Sunday, August 31, 2008

A quick hello!

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

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

Friday, August 29, 2008

Rates and Ratios

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

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

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

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

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

Thursday, August 28, 2008

Education revolution - Bah humbug!

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

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

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

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

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

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

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

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

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

Wednesday, August 27, 2008

Impost of Mathematics NCOS in our schools

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

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

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

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

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

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

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

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

Tuesday, August 26, 2008

Secondary Maths Users Group (SMUG)

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

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

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

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

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

Monday, August 25, 2008

Outcomes based education

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

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

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

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

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

Learning Factors:
D=Developmental level
P=Prior Knowledge
E=Environmental factors

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

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

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

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

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

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

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

Sunday, August 24, 2008

Teaching Jobs in WA

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

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

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

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

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

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

Curriculum development in WA Mathematics

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

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

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

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

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

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

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

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

Updated: 10/12/11

Saturday, August 23, 2008

Solving triangles decision tree

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

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

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

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

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

Friday, August 22, 2008

3D trigonometry

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

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

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

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

Also useful is the discussion on solving triangles here.

Thursday, August 21, 2008

Burnout Week 5 term 3

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

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

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

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

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

At least I hope so.

Saturday, August 16, 2008

Setting difficulty level of classes

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

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

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

And so on..

Friday, August 15, 2008

2009 subject selection

Many graduate teachers and even experienced teachers feel some anxiety when it comes to subject selections. It's one of those times where your judgement can make or break the aspirations of a student.

Ultimately school should be a safe place where students feel comfortable to attempt what they previously thought of as impossible. Too safe subject selections will put students into classes that they will not be challenged in and surrounded by students with weak work ethic / too hard subjects will place students at risk as their self esteem takes a pounding.

Teachers feel this pressure. It is important that any conflict over what students should and shouldn't be doing be overcome before students are counselled into their subjects. The issue over 3A MAS/MAT (old Calculus/G&T stream) subject selection has caused much angst as this is a class in small schools typically with less than 14 students (the DET magic number for whether a class will run in 2009) yet also a draw card for top students entering year 8.

The plus side is that theoretically the new level 3 courses have a reduced difficulty level / the downside is that nobody really knows what the exams will look like and how the CAS calculators will alter treatment of certain topics. With very few true mathematics graduates entering teaching, it has been a concern for some time as to who will teach calculus courses in the mid term.

Cases where counsellors and administrators are counselling 'A' students out of level 3 courses due to misconceptions of course difficulty, available staffing levels, questions over quality of recommendations and issues with grades given to students need to be resolved well before the counselling process. Students being told to pursue higher maths by teachers and then convinced otherwise by counsellors is an avoidable situation that requires clear communication from administration what subjects can run and clear guidance on how to guide students forward.

I think schools need to consider whether the prime role of schools is to guide students into their first job (eg. narrow but job focused education) or into lifetime learning (eg. broad pursuit of highest possible education and widest vocational choice). Where schools assume a split role (eg schools with strong competing VET & TEE courses) close attention needs to be made over who is part of the counselling process and their mandate in giving subject advice and applying/overriding teaching or vocational recommendations.

Wednesday, August 13, 2008

You just don't get it sir!

Yes, the kids do call us 'Sir' still, it's a mark of endearment for some kids - but before anyone gets too excited, there's usually a 'f*ck off' in a nearby sentence.

Occasionally you get a disruptive student that says "I just don't get maths" or "I don't need maths in "... and I think to myself here we go again. Do I have an honest student that has no faith in their ability or a student looking for excuses to maintain poor behaviour?

I have a great test for this but it requires being done in a period before lunch. I suggest that if they don't get it, it's ok, wait behind after class and I'll give them as much time as they need. In fact I insist, it's very important that they master the concept and not fall behind. It's amazing how many students get instant inspiration and get the task done.

Some students think I came down in the last shower and copy another student's work. A quick question usually indicates that I know when they are 'borrowing answers' and then I insist that they remain to get additional assistance to avoid such dependence on others. At this point they can be quite stroppy.

I start them off and they usually take about half of lunch procrastinating over the first question, arguing, complaining and whinging. They eventually realise I'm happy to wait until I see some success and start work..

