A quick hello!

Hello to those reading!! I quick thank you for the tripling of volume this month to the blog (300 unique visitors or so this month), the public and private comments I have received and the 25% of people that have been interested enough to have a good read and spend a few minutes with my ramblings.

Reflection is something that we all find hard to do regularly. Having it here helps keep up the motivation, I would heartily recommend anyone interested in blogging to have a go and start your own!

Rates and Ratios

Rates and ratios is one of those topics that I always have troubles teaching - especially to weak classes with poor fractions.

It is a large topic and covers many areas:

• parts of a whole (eg. 2 boys: 3 girls)
• parts of the whole (2 boys: 5 students total)
• scaling factors (1:100)
• equivalent ratios (2:4 as 1:2)
• conversion of fractions to ratios (2 blue:3 green = 2/5 blue)
• comparing unit values (1.25L of Coke @ $1.15 & 2L of Coke @ 2.35)
• unit conversions (dilute 1mL : 2L -> how much for 5L)

I don't think teaching this topic to 7's or 10's that I've established a sequence that enables students to grasp the concept easily. A few successful strategies have been corners and calculating ratios of m&m's and smarties. Mapping activities have been good (find ten cities in ten different countries and find the actual distance travelled) for large unit conversion activities. The grid activity where students grid a picture and then construct an enlarged grid and redraw the picture inside also works well.

I think next year when the topic is introduced I'll define ratios as a way of 'describing a groups of things' and then launch into proportions.

This is definately one that needs more attention on the programme and the sourcing of more resources for next year.

Education revolution - Bah humbug!

When someone uses revolution in a sentence, I usually put the following talk in the same category as others that include inclusive, flexible, robust and my all time favourite.. well... I try not to be cynical but election campaigns are always full of sensational headlines and little else when you dig a little deeper.

Here comes the usual garbage through my letterbox from state government politicians talking about greening the planet whilst cutting trees putting junk mail into my letterbox that goes direct to the bin. The latest junk being performance tables for schools.

I am not an advocate for school league tables. A better indicator for prospective parents is to speak to local parents about how students were treated by the school over the five year period. A school's reputation is its life blood. Conversely collating data and independent analysis privately reviewed is a great idea. Acting on these issues and seeking remedies over time in the public's best interest would be fantastic.

The only reason to release league tables is to accept that the government cannot act in the best interest of the public and the public needs access to the information to decide for itself. To accept this is to accept that the public has lost the faith in government. This is a direct indictment on the quality of our political leaders and public servants. One only has to look at how elections are won and lost - often on the actions of individuals rather than on their ability to govern. If parents had faith in government, the decision of parents would be geographical or financial as it has always been. Devolution of responsibility to schools is open acceptance that government cannot accept the responsibility/risk associated with governing schools. They are not capable or willing to remedy issues and are relying on market forces to do it for them. This is the heart of the safety net path I discussed in an earlier post (we'll take them if no one else will).

There are many reasons for poor results and to release the data with no analysis of why it has happened is not fair on a school. A school has poor results for many reasons - poor teaching, demographic change, a change in leadership, weak leadership, a lack of experienced staff, a large number of inexperienced staff, behavioural issues with specific students/classes, resourcing, a weak cohort, changing curriculum, socioeconomic reasons, issues with feeder schools. The list is unending.

Will a poor school be able to attract better students to raise its status after negative reports? Will poor reports relegate a school to a slippery slide of not attracting better students or teachers for fear of the school closing?

And what makes a good school? Is it the results of the top ten percent? The number of students without criminal records after five years? University entries? Students that gain incomes over $100,000? Students that don't end up divorced? Students that do well/better on standardised tests? Schools where parents are happy? Low teacher turnover?

How will statistics provide a fair and equitable benchmark for measurement of performance when high and low performance of students, teachers and administration is nigh on impossible to define and measure? People get very clever at analysing how scores can be manipulated.

I must say that I think these questions raise more questions than answers and that politically it seems it is just a smokescreen aimed to reduce inflationary pressures caused by police/teacher/nurse/public service wage claims and take away the focus from economic forces.

Impost of Mathematics NCOS in our schools

Let's look at the impost on schools and students for the introduction of NCOS in mathematics.

Firstly handmedowns instantly become useless to families. Old textbooks cannot be passed on as new courses are semesterised and the curriculum has changed. Students are at a significant disadvantage if using hand-me-down graphics calculators next year and old calculators cannot be resold relegating $147 calculators to $20 adding machines.

