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!

School Fights

Many teachers feel intimidated when a fight occurs in the playground. Fights are things that are skirted around by teaching institutions and rarely spoken of in PD other than in strict legalistic terms.

I'm of reasonably slight build and am considerably smaller than many of the year 11 and 12 students. I'm bigger than many of the female staff also on duty.

So what happens when a fight occurs? How do you, as a teacher, alter an out of control situation when you are physically incapable of stopping students from injuring others and yourself.

The school and how students view the school is a big part of this. I am lucky in that students at our school respect teachers and despite diffusing multiple fights in my career (with male students many times larger than myself and females that had little control over their actions) in all cases my status as a teacher has meant that I have not been at risk. Students seem to know a line that they cannot cross.

Yet I fear this may not always be the case. Students with disabilities are common in school grounds and anecdotal evidence suggest that mainstream students are becoming less able to control their actions.

Practical (not legal) training of staff is necessary before real injury becomes more common. My suggestions are based on practical observation.

1) When on duty stay in line of sight of another teacher on duty. Be prepared to render assistance at short notice. Know the parts of the duty area where you pass from line of sight from one teacher to another.

2) Survey who will take the primary role in diffusing a situation.

3) Issue a command(using full teacher voice) to stop to both parties and (if wise) get between the two students. Hopefully you can skip stage 4 if both students react appropriately. If you are taking the secondary role call for assistance (preferably from a deputy or someone that students are more likely to take seriously.) Seek out the amateur camera people and ensure that they are dealt with.

4) Have the secondary escort at least one of the parties to a safe area (such as the main office, tell the student where to go if you are the only one present and restraining the other student). Do not try to ascertain blame at this point. You may need to restrain the most out of control student for a short time to prevent a running fight towards the office if you, other students or the out of control student themselves are at risk of harm. Speak in a soothing tone to the student being restrained. As soon as the other student is in a safe zone release the student. Be prepared to restrain the student again if he has not regained control and is at risk of causing further bodily harm. Restraint is a last resort and usually indicates that intervention was too late. Holding a wrist is often sufficient. Usually they will seek somewhere quiet although be mindful of students seeking self harm at this point. Damage to property is repairable, staff and student injuries may not be.

5) Diffuse the audience and escort the remaining student to a team leader or deputy.

Students need you as teacher to be in control. Being calm is a key part of this. Don't do anything extra during a crisis time that is unnecessary to the safety of the students. If you are not able to fulfil your responsibilities in stage 4 then consider the legal ramifications of your actions and the risk of injury to other teachers and students.

I am not a lawyer and suggest this article only as a way to promote discussion within your school. I am not a principal - it is your school executive that will dictate what you may or may not do as a teacher on duty. This is an article purely of opinion and you as a teacher need to decide what you are willing to do in the course of being a teacher.

Harry the goat

If anyone missed the Harry the Goat article on the 7.30 report go grab it off the web here.

It's what a 13 year old is capable of.

What a fantastic feel good story that shows the power of imagination.

Catering for gifted students

Catering for gifted students is one of the hardest parts of the job. These kids have been haphazardly accelerated in various topics resulting in them blitzing through some topics and requiring high levels of assistance at other times ahead of students in the normal programme.

It is near on impossible to cater for these students in a true heterogenous classroom as a beginning teacher. There is no possible way that a starting teacher has the skills to run multiple programmes in a room and diagnose issues for these students in a just-in-time manner. An experienced teacher can do it (with difficulty) but a beginning teacher cannot.

An analogy is the best possible way of explaining what I have come across.

Each child in the room has the combined computing power of every computer in the world today combined (there was a great article on this found via /. the other day). I would not expect a just graduated four year programmer to produce a programme that would optimise throughput via every computer in the world.

Yet we regularly ask 1st year out teachers to create optimised programmes (and IEPS)that cater for thirty such brains with 30 times our current worldwide computing capacity. Let's face facts.. the only reason teaching works is that over the last 2000 years we have stumbled across some methods that make the world more understandable for these underdeveloped intelligences.

And here we are again not giving baseline programmes to these graduate teachers. The national curriculum has failed to deliver something easily usable and assessible in the classroom (are we in education forever destined to repeat mistakes - maybe it was the lack of History in classrooms over an extended period??). I was very critical of the lack of production by the maths TDC's but at least at the end they tried to produce something for the classroom that could be modified to suit a learning environment.

As teachers in the system for some time, we need to be constantly aware of new teachers that will need our help and guidance - hopefully willingly, and sometimes reluctantly. Those 2000 years of education have some parts baby that shouldn't be thrown out with the bathwater.

We place our gifted students at risk every time they enter a classroom of where we do not cater to their needs. Without the need to strive, they coast, get lazy or find a private school that will cater to their needs (check to see if your school has a year nine exodus and then ask what is being done about it). We need to be careful that good teachers that need support are given it, students are optimally taught and environments are created that promote the benefits of learning.

I'm currently pointing the finger at middle schools over catering to pastoral needs and the national curriculum intent to remove the ability to provide developmentally appropriate classes in WA senior schools.

Fractions

My emphasis for the last week has been on establishing an idea of "one" with my year 9 academic class. We examined how our idea of one influences how we deal with fractions and algebra.

Firstly we looked at common denominator problems and examined in more detail the method for adding fractions with different denominators.

A common idea is to find common multiples or factors of the denominator and then multiply both the numerator and denominator of the fractions until common denominators are found.

eg. 1/2 + 1/3 -> common denominator of 6 (LCM of 2 and 3)

We then need to find equivalent fractions with denominators of six.

eg 1/2 x 3/3 = 3/6
1/3 x 2/2 = 2/6

Now we have common denominators we can add the fractions..

eg 2/6 + 3/6 = 5/6

But.. why does multiplying by 2/2 and 3/3 work??? Understanding "One" is the answer!!!

1/2 x 1 = 1/2

3/3 = 1

Therefore by substitution 1/2 x 3/3 is just multiplying 1/2 by one. Any number multiplied by one is equal to the original value thus any resulting fraction must be equal to 1/2!

This illustrates two different ideas related to one.. "Multiplying by One" and "Dividing a number by itself".

We also looked at cancelling and why it works..

2m / 3m, we commonly use the skill cancel the m's and 2/3 is what is left.

By re-examining how multiplication works with fractions we find that we can rewrite

2m/3m

as

2/3 x m/m

..but we know that anything divided by itself is 1 (other than zero of course!)

Therefore we can simplify to

2/3 x 1

and we know that anything multiplied by one is equal to the original value.... thus we can see why cancelling works..

Quite a fun little lesson.

Russ.

Moderation - advice for new players.

Moderation is the local equivalent of peer assessment at a teacher level. If your class is small (less than 12), it is assumed that it is too difficult to give fair grades thus you need to find other small schools to check your grades against. If you are having trouble locating a group tell your HoD/TiC then contact the curriculum council.

Moderation sounds like a pain (and it is) but there is one major advantage. Generally, not always, when you do this you share assessment. This means that you may only need to write half (or a third/less depending on the number of schools involved in your group) of the assessment for the course. If your group has teachers that are organised it can create some great discussion and access to course materials that are often hard to find (such as investigations). Sometimes teachers are not organised, are difficult by nature or have a different opinion to you as to the content and difficulty level of assessment. When they are a combination of these you end up with conflict. Especially if assessment is given late and other participants do not have time to check the difficulty level and breadth of assessment. This is reasonably rare and you can always decline letting them into your next small group. It's in nobody's interest to have a slacker in your group. If you are the slacker for a good reason (such as sickness at home or an unrealistic load at school) then make sure you nurture a good relationship with the rest of the group. Don't let the resentment fester.

If you are terrible at investigations (I own up to this one, I rarely get the difficulty level right), then ask for a later investigation in the year and start now, using your mentor teacher as a guide for where to go with the project. Hunt around for one that hasn't been done for a few years at your school. There are some fantastic investigations being dreamed up at the moment as teachers are finally finding that they have more time with courses bedding down.