.. and that's where my real work begins. I ask questions about how relevant they find maths, what do they find hard, I watch their every move and slowly, subtly start helping them with each answer. How can I make learning easier? Where in the class would they be less disturbed? How do they think I feel when teaching becomes impossible due to the number of interruptions? How can I connect maths with their aspirations? Other students come in that I have great rapport with (in senior years) and I give them a hand whilst the student is working. By the end of the period they see (in most cases) that a) they can do maths and b) if they just read their notes they could figure out what to do c) despite being noisy others students get work done and d) most students in my class have had this talk. I then let them in on the real secret - if teachers really didn't care, they would just let students fail and not try to get them to succeed. I suppose it also helps that I grew up in the area, know the type of kids to some degree and was reasonably successful prior to teaching.

If this fails, the next level is discussion with other teachers and the parent call/three way conference with pre-prepared wads of homework and suggestions of reduced TV/sport/PS3 time. Word quickly gets around it's a bad idea to get me 'organised'.

Maths is a confidence game and building the confidence of key students in a class can help make it all work. It's amazing what a class can do when disruptive influences become positive and the right opportunities are allowed to flourish.

Tuesday, August 12, 2008

Avoidant behaviours on the nose

I thought I'd start with a lighthearted post as today this happened in two different classes. I've noticed an increase of stinky kids - I don't mean kids with poor hygiene - I mean the kids (usually boys) that let one rip and fill the room with godawful pong..

There are times when I say don't exaggerate, yes he made a noise, it's a natural function now get on with your work.. but today there was a dark cloud surrounding the little darling. It was capital S, STINKY!

Now, flatulence happens to the best of us I'm sure, but no kid wants to be known as the stinky kid. This is one problem that can be faced and dealt with, although I'm not sure by whom. Do you refer them to the school psychologist, call the parent, have a talk with their health teacher, direct the kid to the loo? I don't know..

From a teacher point of view, you need to hose it down or you get the 'wanna be' funnies making stupid noises at decreasing intervals. In my classes repeat offenders that call attention to themselves get called stinky and soon get the message - especially if it continues past the class by students in the playground. This is a reasonably effective strategy for a popular student but can have long lasting repercussions if it goes too far or with an already unpopular student. Perhaps a quick warning and anecdotal story to the student about how 'another student' was labelled 'stinky' for life might do the trick.

Another common class disruption is the student that hasn't eaten and claims that hunger is preventing them from working. We are lucky that we have good in school process for feeding these sorts of kids albeit they still miss most of class whilst being fed.

I'm not even going to touch on the 'I'm too sick to work/I need a drink/I need to go to the toilet/I need to see the counsellor or nurse' plague.

The armoury of student behaviours to avoid work and teachers strategies to sidestep avoidant behaviours is like walking a tightrope - especially in lower classes. One push and a student/parent complaint, a lack of push and a class of low performing students. It's a tough one experienced teachers navigate naturally. I look forward to the day when I can do the same.

Monday, August 11, 2008

Preparing students for exams

We had a great lecturer (now retired) Kevin Casey at uni. He was of the view that learning was basically a factor of time. Given extra time most students could learn the same concepts.

Confidence in exams is a similar concept. Take one student that had extreme exam anxiety - she would frequently throw up before exams, have shakes and rarely display her progress. Some would say that she is a prime candidate for alternate assessment. I would suggest that in many cases this is exactly what not to do. (In life she has proven that she has great coping skills in highly stressful (eg exam like) situations).

In considering her exam phobia I sat her down and looked into what her core issue was. She was a student that had had repetitively reinforced 'I can't do maths because I'm a girl syndrome,' from both parents and past teachers. She also had an almost photographic memory - anything placed in front of her could be instantly recited back.

So I thought to myself let's fix the confidence issue then fix the maths. I considered learning methods I was familiar with and selected mastery based learning as the key tool. Mastery based learning is a great way to attack confidence issues as students repeat activities to the point of automaticity - the point where they don't have to think. This was important as she was brain freezing in exams, thrashing and stressing to the point of uselessness. Mastery based learning is not the most fun way to learn all the time - but it is a great way of showing to a student that they have ability.

Next we did a lot of boring repetitious stuff until she hated me, maths and statistics. But.. she (for the first time since year 7) not only passed but managed to get 80% on her test... and this was the pattern thereafter in not only maths but in other subjects.

