student progress and to help them."

A co-nomination goes to Caroline Milburn author of the article in The Age that says "Teachers will no longer be the sole judge of a student's work, after a landmark decision by the National Curriculum Board to introduce year-by-year achievement standards for pupils. For the first time, all teachers in Australian schools will have to use the same achievement benchmarks to measure student progress."

We know from MCJ in WA and how league tables are used that standards do not make it any easier to identify student progress as variables that define student learning are (in general) too various to adequately define. The only thing that standardised testing has done has reduced many good schools to "teaching to the test". No test has a better idea of student progress than a good teacher.

Caroline Milburn you are just publishing sensationalist tripe, if history repeats itself, we will just be given a load of generalist edubabble descriptions and unusable work samples that produce unscientific and statistically unsound assessment. Not to mention that standardising results across Australia has minimal use or effect other than for systemic discussion (which has no place in the hands of the public - see below).

My rant earlier today on this topic on the Education Matters forum went like this..

"I thought that we had learned from the smartie chart fiasco [in WA] that standardising grades is an exceptionally stupid idea.

Student A is trying their hardest but has little support at home. They are in a low socio-economic school, have peers in similar situations and have no chance to compete with students from leafy green schools. So each year, teacher has to give them a 'D' or somehow find them a scholarship, remove them from their social peers and hope that they can handle the social stigma attached to being in a higher SEI school.

The student without a scholarship gets sick of receiving D's (despite their attempts at catching up and working really hard). This is the same student that given a higher grade would have caught up and done really well in senior school, be a TEE candidate and contribute to urban renewal in low socio-economic areas (this kid was me - which is why I am so passionate about the idiocy of standardisation in this manner).

It also works the other way around. Student B does bugger all in school, but achieves an A because they have reached the benchmark. Without the motivation to push themselves further they don't learn a good work ethic.. Two years later they fail senior school as they hit their ability curve and have no drive to fall back on. It is just such a b*llsh*t idea.

School is about excellence and doing your best - not about standardisation and "fairness" in grading. Anyone with half a brain can see the flaws in it. TEE examinations provide the cross school moderation and that is where it should stay. I fear though that the drive for standardisation comes from government fear of litigation and the need to defer risk to schools where legislation and procedure provide some protection."

and then again later..

"Standardisation creates the same issues under a different guise. It potentially dictates that I teach material that is clearly beyond the student capabilities. I have no problem with suggested standards nor syllabus (syllabii?) but I do have an issue where I lack the ability to modify it where required. To demand that I teach algebra in term 1 year 7 when my kids can't do simple operations means that I would waste two terms teaching inappropriate material. To have to fill out twenty pages of documents to justify the delay (I know I'm projecting here but I have some understanding of how bureaucracies work) would do my head in.

Whilst we are on the topic of standardisation, to give these same students a standardisation test that tells them they are below benchmark (translate that to dumb in kidspeak) and destroy fragile confidence because the test is effectively two terms early is also wrong. I'm not sure of the purpose of these tests other than to satisfy curiosity of head office and parents. If they were internal tools that we could use to gauge performance and modify curricula to suit I would support them - but as yet all I have seen is judgements made about students, niggling comments about teachers, and misapplication of developmental/environmental causes rather than teaching or intelligence based assessment.

Either we value the judgement of our teachers or we use standardised testing. To continue the devaluation of teacher judgement in lieu of creating a better system needs further analysis as I don't think we are doing the education system any favours by pursuing a course of teaching to tests and the associated pressure of high stakes testing on children. "

Now I feel better.

3A MAT Ex. 8B Annuities and Amortisation

Ok.. AP's and GP's are now a thing of the past (what?? huh?? when did that happen - in 8A of course!).. we're now onto applications of growth and decay.. nope.. (we did that in 8A too.. huh?? what??)..

MAT 8B We're now onto Annuities and Amortisation - growth and decay with payments.

The calculator handles this under the Financial, Sequences or Spreadsheet.