Last but not least are the technical issues. Sort out whether you are running concurrent or sequential. Ensure that you know what the weightings are for each assessment and where the marks are coming from (take home and/or validation). Check if notes or calculators are allowed in each assessment. Send your marks to all members of your group and check where your students lie - this will change your approach during semester. Agree on grade cutoffs for semester 1 well before the end of term 3.

Have Fun.

Russ.

Bullying

In a school with strong personalities, bullying can be a real problem. Typically physical bullying with the boys and psychological bullying with the girls. Bullying can and does break good students. A success story of our school is the lack of bullying despite public perception.

It is one area of the school where the middle school and the counselling group excels. The kids that come through to the senior school typically aren't bullies; those that try get counselled to death and the source of their bullying painfully exposed. I can't imagine being told "you are a bully and you need to have a look at yourself" is a wonderful experience.

There is always room for improvement. Especially with new kids. Assimilation can be tenuous at time especially in well settled groups. Each teacher needs to be conscious of isolates within a class and subtly discourage them. Each teacher needs to be conscious of niggles that rise during the year. Each year an issue defines a group: race issues, bitchiness, physical agression, complacency, lack of work ethic, teacher conflicts, lower than expected performance. How we deal with those issues makes or breaks a year group.

A nice thing is that regardless smart students at our school are looked up to - there are safe areas in the school for them, for the weird kids, for the popular kids, for the sporty kids. Inside a class anyone can answer a question without fear of a smartness stigma. Amongst all the "over" worldliness of our kids is an innocence that comes with a lack of funds and a questionable future. There are few students that have a future guaranteed by a parent's bank account. Education is one pathway out of the poverty trap. It's a source of pure hope.

It's a real responsibility to find a pathway for this hope through education into the workforce for each of our kids, whether VET or TEE and we all have a part to play.

NAPLAN preparation

There are lots of times you are surprised as a teacher. Today I did some NAPLAN revision of decimal numbers with my year 9 class. It really surprised me how difficult students find the concept of decimal numbers.

Here's something to try with your child.

Draw a number line and place 4.5 at one end and 4.6 at the other.

Place a marker in the middle and ask your child what number would go there.

The answer is 4.55 and many students may get this right, but many would not be 100% sure.

Split the number line again so that it is now in four equal sections. Ask your student to label the new sections.

You may get a wide variety of answers and weird looks.

The answer is 4.5, 4.525, 4.55, 4.575 and 4.6

If your child cannot do this they are not alone. Try again using whole numbers and break it into ten equal sections. Try asking for points between intervals.

Errors like these indicate an issue with both division and place value. It can easily be remedied with some place value exercises (to check if they understand that 4.6 is bigger than 4.59), some estimation exercises (to check if their answers are feasible/reasonable), determining how to find the width of set intervals (using division), learning how to add on intervals and how to find midpoints of intervals.

Fractions and year 10

We're reviewing fractions and my academic 10's sheepishly owned up to not being confident at fractions. The issue was traced back to poor tables (without it students get hopelessly stuck with LCD methods).

PARENTS NOTE: TEACH YOUR CHILDREN TABLES.

I'm shouting because it's seemingly not PC to rote learn anything. It is hard to get this message heard. People are too busy to do the little things. Curriculum is too full to teach tables in lower school (nonsense), parents are working multiple jobs and don't have time (you can't afford to not find the time), students are too lazy (they have always been too lazy, this hasn't changed), students have little discipline. We are setting students up to fail if we don't take minimum effort to assist them learn key content.

Anyhow, the second element of students not knowing fractions is a lack of actual teaching of what fractions are and how they work. After 60 mins of learning time they could add subtract and multiply fractions and there were a lot of happier students in the room. Here's the method I used.

I started by drawing two objects, one in halves, one with two quarters (colouring in the selected parts) and described fractions as a way of describing the proportion of an object selected. Both objects were the same size and were split into equal parts. I wrote 1/2 and 2/4 (vertically) next to the objects and discussed numerators were the parts selected and denominators were the number of equal parts in each object

I then asked students what would happen if I added the two objects. Students responded that I would have a whole of an object. This was good as it indicated that they had some understanding of a fraction. We discussed how we would expect 2/2 and 4/4 for a whole.

I then added the numerators and denominators and students could see that this was wrong (3/6). I drew what 3/6 would look like.

I then split the 1/2 into quarters and relabelled the 1/2 object 2/4. We talked about equivalent fractions and lowest common multiples at some length.

I then added the numerator and denominators again. This time we had 4/6. I drew this. It was still wrong. Students pointed out not to add the denominators. We noted that adding denominators made no sense as the denominator described the number of parts. Good! We now had 4/4.

We then talked about multiplication. They were happy to accept that to multiply fractions, multiply the numerators and multiply the denominators.

Now we discussed the effect of multiplying by one, how 2/2, 3/3, 4/4 was really one; and used this fact and multiplication to construct equivalent fractions. I pointed out that without tables it was difficult to find lowest common multiples or factors (for denominators) and that simplifying large fractions was a poor alternative for knowing multiples and factors. We then looked back at the cross multiplication method that many had been taught and how that aligned with what we were doing.

Students completed 60 questions of increasing difficulty. All completed working and checked their own answers. Note that there was no "fractions" specific method (such as cross multiplication and lowest common denominator) used here. It simply flowed from their own mathematical understandings.

Finally we discussed that order was important with subtraction. Division was left for another lesson. Formal notes were then given. 60 mins. Happy faces. Job done. Tick.

I'm not saying that this would work with students that have no understanding of fractions. I am saying that proper consolidation of teaching done in upper primary and lower secondary is not difficult with average students and this topic.

The trick will be to consolidate this in algebra, indices and trigonometry topics so that key concepts are not lost in future.

Russ.

Attacking a subject

I always tell my students to attack a subject and it worries me when I get a class of passive students - especially in stage three courses.

Students that are attacking a course:

a) come in bright eyed and bushy tailed
b) are on time
c) have all of their resources (books, calculators, pens ...) ready on day 1
d) attend regularly
e) have pre-read the chapters
f) get stuck into their coursework and are not afraid to have a go
g) natter about their current question with other students

Students that wait to be prompted and expect to be spoonfed, wait for you to find that they are stuck and look like deers in headlights make me concerned. Students that seek personal information from the teacher, natter during instruction, dawdle in late, are disrupting the whole class with nonsense annoy me. They make me think "Is this student in the right place?". This is after all senior school, the pointy end of education.

My 9's, 10's and 2C course are going gangbusters. They demand notes on everything. They attempt questions that I haven't asked them to do as well as the ones I have. They are working on revision books. They are playing with their calculators. Good for them.

My 1B's and 3A courses are another story. Where's the ego? Where's the work ethic? Where is the focus? Hopefullly they're more awake next lesson.

Multiplying and dividing by powers of 10

I had my academic year nine class for the first time today and had a lot of fun. I had been warned about a few students, but they were arms deep in the trenches having a good go.

I took an experimental approach today with the class examining how to multiply and divide powers of 10. The idea was to create algorithms in student terms for solving simple equations.

We started with simple examples using whole numbers
5 x 10 = ...

"When multiplying by 10, 100, 1000... count the zeroes and put them on the end of the number you are multiplying."

25 ÷ 10 = ...

This time students considered the position of the decimal point:

"Count the zeroes in the number after the division symbol [divisor] and move the decimal point right of the other number [the dividend] that many digits"

We then looked at the case

2.5 x 10 =

and discovered our first algorithm didn't work as by our first algorithm 2.5 x 10 = 2.50

This lead us to a similar algorithm as for our division case:

"Count the zeroes in the multiplier and move the decimal point left of the other number [the factor] that many digits"

Using the whole number cases gave students an additional method of multiplying powers of ten than the messy loops moving decimal places method. The idea of this lesson was not to deny them mathematical language - but to give them an opportunity to explore a mathematical concept before formal language was introduced. It was a lot of fun for me and engaged them during the lesson.

We then looked at a few cases where the multiplier and divisor were not powers of 10. This exposed that students had difficulty with long division and long multiplication and were over dependent on calculators - which has the possibility of causing issues in non-calculator sections in upper school. We'll now go own to examining factor trees and ease into indices.

We also looked at 250 ÷ 10 where we converted the expression to a fraction and cancelled the zeroes - although we didn't consider why this works and will need to revisit it later.