We also went through the main steps when attacking an exam:
  • Don't panic
  • Determine the time per question/mark and monitor regularly
  • Read the whole paper before answering anything
  • Order questions from easiest to hardest - do the easiest first and build confidence
  • Don't get stuck - move on..
  • Don't write comments about how hard it is to the marker or doodle on the page
  • Don't rub out working / show all working
  • Go back over the exam at the end - ensure that each question is attempted
  • Take note of when the teacher/lecturer says 'this is in the exam' - put a star next to it.
  • Prepare your notes 1 week before the exam and add to them throughout the remaining week
  • Don't panic
  • Pick your study buddy carefully
  • If revision sheets or trial/past exam papers are available... do them
  • Complete assignments to the best of your ability - this will lower exam pressure later on.
  • Avoid friendship based group assignments
  • Complete as much as you can in class - keep an eye on what the 'top' students are doing
  • Try and guess the types of questions in the exam - make sure you have attempted the questions at the end of exercises and chapters
  • Ask your teacher or lecturer for direction (they can only say no)
  • Don't panic

Students that do well in mathematics have well practiced skills before they attempt to apply them (in assessment or practical applications) and before they are able to choose between multiple skills to determine an optimal solution.

Practice makes perfect.

Sunday, August 10, 2008

Preparing graduate teachers for TEE exams

In Perth, we have the Tertiary Entrance Exams (TEE). This is a time of stress for new teachers and students alike. If you are a graduate teacher naturally you start to question whether you have done enough to get your students over the line. I covered the yr 12 Discrete course for five students this year (quite a soft entrance to teaching university bound students), but like most teachers we all want our students to succeed and get a good TER(Tertiary Entrance Ranking - score between 1 & 100 derived from scaled TEE exams) for 'front door' university entry.

[I can hear teachers in Perth saying there are no more TEE exams with the new courses of study(NCOS), but there are still external exams at the end of the final school year and it is the paradigm that we are most familiar with.]

Nonetheless graduate teachers can at this time feel the stress of performance as failure may relegate them to lesser classes for some time. It's probably a good time to give graduate teachers a day of real PD or reflection (preferably with access or guidance from a senior staff member) to gather themselves and prepare materials for TEE students for their run home. I hope when graduate teachers put their hand up they will be listened to; and graduates that are 'low profile' are being monitored and looked after.

We've been lucky in that our Discrete group of students have worked hard and agreed to meet before school regularly to complete old TEE questions and have used the great Saddler texts that have been around a long while (that include constant revision miscellaneous exercises). It's also great that the TEE Discrete course is underdone in the amount of required content in comparison to yr 11 preparatory (foundations) course. Oh, as an old course - it's the second last year it will be run and examined for university entry.

Which leads to the problems of the new year 11 2009 where we are running semesterised 1b,1c,2a,2b,2c,2d,3a MAT, 3b MAT, 3a MAS, 3b MAS courses which are 10 new courses of study, no texts available, no written class assessment and limited sample exam material. If I was a first year graduate falling into year 11 (rather than my soft entry yr12 Discrete course with a plethora of materials/experience of teachers/known student pitfalls/existing performance levels) I would be more concerned. Add to that learning how to use and teach with the new CAS calculators effectively.. it adds another layer of difficulty - especially if the calculators themselves are meant to increase the non-computational difficulty of the courses.

Click here to visit the Tertiary Institutions Service Centre (TISC) for more information about tertiary entrance exams in WA.

Friday, August 8, 2008

Favourite Sci-Fi books of all time

Yes I'm a maths geek... I am also interested in science fiction... they go together. Reading is a major factor in student performance and parents modelling that reading is pleasurable and informative is the only path to students getting into the habit. Not just in English but especially in maths with the new curricula being much more wordy and problem solving oriented.

With the demise of newspapers in the home, the humble novel is one of the few physical manifestations of the written word. It is still one of the most rewarding as it enagages the mind, imagination and gives a sense of achievement on completion. One of my most memorable and cherished moments in teaching was in my first practicum when a group of yr 7 students read their first complete book (as a group, one paragraph at a time over weeks).

