Graduation figures

Maintaining 100% graduation is a constant battle in state schools.  It is a combination of students understanding expectations, good subject selection practices, identifying students at risk, providing intervention to put students back on the path to passing and providing effective alternate paths for those that will not pass regardless.

If any of these practices fail, 100% graduation becomes unlikely.  It is not something that is easily rectified when it fails and if anyone in the process underestimates the importance of their role, the graduation measure falters.

Some would say that 100% graduation is a furphy and strictly speaking it is.  All students should not graduate.  There are those that are intellectually incapable of reaching any standard set, those with insufficient support at home, those with behavioural and motivational issues, those that have failed due to sickness should not pass.  Seeking high graduation rates has one positive effect in that it promotes support for those that need it most, those most likely to fail.  Seeking 100% graduation in low SES schools is an incredible drain on resources and to my mind a bit of a folly.  Low SES schools face too many of the issues every year raised above and without parachuting every student out that looks like failing (which I think is wrong because struggling students deserve a chance to defeat the odds if they are determined), low SES schools are unlikely to consistently reach 100%.  Anything in the high nineties would seem acceptable.

One issue that is often grappled with is late assessment and avoidance of assessment.  Common strategies to overcome this include parent contact, mentoring, detention, suspension, deputy intervention.  Older style strategies (used in years prior to year 12) such as deducting marks for lateness and requiring medical certificates are pursued less often as this puts students at risk far quicker than allowing students extra time to complete stage 1 assignments, especially if they are likely to reach the required standard by the end of the year (but have only failed due to penalties).

I have grappled with the fairness of this approach for a number of years and have come to the conclusion that allowing students more time (and giving more "incentive" to complete assignments) is fair.  Students in low SES schools lack academic, intellectual and emotional development.  The extra time allows development to take place and maturity to kick in for many cases (and thus we do get them over the line).  It's a lot of extra work for senior school teachers to coerce, coach, encourage and force students to complete work at the end of the year - but it means that students leave school with their year 12 certificate, something that is difficult to get later in life if they don't pass the first time.  Repeating year 11 and giving students time to develop further is another effective response.  Students that do their work, are still likely to do better and will go on to greater things.  Those struggling do not deserve to be punished further.

It's counter intuitive, but I do believe it is right.

A good day

I don't normally look forward to being left in charge of the maths team but in short spells it can be quite enjoyable. There was a nice feeling in the team today that was jovial, yet productive. There was a combination of teaching students, assisting colleagues, developing skills in student teachers, finalizing marking prior to reporting and generally working collaboratively to promote learning.

The feeling of collegiality is something that can be lost under the pressure of deadlines. Opportunities to work together in a fun environment can be lost to immediate demands. It's nice to finally reach that time in my career where content and instruction practices become easier to achieve, freeing time such that intervention becomes more of a focus.

It's hard for practicum teachers to see the road ahead. We look at them and see the types of teachers they are growing into, a horizon they can't always see. If they can better understand how it gets simpler(if not easier), perhaps we can improve the retention rates of our young teachers. We need to make that collegiate environment that aids their transition.

Russ.

Leaving marking behind cont..

It was a nice idea leaving marking at school rather than bringing it home.. but it hasn't worked..

I'm just sitting here thinking about it.

bugger.

Taking marking for a holiday

A common problem of many teachers is taking a wad of marking home over the weekend and my best solution to date has been to bring it back unmarked and untouched. It's the 'taking exam papers for a holiday' solution.

Being focused on improving the middle can be a trying task. I really enjoy marking.. I really do.. Those around me though... not so much...

I've tried getting up early, doing it late at night, whilst the baby sleeps, a bit at a time, reserving a whole day. Marking the best ones first, last, randomly. They all end with foul tempered dad, saying multiple bad words with lengthy time considering how to improve mean scores further, talking to myself like the mad cat lady.

But.... I think I have finally solved the problem...

Don't take it home!!

Duh!



...I feel better already :-)

The importance of tone and volume

The teacher voice is something that many teachers are told they need to learn.  I think sometimes the 'teacher voice' is a catchall phrase that practicum teachers can have some difficulty learning.. I know I did as a practicum teacher.

Being soft spoken, it is something that I had to approach.  My first teacher instructor was a shouter - to her classroom control was maintained through a combination of fear and volume.  It was something that I was poorly suited to and found difficult to emulate.

My second teacher instructor maintained her classroom through warmth and caring.  She had an ability to develop a rapport with her students and her classes liked her - much of this I would attribute to her sunny, kinaesthetic Phys Ed inspired background.  Not being the warmest of people myself and a little awkward at times in new social occassions,  it too proved difficult to emulate, although I did take much away from that practicum that I have tried to incorporate into my teaching.  I could see how her approach made it easier to break down barriers and reach that zone of intervention.

My third practicum was nearly my undoing, where the teacher instructor was a disciplinarian - a person I highly respect for the results he achieved in his classroom.  I also taught the class next door once a week and found enforcing this approach was difficult - as setting bounds on classes not seen often was difficult - and is a regular issue in teaching high school.  Whilst being observed in this class, my practicum nearly terminated after a lesson failed to achieve lesson outcomes due to behavioural issues.

Yet from each I was able to take a little bit of what I wanted to do (and what not to do) and established my own style of teaching, authoritarian but with a degree of warmth used to encourage students to achieve above their own understanding of their ability.  Raising my voice a little into assertive tone brings attention quickly - raising my voice above this brings looks of shock and silence for half an hour.  I think my students realise that I care about their performance as long as they are pursuing the methods I describe for success and realise that I care about non compliance when it effects their grades.

Anyhow, assertive delivery is a powerful tool in the arsenal of a teacher.  Use of the tone usually requires a number of things

1. establishment of an attention spot at the front of the room
2. a quick scan of the room (seeking eye contact and indication that instruction will follow)
3. a pause (to give students an opportunity to finish and look up)
4. a statement to gain attention (eyes front, pens down, look here or similar statement) delivered without intonation at a slightly high volume level than instructional voice (a voice that can be heard at the back of the room).
5. a second scan of the room to identify non compliant students in conjunction with a number of low key responses for students that need additional attention (hand signals, name, indication to neighbour)
6. a willingness to discuss consequences with students and move students permanently that do not respond after multiple processes

Once attention can be gained and maintained easily, delivery of materials becomes considerably easier.  It's not really the obscure secret many teachers make it out to be nor is it an optimal strategy for all teachers.  It is one of the more successful strategies for practicum teachers to use during practicum where more reliable and effective rapport based strategies really take too long to successfully implement.

Being predominantly a rapport based teacher, I do empathise with practicum teachers that are not 'type A' individuals sport stars and fashion victims that students immediately warm to.  My fear with the current practicum system is that many of the highest potential teachers are lost to the system as they do not have the time to develop a reputation amongst the student population as a great teacher rather than as a new cool teacher.

I love being a math teacher - as sportiness and fashion are rarely problems for us.  No expectation of being cool here :-)

Practicum Teachers

There is another side of taking practicum teachers - the side where the teacher instructors benefit.  A good practicum teacher is worth their weight in gold.  Some of the reasons for taking a practicum student:

• They are the bees of education, cross pollinating ideas from one school to another and from their own educational background
• They bring enthusiasm into the classroom
• They are an extra pair of eyes, ears and hands
• They lack pre-conceived notions and challenge the status quo
• They bring fresh ideas, a level of innocence and hope
• They lack some of our cynicism and crustiness
• It forces us to re-evaluate our own teaching practices
• They bring youthfulness into teaching staff
• It provides some longevity to our own learning when seen in their teaching

Most of all they can be a lot of fun. Once in your fourth or fifth year, I'd heartily recommend taking one for a term.

Lesson plans

I think every practicum teacher goes through questioning why lesson plans are useful.  Some find them odious and don't see the value of creating something that rarely executes as expected.  As a teacher instructor, I find lesson plans a real insight into what is intended by a practicum teacher.  As a tool it forces the practicum student to think about what they intend to do, before doing it.  The lesson plan also provides an opportunity for feedback between the teacher instructor and practicum teacher that can be done before a lesson is run (rather than the trite comment given by teacher instructors with the benefit of hindsight after the lesson).

A quick look at a lesson plan can provide a teacher instructor a wealth of information about how a practicum teacher is travelling.  Here are some things that I look at within a lesson plan.

• Has the teacher connected the lesson to prior learning?
• Is timing adequately considered?
• Is the scope of the lesson being managed?
• Are the main teaching points identified?
• Is the level proposed appropriate for the students?
• Is there adequate opportunity for students to demonstrate competence?