National Curriculum confusion reigns

National curriculum continues to be a source of confusion for teachers. New words such as engage (have a look at it), implementation (sort of run a class with it) and significant implementation (meaning whatever you want it to but it needs to be done by 2014 in WA and 2013 everywhere else). Never mind that curriculum description dot points are vague even to DoE experts.

If you manage to implement something by getting past inhibitors in your school you then have to decide how to grade what you have done. Proper grade descriptors are non-existent, vague C grade descriptors give little idea what an A or a B is. Administration are scared witless that any implementation will impact negatively on NAPLAN scores, especially where they have been good in the past.

Overcoming the urge to use classroom distributions as solutions for behaviour management problems threatens academic programmes. Small class cohorts gives fewer opportunities to distribute difficult students between classes. Teachers need to closely examine classlists to ensure that troublesome or low ability students are found classes to which they can perform. Finally we have some acceptance that heterogenous classes with wide distributions are not optimal teaching or learning environments.

I read the dreaded innovative solutions mantra for the first time this year in a department missive. Give me a solution or identify an opportunity to solve a problem. The wait and see at the moment is becoming generational.

It seems ok for a whole school to get D's and E's if that's all the students can produce despite their best efforts. Just create an alternate school based criteria to distribute to parents at the same time.

The frustrating thing is that NCOS is working ok and this new system is degenerating into a debacle of epic proportions. Yay for our minister putting on the brakes a little. It will be interesting to see how the final implementation is delayed again if ACARA can't get a handle on this monster.

The only positive out of all of this is a push for more academic classes and more protection and attention for our gifted students. For this at least we can be thankful.

Being proud of those making a difference

I'm the first one to say, teachers have a pretty good wicket to play on. The pay is getting better, the holidays aren't bad and when you have a supportive administration, teaching is a lot of fun. There are a lot of teachers taking advantage of this, it's true.. but there are also many going way past what is required, doing what is necessary.

I'm one of those that is very proud of what my school is and does; and I refuse to be negative about what we achieve. Our kids do not come to high school ready with all the skills they require. They have parents that work 2 jobs, many are abused or neglected, have poor nutrition and health, have few positive role models outside of school, have strong negative peer influences, have access to little help outside of the classroom, have few aspirations, no career guidance, already work long hours to help families make ends meet, have low expectations of their own ability and performance, limited access to resources, few options for subject selection.

Yet every year, up to half of our year twelve cohort goes to university. Not just goes, but are ready and skilled to perform at the highest level. Another group enters TAFE, starts apprenticeships and pre-apprenticeships. Another enters the workforce and starts the gradual climb to owning their own home and financial independence.

There's also the hidden statistics, the kids that are the first in their families to get to year 10 for the first time. The kids that raise their attendance from sporadic to regular. The parents that gain an interest in their children's performance. The kids that succeed despite low expectations (or ability) through the intervention of a teacher or two. The kids that get that positive work ethic and attitude that will carry them through hard times. Those that conquer substance abuse in their homes and turn their backs on criminal activities. Those that succeed despite physical and mental handicaps.

As a teacher, I look at the results of year 12 and take pleasure being a part of an education equation. If my kids get opportunities as a result of finishing school, staff at all levels of the organisation should take pleasure, no one teacher made the difference. We as a school have achieved something.

The Aussie battler is not just a person in the bush, it's kids and organisations that do things despite the odds, with limited resources and where others are trying to take advantage of them (yes I'm looking at you IPS staffing!). Our principal, administration and teaching staff are giving it a good go, and for my mind last year succeeded in many areas. If we keep our eye on the ball and support each other, we'll do it again.. and again...

Cheers to that!

Oh, and DoE take note.. support your low socio-economic schools or you will end up with these kids unsupported in large mid socio-economic schools with teachers that cannot cope nor want them. If you create a permanent underclass be prepared to be named as the cause when it happens.

Board games in high school

I am by no means an expert in this topic but I have been experimenting with it a few years. I've avoided traditional games in this list such as Chess, Connect 4, Chinese checkers, Draughts, Backgammon as these form the basis of school games clubs.

Here is my list of alternative games played successfully with students:

Simple Games:

Collossal Arena (~$35, 30 mins, six players) Students bet against gladiators. Students have to evaluate diminishing odds when placing bets and simultaneously use a variety of special abilities to eliminate rival gladiators.

For Sale (~$40, 10 mins, six players) A game where students purchase property at auction and then sell them to each other. Students need to evaluate what is left to be purchased and then try to estimate the best moment to put them on the market.

Set (~$25, 10 mins, six players) Students need to identify sets based on multiple criteria before other students find them. A simple game that uses many of the skills found in visual IQ tests.

Lupus in Tabula (~$20, 10 mins, up to 16 players) Students try and guess who the werewolf is. Students are accused and try and convince others that they are not the werewolf. A great way to introduce polls and tallies within the class.

Apples to Apples (~$50, 30 mins, up to 10 players) Hard to explain but fun if not taken seriously.

Ticket to Ride Europe (~$70, 1 hr, 5 players) Students build networks of track to connect destinations. Students that build the most effective networks win.

Citadels (~$35, 45 mins, 5 players) Students use roles to build their citadel whilst trying to stop their fellow students from doing the same.

Carcassonne (~$40, 30 mins, 3 players) Students accrue points by laying tiles and selecting optimal point scoring opportunities from multiple options.

Nuclear War (~$50, 30 mins, 5 players) What is better than blowing each other up? Blowing each other up with nuclear weapons.. Beware this game has the worst components ever, be prepared to laminate and find card sleeves.

BattleLine (~$30, 30 mins, 2 players) Two players use poker sets to try and win 5 hands. Special cards change the game in a variety of ways.

Dixit (~$40, 30 mins, 6 players) Players use their imagination to get students to guess which card is theirs.  A great investigation into grey areas as black and white answers do not get points.

Say Anything (~$40, 30 mins, 6 players) Similar to Apples to Apples but easier to understand by students.  Have to enforce a G rating on answers or the game gets out of control.

More complex games (require multiple sessions):

Space Hulk (~$200, >2 hrs, 2 players) I wouldn't suggest buying this for a class, but if you have a copy the students enjoy it. The miniatures take hours to paint but the end product is well worth it.

Claustrophobia (~$70, 1 hr, 2 players) The game to play when you can't play Space Hulk.

Battle Lore ($100, >2 hrs, 2 players) A skirmish game where students line up two forces and try and defeat each other. Students have to concentrate to get their forces into battle critical moments.

Smallworld (~70, 1 hr, 4 players) Students use a variety of races to control the largest area of a map.

Indonesia ($100, 2hrs+, 4 players) A game where students use stock techniques to manage shipping, mergers and acquisitions of wheat, rice, oil and spice companies.

These games can all be researched further on Boardgamegeek. Many can be purchased locally at Tactics in Perth, or online (cheaper but with shipping delays) at Milsims, from unhalfbricking, or from PinnacleGames.

Russ.

(Updated 24/4/2011)

Promotion to incompetence

Promotion is one of the hardest parts of management and shows where a lack of career counselling can affect a whole organisation. Teaching is no different to many professions where perfectly good(and in some instances great) employees ask for promotion into roles that they are clearly unsuitable for.

Administration roles in teaching carry pay scales above teachers and therefore attract teachers into the role. These roles tend to accumulate all the detritus that teachers don't want (or can't) do. When these roles attract a capable person, the whole school runs more smoothly. This is not an exaggeration, it is a statement of fact. The sad story though is that these roles are typically the ones on paths to promotion so also fail to be stable.

I have no problem with promotional pathways per se (and good staff should be promoted), but I have a problem when people are put into them that are unsuitable. Conflicts seem inevitable, skill sets are sorely lacking and a lack of understanding of what the role entails occurs due to poor internal job descriptions. People bring their own slant to the role upsetting a whole system that works. A clear lack of understanding of how change management occurs (and when these positions are temporary and will revert to the incumbent) and it becomes just another load placed on teachers.

My favourite fails from promoted staff are: managing teachers as students, the I'm right despite all evidence to the contrary statement, aggressive behaviour (oh my goodness, for this there is no excuse from a manager), the I'll disregard your experience because I know this is a better decision(without evidence) and the inevitable push back of work to the classroom.

