Right Angle Trigonometry Meta-language

My prac student is to deliver the right angle trigonometry unit and I was thinking about all the little things that I like to emphasize to students.

The first thing I would like him to consider is to design the course to make connections to previous courses of work (prior learning) especially with regard to language. Mathematics has such a rich history of precise language that it is important to identify ideas correctly to students in a manner that ties together topics to promote abstraction.

For instance before actually doing anything, we need to remind students what the LHS and RHS of an equation is, and how to identify the subject of the equation that we want to work with. Then we might think about how to eliminate coefficients and pronumerals/variables from one side on an equation, transpose terms/pronumerals/variables and multiplying through/simplifying to remove a denominator. What can we substitute into an equation? How do we solve the equation? Do we need simultaneous equations? We need to use every opportunity to reinforce concepts learned in previous algebra topics.

We have geometry prior learning to consider, three internal angles = 180°, a right angled triangle has one internal angle 90°. Line properties give us complementary, corresponding, co-interior, supplementary, adjacent, vertically opposite, exterior, alternate angles. Also the types of triangles, isosceles, equilateral and scalene help us find other angles. Circle geometry gives us tangents, subtended angles, cyclic quadrilaterals. Properties of 3D shapes!

Only after we consider possible connections to prior learning can we think about actually teaching the relatively small amount of new material. Without these connections we are just teaching students a new trick that will be forgotten immediately after assessment (a key issue exacerbated by the increased assessment required by OBE reporting requirements).

We have to introduce a range of new ideas such as opposite, adjacent and hypotenuse for right angled triangles. We have equations such as Pythagoras' and the three trigonometric ratios. .. and the dreaded bugbear bearings (until vectors makes bearings look easy!!)

We have conventions such as labelling the hypotenuse 'c' and the remaining sides a, b for Pythagoras' theorem problems and opp, adj and hyp in trigonometric problems.

We have good practice such as always writing the symbolic form of a trigonometric equation before substituting values, labelling diagrams, identifying right angles.

We have acronyms to help us remember trigonometric ratios SOH, CAH, TOA.

What is the correct sequence for introducing the material? What resources can we use or have available?

So now prac student, your job is to help students see how their prior learning is necessary to solve these problems!

Touchy.. Touchy...

Often speaking at school you think.. bloody hell.. that's not what I meant.

This seems to happen to me a lot as I am a bit introspective at times but will say what I think - and subsequently seem to live with a constant case of foot-in-mouth.

A couple of students came to me and said, "such and such teacher just doesn't understand.. I ask them for help and they don't listen." I sat down and talked with them about the kind of questions they were asking and it turned out to be a conversation like "I just don't understand anything!", to which even I would respond, "then go back to primary. I can't help you either." I then talked to the students about leading questions, redrafting and investigated what they did know. By the end of it, we realised that they had actually learnt a lot from the teacher already and that the angst they were feeling was that they now had to use this knowledge and that this required work.

.. so I said to myself... job well done.. and mentioned it to the teacher and asked if students resubmitting redrafted work was a problem and discussed the conversation I had with the kids.. this was turned on me as, "don't you think I provide scaffolding for my kids." OMG.. I'd just been praising this teacher to students and pointing out what they had already learned!

Another case in point occurred when I was asked did I have a preference to teaching boys or girls, to which I responded I thought I had a bit more experience teaching girls, therefore found it a bit easier.. to which the scamp teacher cheekily replied.. "I find boys easier to teach, are you saying I have less experience with girls?" ARGH!!!

These were jokey experiences, but sadly in teaching often analysis of our strengths and weaknesses, or sharing our ideas is seen as a prelude to punitive action to rectify a perceived issue. This fear often hampers any reform process and causes much angst with regards to performance management issues.

Oh and don't even think about robust discussion or sharing subject passion or investigating your own perceived flaws.

One of the ways of stopping teacher close mindedness is to nip it in the bud with practicum students and promote sharing of ideas (using new media where a young group of teachers is not at hand) to ensure that we become collegiate as a profession and welcome self and group analysis as a way of improving our performance. With many of our experienced teachers on the verge of retirement beaten down by OBE we will need to accelerate the speed that teachers become competent and we can no longer rely on the "closed door, hide in our classroom and teach ourselves" method of learning. It's inefficient, in a world where people change careers like underwear, it is also impractical.

That's my rant for today.

Unrealistic expectations and belief

As a teacher you hold fragile confidence in your hand every day. Belief in a student is a powerful thing, it can set a child on the path of success and make them believe in their own futures.

When we get caught up in grades and league tables and moderated scores and all other such associated bulldust we forget what a powerful thing belief is. When we believe in the person miracles are possible.

When we don't let students try, succeed and fail, we fail our students. Failure is important when seeking the utmost of our ability.

School is not about high stakes testing, nor about consequences. It is about creating a safe environment for our kids to explore their limits and seek excellence. Sometimes as a society I think we have forgotten this.

...as teachers we see the evidence of our beliefs every day.. as well as the consequences when our belief fails.

It's something to ponder.

The meaning of life

Today, I was talking about the meaning of life with my daughter..

Her response was definitely, "GOOP!".

..and how true she is. We start out as goop, we end as goop and we goop about a lot in between.

In fact there is very little that can't be explained by the word goop..

but.. I was unsure if she was interpreting our existence as part of a predestined global goop entity rather than as individual gooplets with free destiny. Does she lean more towards intelligent goop design or a more darwinistic goop approach? I'll have to check with her later.

Very thought provoking little 3 month old Mackenzie! Maybe she can explain it to me when she learns her second word.

A different model for success for state schools

Permanency has always been a key goal in state schools with teachers falling into permanent positions and then staying in the same school for 7-10 years, perhaps reaching long service leave and seeking a new school.