Without a reasonably detailed and well thought out lesson plan, practicum  teachers are placed on the back foot, forever reacting to issues rather than predicting issues and developing skills and knowledge to compensate.  By setting clear goals for performance before a lesson practicum teachers are able to see improvement measured against the goals of the lesson plan.

A note of warning, lesson plans on practicum have a finite life, as practicum teachers start taking full load, timing constraints limit their effectiveness (and can cause burnout towards the end of ten week practicum if detailed lesson plans are pursued).   The full benefit of a lesson plan is gained whilst a practicum students is ramping up. Even with this limitation, lesson plans (for all their odious nature), tied to reflective practices after a lesson, provide practicum teachers a platform to develop their fledgling skills into skilled teaching practitioners.

Classroom presence

I asked a colleague to talk to my practicum student about teaching.. Often a colleague has different viewpoints on teaching and can get to the nub of a problem faster than I can. There was some great advice about establishing presence in a classroom.

Establish space between the whiteboard and the class >1.5m
- use this as performance space. Move towards the class for emphasis and towards the board when teaching.

Establish modes of voice.
- develop a range of tones that can be used to indicate pleasure/displeasure, tied to a range of volumes

Develop affectations to your teaching
- Tapping a whiteboard marker can be more effective than shouting, as can removing or looking over your glasses.

Change your travel path
- ensure that your travel path is giving attention to all students and is not just a convenient way to travel a room.

All of these things will change your presence in the room and were good ideas. I would add a few more - wait for quiet before starting instruction (be patient.. 5 seconds is longer than you think), establish a spot so students know to be quiet when you are standing in it when waiting for attention, ensure that you are giving positive and negative feedback, be warm but not overly friendly and welcome students on entry.

I'm sure there are many more!

Practicum teachers & Teacher instructors

Practicum is the gateway to the profession.  It ensures new teachers have the experience to have their own classroom and sets clear expectations of performance outside of an tertiary academic environment.

Practicum teachers are a resource that is relatively infinite.  Good practicum teachers are not.  Teaching is an attractive profession to students as it is a familiar environment and one where students see infinite room for improvement.  This gloss can come off to some degree during practicum.

Teachers instructors come in a range of colours and shapes.  Aggressive/passive, lazy/committed,  skilled/enthusiastic (grin),  assessment driven/programme driven and with a range of teaching styles.

Good/bad teacher instructors are relative judgements. They make and break practicum teachers.  Let's see some of the pitfalls for practicum instructors

• Providing insufficient opportunities to fail
• Giving insufficient guidance on expectations
• Providing inadequate encouragement
• Assuming complete content knowledge
• Providing inadequate written response
• Creating insufficient opportunities to show initiative
• Insufficient direction/focus
• Insufficient guidance on required scaffolding
• Overestimating diagnostic abilities
• Assumption of teaching skills (photocopying, marking, using equation editor, CAS calculator usage, fxdraw, whiteboard usage, interactive whiteboards)

When we look at an incomplete list such as this and then overlay behavior management (which is the usually the primary focus of practicum) we start to realise the hurdle that practicum teachers face.  When I hear about accelerated teaching programmes that reduce the time for undergraduate teaching degrees I fear that policy makers are underestimating the impact that good teacher instructors can make.  Furthermore they are underestimating the impost of the shifting of responsibility from the student during practicum, to the teacher during their first year of teaching.  This will be borne by experienced staff and administration dealing with issues typically dealt with on practicum.

Good teacher instructors are using their full range of abilities to ensure that practicum teachers are maintaining their confidence at appropriate levels and by ensuring student learning is continuing.  The ability of the system to identify good potential teachers is based around the practicum system and bypassing this system has potential for lowering teaching standards further.

Apologies where due.

After re-reading my last post, I had a think back to my last performance management review.  Being a male, performance reviews, when I did them, focused on performance.  What had a person done, how had it been done, how could it be done better.  It focused on skills had, skills developed, skills required and skills gained since the previous review.

I learned something from my last performance management.  I lacked soft skills when performance managing.  A good manager knows their staff and steps in to remind them when they are not looking after themselves and can step in and make changes.  I always did this under my management premise rather than under performance management - but I can see how it could fit here too.  If a staff member is not looking after themselves, if home life is not taken into account - performance will suffer.  By talking through the issues (rather than just making the changes) a staff member can become empowered to better manage themselves.

Revising my original statement, under my usage of performance management, admin is poorly suited to analysing content provision and pedagogy due to time and skills constraints.  Using their experience to assist in management of self is a good use of their time, as they see continuous snapshots of staff behaviour and can spot when a staff member is struggling.  Reviewing how often this is occurring is a valid use of performance management time.

I'm lucky in this respect as my line manager (and even indirectly my principal) has had to step in a number of times to remind me of my limitations before I started something I couldn't finish.  For that I am thankful.


Russ.

Rewards for great teachers

Money for teachers.. Aimed at rewarding 10% of teachers.  For what?  Great teachers?  My issue with this idea is that government couldn't recognise a peer recognised 'great teacher' if peers erected a 60 foot high arrow above the teacher's head. I have real doubts at the success of this Commonwealth initiative.

Here are the proposed criteria for rewards circulated by Ms Gillard:

• Lesson observations
• Student performance data (including NAPLAN and school based information that can show the valued added by particular teachers)
• Parental feedback
• Teacher qualifications and professional development undertaken.

It seems the majority of the criteria is through administration based appraisal.  Staff who have been through an appraisal process know why teachers are cynical about their effectiveness.  The general summary is that deputies cannot assess subjects out of their own prior learning area on anything but behavioural matters.  These processes are time consuming and have little priority.  Outcomes from these meetings are negligible.  They are a hoop to jump each year.  I'm not having a poke at admin, they're busy and have a job to do - staff appraisal is not one well suited to them.

Lesson observations are generally futile given the amount of feedback that comes from them.  Without HoDs or subject superintendents, lesson observations only assess classroom management and this can vary greatly from day to day based on happenings within the school or within the home.  They are snapshots done maybe once a year.

How does the government expect this whole process to happen?  Who will pay for the time to collect this information, analyse it and present it for "approval" by government?  Where is the incentive for teachers that make huge differences in childrens lives outside the academic sphere?

Here is a cynical look at the process for gaining the money: 

Step 1: Prepare a lesson with little effective learning that is flashy
Step 2: Overteach NAPLAN and identify students that you can make large value adds and teach the class at that level
Step 3: Make sure parents put nice things about you on a "rate my teacher" type website (the alternative is ridiculous as it is near impossible to get a detailed questionnaire filled in a low socioeconomic school).  Challenge every poor parental response vigorously
Step 4: Seek spurious professional development to bolster your claim
Step 5: Fill out a wad of paper that takes inordinate amounts of time away from the classroom.  Sing your own praises until you sound like God's gift to teaching.
Step 6: Wait 8-24 months for your application to be appraised by a highly efficicent organisation such as WACOT.  Wait another 8-24 months for it to be approved.

I see absolutely nothing here that actually improves student performance, that leads to to gaining employment or higher education.  If the government wants to see this failed model in action - go seek out L3CT's or the WACOT registration and renewal process (that this sounds very similar to and has similarly been highly?? successful).  It's not the best teachers that succeed in these process, generally it's those with a lot of time on their hands and those willing to gild the lily.

This needs to be reconsidered and focussed on where a difference can be made.

Reward those that teach at the highest level (stage three subjects). Reward those in specialist programmes for disengaged students. Reward those in special needs areas. Reward those that consistently get students into university, apprentiships and TAFE courses. Reward those that go beyond their teaching requirements and still do an admirable job in the classroom.  Reward those recognised by peers as exemplary teachers.  Make people aspire to these levels to improve their teaching. There is nothing else easily measurable that teachers do.

NAPLAN in particular does not measure what one teacher has achieved.

Rewards should be an incentive to continue doing a good job.  If people keep doing a good job, keep rewarding them year after year after year.  Strangely enough, seniority captures this more effectively than performance management (generally, teachers that have taught longer are better teachers - those that can't quit or are encouraged to move on).  Couple seniority to more flexible staff movements and a better mix should be possible.

If the government wants change, improve teacher training (increase the subject specific content level appropriate for teaching), recentralise staffing with a focus on school performance rather than 'bums on seats' (moving these higher paid expert teachers into areas they are most required) and install monitors on learning areas such as subject superintendents for each region and HoDs in schools.  Improve pay rates and ensure that schools have the ability to move staff on.  Allow schools to focus on become specialist learning institutions to compete with private schools.  Provide assistance to deal with difficult students outside the general education system (this is where private organisations should be funded - to do the work government doesn't/can't do - rather than becoming a dumping ground for private schools).