Next comes the impost of new texts. Each course (two per year) requires a book at $22 each (thank goodness Saddler books are reasonably priced) - $88 over two years or $8800. In year 11, students need to purchase a new CAS calculator at $187 - adding to another $18,700. In a school that supports 100 senior school maths students, this means that parents of senior school students as a group need to find $27,500 to cover costs just for mathematics.

Now knowing how hard it is to get $6 out of students for an excursion in difficult times, we should not discount the impost this is causing families. Suggesting to students that working and buying calculators rather than MP3's and PSP's may be the only way that some of these kids will be able to do mathematics. Perhaps this needs to be the christmas present for a number of students.

That it has come to students picking other subjects because they are cheaper says poor things about our schooling system. I know that some families have to make great sacrifices to find that $187 on top of requirements for other subjects, stationery and uniforms.

Then we look at the cost of implementation - PD, adjusting to new texts and calculators, course redesign, lack of available TEE materials, adjustments in subject selection, timetabling issues, preparation of new tests/ assignments/ worksheets/ homework /investigations, adjustment to non-calculator sections, the unpreparedness of 10 new courses all implemented at once. The time available for senior teachers to mentor junior teachers over the next couple of years may be severely limited. There will be very few knowledgable in the intricacies of these courses for some time. For confirmation of the limits of knowledge ask a mathematics teacher how the level 2/3 courses are treated in calculating TER scores. Good luck understanding the answer (it's here).

Course change is not something to be taken lightly- nor something that should be done in a rush.

I hate to think what will happen as books and calculators go missing or courses go awry next year - there are going to be some very sad parents, teachers and students.

Secondary Maths Users Group (SMUG)

The first run of the secondary maths users group was today, with a great presentation by Mahendra and his magic show. I'd seen a few of the tricks before and decoded a few more on the fly, but it will be great to look at the tricks in more mathematical detail.

It was a bit strange to be there in the lofty company of Alan Saddler - local textbook god, Greg Williams and the heads of department of many of the top schools in Perth. As one of the junior parties there we gained gobs of materials from Greg Williams but for the most part just listened.. these guys have wads of experience with a vast array of students and my two bobs worth doesn't stack up. One question did prick my ears though, a call for assistance in motivating low performing students - we do have a wad of those and maybe this is one way to give back to the user group.

An interesting topic raised was the running of 2C/2D in year 10 to assist students in year 11 3A/3B. The opinion was that students doing 2C/2D would do ok in year 11 and in 3A/3B year 12 but that the year 11 3A/3B students will do ok but will struggle with 3C/3D in year 12 without firming up some concepts earlier than commonly done now - especially with only the 3 terms available in year 12. Some schools are intending to run 2C/2D as the year 10 course (Scotch was mentioned and others said this was the intent in 2010) to alleviate the short year 12 issue.

Another was that many topics that were quite simple with calculators need reassessment under the new curriculum and non-calculator sections - one mentioned was trigonometry where 'trisolve' will no longer be "the be all and end all" as it is in Discrete mathematics.

It's definitely worth adding SMUG to your calendar if you are local and looking to see cutting edge teaching practices and problem solving in our elite schools. The next event is week 3, Term 4.

Outcomes based education

I thought I'd have a mathematical dig at OBE for a bit of fun.

Let's define a traditional learning environment in terms of mathematics:

Let
T=information taught;
L=student ability to learn;
K=student knowledge & skills;

Let us say that:
T * L = K;
T * L = 1; if a student learns everything taught.
T * L = 0; if a student learns nothing.

Examining Teaching and learning further:
Teaching Factors:
A=Teacher ability to teach content
R=Resources

Learning Factors:
D=Developmental level
B=Behaviour
P=Prior Knowledge
E=Environmental factors
M=Motivation
C=Competition/Collaboration

Substitute these to our equation:
(A*R) * (D*B*P*E*M*C)=K

In an outcomes based world T & K are written differently. What is taught is driven by the students and the knowledge required to be taught:
A = K ÷ (D*B*P*E*M*C*R)

So optimal learning ocurs at:
A = 1 ÷ (D*B*P*E*M*C*R)

Here is where the interesting things start to occur. One only has to wonder what happens if any one of DBPEMCR becomes zero. In the old equation K become zero, you could still teach but no learning occurred. In the new equation A becomes undefined and the ability to teach becomes impossible.

