Thursday, February 25, 2010

Manual Subtraction

An interesting question was posed to me today.

How do I subtract two number manually when the answer is negative??

For instance, 3896 - 4321 (to which the answer is -425).

I originally set up the problem in vertical columns


and tried to subtract..


which obviously does not work.

So I thought about it.. the only obvious solution was to say, when subtracting always put the larger number on top.


As this answer is positive, it is still incorrect. It requires an additional rule, that when the order is changed, the sign of the answer is negative. Thus the answer is -425.

I'm sure everyone knows this (and it's just one of those odd cases I haven't come across before), but it could be an interesting short investigation for upper primary or lower secondary doing directed number exercises.

.. and I have a stupid cold, my nose is dripping like a tap and I can't hug my daughter. It's made my day!

Saturday, February 20, 2010

Evidence based education vs OBE

Educational trends tend to go in cycles. From ultra conservative, tried and true methods (such as direct instruction from defined syllabus) to ultra experimental (such as the whole of language approach).

Recovering from the ultra experimental 'OBE' we are now heading towards the ultra conservative 'evidence based' approach.

Although the evidence based approach has merits and is a very attractive alternative after OBE, I would suggest caution. The consequences of evidence based education is already starting to slow educational change through the inability of educational practices to change in time with social change (by the time evidence is gathered, social change has again occurred).

Current practice would be to identify an educational need, and then find a current practice (with evidence) to use to fulfil this need. The obvious issue with this is that where we have a new social situation, no evidence exists and with current research practices - no evidence will ever exist as typically research today does not seek to find a solution, only observe existing practice (existing practice which we know is flawed or wouldn't require research).

Has the pendulum swung too far, now stifling the innovative approaches that could be researched and widely implemented? To avoid this I think a middle ground needs to be found, where innovative practices are encouraged and then researched before extensive implementation. To have one without the other is to invite poor practices or stifling of positive change.

Friday, February 19, 2010

Time continued...

We were working on applying time calculations today, so I posed a question:

"If [student A] was given detention for 1.4 hours and [student B] was given detention 1 hour 25 minutes detention, who would be in detention the longest?"

Students had a guess and then they reviewed the caterpillar for converting between time units.

We then did a number of calculations with some templates to show how a calculation could be constructed.
3.4 hours = _______ x ________ mins
= ______________ mins
2 122 131 sec = ________ ÷ _________ ÷ _______ ÷ _______ days
= ____ days
1 hour 20 mins = ________ x _________ + ________ mins
= ______________ mins
After we did that, students were just given a range of questions to solve without the templates.
2.8 hours = ___________ minutes
12 hrs 12 minutes = ______ hours
12 hrs 12 minutes = ______ days
Then we revisited our original detention problem and a range of similar problems.
Students then practiced with math-joke type connect-the-answer-with-the-question exercise (the old worksheet with a bad, bad mathematics joke at the bottom to solve). Students were able to solve the majority of problems.
There's nothing to say that with a stronger group I couldn't have taught the same topic by teaching basic time facts (such as 60sec = 1 minute) and then relied on their application of multiplication and division, but in this case I'm glad I didn't do that, the look on the faces of my students when they realised time calculations made sense (that they had found difficult over a long period) was priceless.

Wednesday, February 17, 2010

Teaching Elapsed Time

Teaching time is always a little problematic with a class, as some students will have this well and truly conquered by year 10 and others will struggle.

Elapsed time is a difficult topic for many as it drags in a lot of sub topics. With each step it is important to draw student's attention to possible mistakes and also to any parallels with an analogue clock.

A common method is to find the number of hours elapsed and then add the remaining minutes on either side (eg. for 2.14 to 4.15: 2.14 -> 3.00 -> 4.00 -> 4.15 would be 46min + 1 hour + 15 mins = 2 hours 1 minute)

The usual approach is to
a) draw a number line
Issues: Students don't relate a number line with time, and commonly place decimal marks (eg. 10 between each hour) rather than 12 (for 5 minute intervals).
b) place the start and finish time on the number line.
Issues: Students don't realise that the start time and end time have to be placed in that order. Eg. if the start time is 8am and the end time is 7am they want to put 7am first on the number line.
c) mark on the hour after the start time and the hour before the start time
Issues: Students have difficulty adding the two times inside the interval. If 7.30am is the start time, they might add 7.00am instead of 8am or for a 4.30 finish time they might add 5.00pm or 3pm.
d) mark on midday and midnight if they lie between the start and finish time
Issues: This is problematic especially with times over 12 hours where both midday and midnight are involved. Students are often not sure whether 12pm or 12am is midday or midnight. They also get confused moving from 12am to 1 am (counter-intuitive).
e) calculate the time between each number on the timeline
Issues: This is the bugbear of the exercise. Students are not sure of the answer counting up to the nearest hour and counting back to the previous hour. Eg Finding the time between 1.17am and 2am or 4.00pm and 4.55pm. Many issues here are related to issues in part c)
f) add the elapsed times
Issues: Students write times such as 7hrs 85 minutes not realising 85mins is greater than an hour.