The media release is here for those that want to poke a stick at it.

IOTY nomination 2011

The IOTY has been won by Julia Gillard before, but she continues to make a fool of herself to draw headlines away from real problems, by creating new ones.

Her latest brainwave is to reward teachers that improve NAPLAN scores.  Hey, I'm all for taking money from the government for doing nothing.  Let's see how it will work.

Year 7 teacher gets a bunch of students that have fallen behind.  He works hard with them but he has no hope of preparing these kids for massive improvement before the test.  They are tested in May 2011 and perform miserably compared to their 2009 Year 5 NAPLAN scores.  Sorry.. no bonus for you.   Regardless, with the support of a great administration he continues to work with his kids and they improve dramatically.

The next year the year 8 teacher is good too and the kids continue to improve in 2012.  Sorry... no bonus for you. We don't test NAPLAN in year 8.

One year nine teacher focuses on teaching the kids how to solve NAPLAN problems.  These kids do very well at NAPLAN in May.  Job well done, the teacher plays guitar the rest of the year, the kids learn very little and the teacher gets a nice fat bonus.  Upper school?  That's someone else's problem.

Another year nine teacher for similar kids focuses on what year 10 students need to understand and provides a sequenced course.  Her NAPLAN scores are not as good but are a more accurate representation of the level of the students.  No bonus for you.  She is invited to find a new job next year as she is under performing despite being popular with kids, parents and upper school teachers.

Upper school teachers get jacked off with the system and start applying for middle school roles.  Teachers in the upper school become less skilled and results suffer.  Nobody really cares because school performance is measured primarily through the 10 months of NAPLAN teaching rather than over the whole 5 years.

Of course this is based on gross speculation, but considering her past performance and lack of ability to heed advice or public opinion, a more than likely scenario.

Julia Gillard, you truly deserve to be renominated as Idiot of the Year for 2011.  You are an idiot.

Marble run

Spending time with my daughter has been fun and inspiring. Today we were playing with her marble run. Best $40 I've spent for some time.. She fed the run for at least half an hour. I'm guessing she likes the feeling of starting something that continues for some time without any real effort.

Teaching is like that sometimes.. The summer school started three years ago and I was unable to participate this year, yet it continued. Similarly I am now working with the maths academy kids trying to set something that will grow into a lasting benefit to the school. The programmes we wrote are still being used and adapted. I think the knack is to take ownership until it is working and then gradually step back, keeping an eye and maintaining the vision of the project. If you don't do this you are not really contributing to the school, just your own resumes... The project will die as soon as you leave.

Hopefully the same will occur with the Naplan analysis that we are doing this year.

Similarly, starting things and expecting others to finish it is a common path to failure. A lack of adequate committment and management results in underdeveloped projects with resentment by the participants - those thrown into the breach. Worst of all are the managers that take credit when the project succeeds despite the odds through someone else taking ownership.

Russ.

Emergent vs Divergent curriculum

Early learning in Australia has a great focus on Emergent learning.  I know little of this idea but I see clear parallels between it and failed OBE approaches.  Yet those that go back three years in my writing know that I actually support the ideals of OBE, just not its implementation in WA.

If (as I suspect) emergent learning focuses on letting students travel in directions best suited to their current status as a learner, I would draw notice again to the frailties of this model.

• In general, it is very difficult for any but a highly skilled practitioner to maintain an individual focus on a classroom of children - especially in the first five years of being a teacher.  The skills to diagnose, resource, devise, integrate and execute multiple programmes in a room is near impossible for a learner teacher.  It is a sure path to burnout and disenchantment with the profession.
• Students resist learning in lieu of fun.  If left to their own devices they will not learn optimally.  Pacing a course at the speed requested by a student will ultimately fail the student.  A highly motivated student is a challenged student, not necessarily an 100% happy one.

I would be a poor educator if I didn't offer an alternative, especially for our practicum and graduate teachers.  I call it a divergent curriculum and again I don't doubt it has been suggested before, though it hasn't been brought to my attention.  If we want more teachers that can embrace the best of OBE or Emergent curriculums, then I would suggest this approach.

• Create a baseline syllabus that dictates 80% of the course, when, what and how it should be taught for all teachers under 5 years of experience.  Have these teachers mentored, assisted and monitored by experienced teachers (5 years+) regularly.
• In the remaining 20% allow for remediation and extension. 
• The teacher must return to the syllabus each time a new topic is encountered.
• Experienced teachers that embrace emergent or variant curriculums are reduced to .8, have increased pay, given EA support and set high performance metrics in order to renew courses.  If courses do not meet metrics teachers return to the syllabus.
• Results are centrally coordinated and used to justify changes to the syllabus or suggested alternate programmes for special needs areas or developing teachers.

Thus the curriculum is only allowed to diverge by 20% unless the experienced teacher judges that more is necessary.  The load for curriculum design in the early years of teaching is reduced and by the end of five years the 20% "focus" becomes the resource for when syllabus restrictions are released.  Only teachers with experience to create emergent or purely outcomes based curriculum are allowed to do so (as they have a thorough understanding of what needs to be taught and a baseline for how long it takes to teach it) and it is closely monitored.

If we want to draw a line in the sand of where teacher pay rates should increase, it should be here.  Some might be cynical and say choosing five is because I am five years out.. but being more cynical, even if this idea was embraced, it would take another five years to implement and gain momentum.  I have no idea what I will be doing by then :-)

Learning as a parent

I have a two year old and she is too often my teacher. I learn more about myself through our interactions than through hours of teaching. At the moment she is going through a "wake up at four" phase, waking up screaming (thus the 5am blog). Normally, I'm tired and half awake so I bring her in with us. Being on holidays, I sat with her and after much screaming of "big bed" she let me give her a cuddle and said "scared daddy". So I sat with her on the chair in her room, closed the cupboard door and she fell asleep in my arms.

I wonder how many times a student has felt scared of a new Maths topic and I have gone into autopilot and shortcut the issue by providing a question specific solution that does not generalise for the elementary problem. Rather than giving the answer, I should allow a student to elucidate what the issue is and then provide abstract tools to prevent it happening again. Time notwithstanding, I think this is what maths should be more about.

Experts in their field

According to the Australian council of professions, a profession is:

"A disciplined group of individuals who adhere to high ethical standards and uphold themselves to, and are accepted by, the public as possessing special knowledge and skills in a widely recognised, organised body of learning derived from education and training at a high level, and who are prepared to exercise this knowledge and these skills in the interest of others.

Inherent in this definition is the concept that the responsibility for the welfare, health and safety of the community shall take precedence over other considerations."

As a computer programmer, analyst and manager, I had a group of skills and worked ethically to provide a service.  There was both an effort and reward to what was being sought and achieved.  I was paid well for my knowledge and was accountable for any advice given.

As a teacher I bring my old skills and have a set of new skills, yet demand for this knowledge is limited to submission requests by national curriculum, moderation requirements by curriculum council and occasional tutoring programmes.

As teachers, the transition from seniority based government workers to teaching professionals is not being well managed.  Career progression is poorly defined and clearly needs additional work.  It's in nobody's interest to address this issue as it will make a large workforce considerably dearer to work with.

What no-one is considering is that the increasing requirements on teachers to perform to metrics is creating a specialised workforce that will increasingly require differentiation and alternate wage scales to retain key performing employees within the workforce.  When this starts to happen the knowledge of key employees will gain value, diminishing the willingness to share knowledge especially where a market advantage is gained by the organisation.


It reminds me that when WACOT release ethical standards for teachers (after they finish that wad of registrations that is their revenue source), we need to be certain to ascertain how limiting they are to ensure that the remuneration is consistent with expectations.

Specialisation and professionalism needs to be properly re-established at the teaching training level.  The image of a  teacher in a mortar board and gown, cane in hand, standing over students studiously working on chalkboards, feared by parents, admired for their knowledge is long gone.  Perhaps, with the rise of an 'education first' approach to teaching training, a teacher delivering developmentally relevant content to a group of engaged students that understand the consequences of under performance on their future vocations, teachers will become again become valued members of a community. Maybe this person should be paid more.

A teacher that performs at a high level within a community and is visible in promoting education of parents' children may even become respected again.  Maybe this is a viable pathway to raising the profile of groups of teachers in the profession at a local level.  Maybe these people should be paid more.