With state schools paring down due to reduced numbers, the pool of capable people is clearly reducing placing further stress on capable administrators. I'm sure we'll hear the "innovative solutions" mantra reappear, which will translate to mean"do more with less". Saying that, it's also a time of opportunity "if" situations can be identified that will not impact on teaching roles too greatly.

It's at times like these that I think the old HoD role had advantages. Discipline, year leader and curriculum was shared amongst HoDs; administrative roles (below deputy) were clerical and did not call forth large salaries because they were not highly skilled. Staff that could not handle discipline and curriculum could not do HoD roles, those that could were respected within the school as they were sorely needed parts of a working wheel. The capable staff then went on to Deputy and Principal roles (garnering management skills slowly on the way), were less subject to fads (had a healthy dose of scepticism "built in" that required proof of concept before implementation), demanded an understanding of progress in each classroom and enjoyed coming back to the classroom to fill in from time to time.

Staff that have worked effectively in HoD roles are effective educators (whether in English, Phys Ed (no matter how we tease them), in the shed or in Math). I would much rather see these paths further developed than the flat management (treating teaching as a profession without professional pay scales) strategy currently used in many mid/small public schools encouraging staff away from the classroom.

Russ.

Summer School Day 4

Due to unforeseen circumstances I find myself at home instead of at summer school since day 1. Although frustrating, it has given me time to ponder why I consider it an important part of each year.

These I think are the main reasons:
1. It gives me an excuse to investigate areas of the curriculum in detail and develop my understanding of a topic
2. It provides time to interact with other mathematics teachers and gain insight into their motivation, teaching methods and knowledge
3. It's a great time to spend with the kids outside the pressure cooker that is TEE (and I know we're supposed to call it WACE now, but the pressure of L3 WACE is far different to level 1 & 2) and gain that rapport that helps when you have to give them a nudge to get over the finish line.
4. It's a time where you can develop method/pedagogy and style and measure results in an environment where you are not going to leave yourself weeks behind if it doesn't work.
5. You can work on the motivational, career oriented, aspirational and inspirational components of students rather than just focus on curriculum.

Russ.

Summer school day 1

Today was the first day of summer school and what a great bunch. We worked on some areas that have caused difficulties in past years...

1. Fractional indicies and how to simplify where the numerator of the index is greater than one or where the index is negative.
2. Graphing a variety of different functions
3. Domain and range of a variety of functions
4. Odd and even functions
5. Piecewise functions and domain/range
6. Counting techniques and associated proofs

From an IT point of view it's great to use tools (such as slideshows) and make them highly interactive through joint presentations with other presenters. The students seem to enjoy the change in venue too! Students were actively challenging each other to speak up when they didn't understand and demanding more information when an explanation was incomplete.

A productive day!

Summer School 2010/2011

Summer school is about to start again when we get our year 10->11 and year 11->12 students ready for level 3 subjects. It was interesting to hear the students volunteering this year and plaguing us to run it so lets hope they turn up.

A whole week of students and just maths. Who would have guessed it would have been successful?

I wish I could find our slides from last year!

IOTY 2010 Winner

And the Idiot of the Year 2010 goes to our perennial winner

... (drum roll please) ...



.... Julia Gillard .....




...for her ongoing support of the myschool website, the diabolical national curriculum rollout, computers in schools schemes and her support for the complete an utter waste of money during the GFC on school rebuilding.

Oh, and please do us a favour Julia, get out of the way and let Ms Bligh do her job... although they might need you around soon with your unending bag of cash.

Congratulations Julia!

Funny Quote.

"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." Albert Einstein

Visitors Poll

Who are you?!! I'm interested. The first person that says West Australians are actually Australian obviously doesn't live here :-)

Russ.

Site statistics

7800 page hits and 5500 unique visitors this year from around the world: Turkey to Bolivia, Canada to Indonesia, UK and Spain; hello to you all.

The most popular topics searched were the CAS calculator pages, Hattie's meta analysis, as well as local topics national curriculum and NAPLAN.

National Curriculum in High School

The implementation of national curriculum in WA is fast becoming a farce. It lacks coherent leadership and information is not reaching teachers in a timely manner.

I'm not sure who we are supposed to be listening to or what the correct pathway is for our kids.

Some of the emerging issues.

• WA & Queensland have year 7 in primary making it difficult to implement subject specialisation (such as requirements for science labs in science and adequately trained mathematics teachers for geometry and algebra courses)
• The deadline for substantial implementation is two phased with all states other than WA set for 2013 and WA for 2014.
• A definition for substantial implementation is required. It is not clear whether substantial implementation means k-10 will be implemented by the deadline (eg, for high school: staged over four years - yr 7 2011, year 7,8 2012, yr 7,8,9 2013 and 7,8,9,10 2014) or that schools will have programmes ready to start implementation by the deadline set (do we just sit in secondary schools and hope that primary feeders have it all sorted out so that we can start in 2014??).
  
• Detailed curriculum documents and sample assessments have not been released, with state agreement for the curriculum dot points only happening last week.
• Agreement on how to handle deficiencies across primary and secondary school boundaries have not been finalised. As found in the WA implementation of OBE this is indeed a real issue with grading standards vastly different across each segment (remember level 3 mathematics anyone??)
• Urgency within the secondary segment has not occurred and a watch, wait and see mentality exists - and rightly so given the amount of change thus far.
• Preparation for NAPLAN (being a key metric for school performance) is causing issues disrupting year 9 curriculum with half to all of term 1 being dedicated to NAPLAN preparation.
• NAPLAN itself becomes an issue for WA as NAPLAN will be attached to National curriculum objectives and as WA will lag in national curriculum implementation we would expect WA to lag in NAPLAN results also (for a considerable time as other states will continue to improve in their understanding of national curriculum objectives whilst WA grapples with implementation and the required modifications in primary and lower secondary).
• With declining NAPLAN scores, this has the potential to further exacerbate the decline of student enrollment in state schools as parents view poor results as further reason to enter private schools where students are already on national curriculum, having access to specialist teachers and materials in year 7.
• It is unknown how to grade students. C Grade standards have the potential to relegate low SES schools to D & E's for all students and provide ongoing failure for our students. This is not fair nor equitable. It is also unknown what an A student looks like. Direction here is required and it is a real pitfall for early adopters.
  
• Independent public schools are also affecting staffing equations in low SES areas as teachers are being poached to IPS schools and EIP's are being parachuted into these positions. This movement of experience restricts schools ability to respond to national curriculum objectives.
• As public schools shrink in size their ability to manage content, subject and student knowledge becomes much more difficult with the loss of redundancy (more than one teacher able to teach a topic) and subject selection (fewer subjects are offered or schools are forced to distance education or busing solutions). The size of a school places the burden of implementation on a relative few (as it did during NCOS implementation) at a time where schools are feeling staffing stress both in administration and teaching roles.

It is not a good equation. At least with the OBE farce behind us, we should be better equipped to handle this one.

Click here for previous posts on national curriculum.

Increase in WACOT fees

WACOT fees have been increased by $6 to pay for increased costs of disciplinary actions and registration costs of teachers to $76 per year. This means that 3.5 million dollars is required to run WACOT or ~46 FTE at $76000 per year. Net gain to those paying the fee - really... nil.

According to Brian Lindberg (chairman of the board at WACOT) in a recent email to all teachers:

"The increase in the Annual Fee should be seen in the context of the development of the College. Bi-partisan political support was given to a discussion paper on teacher registration in 1999. "

Can you believe it is 2010 and they are still needing to justify their existence?

"Based on the 348 submissions, a Position Paper was published in 2000. It indicated that there was wide support for a non-industrial body for teachers providing that its activities would be wider than just the regulation of the teaching profession."

Not within the teaching fraternity - and given the lack of teacher involvement during formative years and questionable independence of the body it is no wonder.

"In responding to the Discussion Paper teachers indicated a preference for a body that was independent of employers and the Minister of the day, and that had a majority of elected teachers on the Board of Management."

Another reminder about how long our ineffective body delayed this happening and that our body is not independent!!