An alternate approach is to go up in hours and add the remainder (eg. 2.14-> 3.14 -> 4.14 -> 4.15 = 2 hours 1 minute). This may help struggling students and reduce the amount of calculation required.

Monday, February 15, 2010

Heroes in mathematics education

There are some heroes in mathematics education in Perth. They're the ones that share their resources freely, commit to projects and help out. Most are quiet, private and retiring soon. I feel sorry for the public heroes like Rom Cirillo at Curriculum council who is trying to help everyone and is succeeding most of the time. If only there were four of him.

Then there's those that are paid to help and are more talk, little knowledge and bugger all action. I've labelled them the West Australian New Kurriculum Education Resource (the acronym is all important - feel free to put it after your name - no charge!). They join TDC's, MAWA and teaching groups and are paid to produce resources and assistance. All too often they send out untried resources that cause confusion and show their lack of knowledge, they provide advice that is the flavour of the month and denigrate anything functional (their favourite seems to be the Saddler texts). Their advice is ill researched and they often don't answer the question posed. I often have a good laugh at their email sigs that are fourteen lines long outlining their projects as if this means something.

Numeracy consultant, Leaders Facilitator, Specialist teacher, TDC coordinator (yawn - and all in one sig!). It seems rampant self aggrandisement. I've seen title based nonsense before in IT, it's not something we need in teaching. The word 'consultant' brings about shudders - tell me what you're doing and then I'll record it so that you will know what you are doing (and charge at $400 per hour), tell you how the latest fad might help and provide insanely conservative advice as any real advice I give could lead to litigation that might hold them responsible.

One only has to look at how well these experts do during in school PD to realise how out of touch they are.

No thank you.

To me - it makes more sense to signoff Mathematics teacher. Add BEd, if you need qualifications. Sometimes I might add senior school to make it easier to find me within the school. Anything more seeks to diminish the reputation of a classroom teacher.

Give me a teacher that can teach a TEE student and a year 8 effectively any day (or a primary equivalent).

Show me a "super teacher" and I'll show you an idiot. Teaching is too wide a profession with too many different contexts to be an effective specialist or specialist trainer. To specialise is to remove yourself from the coalface and limit your student involvement (eg. reduce your ability to teach). I fail to see how this is a good thing.

Sunday, February 14, 2010

Creating a positive learning environment

Positioning kids for learning is an underestimated part of teaching programmes. If a student understands that creating a good impression is important, then this creates a pattern of behaviour that can continue throughout the year.

As a form teacher, it's important to remind kids of this, take a personal interest in their successes and reinforce disappointment when they step out of line. This creates a culture of success and reinforces the positives.

It can also snap a student out of negative behaviour before it becomes habitual.

Homework is one of those things that needs to be positioned early. It is time consuming to check homework daily, but initially there is no way around it. There needs to be real punishment for non compliance (I use check ability -> detention until complete -> blue note with letter for non-attendance -> phone call -> demotion to lower class). The letter part is my favourite as I can suggest a number of activities that might be suspended such as PS3/Wii/XBox, MSN, TV, sport, going out etc. until regular homework becomes established. Diaries and journals play an important part in this process to keep parents informed.

I have heard that imposing homework is too difficult (and it is difficult if done in year 10, without having the habit instilled earlier) but without it, we are expecting low SES kids to perform with potentially 3 hours per night less work completed compared to independent schools. This means state school kids are expecting to compete with 2/3 the effective work time.

The need to stop and rethink

Sometimes after assessment you need time to stop and rethink. When a course of work has succeeded for a number of years and fails spectacularly with a particular group, it's a good thing to reflect on what has happened.

If a group of students can't follow instructions to complete a task the underlying issues should be examined.
a) Has your teaching changed(content/pedagogy)?
b) Are the students somewhat different to other groups and how(ESL/refugee/migrant visa/disaffected/gender specific/generational change/indigenous)?
c) Has the environment changed (bullying/timetable/family/schooling structure)?

