NCOS and consolidation of knowledge.

One criticism of senior school and mathematics in general is the lack of consolidation of topics - especially when the course is prescribed as is the case with NCOS. Funnily enough, the NCOS has brought about an opportunity for consolidation that did not exist under the old courses.

The new courses allow for repeating of yr 11 subjects - which makes sense under an outcomes approach where learning speed is not being measured, just knowledge and skills gained (this is an issue in itself that needs investigating if TEE scores are to remain a predictor of university success).

Students that cannot withstand the pace of the course in year 11 have in year 12 the option of consolidating (by repeating the course), remediating (by completing a lower course) or advancing to the next course. This approach allows teachers to make more aggressive subject selection recommendations in year 11 that promotes striving for excellence without fear of being locked into advancing and failing the yr 12 course. The recent trend of conservative subject selection could be broken!

For example, a student doing yr 11 3A MAT has the option in year 12 of doing 2C (remediating) 3A (repeating) or 3C (advancing).

I doubt this was the original intent (in other subjects teachers must teach another context - but only one context really exists in maths/science courses).

I fail to see the issue in repeating or remediating although I know some humanities teachers think it unfair - students that repeat will have the option to gain a deeper understanding at some level and a further opportunity to apply their skills - having a second bite at the cherry.

It will be interesting to see if the old adage that 'repeaters don't succeed' will bear true next year. For the lazy student - repeating/remediating will not work, but for those that have good work ethic but need more time logic says they should succeed (more time better results!).

My prediction is that (when counselled and supported correctly) repeaters and remediators will do far better than advancers and scaling will be applied to these students (compared to advancing students) in future years. It will be interesting to see if the scaling factor of 10% between 3AB and 3CD will be enough to compensate (I can't see how having two years to master a course can't cause better than a 10% increase in low/mid performing students between the two groups). The scaling may already be heavier for repeaters - but I'm not aware of it.

Don't forget to vote in the new poll!

There's a poll on the right hand side asking how we found the new courses - are they better than the ones they replaced?

For parents who are interested:

The harder parts of Intro Calc / G&T / Applic / Calculus (for strong science/maths/engineering bound uni students) was replaced by 3ABCD MAS (with some changes)
The easier parts of Intro Calc / G&T / Applic / Calculus (for capable science/maths/engineering bound uni students) was replaced by 3ABCD MAT (with some changes)
Foundations / Discrete (for capable Uni bound students) is now 2CD 3AB MAT
Foundations / Discrete (for weak Uni bound students) is now 2ABCD MAT
MIPS /Modelling (for students needing some maths - TAFE/Uni bound) is now 1DE2AB MAT
MIPS /Modelling (for remedial maths students - work or TAFE bound) is now 1BCDE MAT
No real maths course under old system (for Ed support or struggling maths students) is now PA PB 1A MAT

Now don't forget to vote on the left!

3B MAT/MAS course review

The 3B MAT course finished spot on 13 weeks (I used the remaining 6 weeks for revision and consolidation), which bodes well for the year 12 students moving into the course next year. The second semester is longer to cater for combined year 11/12 classes.

The 3B MAS course ran right down to the line finishing in 17 weeks and the vectors course was barely completed. It is quite full with Trig Identities and Vectors taking up large wads of time to do properly.

Some of my yr 11 3B MAS students are repeating 3B MAS in year 12 (with me again) and I need to lift the pace a little to make sure there is a little more revision time.

3B MAT exam
We used an external exam and the students were able to easily complete the project networks, correlation, linear programming, moving averages, optimisation and simple differentiation questions. Next year when teaching 3B MAT we will need to focus on interpreting graphs and their derivatives, conjectures and applications of differentiation. I'm happy with the two results over 80% (out of 10 students), but kicking myself that I missed one of the students that fell under 30%. I should have picked this one up sooner.

In particular I would find an alternate text to teach problem solving/conjectures with as the Saddler text is a little short on this topic.

In general I am pleased with their results (pat on the back guys) as I gave little in the way of exam tips (I didn't do the exam beforehand for fear of giving too much away!) and there was a 6-8% average increase across the class.

3B MAS exam
Urgh! The lack of revision showed, compared to the MAT paper. The exam also showed that working consistently through the year can work, with marks between the most gifted student and the conscientious student closing to just 3 marks in the calculator section. More work in vectors is required for the three students repeating next year to improve their C&D's to higher marks. They showed great improvement in the calculus sections of the test. With a bit more experience, they should be better able to identify what methods to apply to what questions. My results are skewed to the left with more C & D's than A & B's, but with 5 students, it would be a surprise to get a true bell curve (I would have liked it skewed more the other way!).

The MAS paper was a bit narrow compared to the MAT paper.. I would have liked to see more opportunity to show what they knew - rather than the imbalance of an overly large number of marks for questions that only an A or B student would be able to complete. Some questions were very misleading in their no. of marks compared to the actual work/knowledge required to complete them. Yet this is the price to pay for using external exams to judge how well the course is being delivered.

On to reports now!

School report cards

Last year Julia Gillard forced through school report cards to be made available based on the statistically questionable NAPLAN results. She stated that league tables would not be made from them.

Anyone with an ounce of sense realised this was nonsense. Then she linked agreement to funding - "Do it or else!"

Here is an excerpt from what the report cards are to look like:



Through a simple examination of the card you can see that each school is compared to all schools and to a socioeconomic band.

It is a five minute job to create a league table from this! Promise broken Julia!