Similarly in traditional teaching one equation would fit the whole class and if the factors were affecting one student on any given day, the remainder of the class would still continue learning. Under the new model, one student with a factor at zero can cause complete disruption as you attempt to redress the factor impeding your teaching ability (and making your teaching equation undefined).

Furthermore, whereas delivering content from syllabus is under teacher control, understanding DBPEMCR and using it to drive the delivery of the teaching content makes the job of a teacher considerably more difficult in a heterogenous classroom especially as a new teacher with limited experience/ability/control over these factors. The smaller the value of DBPEMCR, the more difficult it is to establish a teaching moment.

Ok so it's all a bit fallacious but it does make one think.. perhaps sitting at home sick isn't the best time to philosophise and I'll go back to bed.

Teaching Jobs in WA

I was looking through the logs and many of the searches are for Teaching Jobs in Western Australia.

There are a number of hurdles to jump to teach in WA. You will need a WACOT registration number. Information can be found here. You will also need a working with children (WWC) check and a Federal police clearance. All four local universities have teaching programs ranging from 4 year BEd to the one year Dip Ed (completed after a three year degree).

Teaching in the state school (public) system requires applying through the Department of Education and Training. If you are from overseas it is likely you will get a remote posting as metropolitan postings are generally taken by the leading graduates and those returning from the country. Jobs are advertised here. The state school system is a rewarding learning environment and ranges from low socioeconomic schools, to GATE (Gifted and Talented) and distance education. Generally there are more behaviour issues in state schools than private/independent schools with the compensation of lower extra curricular requirements.

Catholic schools in WA generally advertise here. They and the remainder of private schools also advertise on SEEK. The local newspaper, the West Australian usually has a few jobs that fall outside the norm.

It is worth checking the location of the school you are applying to and the cost of renting in a local suburb. The real estate institute is usually a great place to start. A general idea of schools can be had by looking on that ratbag site rateMyTeacher or on school league tables mentioned in a previous post. Public transport in Perth is generally regarded as woeful unless you are in the centre of the city and then it is just congested and rarely less than a one hour trip.

Salary is between $45,000 and $70,000 AUD depending on levels of experience. Currency converters can be found here. The wage scales are a bit of a mystery to most and usually require some lengthy discussions with the paymaster to get right.

Curriculum development in WA Mathematics

You'd be human if you felt confused by the number of documents that guide WA education. Some are used more often than others. These are the ones I refer to most often.

NCOS Yr 11 & 12 Courses - outlines mathematics material to be taught in Yr 11 & 12 for cohort starting in 2009 (1ABCD, 2ABCD, 3ABCD MAT). Many materials for these courses are still in development including texts and sample exam papers. At this stage generally seen as an improvement on the old courses. Specialist maths course information (3ABCD MAS) can be found here. It is unclear how the implementation of the NCOS will affect university entrance.

K-10 Scope and sequence documents - outlines materials to be taught in each year group for each subject. Not mandated by government, can be varied depending on the developmental level of students. The most recent and useful by far are the ones labelled "scope and sequence".

Progress Maps - Used as the major curriculum guide prior to the K-10 Scope and sequence documents being available. Outlines the various assessment bands. If your student is "level 5, Number" this is what describes what level 5 number contains. Its use is mandated by government and is currently the subject of much debate over its effectiveness as an assessment tool. Also known as Outcomes and Standards Framework.

Curriculum framework overarching statement - outlines the framework for teaching. This forms the basis of any response to what teaching is done, how it is done and the aims of WA education. Its use is mandated by government.

Smartie chart - Most controvertial element of school assessment in WA. As part of Commonwealth government funding A-E grading was introduced in WA. The conversion chart or "smartie chart" shows how levels are converted to grades. Has proven difficult to use in producing meaningful grades especially in "leafy green" and "low socioeconomic" schools where the geographical differentiation skews results to either end of the A-E spectrum resulting in classes of A's or E's if applied as designed. Used as a replacement for normalised A-E grades within a class.

Expected standards - outlines what a student needs to be doing to get a C grade for each year group. Controversial as it lifts the bar a long way. Replaced the "smartie chart" in 2010 when using levels for reporting was deemed ineffective.

National Curriculum - The new standard that WA is grinding towards.


Updated: 10/12/11