A teacher that brings a wider knowledge of life through experience would help make better citizens.  Maybe this person should be paid more.

Maybe when those in high places actually consider the fiscal issues of a metric based educational economy they will reconsider this whole notion.  Who is looking after or taking chances on the kids that don't make good metrics?

Teaching is and should be always be a vocation well supported by all so that what needs to be done, gets done.  Let's hope it stays that way.

Russ.

More work not less

Students in low socio-economic areas need to do more work in high school despite behavioural distractions.  I've listened to colleagues that studied in NSW espousing the benefits of a multi stage course in senior school. I've never really bought into the argument for the majority of students, but for our top end I'm not so sure.

We have the maths academy twice a week after school.  The year 10 students are a keen bunch and are willing to work.  Taking out the two advanced students (and placing them in with year 11 and 12's), the majority of the rest have shown a vast improvement through the extra two hours a week.

This attention for the middle has raised class averages from sixties to eighties (resulting in an avalanche of praise) something I have never been able to achieve before.  Given the statement - students that are behind have to work harder (such as in areas where students start with a social disadvantage) and the fact that extra attention can work for these students (who come in their own time for nothing but the potential for a better grade), it identifies an equity issue that is difficult to ignore.

We put vast amount of effort (and money) into students with behavioural issues - but in many cases we ignore those with academic needs because they cause little trouble and parents are unaware of their potential.  With the lack of performance data in this area - I would say not only parents are unaware of actual potential, I would say schools, teachers, administration and society are also unaware of this potential.  Since our middle management and bureaucracy comes from this pool, we endanger future performance with this neglect.  We are creating a large welfare/low income group onto which we will have to support well into the future.

Teachers are in some part to blame for this - as we individually protect these students by investing our own time, allowing the system to abuse the goodwill teachers have towards their students.  Why pay teachers for putting in extra time if they are willing to do it themselves?  Private schools take this one step further and write donations of family time into school time as a part of extra curricular requirements.  Good people enter teaching - and as such set themselves up to be burned out by unscrupulous employers.  It takes other teachers within the system to identify when this is happening as teacher management itself is near non-existent (as management focus is placed on behavioural issues with students rather than optimising teacher delivery).  If teacher management is attempted it usually a band aid prior to slingshotting them into another role or school.  Result - students fall through the cracks (chasm) on a regular basis.

Once upon a time schools protected academic performance as the core business of a school.  Since losing this focus schools now have other metrics such as attendance and suspensions (resulting in lower crime figures) and year 9 performance on standardised tests (resulting in funding advantages).  Neither of which examine the output of a school vs the input of a school.  It is difficult to take a snapshot of a school as the main metric is measured over 5 year periods.  During this time anything could have changed - especially as student performance can be greatly modified through teacher, principal or community involvement (positively or negatively).

Where schools seek to keep out of the news and have a status quo with students, rather than seeking excellence and pushing them to their limits, it raises students with little resilience and little understanding of their own capabilities.  This is a poor outcome for everyone.

Singstar Competition

It's interesting to see those that are willing to put themselves out there for kids, those that aren't and those that can't.  I've run Singstar competitions at the end of term 1 for a number of years.  I do it for a number of reasons:

• We don't have a music programme at our school, and it gives kids an outlet to express themselves
• It encourages students to make a fool of themselves and know there is no lasting consequence
• It's an opportunity to teach empathy - laughing with, not at
• It builds confidence for shy kids, who over a number of years learn to have a go
• It's an opportunity to talk about why building confidence is important
• It's class building
• It builds school spirit
• Students I don't teach get to see us have fun and the learning environment I expect (mildly chaotic but productive).
• It's a but of fun

Bridges get built during these lessons where students that don't perform academically are allowed to shine and it provides a talking point with those that can perform.  There is a purpose to it, a pastoral care activity with real academic outcomes.  We know from past experience that classes that participate are more willing to ask seemingly "stupid" (to them) questions and resolve issues quickly rather than hiding at the back of a room.  If I can sing in front of peers, then I can ask a peer of the class a question that everybody might need to know.

Our principal had a go at David Bowie, TA's had fun (best Math's lesson ever supposedly!), one of the other maths teachers beat his highest score of 850 (he doubled his previous best), an English teacher was mildly inappropriate but very humorous.. and my poor prac student looked like she was going to die when she was gently "encouraged" to have a go.  Our chaplain went white as a sheet when asked by 60 students to sing.  One of the deputies ran in fear.  I don't know if that was the best role modelling - but it was funny.

I was giving rewards to students randomly, to those that wouldn't normally perform (although I endeavoured to not make this obvious).  One performing/drama student felt that she deserved one and had a wee tanty when I declined.  It's interesting that students still believe that they deserve a reward for doing something that they enjoy rather than for something that extends them.  I felt like quoting the workers in the vineyard parable to her.  They're my rewards, I can give them to winners, losers and anyone inbetween.  The tanty showed an area we can work on before they go into the workforce and forever feel hard done, yet not knowing underlying strategic reasons for rewards!  Take pleasure in what is given - enjoy the pleasure others get by being rewarded.  Resentment is not a good path to be on.

The great thing is, from year 8 to year 12, by the end of each period the majority of students wanted to have a go and it identified those that could benefit from some leadership training to extend themselves.  I was later told that you could hear the better part of 60 students singing, enjoying themselves from 50m away outside the school.  It's days like this that remind you of why you teach.

Five hours and five classes is a bit much to do on my own, with typically 60 students in a room each time.  By the end of the day my head was throbbing.  Being careful to limit the songs that students can use, I would heartily recommend it, though be aware it may take a couple of years to create groups in the school that can "get the party started", a PS3 and about $500 worth of songs/microphones/CDs.

Knowing the quality of the singing I would always suggest turning the mics down to zero ;-)

Welfare and schooling

I read this article today and wondered at the effect welfare has on education.  The article discusses how different areas have large welfare elements and inferred that it needed fixing.  The Balga area (30% on welfare) and the Girrawheen area (21% on welfare) were mentioned as two of the highest areas on welfare in Australia.  They also happen to be two of the areas that I grew up in.

The cost of housing drives the low/no income population into areas,  welfare and those on subsistence incomes. Both areas mentioned in the article were also state housing areas before policy distributed state housing across all suburbs.  This population will always be grouped to some degree.  The article identifies how concentrated the "have nots" have become in WA compared to other states.

Gentrification is the only thing that "fixes" an area.  As the area becomes more desirable (due to proximity to jobs in the city), low income earners will "cash out" and move further away or be forced out by increasing rent values.  Although it does just create a new area elsewhere with the same issues.

Low levels of education drives this segment of the population people into low paid/subsistence jobs or welfare whether due to lack of language skills, poor health and hygeine, poor diet and obesity, large family caring requirements (3+ children), poor financial management ability, low base EQ or IQ, low levels of schooling or mental health issues.  Many see the education system as failing them (and it does in many cases fail to provide them with pathways into the workforce) and pass this prejudice onto their children.  This article talks about the entry point of children into year 1.  In these areas it is not surprising that children cannot read, where parents cannot model these behaviours to children prior to school.  Thus the cycle occurs from generation to generation.

This is most obvious in our indigenous or welfare families.  Those students not affected by alcohol and drugs in vitro, have difficult home environments in which to learn.  We need to rethink "quick fix" solutions and focus on long term measures.  Schools are succeeding across the state if with every generation (16-20 years) one level of schooling is achieved.  Education to year 7 and wishing for higher schooling, education to year 10 and work ready, and finally the holy grail of education: education to year 11/12 and achieving TAFE or  university entry.  This is not shown in NAPLAN results.  Furthermore, the problem doesn't go away with each generation, as the next wave of immigrants will have the same issues.

I don't know if any amount of "fixing" can actually correct this number of issues.  Certainly lack of public transport as mentioned in the first article is not a major solution.  Breaking up public housing was certainly a start as it gives families better role models than was available by grouping them together in state housing slums. 

The message that "education" is the only way out of the rut will not work until educational equality is again established for this group from a very young age.  This has been lost as many schools have a pastoral, rather than academic focus - attempting to ensure happy environments rather than taking a narrower focus and focusing on the long term issue of education.  Pastoral approaches need to be tied closely to curriculum success. To reach parity, students that start at a lower level, have to work harder and/or smarter.  They don't need pampering, school will not be the best time of their lives (if it is then it is to the detriment of their adult life).  Eggs will get broken along the way and they need caring for by a different system outside of schooling. 

Schools cannot be a catchall for social change.  They are one element of a big picture that can work for the majority of students.  If we allow diminishing returns (increasing support to students that cannot be supported without additional funding) then we will fail the majority of our students.