"The Board kept faith with all the recommendations and desires of teachers despite having concerns that it would be difficult to carry out all ten functions of the College without Government financial support or much higher annual fees. "

Grin - yes, we wanted value for money because we could see that this was just a way to make us pay for something we already had. Sheeting the blame back to teachers because we were right is hardly fair although predictable. I imagine only one of the 10 functions serves a purpose and that is to keep questionable members out of the profession. That is a regulatory action and should come out of tax dollars (as it is primarily an action in the interest of the public) not through a reduction in pay. Why should employees pay to police the misdeeds of a few?

"Accordingly, the Board will concentrate the functions of the College on registration and discipline only until all 46,000 re-registrations are completed." Why does it cost $76 per year for a police check to be done and a register to be maintained of teachers that have had disciplinary action?

I'm a little confused how reducing the role of WACOT to registrations and discipline will cause a $6 increase and wonder what the cast of thousands in Ascot that were doing the other 8 functions are now doing. Given that much is done electronically and most registrations should require nothing to be done by WACOT - only inefficiency can be to blame.

Most annoying things that WACOT have or have not done (regardless of who is to blame):

• Waste money on glossy brochures (now stopped)
• Re-registration requiring full 100 pt check again
  
• Pointless accredititation process lacking any credibility
  
• Organise discounts for things I don't need
• Lack of real independance or voice on teaching matters
  
• Involvement with conferences for beginning teachers (leave this to private enterprise until truly independent to prevent political interference)

Most useful thing done by WACOT

• Prevention of accreditation of short teaching courses in WA
  

If a review was done, I would love to know how many people are needed at WACOT throughout the whole year (rather than just between October and February when most registrations are required to be done).

My guess is that not many are required to produce not much.

Making errors!!

Sometimes long time errors can sneak up on you and beat you over the head. I have avoided the term bar graph for a few years and was under the misconception that the width of the bar has as much meaning as the height. I always use the term column graph for discrete data drawn in bars.

I have no idea where this misconception comes from, but I will have a look through texts I have used over the last few years - I must have misread one of them (I did find a strange Histogram in one of my stat books when width of the columns was important to do with graphing different sized class boundaries). This all would have been fine if I had figured it out myself.

That would have been too easy.. Of course I was asked the question by my HoD whilst he was teaching his class and using my room (as it was air conditioned and empty) and I corrected him calling it a column graph (cringe). I should have known he was right - as he is rarely wrong.. I had to come back and eat some humble pie..

That's life I suppose.. I'm glad it doesn't happen too often!

Greenfoot

Greenfoot is another attempt to bring programming to students. It has a textbook that can be purchased and an established user group. It is well worth a look if starting a computer programming class and you wish to use Java.

Here is a link: http://www.greenfoot.org/.

Have a look

Russ.

Hattie's Meta-analysis

Hattie's meta analysis is something as teachers we will hear a lot about. It is a study that brings together a wealth of research in one place. We won't hold it against him that he did it in New Zealand.

My reading of his findings is that he finally cuts through the nonsense and gets to the core of what makes a difference beyond what is normally done in the classroom and also what is detrimental to a normal classroom.

It is an astounding in that it confirms what many crusty teachers have called the "bloody obvious" and stripped away the rhetoric. His commentary on his statistics is well thought out and constructive. I feel a bit for these teachers that have felt the brunt of the new wave of teaching (that fell flat well before the shore). They were right and all you new wavers were wrong. :-)

Well.. it's not quite like that, but here are some of his findings.

d= -0.1 - 0.16 (what a student would learn if not in a classroom)
d= 0.16 - .4 (benchmark of a normal classroom)
d= .4 + (desired improvement beyond a normal classroom)

Improvements can be made by:

• Having a cohesive classroom (0.53) p.103
• Maintaining a positive climate (0.52) p.102
• Strong teacher-student relationships (0.72) p.118
• Teacher clarity (0.75) p.126
• Clear goals (0.56) p.164
• Concept mapping (0.57) p.168
• Mastery Learning (0.58) p.170
• Effective Feedback (0.73) p.173
• Worked examples (0.57) p.172
• Formative evaluation of teaching programs (0.9) p.181
• Questioning (0.46) p.182
• Spaced practice (0.71) p.186
• Peer tutoring (0.55) p.186
• Effective study skills (0.59) p.189
• Meta cognitive strategies (0.69) p.189
• Self verbalisation and questioning (0.64) p.193
• Direct instruction (0.74) p.204
• Problem Solving teaching (0.61) p.210
• Interactive video (0.52) p.228 (such as mathsonline)

Things that don't work:

• Student control over learning (0.04) p.193
• Individualised instruction (0.23) p.198
• Inquiry based teaching (0.31) p.209
• Problem based learning (0.15) p.211
• Cooperative learning (0.41) p.212
• Team teaching (0.19) p.219
• Computer assisted learning (0.37) p.220
• Web based learning (0.18) p.227
• Audio Visual (0.22) p. 229 such as slides, video presentations
• Distance education (0.09) p.232
• Home schooling (0.16) p.234

One reservation that I have is that it is hard to evaluate where the quick wins could be for a school. A number of small gains (such as the 0.45's) may require less change than a large gain. Some of the strategies that are not achievement driven may provide motivation to complete higher gains in other areas. I don't think it was ever Hattie's intent to make it a recipe book for success, but can give clear indicators to where effort needs to be made.

The book is well worth a read:

Visible Learning : A synthesis of over 800 meta-analyses relating to achievement. John Hattie. Routledge 2009.

New fun games

Well, it's been a busy year and playing games has not been high on the agenda.. but for a change I thought I'd write about the couple of games that have been fun in the classroom and others that have been fun at home.

The three big success stories of this year have been Lupus in Tabula, For Sale and SET. All three are relatively inexpensive (<$40) and can be played with groups.

Lupus in Tabula is a game that can be played with a whole class, basically heads down thumbs up with Werewolves. Some students are the werewolves, others are the villages and we all have a bit of fun lynching the wrong people. I get to stand at the front of the class and describe in graphic detail how students are ripped apart in the night. From my top to bottom class, all have enjoyed the theme and it has allowed me to discuss problem solving strategies such as limiting choices and probability to resolving social issues such as how to play fairly and that being involved can be fun. It's probably the new favourite over Apples to Apples for a whole class.

The next one is For Sale, an auction game where students buy houses and then sell them, the person that sells their houses for the most money wins. We have great laughs about who will end up living in a cardboard box (one of the houses for sale) and who will end up in the space station. This one requires a little mental maths, ordering of integers, a little recall and a fair amount of fun.

SET was the big surprise. A bit of a brain burner, students have to pattern match cards to find groups of patterns. It plays a bit like an IQ test and after you get the hang of it, can drive you batty. It's interesting that the 'smartest' kids are not always the fastest, it's an occassion where 'visual learners' (how I hate that term) can show their mettle.

Honorable mentions should be given to Leaping Lemmings, Battle Line, Ticket to Ride - Europe and Cave Troll that had some table time, but weren't all that successful.

At home, the big winners are Campaign Manager 2008, Arkham Horror, Runewars, Space Hulk and Twilight Struggle. I'd still love to get Die Macher & Brittania to the table, but I'm not holding my breath until TEE exams are over. We still have to complete proofs and stats/probability, so I'll have to have a sit down and figure the rest of the course out.

Until next time...


Russ.

Ability and performance of students in year 10

Today I focused on the performance and ability of year 10 students. I really wanted to know what caused the lack of performance in students coming through from the middle school.

Issue 1: Middle School and Middle Schooling.

Funnily enough these are two different terms. Middle school is the structure - the buildings, the leadership model, the way students move between classes and the like. Middle schooling is the teaching pedagogy and curriculum. Neither came out unscathed.

Research was not positive about progress in middle schooling.