Stability, one would think, would be a key advantage over the private sector. I would suggest that it is the exact opposite. What tends to happen is that schools in adjacent suburbs function like teachers in classrooms. Many not knowing what is going on in the school/classroom next door.

Another key advantage would be the non competitive nature of schools is of a reasonable distribution of students, with students being part of catchments removing competition between state schools. In the private sector it is counterproductive to assist neighbour schools find talented students as they are potential customers. Yet in state schools we find it is common practice to poach students (and thus lower a school's potential results) either through systemic planning (eg. G&T schools) or through informal discussions with year 7 groups across catchments.

I think that increasing the rotation of teachers in schools within a district would solve this problem. Teachers would be attached to districts rather than schools and key teachers (level 3 CT's perhaps) used as troubleshooters for schools that cannot reach benchmarks. Benchmarks would be created for districts rather than schools. Funding would be linked to performance of the district with underperforming schools being given proven troubleshooters to improve performance (Think similar to the AFL draft!).

This would promote common frameworks to assist teachers with transitions between schools (the new system couldn't work without them). It would also lessen the poaching aspect as we could distribute students freely between schools in the same district knowing common teaching methods were being used and that school based performance was irrelevant.

By being district teachers rather than school staff, needs based movement could be made based on cohort size and specific needs of schools. I imagine this was the original idea of central staffing. To maintain consistency of approach, pastoral, teaching assistants and administration staff would remain school based but would need to agree on baseline standards. Consideration could be made on how HoD's and level 2's are distributed and moved and on what basis. Movement of HoDs and level 2's would give graduate teachers a wider exposure to teaching methods and promote exchange of ideas and resources between our expert teachers. Similar to the movement of principals in the metropolitan area.

It would require a change in mindset from 'development of a school' to 'development of students for a district' - seeking the betterment of the system rather than the betterment of a school. It's a philosophical change of mindset.

I like this idea. I doubt many others would.

Dancing...

Often I bop about with Mackenzie when music is on and she quietens.

Today we were at Woolworths and she was crying...

So here I am at the checkout..


"We are, We are.. the fresh food people..."

Dancing.. Singing.... baby in arms...

What a rocking tune.. The poor checkout girl thought I was nuts and Kendra is still laughing..

Milestones

6000 hits since July last year.. 750 hits & 499 unique visitors for May.. passed the 200 post mark... not bad if I do say so myself..

Hello to everyone out there !!

Career development & Half cohort musings

Today I was thinking.. what's the best way to get better early in your teacher career and do the most good in the community? Is it better to stay in one place surrounded by people that are supportive and appreciate your contribution, developing your own ideas with a small group or move amongst a range of schools, view what they are doing and use that to cross pollinate ideas whilst developing your own skills?

The half cohort is a critical moment in state school teaching in WA, with DET very late realising that it is having a negative impact on both school morale and student intake. For Ms O'Neil to release a missive saying the half cohort is being managed properly is to ignore the fact that it is not! Something that is being managed properly would not endanger subject delivery at schools, would not reduce student numbers over a five year period (which to my knowledge is not happening at private schools), cause further loss of teachers, leading to a loss of teaching knowledge (both about content, cohort, process and individual students) and further loss of confidence in your employer.

Schools are contemplating busing students between schools such that they students will have access to courses that individual state schools will not be able to offer due to small cohorts (this includes core subjects, Maths, English, Science and S&E). This means that students are taken out of their social settings, have reduced access to their teachers, lose contact time due to travel. Teachers lose access to certain courses for periods of time, have to teach more often across learning areas, have to teach subjects with gaps or years between offerings (eg. 3A subjects offered in 2010 & 2011 at one school, would move to another school for 2012 & 13), teachers may have to flit between schools with all the associated issues with managing split shifts, marking, load and travel time (equivalent to moderation issues 8-12 all subjects, all year round). Schools have to manage timetabling across multiple schools reducing the flexibility for change and development, manage attendance, manage the different acceptable behaviours/pastoral care, the consistency of assessment requirements and manage differing academic, literacy and numeracy standards.

Other options include merging 8/9, 9/10, 10/11, 11/12 classes.

There is more potential for students to fall through the cracks; it is an awful lot to deal with.

Subjects with low numbers (typically academic subjects such as maths specialist, physics, chemistry, lit, politics, history, economics), drawcards for students when selecting schools, all of a sudden may not be offered by a school unless under the busing students model (parents will really need to read the fine print!).

Busing students could be positive especially when tied to more options for students - with adjacent schools specialising in areas such as aeronautics, dance, LOTE, drama, specialist science courses, maths enrichment, sporting initiatives, computing, shed work, VET courses and the like that could not normally be offerred in a single school of 400-700. My concern is when schools are diminishing their offerings rather than enhancing them. Perhaps restricting busing to non core subjects and limiting it to one/two afternoons a week is the commitment that could be made by DET to limit potential issues. MESS teachers would need to take an option/specialist class or have all their DOTT at once. Anyone with VET courses at schools knows the timetabling issues caused by kids being out for half or whole days. Running specialist courses over schools is something that could have been done without the half cohort issue which leads me to think that more than likely it has already been tried with limited success.

There are other potential indirect benefits: in small schools, class sizes of 5-6 are more difficult to develop cooperative learning opportunities; it is also more difficult to instill some level of competition between students; (and the big one) these classes are more difficult to justify in terms of cost per student. Courses that may only be offered occassionally based on demand may be able to be offered consistently under a busing model.

So... going back to my original question, in amongst all this uncertainty, what is the best option for doing good in the community and developing my teaching skills? Sadly, it could be the private system for the first time in two years, especially with my family on one income and having a temperament like mine that needs a level of stability. I'll continue to think it through and seek more of the positives in my current situation as I love working in the state school system otherwise.