Where parents cannot provide adequate support, the welfare state must step in to assist and parents must support this assistance. It is a public service message that needs to be supported with real results for the majority of students and ultimately for Australian society as a whole.

Otherwise, sadly, a two class system (with the "haves" in private schooling and the "have nots" in underfunded public schooling) will be the result as opposed to the "occassional" problem family causing issues for society.  Creating and promoting a two class system through education would be a sad event indeed.

Hello out there!

Last month we hit 1000 visitors in a month for the first time (1111 in fact).. which is a fair bit for my little blog.. hello to everyone out there.. I hope there's a snippet you can take something from.

I'm sure that there's a few teachers looking forward to the holidays and wondering how we can finish off the mini term and get into exams before starting semester 2.  Gathering up the last of my tests for the term has left a load of marking that needs to be completed next week.

It's usually about this time that I reflect on the term and try and figure out how I could do it better next time.    I'm very cynical about NAPLAN and can see on a daily basis the negative side of it.  There is pressure being put on administration to make difficult cohort's perform.  There is pressure on teachers to put curriculum aside to teach topics out of sequence to "optimise" student NAPLAN results.  There is pressure on students to learn techniques to optimise their performance as it is a significant factor during their subject selections in year 10.

I tried to analyse NAPLAN pre-tests this year to get an indication of expected NAPLAN results.  Having done the analysis myself, I have confidence in my analysis but comparing results to past years makes me question the validity of the data or the value in repeating the exercise next year.  After looking at individual student performances in year 12 and their NAPLAN results, I see little correlation between the two - in fact in many cases the results are contrary.  Comparing year 7 results with year 9 would indicate that many students are in fact going backwards during their transition to high school.  Performances in individual outcomes is disturbing, with some areas of the syllabus lacking depth to any level.  Some individual student results were bizarre to say the least, with some very high results in some classes from some students that had no opportunity or ability to learn the work that they managed to get correct.

Given the change in syllabus, this year I had the opportunity to align year 10 and year 9 coursework for a short period.  I noticed not only a maturity factor affecting performance, a cohort ability factor but also a significant NAPLAN factor.  Whereas the yr 10's were given a structured sequence of algebra lessons, the yr 9's were given a fractured course, interspersed with NAPLAN revision.  My feeling is that the 10's understanding is far greater and more likely to be retained than the 9's (both having similar backgrounds in the material presented) after completion of the course of work.  Given this I can only conclude that NAPLAN is disrupting learning in year 9 - potentially for a term and a half (which in any case has always been typically a slow group to settle) preventing them starting serious learning.


I'm sure we are not the only ones spending inordinate amounts of time on NAPLAN especially as the measure of a school's performance rides on the public perception via myschool.edu.au.  It seems a little unfair that the reputation of a high school rides on what can be done in 4 terms during year 8 and one term in year 9.  Sadly all the good in making students work ready, TAFE ready and University ready up to year 12 is disregarded and stupid charts in a stupid website designed by stupid people is used to measure a school instead.  More important is how many indigenous students are present, how much money the school is given for each student and whether the school compares with a dubious set of like schools.

I can say two things with certainty this term.  Firstly, teaching middle school is significantly easier than senior school.  I look forward to attacking it with gusto without the overhead of NAPLAN nonsense.

Secondly, middle schooling has lost its way and needs to refocus around curriculum rather than pastoral care.  The lack of programming and consideration of actual learning (especially in the mid to top students) is frightening.  I don't claim to be a genius at planning but I can show at all times what the intent is of my teaching, have it vetted by a teacher in charge and supported by text and resources.  I can't and don't condone the time wasting that is done with rewards programmes, homogeneous programmes in heterogeneous classrooms, mental mathematics and the general avoidance of teaching, assessment and grading standards.  With the loss of staff that can measure the effectiveness of learning programmes and the movement of responsibility for curriculum to administration incapable of monitoring progress, middle schools are languishing in apathy and poor performance.

I don't think I am alone in this thought.  I love the idea of middle schooling but am yet to see it work in any but very affluent schools.  Maybe, as I was informed early in the year - as a "classically" trained teacher I lack some flexibility in this regard.

I'll try and keep a more open mind.

Outstanding Teacher... Nonsense.

I was in school.  I had an English teacher that was rude, abrupt and many students couldn't stand him.  He changed my life in that he found issues with my essay skills and fixed them.  Every Friday afternoon for two years we wrote essays.  On the day before we finished he said to the class.. whatever you do.. leave the creative question alone in the university entrance exam.  After class he took me aside and said.. do the creative question.

Despite being a Mathematics teacher, it was my English score, followed by my History score that lead me into university.  My Maths and Science scores came next.  I attribute my success to him.

I remember another teacher in primary that let me get away with murder in the classroom because I always finished my work.  I needed to be mobile, so she let me, on condition that the same work was completed that all other students did.  Over time, (and after some work on diet), I settled down and was able to work with others.

Yet, on another occasion I had the lead English teacher, who was adored by my peers that I couldn't get along with at all and I failed her class.

By declaring "outstanding" teachers we fail to recognise that it takes a variety of teachers to raise a child, especially those with different social, emotional, physical or intellectual needs.  Sadly, generally the rule is that an outstanding teacher is one that sings their own praises loud enough or one that creates the time to write spurious documents about what they had achieved.  Not the one that knuckles down and gets the job done (or the experienced teacher that has done the hard yards and makes it look easy).

An outstanding teacher (in a student centred world) is someone that makes a lasting difference to student lives, something that is not often measurable until after students have left school.  I'm not sure what is hoped to be achieved by awards such as here except another media release for Peter Garrett in the future.  Parents certainly don't want to know that a great teacher is in another state and teachers know that the odds of being recognised for doing their job well is highly unlikely especially in difficult environments.  Students would likely dispute it even if it was won.  There really is very little upside for the majority of teachers short of political posturing.

I remember the year a teacher won the award for taking her class on 400 (exaggeration) field trips.  One wonders how direct teaching requirements were met?  Same could be said for excessive IT, collaborative learning and any one of a hundred "innovative" approaches.

If awards are an attempt at raising the profile of teaching, the idea fails as it only rewards a few - creating an elite rather than a college or fraternity.  It really is a daft idea.

Quick and easy game to promote retention

I gathered up some practice for students and was thinking about how I could get them to do some revision.  I hated revision as a student as I had a quick memory and remembered things fairly easily.

It's not true of all students though.  So I found 300 questions on the topic (simplifying and balancing equations) and made up an A5 booklet of 12 pages.  Then I made up some little reward packs and said that the first three students that completed page 1 with 100% accuracy would get a pack. Whatever revision work was left at the end of the period would be done for homework over the next week (to give encouragement for those that for a second considered loafing).

In the past marking of each page has been an issue.  To get over this I combined two of students favourite things - writing on the white board and finding errors in each others work.  Students wrote their name on the board and had to mark the work of the previous name on the board. Five students (randomly chosen from the rest) that had completed a page of work and had marked another students work would also get a reward.

We all had a laugh when the last and hardest question was repeatedly incorrect so that the 3rd place prize was ultimately won at student 15.  The random draw was good incentive to keep going.

All in all students completed about 75 questions each in an hour (writing the question and answer for each sum).  At the end of the lesson we talked about how it was important to develop concentration for the full 60 minutes in preparation for 2 hour exams later in the term and the need to strengthen muscles in the hand to withstand the onslaught of essay writing.

I tried it with both 9's and 10's and had success in both classes with 90% of students engaged and only a couple of students needing to "have words" with at the end of the lesson.  Many students asked if they could complete the remaining questions over the weekend and I supplied answers for them to check as they progressed.

Teaching Linear Equations and Functions

Linear "anything" can send chills down the spines of many adults.  For many students it is an exit point from mathematics.  The inability to grasp the connection between an equation and its graph can mean a student languishes in any but "maths for living" type classes.

Yet there seems to be different reasons why students don't like linear algebra and linear functions.  My top ten suspicions why students don't understand linear topics is listed below.

Mum says its hard
We should not estimate the impact we have as parents.  By placing the kernel that we found it hard, our students will have to face the likelihood that they have the potential to know more than the most respected person in their lives.  It's ok for it to conquer them because it conquered you.  As an adult it really is rather easy to learn!  Before passing on our prejudices, we need to find time to grab a text and figure it out from a worked example.  It will make you feel good and your student will benefit from someone that can help too.  Excel books can be found at booksellers for around $15 and can be a good starting point.