My reading habits have narrowed over the years and I read Sci-fi nearly exclusively. My favourite books of all time (I have some very worn and well loved copies) are:

The Moon is a Harsh Mistress: Robert Heinlein
Starship Troopers: Robert Heinlein
Enders Game: Orson Scott Card
Foundation: Isaac Asimov
Dorsai!: Gordon Dickson
Hovercar Racer: Matthew Reilly
Neutron Star: Larry Niven
Voyage of the Space Beagle: AE Van Vogt
Dune: Frank Herbert
Neuromancer: William Gibson(Yes I know it's cyberpunk- but close enough)
Snow Crash: Neal Stephenson(ditto)

Out of Genre:
Magician: Raymond E Feist
Bourne Identity: Robert Ludlum (the movie does not compare with the pace of the book)
Animal Farm: George Orwell
Catch 22: Joseph Heller
Harry Potter and the Philosophers Stone: JK Rowling
The Lion the Witch and the Wardrobe: CS Lewis

Watching my father read, gave me the impetus to try, and continue trying to read complex and more complex books over time. I've never shared his love of the books he read - they had special meaning to his generation, but I do still read for pleasure, it is my primary method of relaxation.

We have to thank the internet for the resurgence of students writing to each other for pleasure - blogs, instant messaging, facebook/myspace portals (which all have their issues too).

Is it possible to re-engage not only student love of short form writing but their creative centres to design more complex works? JK Rowling showed that the task is not insurmountable.

Instant gratification is fleeting, a feeling of true achievement only comes through effort. Building resilience into our kids means demonstrating that long term effort is worth it.. well past 5 mins.. well past the end of the lesson.. past the term end and year end.. past school.. and hopefully past their own generation.

Newby teachers, sickness and tolerance levels

The first two years are the worst I'm told. Being in contact with 150 kids or so with variable hygeine habits over the course of a week means that you face a lot of potential sick leave. After those first two years, your immune system (I'm told) kicks into hyperdrive and you stop getting sick.

I hope so. I'm so sick of being sick. Never enough to take a day off.. Just enough to make your nose run, throat sore and generally turn me into a REALLY grumpy person. That's not to say I'm especially pleasurable to be around at the best of times but when sick my tolerance drops to near zero. When in the workforce my staff knew this and would stay clear and (on occassion) appeal to higher authorities to send me home. I would tell them to get stuffed too.

Unfortunately our little darlings can't do that. Other new teachers are much more pragmatic and just stay home if they are sick. I find though that the preparation of relief and clean up in the aftermath is just never worth it.. I'm better sick with kids I understand than dropping a relief in with limited maths knowledge or with limited preparation(<24hrs). I'm a hopeless relief in (insert subject here) and know it. It takes me well into a term to establish a rapport that works with my teaching style - without that rapport it's a case of tell them how mean I am and scowl a lot. Generally that's not near optimal learning.

I'm Mr calm 99.5% of the time, but if a student has been putting effort over a long period of time firing me up.. this is prime time where they might meet the person who explains to them that they've finally given me a little more than I'll accept. Very honest, very public, very abrupt and to the point - typical math teacher style.

The responses vary from 'ok I'll pull my head' in to 'I'll tell my mum'. I don't mind what the response is as long as the message is clear. Yr10/11/12 students have a clear choice - work in school or work towards employment. There are now a heap of options other than come to school and make life difficult for other students and the teacher. Education in school is the right of all students and a few ratbags do not have the right to disrupt the rights of many. Allowing them to do so reduces teaching to low quality child care.

When my tolerance levels are low.. WATCH OUT!

Oh.. and some good/bad news today. 12 of my top 14 students elected to try two stream maths. Sadly, their progress in their exam when reviewed by the head of department indicated that only 8 would make it. That's probably not going to be enough for it to run despite all their work. It does say that the message of 'trying' and believing in yourself is getting through. Well done guys!

Tuesday, August 5, 2008

Board Games in Mathematics

One strategy for investigating decision making, statistics and probability is through games. Common examples are Scrabble tile frequencies, board distribution in Monopoly/Snakes & Ladders, card/dice probabilities, chess, chinese checkers, draughts, dominoes, Uno, Numero.

I have been experimenting (in the "play needs to be taught" theme) with a number of different board and card games with some success. My favourite six games used at end of term are as follows:

Ticket to ride (Europe): 1 hr duration, Networks, probability, mental computation, decision making.
Carcassone: 1 hr duration, Networks, probability, mental computation, decision making.
Dork Tower: 1 hr duration, Probability, decision making, estimation.
Portabello Market: 1 hr duration, mental computation, probability, decision making.
Munchkin: Decision making, reading, mental computation, probability.
Thurn & Taxis: Set construction, probability, decision making, mental computation.
Apples to Apples: Reading for understanding, proportion, decision making.