“middle schools are in serious decline in the US and UK... What is actually done within classrooms and schools is the most important thing, not structures... The most important factors for high-quality education are quality teaching and learning provision; teaching standards; and ongoing teacher professional learning focused on evidence based teaching practices that are demonstrably effective in maximising students’ engagement, learning outcomes and achievement progress.” (Dinham & Rowe, 2009)"

“the report called for a “second generation” of Middle Schooling philosophy with a focus on relationships, relevance, pedagogy and rigour, which is informed by students’ experiences and enabled through sound educational research.” (OBrien, 2009) [Referring to the Beyond the middle report]


" In a region with very low student retention, the middle years when curriculum becomes compartmentalised and fraught with judgmental selectivity was a crucial locus for confronting serious consequences, in student lack of engagement, for later achievement and retention" (Hattan et al, 2009).

“Middle Schooling movement that has been variously described as “arrested”, “unfinished” and “exhausted”." (Prosser, 2008)

"There needs to be a more systematic emphasis on intellectual demand and student engagement in mainstream pedagogy that moves beyond and capitalises on current foci on increased participation rates and basic skills development for target group students." (Luke et al, 2003)

A great article to read is Beyond the Middle Years (Luke et al, 2003) by DEEWR and then follow it up with Dinham and Rowe (2009) article available from ACER. If students don't have a workable learning environment then learning is highly unlikely.

Issue 2: Home environment

Home environment is a key aspect of demonstrable learning ability. Although the gloss has come off this idea since the Campbell report (1960) in the US which prompted black students to be bussed away from their homes into "better" environments, it is still a factor in understanding student ability and performance.

"Students performance in low SES schools significantly lower than high SES schools. Internal school-based determinants of success do not operate independently of external, context-based determinants" (Angus, 2009)

“Cost of school represents a disproportionate amount of household income in term 1 for sole parent families” (Bond & Horne, 2009)

" In the 2007 Education Costs Survey, most parents reported having difficulty paying aspects of their children’s education during the last year, particularly for sport/recreational expenses (69%), for camps (62%) and for books (60%). Almost half struggled to pay for equipment (48%) and excursions (47%)" (Bond & Horn, 2008).

“If education is going to be the means to personal fulfilment and opportunity, we need to ensure that all these young people and their families are given the support they need to succeed. If not, then the education process will reinforce disadvantage, not overcome it, to the detriment of us all.”(Dinham, 2008)

"Schooling reproduces the structure of inequality itself" (DEEWR, 2009) inferring that prejudices and low expectations are placed on working class children by the system and re-inforced by parents

Lower expectations by parents impact on adolescent performance (Crosnow, Mistry & Elder, 2007)

High level of aspiration, low chance of success (p.162) – ESL students with non-english speaking parents (Windle, 2009)


Issue 3: Ability is often not recognised

Students are unaware of their underperformance

“Honesty in recognising and reporting student ability levels (p.163) Students reported that their skill in English was much higher than assessment indicated” (Windle, 2008)

“Ability may not be recognised due to teachers failing to recognise high ability students manifesting typical low socio-economic behaviours.” (Petersen, 2001)

“Further, social and individual factors were found to affect students' attitudes and academic choices; in particular their identification with peers, school and family and student's perceptions of peer, school and family attitudes towards HE. An interesting finding arising from stage one data was that there were significant age related differences in students' attitudes toward school and learning. Students in year 10 were significantly more negative on nearly every measure than students in Year 9 or 12.” (Maras, 2007)

Issue 4: Underperformance of teachers

Poor application of new ideas has resulted in lower than expected performance for a generation of students.

"Research conducted over the last 40 years has failed to show that individual attributes can be used to guide effective teaching practice. That ‘learning styles’ theory appeals to the underlying culture’s model of the person ensures the theory’s continued survival, despite the evidence against its utility. Rather than being a harmless fad, learning styles theory perpetuates the very stereotyping and harmful teaching practices it is said to combat." (from abstract only) (Scott, 2010)

"Practice, grouping of concepts and direct instruction/frequent modelling are key element in addressing learning difficulties. Independent learning and discovery based learning is inappropriate in a learning difficulty environment." (Bellert, 2008)

“Many primary teachers feel under-equipped to teach mathematics and science. In a 2007 study of 160 Australian primary school teachers, they devoted only three per cent of their time to the teaching of science and 18 per cent of their time to teaching mathematics. There is concern that if students receive an insufficient grounding in mathematics and science in primary school, this will cause difficulties in secondary school.” (quote taken from http://www.acer.edu.au/enews/2008/03/study-of-mathematics-declines) (Chinnappan, Dinham, Herrington, & Scott, 2008).

“Curriculum alignment must occur to clearly connect outcomes to assessment.” (Hedemann & Ludwig, 2008)

“Curriculum Mapping is required to ensure minimum standards are met. Every student must have multiple opportunities to attain minimum standards. Choice of actions is required to improve performance.” (Falls, 2009)

And that was today's research!!

Thinking about information thus far

Ok research thus far,

So for students to succeed in low socioeconomic schools we require the following:

a) Parents to encourage students towards realistic academic goals
b) For students to be educated into valuing academic success and aspire towards it
c) For teachers to set high expectations and go well beyond the average expectations of a normal teacher
d) For schools to find, support and appreciate teachers that can satisfy c)
e) For government to accept that low socio-economic schools (no matter what is done) will not succeed at the level of mid to high socioeconomic schools for a myriad of reasons.
f) For tertiary institutions to get involved at an earlier stage than year 11/12
g) For corporate entities and employers to realise that there are many capable late developing students from low-socioeconomic schools able to participate in the workforce (that under different circumstances could have achieved in a tertiary environment)

That's that.. done.. tick!

Unrealistic expectations

Some students have unrealistic expectations. In the same way that some parents lower the expectations of their students, it does also go the other way.

One sector of the school population where this is common is with students of non-english speaking backgrounds. Students can be put under extreme pressure to perform, often after going through very limited schooling. It's not just a Perth thing, it was also observed in Windle's study (2009) where students reported higher understandings of English than their assessment recognised, the students had high levels of aspiration to attend university but a very low chance of success.

In the refugee population, this is a common problem, with many having had limited schooling prior to gaining residency or refugee status. It leads to exacerbate the demands on teachers in low-socioeconomic schools (as observed by Campbell Cook and Dornen, 1995), with teachers recognising ability, but requiring inordinate amounts of work to see these students through. In talking to a care worker outside the system, they raised that other issues are also common such as sleeplessness (due to hyper awareness), distrust of authority and reluctance (or over demand) when seeking assistance.

When you consider that many of these students are not eligible for additional funding, yet require lower primary assistance within a high school environment, it is easy to see why their performance can fall below school norms. Yet these same students are averaged into "my school" results. From a school perspective these students are a real problem.

For these students to be seen as a problem is a social justice issue that needs resolving. It is a real problem when moving from a searching for excellence paradigm to a market driven approach. In a pure market driven approach, these students would be excluded from mainstream education (to preserve school results and ensure that the calibre of students at a school is maintained) and placed in segregated specialist programmes. Yet from an ESL perspective (as discussed with ESL teachers) this is detrimental to their progress as their immersion to common language is a requirement for their improvement.

As a teacher it is a frustrating problem as you need to help at-risk students, but know to do so will draw attention away from kids that have higher probabilities of success. The 'greatest good' model vs the 'rights of an individual' is in firm conflict. Couple this to the higher risk that their 'other' issues may undermine your teaching programme for these at-risk students and the opportunities for success further decrease. Reverse racism (predjudice of non-minority but equally disadvantaged groups)is common, as are claims of racism if direct assistance is withdrawn. It can be a real catch-22 situation.

Literature Review

Research is one of my favourite pastimes, sitting in a library with purpose is quite a fun thing. Yesterday I sat and read about some of the issues faced by disadvantaged students. As I work on my literature review for my masters I'll keep updating this post.

1. It's not a new problem.

The Coleman Report in 1966 was a seminal report in investigating disadvantaged youth in schools (commonly referenced). I need to read it!

To address the issue in Texas, standardised testing was introduced and showed a high degree of success, but at the expense of a narrowing curriculum (Smith, 2005). This was again seen in the UK (Cox, 1999).

The Australian Government recognises disadvantaged student performance as a problem and have produced a paper outlining some effective measures that can be taken. I need to find references, I've read DEEWR articles in the past(here), now I need to use them!

In general though, Australian mathematics education fared ok when in 2000 we were compared to 31 OECD countries (OECD study, 2003), Australian education was significantly higher on the PISA scale for 21 countries and only significantly lower for two (Japan and Korea).