Starting with Financial:
Once in Financial, select Compound interest.

n - represents the number of installment periods
I% - is the interest p.a.
PV - is the present value (the initial investment)
PMT - is the payment per period
FV - is the future value (the investment at period N)
P/Y - is the number of installment periods per year (how often a payment is made)
C/Y - is the number of times interest is compounded

Let's look at a simple problem say 8B q.3 in 3A MAT. Kelvin invests $620,000 into an account giving 5.8% pa. interest compounded annually from which her withdraws $50,000 at the end of every year.

a) How much is left after 10 withdrawals (N=10, FV=?).
N=10
I%=5.8
PV=-620000
PMT=50000
P/Y=1
C/Y=1

Leave the cursor on FV and press solve (at the bottom left hand corner of the window)
FV=436670

b) For how many years will Kelvin be able to withdraw 50000 per year

Find when the account is exhausted of funds (eg. N=? when FV=0)
I%=5.8
PV=-620000
I%=5.8
PMT=50000
FV=0
P/Y=1
C/Y=1

Leave the cursor on N and press solve (at the bottom left hand corner of the window)

N=22.52 therefore for 22 years.

If anyone can explain why PV is negative I would be very appreciative. I know from last year's course that it is but have no idea why.

Now Sequence:
This could also have been done through the Sequence tool using recursion
a) Tn+1=Tn*1.058-50000; T0=620000. Find T10
b) Tn+1=Tn*1.058-50000; T0=620000. Find n Where Tn=0

I'll leave the spreadsheet method for another day.

Here is a link to other CAS calculator posts.

3A MAT recursive formula, AP's & GP's

Those of you attempting Exercise 8A without students with a thorough grounding in AP's & GP's in year 10 will be scratching your head at this chapter.

Q1: creating recursive formula from word descriptions

Q2 -5: creating sequences (tables of values) from recursive formula in the form Tn=...

Q6: identifying AP's, GP's or neither from sequences

Q7-9: creating sequences (tables of values) from recursive formula in the form Tn+1=...

Q10: creating sequences (tables of values) from recursive formula in the form Tn-1=...

Q11-12,15,16,17: creating sequences from multiple previous terms

Q13: recursive formula using the term counter(n) in the formula

Q14: finding unknowns in recursive formula

Q18-22: Growth and decay problems

My recollection of when we did this in Discrete was that these topics were covered over multiple chapters. When attempting 8A students faced difficulties in that the calculator has some limitations. I can usually maintain 1 chapter per lesson but in this case I let it run over three lessons and found some extra resources to supplement the topic as it left many students scratching their heads. This was hard as it chewed into the revision time I had left for exams.

Things to remember for next year:

1. Present multiple examples of recursive formula for the same sequence for Tn, Tn+1 and Tn-1.

2. Introduce the limitation that the calculator (in sequence mode) can only use up to two previous terms in its definition (eg. Tn+2=Tn+1+ Tn not Tn+3=Tn+2+Tn+1+Tn). We wasted a lot of time on this.

3. You cannot move freely between Tn-1, Tn, Tn+1 and Tn+2 representations if n itself is used in the formula. eg. Tn+1=Tn +3 is equivalent to Tn=Tn-1 +3 but Tn+1=Tn + n is not equivalent to Tn = Tn-1 + n

4. Be careful with the position when dealing with growth and decay. It is usually much easier to define T0 (Tzero) and Tn+1=.. as the initial value and formula. Thus when solving for n, n is the answer rather than n-1 (which caused no end of confusion amongst students).

5. Make students do the examples without a calculator unless it states otherwise. A lot of time can be wasted trying to make Sequence mode do things it is not intended to do.

Sequence mode and Calculator usage (What not to do).

Most sequences can be done in Sequence mode. Some cannot. Here's how to get into Sequence mode.

Let's put in Tn = 2Tn-1 -5 where T1=3 (q.11 from 3a MAT). We are looking for T1 to T5. Press Type in the menu.

Figure 1.

You will notice that the notation to the text is different in that "an" is used instead of Tn. Ignoring that, you will also notice that there is no option for "an", only for "an+1" or "an+2". (Blogger can't do subscripts so just put them in where needed!).

In this case it is not such a problem, we can just transpose our equation to Tn+1 = 2Tn + 5 as n itself is not used in the formula; The given value T1=3 now becomes T2=3, remembering that we are looking for T2 to T6 now (which is really T1-T5 of the original formula).

So now we put in T2.. Easy no? NO! If you look at Figure 1 we have options for Tn+1 where we are given a0 (the zero term) or a1(the first term). No option for a2.

The Saddler text does a pretty good job of making the calculator look clumsy and painful to use compared to paper and pen.

Here is a link to other CAS calculator posts.