This happened to me recently and I learned a lot from it. My final conclusion in this case was that the kids had changed - I had a weak group, caused by frequent absenteeism over many years and a raft of 'community' issues. These were kids lost in the system. I became a better teacher as I had to think of new ways to teach content that I had taught successfully a number of times before. In a heterogeneous class, I never would have had the time to backtrack, but in a streamed class destined for 1B in year 11, just this once I had the time these kids needed.

I had to diagnose the core issues, backtrack and reteach basics that are normally assumed to be in place since primary school. This in itself was a new experience as teaching solely upper school classes removes you from some of the resources and skills necessary for primary content.

I had to face issues similar to I imagine that of low literacy English classes, where finding age appropriate basic reading materials for adolescents can be difficult.

After they had learned the basic materials, I had to consider topic fatigue and put the desired year 10 learning aside for a time, giving them a break whilst they digested the new material. This gave me time to retest for retention, to make sure this time the learning 'stuck'. I had to be careful that the prerequisite material had actually been learned where previous teachers had been unsuccessful. For some, the motivation to retry a topic failed (where they had multiple failed attempts over multiple years). It was a lot to bear, difficult for them to face and hard to kick start. Kids are proud and rarely want to accept that they can't do something their peers can do readily. In a large class, it's easier to give up and hide in the sea of faces.

The turning point was when we finally revisited the topic and we looked back and could say, 'that was pretty easy now I know how'. Like with most things, unless the end point is well defined (the goal) it's impossible to see when something is achieved.

It's a real reason why wafty curriculum fails inexperienced teachers.

Thursday, February 11, 2010

Belief in teaching

We have a building crisis in confidence in our teachers, a crisis coming about to deflect blame for poor government curriculum decisions and poor staff management procedures over an extended period of time.

It seems we are forever looking for magic bullets, where only hard work and dedication will bring about lasting results. It seems counter intuitive to expect hard work and dedication when your federal minister releases press on a regular basis about how improvement is needed - creates metrics to measure improvement but offers little in proven programmes that bring about that improvement.

I wonder how long it will take the penny to drop that the difference in student performance is rarely school performance but is actually the difference in parental support. This accounts for the difference across postcodes in a way that blaming schools does not. It's not parents fault either - their education level is what it is, generational change is the only thing that will eradicate the issue.

Until then, these kids need more time and instruction to succeed - yr 13, university bridging courses, after school tutoring, summer schools. To have effective courses we need a bunch of people that care about students, are motivated, skilled, nurtured and valued. These people have always been called teachers, lecturers, youth workers, aides, social workers, librarians and more recently chaplains. To continue to score political points against teachers is to shoot people that can make a difference.

Do the world a favour and encourage those making a difference. Chucking around money like confetti rarely brings this about. In fact it usually starts attracting vultures and those without community values that firmly have profits in their sights. The ABC Learning centres fiasco should have brought the effectiveness of profit driven public service firmly into the light.

We know our kids lack values, values previously imbued by parents and religious backgrounds and ethics. Today we need the people willing to set an example and do superhuman things with groups of kids that most people would fear talking to for 5 minutes, heaven forbid five to seven consecutive years.

Technology in the short to medium term can't fill this role. A new curriculum or statistical analysis will not fix the problem. Perhaps we should accept that social change is not the sole role of schooling and put the boot away for a while whilst the community pulls together and is assisted to do what is necessary in a practical, tried and accountable manner. Stop trying to make teachers and schools scapegoats.

Yes Ms Gillard, I mean you.

Updated 13/2/10: Here's another media release about a scheme to 'improve teacher quality' and improve 'teaching standards' (more than likely by those same teachers that require improvement) without details on how it will be done - but with wads of money attached to do whatever it?!? is.

Tuesday, February 9, 2010

Week 2, 2010 reflection

Had a great couple of weeks thus far: students are working well, keeping out of trouble. My aim this year is to increase the amount of learning that is going on in my classes.

To do this I aim to:
  • increase the amount of direct instruction
  • increase the amount of on-task time
  • reduce the number of behaviour issues
  • promote 'the search for an aha moment' as an enjoyable experience

Thus far things are going swimmingly. I started by randomly seating students, explaining to them that by increasing their circle of friends they were more likely know someone that could help them if they were stuck.

Then I set about increasing the expectation of performance, setting regular homework, giving time limits on completing tasks and setting a pace from the time they entered the room.

I paid special attention to student dynamics in the class, emphasising that performance was required to stay in the class. There is competition to get into this class as a precursor for 2A/2C/3A in upper school, so students need to perform well to remain.

