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

Solving triangles decision tree

Before entering declination and inclination in year 10 I wanted my students to really consolidate how to solve a variety of triangles.

I set up a decision tree on the whiteboard splitting the various methods for solving triangles.
My students are heavily reliant on notes to solve problems but now can see which parts of their notes to use for a variety of problems. They are even labelling triangles correctly!

Obviously the tree has limitations - finding third angles when two angles are given, finding the unknown angle with the cosine rule (when not the central angle) and the "ambiguous angle" with the sine rule.

Another area I have focussed on is providing differentiation for students of varying levels of algebraic skill. For some I have written all variations of the various rules on their notes page and ensured they can find the correct rule and use correct mathematical notation when recording their logic for solving a problem. For more capable students I have suggested only the bare minimum in their notes and encouraged them to identify the subject and manipuate equations to suit (as it is great practice). Some students have worked more on mastering sine & cosine rules, others have experimented with 3D trigonometry.

After discussing the limitations and completing a number of examples, suddenly the lights turned on for many of my students.. for the first time in a while I felt they were ready to move on. This is my cue to run a revision session of mixed and composite examples and check for further issues.

3D trigonometry

3D Trigonometry in year 10 is one of those subjects that lots of kids have issues with. Students traditionally learn just one topic at a time, are tested and then move to the next topic. With 3D trigonometry are all of a sudden faced with using lots of maths all at once.

Topics that all come together:

• Parallel lines (in 3D)
• Alternate/Complementary/Supplementary etc angles
• Polygon properties
• Trigonometric ratios
• Pythagoras' theorem
• Sine Rule
• Cosine Rule
• Oblique and isometric drawing
• 3d visualisation
• Volume, Surface area
• Algebra (in all its guises)

My students have seen some success in this topic through the use of "wireframes" (made of skewers and connected with a hot glue gun) and templates placed in the wireframes to indicate various right angled and non right angled triangles. It also helps them see parallel lines and equivalent lengths/angles. This seems to be the concrete element they need to put all the other stuff in place.

I also try to introduce the topic multiple times throughout the year as new concepts are introduced (eg. parallel lines - > volume -> pythagoras -> trig ratios -> sine rule -> cosine rule)

Also useful is the discussion on solving triangles here.

Burnout Week 5 term 3

As a new teacher we have to cope with a lot of things.. The kid with the difficult home life, the aggressive learner, physically agressive students, bullying and social issues between students, unachievable aspirations of students, students with low self esteem, politics between teachers, goals of the school, TEE, the list goes on.

And sometimes you feel it is all a bit too much. You grit your teeth and look forward to the next break. This is especially prevelent in term 3. You can see it even in the senior teachers as they confide they are not coping. I think to myself if they're not coping, how can I do it?

Then you stop sleeping and eating.. You get a little grumpy.. classes stop responding to your teaching methods. You're not as quick at coming up with alternate responses to poor behaviour and end up being the teacher you said you would never be.

At this point, talk to someone you trust - hopefully a team member that has gone through it all before. Don't pick someone struggling that will reinforce your issues, but someone that is doing well. Listen to what they do and why they are having success. Ask for some time out. Don't talk to your line manager - my past experience is that their responsibility for performance causes an imbalance in their judgement as they look at the now and only have time for a quick fix rather than investing in the whole picture.

I suppose the main thing is not to burn out. Your classes can suffer for a little while whilst you slow down a little. The profession needs you - three years from now you can laugh at what caused you such grief before, even if sometimes you can think it doesn't care. At the end of term four you can reap the rewards and next year be recharged. This is the hump - know this and just get over it the best way you can.

At least I hope so.

Setting difficulty level of classes

I've copped a bit of criticism about the level of difficulty of my classes. Some students have found it too hard, others too easy. This to my mind is an indicator that I'm probably doing ok.

After all it's better to push kids too far and get the difficulty level wrong occassionally than not push students and get the difficulty level wrong all of the time.

I try and manage the difficulty level through a number of factors:
1) Are the majority of kids engagaed in learning?
2) Are mean scores in tests increasing?
3) Can those not engaged be moved next to engaged students?
4) Can I make the course more difficult?
5) Is the top student being extended?
6) Are students endeavouring to pass the top student?
7) How long have we been on the current topic?
8) Where are similar classes at?
9) Have I covered the intended content?

And so on..