These sorts of games can be used to assess how able students can follow instructions, work with others, stay on task, cooperate, teach others, analyse probabilities and statistics from scenarios or how to create an instruction set.

Favourite other games from my childhood:
Battletech, BattleLore, Illuminati, Paranoia, Risk, Shogun, Talisman.

Updated here

Support for regular homework in primary school

Here's a study of the blatantly obvious:,,24115399-2702,00.html?from=public_rss

Apparently, if you establish study skills during primary our students are more likely to be academic. If you have a work ethic, you are more likely to succeed. Duh!

I'm sorry about the primary rant.. I'm still fuming from the comments made at the PD session. I promise to go back to supporting my primary brethren and the great work they do tomorrow.

PD day 2 Yawn...

They say you only get what you put in. It's a bit hard when the opportunities for comment are limited to predetermined answers. The issues with planning in today's environment were clearly circumnavigated. It amounted to, plan guys, you're professionals do what you think is right. Oh, and here are five teaching stratagies.

Here were some of my questions and comments by PD staff
1. How many schools engage in values based education planning: few
2. Has middle schooling research been analysed before implementation at new schools: no, currently being investigated by ECU
3. It is important to know what is taught above and below your year group in any subject as kids may be at multiple levels: Duh!
4. There is significant slippage in year seven and nine due to adolescent hormones: True for some, excuse for most.

Here were some answers given by my fellow primary teachers.
1. "It is more important that students enjoy maths than have developed skills that they will retain."
2. "It is ok to teach to level three as lower ability students will switch off if they don't understand."
3. "Oh, is that what is taught in year 8. Why are you complaining - you don't have to do that much!"

..and I suppose it is ok to be able to write sentences with poor spelling, without capitals and full stops too. Numeracy is as important as literacy. Maths should not always be fun - it should have a fun element but there is a need to learn the skills too. Understanding without the ability to retain knowledge is a useless pursuit; you are building a house of straw without retention in mathematics. This is not rocket science people!

Here is some other useful stuff that is not common knowledge (apparently):
1. If a student is meeting outcomes and standards framework 'targets' then they are performing at the level of a reasonable student (eg. a 'B' student). Targets are meant to be the mean teaching point.
2. If a student is just reaching a NAPLAN benchmark, it describes a minimum performance requirement indicating assistance required. The child probably requires an IEP to lift him off the benchmark.

The obvious conclusion here is that many teachers are only teaching to targets and not extending into higher levels. This has always been the concern with developmental strategies - a developmental strategy in a heterogenous class relies on teachers teaching multiple levels nearly all the time and having strategies available to monitor performance and stretch students (a notoriously difficult task) - saying that good kids will pick it up later is clearly not good enough.

Monday, August 4, 2008

PD, direct instruction, collaborative learning

Ok, I'm at my PD for this semester. Two days about hearing the great uses of placemats, four corners, PMI's, Y charts, jigsaws and blahdy, blah, blah. Yes, they're great. But when it comes down to it, a modelled lesson, some great notes followed by practice, practice, practice in a room of engaged students is still a more efficient use of time. Direct instruction and teaching vs facilitated learning and collaboration in a low ability environment - there's no comparison. DI wins each time.

For high ability students the collaborative stuff works, but it is still slower than a modelled lesson or students investigating worked examples. Good students don't become unmotivated whilst learning new content or seeking their next good assessment mark and don't need the Heinz 57 varieties teaching methods. Entertaining students and teaching are not synonymous. I hated some of my best teachers, and learned more from them than necessarily the classes I liked and were more wafty in their outcomes.

For low ability students I am sick of being told students just need to be taught how to do (insert strategy here).. if junior school teachers haven't managed to use these strategies and teach them effectively I don't have a hope at year 10/11/12 level. (I did see multiple strategy coordination done well at one school where teachers had recorded which year groups had been taught which strategies). And whilst we're at it, First Steps numeracy - please get the kids to do some work and not so much nonsense. Show me some real evidence (research with a valid statistical sample) that it works better with high ability students than traditional methods. I don't think it can, and am challenged to find a large number of low ability students responding to it in a high school either.