Girls can't do Maths, Boys can't be neat.
BS.  I don't accept this from students and nor should you.  Girls have outperformed boys for many years in mathematics, (esp. up to year 10).  We have to be careful to walk softly when girls start noticing boys and don't want the nerd slur.  Similarly, boys seem to think that sloppy work is acceptable - it's not and they can do better when monitored and prompted.  It also improves their accuracy and notation.

Lack of primary algebra & directed number knowledge
This is not a dig at primary teachers, but it is a dig at the Curriculum Council.  The lack of a syllabus has harmed education in WA and the implementation of OBE failed our students.  In saying that, the CC is trying to make amends with the new courses in senior school and if the do-gooders don't get started again, we may have some reasonable curriculum reform.  The trick will now be to get year 7 out of primary and get students into the hands of specialists in mathematics, whilst upskilling secondary teachers in ways to deal with younger students.

Lack of sufficient practice and connections to context
Many students grasp the major concepts quickly (like finding an equation for two points) but lack scaffolding in their understanding to establish lasting recall.  Those eloquent in eduspeak will know the edubabble for this concept but the idea is sound.   The motivation for this blog entry was a group of year tens currently struggling with remembering how to create a linear equation.  In after school classes we have worked to connect the idea to shooting aliens (with an equation driven gun), distance time graphs, ice cream sales (using tables and difference patterns), intersection points, changing slope, y intercepts and x intercepts over a three week period.  With a solid understanding of linear, extending concepts into quadratics and other functions is considerably simpler.  These simple (but growing in numbers - we're now over 30 students) after school classes are leaving students enthused and ready to work once classes start.

Limited value seen in abstract knowledge
Sadly, many students are unable to see value in abstract algebra in year 10 and this limits their development.  Without rudimentary skills in linear algebra much of the senior courses in mathematics are inaccessible by our students.  A lack of rote learning and a focus on problem solving has reduced the ability of students to value skills based work.

Lack of connection between reward and effort
This is a huge concern not limited to linear algebra. The year 9 C grade standard lists linear algebra requiring fluency by year 9.  If students don't meet this standard - their grade in year 10 will be a D or worse, even if developmentally they are finally able and work hard to understand abstract algebra.  This lack of reward for effort will start to be seen throughout the mathematics course if we (and our regulators) are not careful.

Poor environment to complete assignment work
Many students in low socioeconomic schools do not have home environments conducive to homework.  This is especially prevalent in at risk students.  Schools need to encourage usage of safe areas to complete such work either under punitive (which can be more socially acceptable) or extra curricular environments.

Lack of study
An average student will not gain a lasting understanding linear algebra if they do ten questions and then move to the next topic.  Given that the key concepts need some level of memorisation (how to collect like terms, establishing the equation of a line, the connection between an equation and a plane, creating ordered pairs, plotting them, difference tables etc), students needs to spend some time considering what they know and what they would like to recall freely.

Lack of in class revision
It is a topic that must be revisited over and over again throughout the year until it is as fluent as order of operations or times tables.  It is the next key plank after basic numeracy is established.

A reluctance to start early
We need to ensure that linear algebra is introduced as soon as directed number, fractions and place value beyond thousands is understood.  Those capable of dealing with abstract knowledge need it and we should not delay because heterogeneous classes typically teach to the middle.  We need to challenge ourselves and seek to find when students are capable of starting algebra and find ways to provide opportunities to these students to advance.

There we go.. It's everyone's fault - students, parents, teachers, administration, regulators.  Now let's get out there and fix it!

Developing deeper understanding

Progress maps and outcomes have damaged mathematics in WA. By making distinct learning points without a web of links to outcomes, mathematics in WA has become disjointed and subsequently students lack fluidity between topics.

I doubt this is a new complaint and has been a fault of many attempted curriculum reforms, but it has been exacerbated by a renewed focus on assessment and the lack of credible assessment performed in early years.  In many cases a year 10 student can perform a percentage calculation if (and only if) it is preceded by 10 examples of exactly the same type.  A student can get 80% in their test by teaching study skills for a percentages test and by creating decent notes... but do they have an understanding of proportion and how it applies to percentages?  In many cases they do not.

As a teaching group we have been talking about percentages (as OBE pushed many decimal concepts into high school and they are now being pushed back by national curriculum). It is important to learn how to teach it more proficiently in lower school and to our lower ability upper school students.  One of the more successful ways we have encountered is to use relationships with ratios.

Problem: Find 50% of 50.

Using a ratios approach
100% of an object is 50
50% of an object is x

To get from 100% to 50% we have to divide by two (100% ÷ 50% = 2)

100% ÷ 2 = 50%
thus to stay in proportion
50 ÷ 2 = 25


Using a paper strip it is easy for students to see the proportions in action.

They can readily see that 50% is between 0 and 50.  It's easy to experiment with a wide variety to proportions and it readily extends to percentages greater than 100%, percentage increase, percentage decrease, finding percentages given two amounts and negative percentages.


Using a formulaic approach
Take the percentage, divide by 100 and multiply by the amount.
or
Take the amount, divide by 100 and multiply by the percentage.

I know which of the two approaches is quicker and easier to teach.. but to extend the formulaic approach to other types of problems requires new sets of rules to remember and apply.  Without a basis of understanding it becomes difficult to know which formula to apply and when to apply it (unless it was proceeded by a worked example - which leads us back to the original concern).


Using ratios and an algebraic approach
x ÷ 50 = 50 ÷ 100  (rewrite ratios as an equation)
x = 50 x 0.5  (multiply both sides by 50)
   = 25

Once students understand some basic algebra and proportion, the solution becomes trivial (as it is for many of us).  Sadly many students today do not reach this level of proficiency.  I'm sure there are other more effective and efficient ways to teach proportion and percentages (and even some that don't use pizzas) but I think my point is fairly obvious.




I think sometimes we can get carried away by the need to meet an outcome and teach the how (as is driven by a packed curriculum) rather than using an exploratory approach that provides students with understanding which can have lasting consequences (often unseen by those that don't teach senior school topics).  I originally saw the paper strip approach (or something similar) done by Keith McNaught at Notre Dame university.  It has stuck with me throughout my teaching.  When I am tempted to get curriculum dot points completed and tested (disregarding deeper understanding), it is always a good reminder of what should be done.

As a final note.. I do believe that nothing replaces practice and students need skills based work that requires rote learning (such as what is done with the formulaic approach).  Which means as teachers we have to get better at providing pathways through the why (such as via the ratio method and with formal proofs) into the how (such as with formulaic approaches) and then making connections to other techniques (as seen with the algebraic approach) - always remembering that students shouldn't have to re-invent wheels which in many cases took millenia to form.

Review of material written

Well, one thing was obvious.. the 3A MAS kids aren't quite at the level expected yet.  We barely reached unit vectors which meant that we didn't get to the meat of the topic.  This was a shame as the helicopter example is a great example of how vector topics fit together.   It has indicated next time I need to go a bit further backward and put a few more examples in for unit vectors.  We also need to look at the difference between adding and finding the difference between two vectors.  Possibly also looking at examples of each in action. Easy fixed.  The year 9's and 10's were comfortable with Linear functions and could use difference tables capably according to the tutor, if anything the work was a bit easy!  This is good news and unexpected! 

Unfortunately the 2C finance EPW was as expected and underlines that the group is a bit weak.. the students stopped after they thought they had learned something, which meant that they didn't get to the meat of the assignment (rookie mistake!).  I think in more than a few cases social life and sporting interests come first.   One student had done the work.. the rest were a bit of a shambles.   My feeling is that the EPW is right, we should be able to make an assumption that year 10's have done compound and reducible interest and (with a bit of revision on their own) should be able to answer reducible interest problems with a calculator.  One in the 80's, a couple of high forties and that's about it.  Very disappointing result but hardly surprising given the incomplete take home sections.  Hopefully what they have done will help them understand it properly when the topic arrives.  These are students entering 3A and they can't be spoonfed and expect to do well.

Writing lasting material

It makes me laugh that we invest time in our teachers, but rarely invest time in the resource bank of a school.  This causes a massive information loss each time a staff member leaves the school and requires significant effort to regain capacity back to the previous level.

We are at present putting material together for our after school classes and the lack of extension resources is amazing.  The most common response is that extension classes after school are usually just repackaged classroom material at a higher level.

