Composite Area problems

With my year 10 "literacy focus" mathematics class we have been looking at the language of measurement, specifically area and perimeter. The idea has been to get students to clearly understand the importance of units and how to interpret what questions are asking.

When thinking about perimeter we are only thinking about the boundary outside a shape. We then looked at some real world shapes and measured their boundaries, followed by drawing some scale diagrams of shapes and measuring their boundaries.

We then tried to describe how much space was in the shapes. I tried to drive them to describing dimensions, but some students had enough prior knowledge to say calculate the answer by multiplying lengths.

The main issues came as we arrived at composite shapes where composite shapes had to be split into basic geometric shapes. Deriving missing measurements really brought home how much trouble low literacy students can have with basic mathematical concepts such as subtraction. Assuming that a student can see how to find missing sides is in many cases overestimating their ability.

Even at year 10, the majority of low literacy students fail to see f- c = a whereas they are more likely to be able to see a+ c = f.

Because of this to use a scale drawing to assist these students see subtraction in action requires some thought. If a student drew the above diagram with the following measurements they would
not use subtraction to find the missing side on the top rectangle. They would count the squares (if on grid paper) or measure the vertical gap and put the measurement of one on the page.

To encourage students to use subtraction I needed to encourage students to first look at the diagram and do a number of examples with them without using scale diagrams, explicitly doing subtraction sums. We checked our examples with scale diagrams, rather than finding the solution using scale diagrams.

Though a subtle difference, this was far more successful.






Another successful strategy used during these lessons was using formal layout during the early stages with simple examples. By doing this, students were able to see the connection between diagrams, algebraic substitution and the usage of formulae.

For instance:

















By learning this and ensuring each example was completed thus, when triangles and circles were introduced it was a trivial case of changing the formula and adding a line to the bottom

Area(Shape) = Area(S1) + Area(S2)

It was interesting to note that students at this stage had now forgotten that perimeter was the outer boundary and were including the S1 - S2 boundary in their perimeter calculations. It had to be explicitly explained that

Perimeter(Shape) != Perimeter(S1) + Perimeter(S2)

and that the intersecting boundary needed to be subtracted. For me, this is learning real mathematical literacy. Students are becoming able to exactly describe their intent on the path to a solution.

Issues with national curriculum

Today at a PD of five secondary schools and their mathematics teachers, we had a quick look at the national curriculum. As an upper school teacher, the demands of teaching upper school are significantly reduced under national curriculum with many upper school courses being pushed back into middle school and a lot of middle school algebra pushed into primary school. I don't necessarily think this is a bad thing.

Strengths that were raised by presenters were that it was put together by experts, that the course was being simplified (would contain less material with more depth), that when questioned by parents for course suitability teachers could point to the syllabus (reducing uncertainty) and that it assisted in course transferability (eg. between states).

The first issue identified by the audience was that it was a one size fits all approach. This means that many students will fail a year and then be unable to do the work in following years leading to students unable to achieve anything higher than a 'D' causing reduced motivation and higher instances of behavioural issues (for this reason alone I will re-iterate that anything other than normalised grades in classes is a poor solution).

The second issue was that for at least 5 years students will not have the capacity to complete middle and upper school mathematics as there are a considerable number of missing attributes in our current curriculum. Students taught under the current system will not be able to effectively participate under the new system without extensive remediation especially in operations and algebra. Given that this remediation needs to occur during an 'increasingly packed' lower school curriculum this is unlikely to occur.

The third issue relates to WA primary extending to yr 7 (resulting in a lack of specialist mathematics teachers in year 7) and primary schools being ill equipped to teach pre-algebra and algebra. Given the number of students that currently enter yr 8 'algebra ready' I tend to concur that this is a problem that could be solved by national curriculum (although nobody is saying how this will occur). I have no idea how long it will take for texts to be prepared and primary teachers upskilled to be able to present the material, but it will be longer than the current implementation date of 2011. No allowance for upskilling has been allocated to schools in low performing NAPLAN states WA, QLD, TAS and NT where the current curriculum is less rigorous due to population and historical factors.

The fourth issue relates to endpoints mapped in the current NCOS of study for year 12. Under the current plan there will be little requirement for 1B-2C as students will theoretically be well past the 2C benchmark if they successfully complete the yr 10 national curriculum. This caused some laughter and raised the more important point that we really need a range of courses 8-10 (focus, intermediate, advanced) to cater to a range of student abilities and to stream courses into NCOS subjects.