It would ignore improvements to the school, discourage entry to the school and undermine any improvement model as students entering the school would be of declining standards (better students would go to the better performing school despite overcrowding/bullying/lower teaching standards etc.)

Of more concern is the second part of the page:

Of interest is the last category: % indigenous students.

What ?? Why should it matter that there are indigenous students in a school?

If we are to encourage students to become Australians, why single out any one portion of the population, why not caucasians, South Africans, Sudanese, Italians or Chinese. Remember this idea is from the minister of social inclusion!

Teaching staff ratios are also misleading. What are teaching staff doing? Quasi administration/pastoral care, specialty positions such as HOD on 0.6, GIRL or GIRN positions, in low ratio classes such as ESL/additional needs.

Whilst we are considering these factors how do refugees, ESL and additional needs students impact on NAPLAN results and school performance? Should they be discouraged from entry to avoid poor results?

This whole concept is just a bad idea. Poor over generalised statistics, designed to mislead the public and is a populist vote grab. This sort of information is best kept within the education system and used for valid statistical purposes until it can be presented in a valid and straightforward way to the public - personally I don't believe this can be done, it is just too complex.

If you are interested in reading more, here is the link to the mySchool website.

Updated 18/11/2009: Seems I'm not the only one concerned. Click here and here.

Updated 18/11/2009: Seems Julia is also the Minister of "wasting public funds", "rhetoric" and "denying the obvious". Click here to read her address on education.

New Poll

I've added a new poll. The last poll clearly showed that maths is the greatest because calculus rocks, closely followed by 'because English teachers are all nuts' and 'you have to be loony to teach science'.

A more serious one this time.. are any of the new maths courses an improvement on the old courses? I've enjoyed teaching 3AB MAT/MAS but have nothing to compare it to. The poll is on the left hand side.

Saddler 3C MAT/MAS books

Saddler has released his 3C MAT/MAS books.. time to take a trip down to Wooldridges - $23.95 or so per book.

Teaching Surface Area

I've been examining the issues with teaching surface area.

Here's an approximate sequence:

Prior knowledge required
(easily takes 3 weeks+ yr 10 with a weak group filling gaps)

• Notation for parallel and perpendicular sides
• Perimeter of Rectangles, Squares, Triangles (with all sides given)
• Area of Rectangles & Squares, Triangles (with all sides given)
• Circumference and Area of circles
• Area of Trapezium, Sectors
• Area of Composite Shapes (with all lengths given)
• Area of Composite shapes (finding missing sides using subtraction)
• Area of Composite shapes (using ratios of the area of known shapes to find area eg. 1/2 circle)
• Arc length
• Pythagoras, Trigonometric ratios
• Area of Composite shapes (using Pythagoras & Trigonometric ratios to find missing sides)

Surface Area Topic

• Identifying 3D shapes (cylinders, spheres, pyramids & prisms)
• Constructing 3D shapes using Nets (cylinders, pyramids and prisms)
• Identifying cross sections of 3D shapes
• Finding the area of cross sections of 3D shapes
• Finding the surface area of simple 3D shapes using defined formula (cylinders, spheres, pyramids and prisms)
• Using surface area of simple 3D to solve composite surface area problems (and using subtraction to subtract shared hidden sides)
• Deconstructing 3D shapes into constituent 2D shapes
• Finding the surface area of composite 3D shapes using deconstruction and 2D shapes
• Finding surface area of simple 3D shapes that have had sections removed using ratios
• Finding the surface area of composite shapes using simple 3D shapes, deconstruction and ratios.
• Using Pythagoras and Trigonometry with planes in 3D shapes to find surface area

It's a big topic!

Favourite teacher

I had a student once say "you're my favourite teacher" so I said to him, "I'm a maths teacher - is there a) something wrong with you or b) do you want something?"

I did ask him why and he said, "I can do the work in your class". This class was special as we had halved its size by splitting it between two teachers during the quiet period after the 11's and 12's finish. I'd been given the students that had potential but were struggling or that were destined for courses with low maths requirements. I'd been pretty strict with them in the first two weeks sending some off to isolation, having a number of one sided discussions with the boys, a few BMIS' and a few blue letters to parents.

There's nothing here that would make a student like the class. Yet, I sat back and listened to the student. In fact he went on to say that in other classes he went from 'bored because it was too easy' to 'giving up because it was too hard'. They had come from a class with a very popular teacher that had consistently good results, so I knew it was a student issue.

I explained to the student that in a smaller class it was easier for me to tailor the lesson to his optimum speed of learning - get on his back if he was loafing, fix his errors in a timely manner and acknowledge his successes. He had to work on his resilience too, and had to try more before giving up!

He understood that. I'd go on to say that when classes are getting feral or unmotivated, splitting them and resetting them into smaller classes is a legitimate and positive strategy.

Another yr 11 student at the end of the same day said that he liked our school because the teachers really cared and were willing to spend any amount of time outside of class to fix a problem. I like that students in our school are willing to spend inordinate amounts of time outside of class identifying and fixing up issues in their understanding. It can get a bit wearying sometimes on a full day. I have seen in another school "maths club" work well, where knowledge or skill issues are corrected in a math teacher overload situation (often 5 students to one tutor). This could take some pressure away in the earlier months of the year and give access to alternate learning sequences for topics.

I do love this end of year when we can consider our teaching practices, do some experimental class arrangements, have extra time to spend with students and test ideas for motivating students.