This can't be right.  If a student seeks extension it's because they want material not found in the classroom - this is one aspect of summer school success we have.  We don't just teach year 11 material to year 10's, we repackage it such that it is context specific, timely and interesting.  One of the joys of an after school class is that you are not confined by syllabus and delivery points and you can delve into topics in a little more detail if students are interested.  Hopefully students that didn't quite get it can now see where the majority of students are.  Students that have a solid understanding can draw connections to other areas of mathematics and other learning areas.

I believe the resources I seek have been written and are sitting in drawers around WA.  I understand why teachers are proprietary about their resources.  Little time is given to developing resources and they have to be done in your own time.  DOTT is taken up with marking, meetings, behavioural resolutions, recouping sanity time and parental contacts.  It leaves little time for planning and developing of resources.  If schools were better able to value what after school programmes could achieve, monitored what they did achieve, set goals to maximise future achievement and provided time to prepare resources to meet these goals then just maybe a few more students in the middle would find success and a few more high achieving students may be able to seek the stars.

Given the changes in curriculum, I'm not writing material to fit state or national curriculum, IB or NCOS.  I'm sticking to topics that can be used across year groups and ability levels.  The first two topics students have asked for are Linear functions (lower school) and Vectors (upper school).  I've designed a written format and a method of delivery and I have some material on Finance that I can bend into this format.  We'll see how it goes tomorrow and Tuesday.

There are opportunities "beyond the classroom" where schools can and do make real differences.  It's a shame that all too often it is because of individuals rather than by initiatives by the school itself.

CAS calculators

The importance of using calculators appropriately cannot be underestimated.  Percentages and compound interest are two of the most misunderstood topics in year 9 and 10 and many student errors could have been prevented with effective use of calculators.  This year my year 9, 10 and 2C classes all did compound interest at about the same time.  All three classes were able to use the CAS calculator to construct the equations required for reducible interest. 

Teaching calculator usage in year 9 should prevent some of the errors in year 10 and 2C because:
a) they will not be struggling with "how to use the calculator" next year (modes, cell referencing & formulas)
b) they will be able to calculate percentages of amounts with or without a calculator
c) they will be able to work with the idea of a period of time and know that this needs to be consistent across an equation
d) they will be able to work with interest periods other than annually
e) they will be able to identify simple and compound interest problems

There are many times calculators are inappropriate but in this context it is an engaging tool and the novelty helps focus students on a fairly dry topic.  It is unfortunate that the 2C class did not have this benefit as they are struggling with remembering what compound interest is and how reducible interest relates to it.  Finding time in the curriculum to promote appropriate usage is well worth the effort as this is one of the occasions where a calculator/spreadsheet is used in a real life context over pen/paper.  A good series of worksheets can be found at classpad.com.au under the intermediate tab.  It does take some patience but students will quickly learn how to create spreadsheets well.  I would also show students how to use the fill range tool (under the edit menu) to make the process a little quicker.  It may be worthwhile to use MSExcel first in a computing lab.

It is obvious that many students have not seen how spreadsheets can be used in computing classes or are not making the cross curricular connections of how that knowledge could apply in mathematics.

A byproduct of the classes is that it was a good assessment checkpoint to see if they understood how to apply percentages of amounts and whether students could see how it fits within a multistage question.  The tens did very well making the transition from spreadsheets to the compound interest formula and I now anticipate that it will be an easy transition to finance mode for more complex worded questions.

Calm before the storm

Crossed the half way point of the term and things finally calmed down for a few hours.  Most of my nine's have now completed their NAPLAN revision and we have a few lessons up our sleeve for the end of term.  They're settling down now that they are starting to realise

a) don't come to lessons unprepared or you will have to sit down the back doing lines and redo the lesson at lunch time.
b) don't do homework or you will stay in until it's done
c) refuse punishment and the number of lunchtimes double - the first with me and subsequent ones with the team leader.

It's old fashioned but the results speak for themselves.  Students that do their work feel good about themselves and students that would otherwise have fallen through the cracks are slowly coming online.  The next lesson is using the CAS calculators - so at least it will be a break from NAPLAN preparation and book work.

Our academic extension class started this week and the first five year 9 and 10 students experienced linear algebra ala aliens. We created bullets using linear equations and shot aliens with them.  Using CAS calculators made this quite fun experimenting with different spots on the hill (the hill was the y axis and we modified c for different points on the hill) and changing the angle of the laser (modifying m). Next lesson we'll use a series of linear equations to reflect bullets off mirrors.  I hope to extend this to matrices later as it is an obvious fit (even if it is only linear equations).  We'll do four lessons of this and then do some isometric and oblique drawing outside to help them visualise objects in 3D before starting some ballistics using quadratics and calculus before revisiting linear equations (with the ice cream example) and optimising some finance solutions.  At the end they were asking whether we could go for two hours instead of one (groan!).

A number of EPW's went out for my 11 and 12's including the Finance EPW I wrote over the last four weeks.  It seems common that 2C students don't know how to use their calculators and teachers are not confident an investigative approach is the best way to learn them.  Three teachers in my small group have all raised concerns about the EPW (seemingly without reading it) but we shall see how it goes.  Given that the answers are provided, online links to assistance has been given and they have a week to investigate, I lack understanding why this is so hard.  We shall see.

My tens are confidently using spreadsheet and finance mode on the CAS to solve a variety of compound interest and repayment problems.  I hope they don't face the same issues as the current year 11's when doing 2C and 3A with regards to using the calculator.

As always 1B's seem to underestimate the difficulty of the course and seemingly need to fail a test before they realise that they need to study.  I'm pretty sure my bunch are not going to top the three groups this time - but I have hope yet that some in class revision will turn them around.

A profession that consumes the individual

One of the things to consider as a teacher is how isolating the career can be. As someone responsible for 100 students and their individual well being, it can be easy to fall into the trap of allowing the job to consume all of your available time to effectively respond to their needs.

The better a teacher you become, the more you realise you can do. The more pressure there is to perform.

Focusing on one class leads to deficits in other classes. These deficits are then questioned and you start to doubt your ability and there starts a downward spiral difficult to arrest on your own.

Then there are personal considerations when faced with students that relate directly to your life story. The child that is facing issues that you faced as a child and believe you can make a difference to their lives. A laptop computer given on loan, buying a student text, giving a few minutes extra tuition, making sure they have enough money for an excursion, advocating for a student - I know teachers regularly do these things. Knowing that it would be difficult to enjoy your weekend and satisfy your conscience if you didn't act when you had the opportunity.

Another trap is allowing a deficit of time to let you lose your support network. Being consumed by teaching can lead to a one dimensional person, having only one interest and thus having limited interest to others. This can make it a lonely profession especially when the majority of conversation you have is with minors.

It doesn't just affect you, it affects those around you. Supporting a teacher is a full time occupation. You come home tired and spent. Events of the day can overwhelm you. It can be a real pressure cooker at times, especially around TEE and reports or when the playground is on fire.

Somebody told me about the monkey analogy and how if someone passed you the monkey - it was important to pass the monkey to another (yes it was an admin person). As a metaphor for problems I think as a teacher, the tribe of monkeys needs a support network capable of dealing with them. Admin sometimes needs to remember this.

Maybe I'm a bit old fashioned. Maybe I have to look at it a bit more like a job and less like an opportunity to make a difference. I wonder if I would be able to do it anymore if I thought about it that way.

It's no wonder many teachers are a little bit more than strange.

A bigger worry is that you fail to notice it after a while :-)

Good Day

After the issues with the 2C test it was nice to have a good day. My 10's were responsive and worked well whilst our Principal was in the room for a whole hour doing his impromptu visits. It's good that he does them, but it can be a bit harrowing. We investigated how to use our CAS calculators to build spreadsheets and will now start looking at the results to investigate compound interest further.

There were lots of things I would do differently with the lesson itself but I can't fault the kids in that they followed instruction, were able to use formulas and solve a compound interest problem using technology by the end of the lesson. After replacing most of the batteries in the morning, only two failed during the lesson which was ok.

I checked my 9's homework and that was a different story. I used some old fashioned "I will do my homework when my teacher asks me to otherwise I will have to write this." x 100 to ensure that students had some encouragement to do their homework in future. Those that did their homework enjoyed it if nothing else.

My 1B's are going ok, they finished the exercise but are not fully understanding cumulative frequency, so we will need to redo that lesson. I must remember tomorrow morning to hunt out a worksheet that will reinforce the connection between cf and median (and xf and mean).

A nice change from Friday.

Russ.

Making mistakes

You know.. it would be nice to not make mistakes. It's even better when your mistakes aren't distributed to multiple schools for scrutiny. I had the wonderful opportunity of writing three assessments for moderation groups all at the same time, two tests (one for 3A MAT and one for 2C MAT) and an EPW (for 2C). Tests did not exist that could be pulled off the shelf and I didn't want to use a Curriculum Council EPW as they have been widely leaked (yes I'm looking at you Curtin University!).