Students that study in state schools have significantly lower funding that independent and private schools (Edwards, 2008).

2. Environment is a key factor

In a US study, a pre-primary student given extra assistance by a university eventually graduated with two degrees. Nothing spectacular here except her parents had sub 40 IQ (Wickelgren, 1999).

3. Students require attitude adjustment

In a Queensland study in 1995, an observer recognised that until students are assisted in changing their perspective they cannot begin to appreciate any assistance given to help them gain access to university pathways (Campbell, Cook and Dornan, 1995).

I saw as a result of my action research in term 1 & 2 that students need to understand what academic behaviours are and why they are important. This can result in quite spectacular short term success. These behaviours in themselves are not enough to ensure ongoing success as retention requires repetition and a long term committed approach to provide lasting benefits.

4. Students require a range of motivational support

There is no one way to motivate students. Many theories exist and none are perfect. Common theories are Expectancy x value theory, Attribution cognitive theory, Attribution Achievement motivation theory and Achievement goal theory (King, 1998).

5. School can both improve future prospects and reinforce existing expectations.

For some students schools can inspire them to levels higher than their parents. For others, schools will reinforce similar job prospects to their parents (Campbell, Cook, Dornan, 1995) and schooling reproduces the structure of inequality itself (DEEWR Component A, 2009, p.29).

High SES students are over-represented and low SES students are underrepresented because students from different SES backgrounds are differentially prepared by schooling for entry into university (DEEWR, 2009, p.29)

6. It is possible to improve university pathway access

There's nothing easy about it, but it is possible with the proper long term approach. Now the task is to create a way to find that correct method for our school.

Russell.

Career progression and an idealistic approach

I sit here still wondering if I am doing the right thing. A senior school teacher has the world at their feet, being able to teach to year 12 across all areas of your specialist curriculum is what gives you worth when seeking to further your career. I'm considering applying for a position in the middle school.

In a small low socio-economic school rarely is the full curriculum offerred (1B-3D MAT and 3A -3D MAS) and rarely will you get to teach the upper subjects as there is competition for them among those in your department. I've been lucky to be given an opportunity to teach all levels of year 10, MiPs, MwM, Discrete, 1BC MAT, 3ABCD MAT and 3AB MAS, but have rarely been able to teach any of these courses more than once. School collaboration (where students are bussed between schools for small class subjects) only makes this cycle longer. Being at the end of a cycle of students, my run at these subjects would take at least another three years (following students through from year 10) and I'm not looking forward to the slog of working with another lot of under prepared kids.

The fatigue and long repeat cycle is a factor in the constant turnover of teachers as they seek to develop depth to their understanding of the curriculum and pedagogy - many at this stage of their career seeking independent sector jobs and more pliable students. Being four years into my career, I'm looking for an opportunity to further improve my teaching and I know there is a job to do in middle school to better prepare students for high school. I've taught senior school for three years and the whole time have yearned to go back to middle school and do what I was trained to do, despite all evidence that says I am a better exclusively senior school teacher than an exclusively middle school teacher - oh for a position where I could do both!.

It has been pointed out to me by many that to not teach any senior school is career suicide. To lose the perspective senior school offers reduces the ability to bridge students into senior school and reduces your attractiveness to a potential employer. Furthermore, from the outside it would look like I was 'encouraged' away from senior school because of under performance, inability to handle the stress or lack of ability. Maybe subtly this is the case (I hope I'm still my harshest critic, my results this term have been woeful by my standards) but I think the want to move to middle school is still my choice and not something that I am not being directed towards by administration. I may also be walking away from a leadership issue in senior school as if I'm not in senior school, I won't be considered once senior maths staff seek new opportunities (conversely what would a future employer think if I'm eight years into my career and still applying for a senior position!).

Despite this, now that a middle school position has finally arisen, I have put my hand in the air and said, 'I would like to work in the middle school if I am the best applicant.' Many people have supported me in the senior school and I feel I have let a few people down by deciding to do this, as it would leave a hole and cause some instability whilst a new teacher is settled in (whereas a new teacher would have less impact in middle school especially mid-year) but I feel I can't complain about student preparedness if I'm unwilling to roll my sleeves up and do something about it. It may set me back a few years in my quest for readiness for a HoD or TiC position but if there is a job to be done (and the middle school needs to gear up for national curriculum and year 7 introduction (if it ever happens)) this is a job I can do well.

After all, I'm only really happy when engrossed in what I am doing and striving for excellence. I'm reliant on others to find areas where I can do this and need faith that they are cognizant of my career progression when utilising my skills. It's a bit harder with a newborn as I have to think about career progression a bit more than in my idealistic past, but I still feel that making it 'career' rather than 'best interests of children' the prime focus of my teaching (as I see in other 'driven' teachers) is a mistake in my case.

Ultimately, if the school needs a senior school teacher, I can do that. If they need me as a middle school teacher, I can do that. If they can find a way to allow me to do both, that would be good too.

Pride in your work.

It's taken half a year but I think the message is sinking in. This week I have focused on getting students to perform to a standard rather than some fictional developmental level. I am the teacher, I set expectations on how I want things to be done and no, I don't really care how your last teacher let you do it.

Hard up against the left margin, work down the page, rule a new column if there is space for it and use it, exercise number before you start in a column, work marked from the back of the book once an exercise is complete with a red pen, one line for each line of working (why do students miss spaces??), a space between each question, each question should be written as if to be read by another human being - not in some chicken language from outer space.

Also, if I give an instruction on how to do something, pay attention and do it that way. If you are writing 4709 in words, it is four thousand, seven hundred and nine. The 'and' is important. Ninty, ninteen, forteen and fourty are not words. One equals sign per line, the question is always to be written unless a lengthy worded problem. If you are adding, subtracting, multiplying or dividing vertically I expect to see clear columns for place value.

When I come into class, don't wait for me to say get out your books - just get them out. If I write notes on the board, write them down verbatim - I haven't met many students that can paraphrase sufficiently to make more succinct notes than mine. Asking what time the period ends is a waste of time - the answer will always be two hours fom now. If you fail a quiz, expect 60 questions for 'practice' over the weekend. Don't talk in my class about social events unless you can consistently get 80% in assessment - you obviously haven't got time to lose.

If you have a problem, seek help. If the problem has to do with a boyfriend, seek someone who cares - I'm only ears for maths and things that need mandatory reporting. I'm not your friend, please remember that - I'm your teacher.

.. and the funny thing is, when you lift expectation, it's easier to teach. The students respond and start to realise that you only want the best for them - tell them it's much easier to just sit back and watch them fail (or to give them phony grades that make it look like they are learning). To me setting high standards is just showing students how to take pride in themselves and their work. Building self esteem is not mutually exclusive with negative responses. I think that in many cases students need to have the bar lifted for them before they can start to do it themselves.

Fatigue... and a poke at Julia..

Teaching is one of those careers where fatigue is a constant enemy. It's important to recognise (especially at this time of year at the end of an 11 week term) that you're not going to be at your best. Week 8+ is always a bit of a danger time where you can lose perspective on your successes and fall into the trap of seeing defeat in what you are attempting to achieve.

With the NCOS things have changed a little, it means that you have to press on at a time where typically you would wind down into the end of term. You really need to fit two good weeks of work in to make a good run at the mocks at the end of term 3. Kids will be feeling the pressure, admin needs reports completed, exams need marking, tempers will fray.

Yet this is also a time when teams come together and there are opportunities to do small things that can make a lasting impression. Take the time to smile at someone, guide them through a nasty spot, do an extra duty, smile when you get relief, go on an excursion, offer around a chocolate bikkie or grab some take away for the staff room. In the crucible great things can be borne.

Take inspiration from wherever it stems, much of mine at the moment comes from my daughter, where in the past I may have given up and sought another challenge, I now dig in and look at the problem again seeking new solutions. A challenge is just an opportunity yet to be realised.

I was working with my 10's and we are looking at their ability to perform in non-calculator situations. Many can't divide, and many of those can't multiply because their tables are weak. Any idiot can teach kids tables. Maybe it's time I rolled up my sleeves and planned a tables club for next year, to fix a core issue. If numeracy is the focus next year, perhaps this is one path to finding long term success.