That's not to say I am disparaging alternate tasks such as investigative work on the white board (such as the graphing question posed in a previous blog entry). This does work, as long as it is strongly teacher directed. Teaching kids to play board games works as long as I am there playing adjudicator. I would love to see some of these 'I've been out of the classroom 5 years' or 'I like being home with my kids 3 days a week' presenters doing this sort of stuff with kids who like to stab calculators or will fly off the handle because a new student enters the class that they don't like.

Stability, a firm hand on behaviour including clear boundaries, an understanding of effective learning styles for each student and low student teacher ratios is a good recipe for low ability student success.

Give me a month, I'll dig out my Spencer Kagan/Developing Minds books again and go have another hack at collaborative strategies. Maybe I'll even be uni student enthusiastic about it again. I'll keep you posted.

Politics and education

Well, today the next round of would be state politicians destroyed a few more trees and wanted to make sure that I would vote for them at the next election by filing my mail box with pamphlets and questionaires. On one side we have the local Liberal candidate who does not know the current education policy of his party (because I dare say they don't have a leader or a policy) and on the other side our Labor candidate(..yes the spelling is correct for those reading from overseas) thinks that the most important local issue I need to consider is whether we need a skate park to alleviate local misdemeaners by our youth.

I wish the pair of them would take a wider viewpoint than this and discuss policy - particularly education policy. At least this election they seem not to be spending the whole time attacking the personality of the other.

My favourite nonsense was the bit at the end of the Labor pamphlet where the Labor party announces they are building WA. Selling WA and privatising it may be more accurate. A key component of building WA is our youth and both parties need to consider the state's role in education and the inequity growing between state and private schools. It would be great to see either party commit to rebuilding public faith and support in the teaching sector by addressing key issues raised by teachers. That would be building WA more than any stadium.

.. and I'd rather they stopped filling my mailbox with garbage and nonsense.

Sunday, August 3, 2008

Learning times tables in 1 semester

For many kids it takes all primary school to learn their tables. It seems a 100% of these students have forgotten them week 1 year 8. Then they hit fractions and have all sorts of trouble.

I recently had the opportunity to teach a young lad (11 years old) at a local catholic primary school, two days a week in class for an hour. He could not recognise numbers, could not perform operations and misbehaved constantly in class as he was unable to contribute to lessons. In two terms we had turned him around and these basic concepts were grasped. His mum thought I was a miracle worker. Nothing of the sort, he just needed some old fashioned one-on-one teaching.. After we fixed up some of his other problems, here's what we did with his tables. It works with any age of student that wants to learn or is given sufficient motivation to try.

a) Create an 12x12 grid, In the top left put an x(multiplication symbol). Number the top 0 to 11 and the left hand side 0-11
b) Start with multiples of 10, 5, 0 , 1, 2. Get students to fill in those columns. Identify patterns in the columns to help them remember (eg. even numbers, end in zero etc.) As time goes by get the student to fill in more columns. Time them and re-inforce the need for legibility.
c) Once they master each multiple set (eg. multiples of 2) create palm cards, one set with the left hand side of the equation (eg. 1 x 2 = ) and another with the answer (eg. 2). Use these to either play bingo or concentration.
d) Get students to copy out the current table being learned 5 times (eg. the 2 times table), rewriting any errors 5 times. Make sure that the commutative property is reinforced all the time (eg. 1x2 =2; 2 x 1=2)
e) Create worksheets that show the connection between addition, multiplication, division and subtraction (eg. 2 x 3 = 6; 2+2+2=6; 6 - 2 - 2 -2 = 0; 6÷3=2). Use colour on the sheets and repeat the sheets regularly without changing them. Create them such that they can be completed in less than 5 mins and have many different sheets prepared. Allow them to choose which to complete. Keep all of them as a measure of progress in a file. Only when they get 95-100% of the sheet correct change them.

I know it all sounds obvious. You will find by the 7,8,9 times tables the student only has to learn a few equations (as most of them were already mastered when doing 1-6 times tables (eg. 1x9..6x9). The key is regular repetition. Be careful though - in the early stages my student was very mentally drained as in each lesson a lot is being memorised. The learning curve can be quite steep. This mental drain turns into how many worksheets can I complete in one session. By th end we had introduced another student and started using competition as a motivator.