I've talked to students a lot about the need to understand what it takes to learn, digging up my old "huh??!!, Doh!, OH!" model, emphasizing trying and practicing as a pathway to learning and long term retention of information.

I've also worked to modify my often unrealistic expectations and drive kids towards work where they can see real achievement. I've slowed my content delivery pace a lot (students are doing more work with a more limited focus), and it has shown a vast improvement in the general demeanor of this year's class.

I've looked at the class and tried to determine who will form the heart and motor of the room. These kids set the tone, mood and pace of the class. I'm more conscious of when they are behaving abnormally and investigate more quickly. The class picks up on this as an indication that I care about their well being as a whole.

I've set class goals which include rewards for outperforming the 'A' class and ever increasing goals for the class average, daily performance goals tied to the school reward scheme and try and give more incidental verbal acknowledgement of achievement.

I've surveyed the kids to determine their benchmark enjoyment of mathematics and then see how this changes over the year. I've recorded their friendship groups and attempted to identify any isolates.

It's vibrant and fun.

Saturday, February 6, 2010

In school research

I started my studies for my masters this year and it's good to be doing something thought provoking again. There's a bit of a rush on post graduate studies at school at the moment, with many feeling more comfortable to start now that many NCOS subjects are bedded down. Lots by coursework, I think I am the only one doing it by thesis.

This term I'm looking at group dynamics and seeing how student/teacher interaction can be made more fruitful. Everyone that I explain my topic to seems to think I'm trying to do groupwork with my students (and I get a lecture on the validity of groupwork and assessment). These discussions have helped crystallise my resolve to assist students use their classtime more fruitfully and have students engage in meaningful conversation with a wider range of students. It's not really about collaboration and groupwork in the "put four people in a group and watch one do the work" mould.

It goes back to the 60 minute period - ~20 minutes instruction (10+ 10 or 7 + 7 + 7) and 40 minutes intervention time. In a class of 20, if all students are relying on the teacher for help, that's two minutes per student and a lot of time wasted waiting for the teacher, in a class of 30 it's worse.

A few minor issues have arisen that has forced me to widen the scope of my project. The first being that I need benchmark information at the start of the year but classes are fluid until week 4 when streams are set in stone. The second being the raft of hurdles that need to be jumped before research can begin.

The hurdles thus far:
Acceptance by university into the Masters course (a discussion, two phone calls and an email).
My WACOT registration expired whilst the transition from registered teacher occurred (and was an absolutely painful process to resolve with the same document lost multiple times by WACOT).
My WWC expired during the break (and required signing by the principal before a new one could be applied for and something that the screening unit needs to consider)
Approval by the university that the topic would comprise valid research (relatively painless as was done as part of a summer school unit)
Human Research Ethics Committee approval from the university (relatively painless as was done as part of a summer school unit)
Approval to proceed by the department (this was the big surprise - Policy and Planning at DET are a well oiled machine and made this a really pleasant experience with a fantastic turnaround)
Approval by my site manager (our principal).

Still to go:
Approval by parents
Approval by students
Approval by staff

The good thing is that now I have passed all of the third party stakeholders, I only need approvals directly related to the participants.

Tuesday, February 2, 2010

IOTY nomination 2010

The first IOTY nomination for 2010 is Kevin Rudd, Prime Minister of Australia and general all around idiot.

First we had to put up with Rate-my-teacher, a website prone to defamatory comments. At least with rate-my-teacher a comment could be challenged and removed.

Now our good-time-guy, hop on the 9 million hits bandwagon Prime Minister, has proposed to add parent comments to the myschool website.

There are so many issues with this idea it is laughable. Anyone that has run a public company and knows the issues around "running stocks" would identify the main problems with this idea.

a) the person running the myschool website would have to ensure that it is a parent making the comment, not a disgruntled student (authentication).
b) if it is a parent, there are a lot of parents with rose coloured glasses and interesting opinions of their little darlings that do not relate to their actual behaviour in class (authenticity).
c) a skew of opinions tend to occur, as happy parents rarely put their statements online (bias).
d) ensuring that malicious and slanderous comments are removed without damage to the reputation of teacher or school is a full time job (for just one school), it would be near impossible for 10,000 (legal liability and overhead).

These issues alone are enough to make this idea stupid. Another government idea taking pot shots at a system nearly destroyed by government curriculum policy. The resilience the system has shown in trying to compete with independent schools has been astounding to watch. It would be nice to get a break from those putting the boot in now and again.

If this is the government's way to take the mind of voters away from rising interest rates and climate policy issues, it is a poorly crafted stunt.

Kevin, you are the first IOTY nomination of 2010.

Link to media statement here.