It's also a time where many decide it's time for a change and the inner conflict occurs of the desire for stability vs career opportunity. Do you talk people into staying or encourage them to pursue other options? I don't know the answer for this other than to encourage them to seek someone with more experience to help them with the answer. Other than this blog, I have no desire to lead (or even influence) as my best leadership option is to lead by example. Whilst still learning content and gaining an understanding of leadership roles I am in no position to lead with expert power. With time, my masters, a bit of experience and teaching year 12 courses may lead me there.. but I think I have a way to go yet.

If that idiot Gillard can become Prime Minister, who knows which lump headed student will solve world hunger, cure cancer or bring about everlasting peace. Some even might remember that teacher that gave them a hard time or a bit of encouragement that put them back on a path to success.

April Fools Joke - Not!!!

Today I had a look at the expected standards "C grade descriptors". This document outlines the requirements of a C grade for a student yrs 8-10.

"The descriptors have been informed by population testing data [NAPLAN], draft national curriculum materials and the professional knowledge of experienced teachers. During the consultation process teachers strongly supported the production of concise descriptors and welcomed the inclusion of examples." Department of Education April 2010.

The issue is that the end product was written devoid of common sense.

Here is an outline of the expectation for year 9 students from the C grade descriptor document.

"By the end of Year 9, students use number and algebra to solve routine and non-routine problems involving pattern, finance, rate and measurement including the calculation of area of triangles, circles, quadrilaterals and the surface area and volume of prisms, pyramids, cones and cylinders. They solve problems using Pythagoras’ Theorem and proportional understanding (similar triangles and the tangent ratio). They have a sound understanding of linear functions and are developing fluency with using quadratic and simple non-linear functions, such as with patterns involving doubling. They have a sound understanding of index laws pertaining to positive integral powers."

My issue is that this is a C grade description. The number of students with "sound" understandings of linear functions (by my definition of sound) during year 9 is minimal and students that have a conceptual notion of quadratic and other functions at this stage are the "A" students that have been extended - not the C students. In fact given this description it would be difficult to give many C's or even a single A in many state schools.

If students entered high school have some algebraic knowledge, they may have some chance at reaching this standard. At present I would suggest that this is highly unlikely. As students delivered by national curriculum are 5 years away - starting assessment now at a national curriculum level is ludicrous.

It is obvious the scope and sequence has been modified to include national curriculum requirements (look for the * in the scope and sequence). You can see that linear functions was the main focus of year 9 and then quadratics and 'other functions' were dumped into the sequence with little consideration given as to how time will be found to implement the new curriculum especially as it was hard to fit in the old curriculum (I sat and wrote a lesson by lesson plan for year 9 based on the old scope and sequence and challenge anyone to do the same on the new scope and sequence given the current entry point of students in year 8).

I have no problem with lifting the bar for students, but it requires time to re-instill work ethic at a younger age and subject specialists having access to these students.

To grade students that have not been adequately prepared for national curriculum assessment is grossly unfair. How anyone could propose this for semester one grading 2010 indicates a lack of understanding of the change management required. Either schools will need to fudge grades (easy to spot when comparing NAPLAN to school grade) or masses of students will not get grades higher than a D or E.

When teaching students in low literacy settings, handing out D & E grades to students trying their utmost to succeed is tantamount to child abuse. It is demoralising, unfair and sets up an expectation of failure. I can't say this in stronger words. Someone needs to have a good think about what is being done to our children.

Link to national curriculum media release (Julia Gillard)
Link to expected standards (Department of Education)
Link to mathematics scope and sequence (Department of Education)

Teaching of mathematical literacy

I have been teaching a low literacy class this year and it has taught me the perils of relying on the immersion technique to teach mathematical literacy. After seeing the positive effects of direct instruction of low literacy students, I see immersion as a lazy teaching technique for low ability students - immersion is slow, ineffective and generally detrimental to these students, especially in a large heterogeneous class.

Let me explain. When I teach area, I generally teach students to write a story that I can read. They draw a diagram, label the sides, write a general equation, substitute the values, evaluate the solution and check their answer. Once this technique has been learned I can then easily teach other concepts such as Pythagoras' theorem, trigonometric ratios, surface area and the like.

The explicit teaching of mathematical literacy (requiring specific layout and explicitly explaining the meaning and need for each component of the layout) is the key component in this exercise. By year ten, most can answer the area of a rectangle and write the answer, but cannot abstract the method to a circle. I attribute this to a lack of mathematical literacy and a failure to appreciate the true need for mathematical literacy.

Although modelling has a place in teaching mathematics (a key tool in immersion), we must be mindful that we need to teach literacy explicitly and not assume students will just pick up major concepts by observing a question being completed. The difference between a student answering a question correctly (after being given an example on the board) and being able to identify how to answer a question correctly from a range of tools (without prompting) is considerable.

Mathematics has grammar just like English. If students understand the grammar of mathematics, the meta-language of mathematics and the algebraic/arithmetic/visual representations/tools of mathematics, then their ability to solve problems increases exponentially.

And as mathematics teachers we can appreciate the benefits of exponential growth.

Functions and the Casio Calculator fog(x)

When finding fog(x) the CAS calculator does a good job of simplifying algebraic steps, often to the point of making traditional questions trivial in the calculator section.

I'll start by defining a function f(x) =2x+1 and g(x)=x^2 and attempting to find fof(x), fog(x) and the inverse of (fog(x)).

To define a function f(x) go to the Main window and select

Interactive->Define

A window will appear

Enter the function name (eg. f)
Variable (eg. x)
Expression (eg. 2x+1)

The main window will reply:
Define f(x)=2(x)+1
done

Repeat:

Interactive->Define
Enter the function name (eg. g)
Variable (eg. x)
Expression (eg. x^2)

The main window will reply:
Define g(x)=x^2
done


To find fof(x)

In the main window
Action->Transformation->simplify
f(f(x)) (using the soft keyboard)
press exe

The main window should say
simplify(f(f(x))
4x+3



To find fog(x)

In the main window
transformation->simplify
f(g(x)) (using the soft keyboard)
press exe

The main window should say
simplify(f(g(x))
2x^2+1



To find inverse of fog(x)

In the main window
action->transformation->simplify
action->assistant->invert
action->advanced->solve
y=f(g(x)),x))) (using the soft keyboard= don't forget the "y=")
press exe

The main window should say
simplify(invert(solve(y=f(g(x)),x)))

Here is a link to other CAS calculator posts.

Inverse Functions and the Casio classpad 330

The 3CD course requires knowledge of domain, range, co-domain and inverse functions. The classpad can handle these in a number of ways.

The most obvious way is in graph mode (Menu-> graph tab). Set up a graph (say y=(x+1)/(x+2), and visually examine it to find the domain and range. To find the inverse, click on the graph and select Inverse (Analysis->Sketch->Inverse). The equation of the inverse can be found by selecting the inverse graph and examining the equation bar at the base of the screen. Be careful with this method, as the resultant inverse graph is not written in "y=" form.

The less obvious way to do it is in the main window. I have not found an "inverse" function yet, but the following is a workaround to find the inverse.
Go
Action->Transformation->Simplify (to simplify the resultant equation)
Action->Assistant->Invert (to swap the x & y variables around)
Action->Advanced->Solve (makes x the subject of the equation)
Enter the function
Press ",x)))" using the soft keyboard (to make x the subject of the new equation)

It would look something like this when finished:

simplify(invert(solve(y=((x+2)/3,x)))

In a way I prefer the main window method as it mirrors the algebraic method. I think students need to really understand the parts of an equation to effectively find the domain and range. I explicitly draw students attention to critical information such as the inability of the function to equal zero or where the function is undefined

a) Look for possible values of x where y=1/0 will occur (eg. {x≠-1} for y=1/(x+1) ).
b) If it is not possible for the numerator to be zero (eg. {y≠0} for y=2/(x+1))

If the range is not obvious it is often easier to examine the domain of the inverse of the function.

Here is a link to other CAS calculator posts.

Purplemath has a good explanation of inverse functions.