I still have all the worksheets I made if anyone needs them (it might save you a little work). Drop me a comment and I'll dig up the server I've uploaded them onto and post it here.

If anyone is having second thoughts about the repeated addition part above - here is a great addendum to the article.

EBA3, heroes and the teacher wage claim

I was wrong. I admit it. I underestimated the resolve of key elements pushing for a significant wage increase and the ability of the union president to annoy her members. The wage claim is not dead and the latest EBA is likely to fail, so says the West Australian. It sounds like arbitration here we come.

If not for Anne Gisbourne (SSTUWA president), I would have thought that the wage claim would have been accepted and we would have had our conditions reduced for minimal additional remuneration. She, through her support for an ill defined pay increase, polarised teachers against the deal and has taken the focus away from Professor Twomey's support of the proposed pay rise. I would suggest her internet monologues selling the agreement have not helped matters - better silent than inflamatory.

A second smaller group of people(7) in the union executive has now split from Anne and openly condemned the new agreement. These people have been labelled heroes as they are standing against their employer and against the union president, will be marked as activists and may have their opportunity for advancement in DET and the union limited. Marko Vojkovic (quoted in previous blogs) stands with these heroes as the one with most to lose. Employed in a DET school he openly is criticising his employer and the union executive. He is standing for a principle. If the current agreement was accepted he (I imagine) knows that the morale and conditions of DET schools will continue to decrease and quality of education continue to erode. He has made a rare stand and is to be applauded.

We now stand at a cross road. Can the government back down from its current position and make a statement that it supports state school education? Can teachers get the message across that teaching in WA is in crisis and that the pay claim is not an inflationary increase but a redress of the inequity in teacher wages to other equivalently trained occupations? Can other unions be convinced that teachers are a special case (police, nurses, public servants, building industry) and not press for similar claims at this time?

How can this wage deal be done, have a public supportive of the agreement and not trigger inflationary pressure?

Watch this space.

Saturday, August 2, 2008

Issues with teaching graphing

Graphing is one of those topics where we underestimate the difficulty some students have interpreting and plotting data.

Try this at home. Plot a graph using height and weight as the axes. Show on the graph that Sue is heavier than Mary. John is the same weight as Sue. John is taller than Sue. Now, is Mary taller than John?

Of course it's a trick question but student answers are interesting and it is always worth investigating whether students are actually thinking when plotting data.

The next one comes with the age old problem of students not able to check answers. A student has ten values between 1 and 10. The calculator reports n=9, a mean of 11 and a standard deviation of 6. The student writes down the answer and moves to the next question.

To overcome these problems we need to model how to detect errors, make them on the board occassionally, reward those that spot the errors (and it's always a good time for a joke and prove that you are human after all) and emphasize how important error detection is. The teacher training adage that teachers are always correct and to hide or 'make intentional' any errors is to my mind poor modelling. My limited experience is that students connect with you as a person when you make 'honest' mistakes and own up to them, they are more willing to take risks and learn to use errors as a path to understanding.

At a content level, students find it difficult to grasp transformations of data within graphs (eg. scores->f->cf), pie charts (and the lack of understanding associated with ratios); relationships of median, quartiles and cummulative frequency in year 11; and mean weighted averages and seasonality in year 12. These areas require clear preparation and care especially when used in conjunction with graphics and CAS calculators.

Setting standards and the responsibility question

It is interesting how we talk and investigate the 'whole student' but rarely the whole cohort. I propose the following exercise done every year. Each teacher for each class is given a file with a plastic sleeve for each class.

By the end of term one, each sleeve must contain an example of an A,B,C,D,E piece of work for every class taught.

The files are submitted to the principal for review and issues discussed that is seen in particular pieces of work. Alternately each assessment, the best and worst are sent to the principal. The principal at their discretion can book appointments with students, parents, teachers, team leaders and heads of department. This was something done on a regular basis in the past and was something tangible that connected students to the principal.

This would create a very direct link between student - teacher - admin and promote dicussion on the level of students and areas, where we are going right and where we are going wrong. These portfolios could be used for yearly teacher assessments.

Getting administration away from managing behavioural issues only and into effectively (and time efficiently) coordinating academic performance needs to be a key objective for state schools to perform at higher levels - especially where clear lines of responsibilty for subject (not class) performance are not evident. This does not mean more committees, we need individuals with experience willing to take responsibility for results, able to make considered and decisive action.