Anyhow, the 2C paper had an error (three circle Venn diagrams aren't part of the curriculum) and it was one of my complex questions along with another question that I changed at a teacher request to set notation. Unfortunately by doing so it also reduced them to non complex questions. The test (although broadly covering key concepts) did not have the required complexity.

Once marked the curve for my class was badly skewed. It's a bit embarrassing as it's the first time I've taught 2C and really wanted to do the right thing by my moderation group. The test had an error in it and I had to re-issue the marking key as well as the original one had mistakes in it too.

Hopefully the 3A paper is ok (it's harder than the 2C paper and I think my students are going to get a little wake up call) and I must say - the amount of work required to write a 2C EPW should not be underestimated. If you're interested in an original 2C Finance EPW based on spreadsheets leave a comment with your DET email address and I'll forward it to you (Your email address is safe, - I moderate all comments before release and I'll delete the comment before it goes online so that the email address is not made public).

I've been flat out trying to get it all done (and interim reports) and bed down my classes. Hopefully now it will settle as all of my NCOS assessments for term one have been done and I can start enjoying myself again working on the lower school courses. Ten year 9/10 students approached me today to run an afterschool extension class again. They're fun but a lot of work when you and the kids are hot and tired.

We'll see how it goes. Bring on the long weekend!

Solving Venn diagrams where the intersection is unknown

n=40

Today in 2C MAT we came across that old chestnut, the Venn diagram with the missing value in the intersection with a number in A, B and the outside region.

In many cases the easiest way is to use a guess and check approach and a lot of the time the answer will fall out by substituting into the intersection and revising your result based on the values
A union B + the outside region = n.

n=40











Another approach is to name the segments and solve a series of equations:

a = 20-b
c = 30-b
a + b + c + 5 = 40

By substitution (20-b) + b + (30 - b) + 5 = 40
Therefore b=15

Once the intersection(b) is known, finding "A only"(a) and "B only"(b) is trivial.

I was asked the question "why teach this technique?" and my response was that it was not formally taught, it was a logical answer for a question given. We have some unknowns, we have some equations, why not solve for them? This sort of problem solving "setting up of equations" technique is common in optimisation and linear programming - why not use it in a probability setting?

I remember a particular student that was renowned for having solutions of this nature where his answers always deviated from the answer key and he had the right answer (or was on the right track) more often than not. We still call intuitive answers like this after "that" student as they forced the marker to find the underlying logic rather than application of a given method (if that student is reading this - get offline and study for your uni courses, scallywag!)


Anyhow, a third and more common approach is to rearrange the property:
A U B = A + B - A intersection B

By rearranging the equation
A intersection B = A + B - AUB

Since we know that:
AUB = U - (the outside region)

to find AUB is fairly simple:
AUB = 40-5
= 35

Therefore:
A intersection B = 20 + 30 - 35
= 15 (as before)

This approach does have the advantage that you can talk about the intersection being counted twice when the union is calculated by adding A + B where A and B aren't mutually exclusive.

I can't really see how this problem could be classed complex given the second method exists. Perhaps, if combined with a wordy explanation, a question of this sort could be made complex but to my mind that would defeat the purpose of the syllabus points in defining complexity. After all, why should something be classed a "complex question" if the only reason was that the question was worded to be understood by students with strong English comprehension?

Further exploring the properties of one

To find an equivalent fraction of a decimals, one way to explain it is to take the decimal part of the original number and place it over the lowest place value. Leave any whole numbers in front. (This only works for non-recurring decimals)

eg 0.123

The lowest place value is thousandths, the decimal part is 123.

therefore:

0.123 = 123/1000


An alternative way to explain it is using properties of one. The idea is that
a) numerators of fractions should be whole numbers and;
b) the fraction should be equivalent to the decimal.

We can ensure the fraction is equivalent if we only multiply or divide by 1 or more importantly a fraction that is equivalent to 1.

To satisfy part a)
To make 0.123 a whole number we have to multiply it by a power of 10 - 1000 (10^3). This was a concept we had investigated earlier.

..but if we multiply by 1000 we will change the original number from 0.123 to 123 - it will no longer be equivalent.

So to satisfy part b)
We multiply by 1000/1000 (or 1!)

Thus:
.0123 = .123/1 x 1000/1000
= 123 / 1000

I like this because it continues to explore how fractions are constructed, the connection between decimals and fractions and why decimal conversion works. I wouldn't try it in classes with low ability due to the possibility for high levels of confusion if understandings of multiplication and commutative properties are not properly understood.

An earlier article exploring one and fractions can be found here.

Viola.

PD Days & Collegiality

One of the bugbears of PD days is the difficulty of engaging 60-70 university trained professionals of widely diverse interests, usually during times of high stress with timelines bearing down on you.

One idea is to use this time for learning area planning. This is usually unsuccessful and the planning time instead used for a wide variety of other tasks (general discussion, marking, personal planning). Why?

Some suggested reasons:
a) No deliverables are defined
b) Time frame for deliverables are unrealistic, ill defined or aspirational
c) Require sharing of resources that are thought of as proprietary (such as programmes developed in own time)
d) Require interaction between staff members that are oppositional
e) Processes are poorly lead and easily high jacked
f) Deliverables are not measured
g) No consequences for not meeting deliverables

Most of these are just indicators of poor school based management but many are problems that have arisen due to systemic ineptness. The lack of collegiality is a growing phenomenon that is occurring as competitiveness between teachers for promotional positions is rising and teaching moves from a vocational profession to an occupation. If schools do not actually manage the transfer of information and the information loss as teachers move between positions and schools, the school loses knowledge and effectiveness (especially cohort or area knowledge) with each transfer. Teachers tend to gain knowledge working in schools such as ours (on their path to effective teaching in low SES schools) rather than the other way around. Those entering these schools can encounter strong resistance to new ideas (especially if it is thought the ideas have been tried before), underestimate implementation issues or be unwilling to share until quid-pro-quo is found.

It should also be recognised that with the rapid changes in syllabus, the ability for a school to develop a working curriculum (that can be further developed over a number of years) has been made significantly harder. The weight of curriculum development has been placed on many occasions in the hands of the incompetent through no fault of their own (teaching out of area, beginning teachers, sole practitioners rather than team members, those lacking analytical skills but are fantastic teachers, administration staff that cannot measure effectiveness of a programme etc)

PD days are one opportunity to stop this information loss but it needs people that can define clearly a task to be done that would serve a real long term purpose and then measure the effectiveness of it. It is just another aspect of change management.

Drawing the first derivative

Teaching students how to visualise the first derivative in 3B MAT has been problematic over the last two years. This morning I had a bit of a breakthrough in that students weren't looking at me as if I was speaking Alien.

The major difference was that I didn't use the arrow approach. Here's what I did.

I drew a positive cubic on the board and identified the turning points. I identified clearly the x axis and the y axis and identified the coordinates for each TP. I drew their attention to (x,y)

Then I drew a second pair coordinate plane directly underneath and identified/labelled the x axis. I then deliberately (as in made a big song and dance) labelled the other axis y' asking students to think what this might mean.

I then went to the first turning point on the x,y plane and asked students what the gradient was at this point. They said zero straight away.

I then went to the second axis and said coordinates on this plane were (x,y'). Given that the TP we were examining was at (0.25) and y'(0.25) = 0, the coordinate(x,y') that we needed was at (0.25,0). We repeated this for the other turning point.

I then drew vertical dotted lines through both coordinate planes. We then looked at the slope to the left of the TP. Being a cubic (with a positive coefficient of x cubed) the slope was +ve. On the second plane I wrote +ve above the x axis to the left of the TP above the x axis. We then examined the second area and noted the slope was negative (making special note of where the point of inflection was - it wasn't mandated by the course but made sense in the context). I labelled the graph -ve underneath the x axis to the right of the TP. I then wrote +ve in the third area above the x axis.

<- It looked like this.

















Once the areas were labelled it was trivial to join the dots starting where y' was positive (y' at +ve infinity), leading to where y' was negative and then changing direction midway between the x intercepts on y', back towards to the x axis until y' was +ve again (again until y' at +ve infinity). It was also a good time to discuss the type of function produced (eg a concave up quadratic) if you differentiate a cubic with a +ve coefficient of the cubed term and how that related to our y' graph.



















We then repeated the process for a quartic.

yay!