The fifth issue related to students in low SEI areas, where developmental lag is a real factor. The new curriculum has the potential to completely destroy students chances of catching up over the schooling years as students with a poor starting point are more likely to fall further and further behind as each year progresses. Furthermore, there is no allowance for students in current cohorts that are six months behind due to starting age differences between the states.

The sixth issue is that population size has to be a factor in determining the best course for a state. It will be harder for smaller states to generate the critical mass for harder courses, as the geographical aggregation of higher socioeconomic students is going to be attained in fewer areas. Running courses for 2-3 students is not going to be viable for many schools (especially with the attention on student/staff ratios) although not running these courses has catastrophic effects on staff retention (the best teachers will not go to schools without these courses running), student attraction (students that may have the potential (eg your top 10-15% will go elsewhere) and school morale.

One way to alleviate these issues raised by the group was to start holding students back if they could not meet the standard (eg pass the course with a fair chance of success in following years). This was dismissed as an unlikely solution by presenters although is a common solution in upper school courses.

It was not known by presenters whether accreditation to teach subject areas was being discussed (although that inference that this is a current agenda could be drawn from this media release by Julia Gillard yesterday). It's not a difficult prediction to make that implementation issues will be ignored, blame laid at teachers feet when the implementation fails in WA, QLD, TAS, NT, then an 'accreditation programme' instituted to identify capable teachers to deflect from the real issues listed above and the government policies that created the situation in the first place.

It was put by presenters that teachers had discussed all of this before at the start of (unit curriculum, OBE, 'insert other fad here') and we needed to just roll with the punches and get on with it as we always do. I think this is my main gripe about Julia Gillard, her inability to accept that this is the reality and that change is driven by government - not schools and that poor performance should be laid squarely by policy makers and change agents - not teachers. Furthermore, ill conceived ideas and implementation causes much angst amongst the teacher population and further resistance to change.

I don't think it is that the issues can't be overcome and that national curriculum will ultimately fail but a rushed implementation to political (4 year cycles) rather than educational (12 year cycles) is not appropriate. I still can't understand why this could not have started with a limited rollout and then moved across the country over the following decade using a staged approach. Given the rush for implementation and the suck it and see approach "the acceptance of ongoing failure before we find success", I think that this has the potential to cause a lot of heartache in the short to medium term.

I really hope those with the experience (and will) to guide us through this stand up and be counted. It's not only the students that will suffer in the long term.

Reflection prior to term

I can't say it's been the most productive or relaxing break, but it sure was needed. It helped focus what needs to be done, what I would like to do and what has to take a back seat for awhile.

Top of my list is making sure my year 12's are well supported on their way to finishing school. This means resolving the issue of the missing moderation group in the first couple of days of term. I have to get this PD out of the way on the first day back (both the presenting and participating sections)

Next is looking at my yr 10's and completing the action research checklist as put forward for my masters course. I think I need to complete this unit if I am to have any chance of getting the confidence back to complete my masters.

Next is to establish the yr 8-12 maths club for those wanting to promote their academic performance.

Last is to start preparation for semester 2. There are some elements of the yr12 course I haven't taught before and I need to work through the exercises and identify the key points.

Everything else can wait.

Study that supports extrinsic reward

News aggregator Slashdot reports that paying yr 2's to read has fantastic results in encouraging students to read. Kids were paid US$2 for each book read and answering questions on the book answered correctly.

It's worth a read.

Sorry, no $2 for doing it.

Julia refuses to show common sense

Another article showing the arrogance of Julia Gillard in the face of good advice.

Click here.

I hope the "We told you so" that is coming does not cause a complete breakdown in low socio-economic schools and foster the creation of a two tier system. The longer time passes, the more likely this is to become.

Update 13/4/10: Here she is again sounding like a petulant child.

Comment Moderation

I've had to add comment moderation temporarily as a spambot has found the blog (from an Indian University). It means any comments posted will be vetted and will not appear immediately until I've seen them. Hopefully the spambot will move on soon and I can turn it off again.

Russell.

Websites found whilst on PD

I'm not a fan of PD, but I do like the networking possibilities. One of the good things about recent PD was picking up a few online resources.

Jigsaw planet allows you to create a jigsaw that students can reconstruct.

Search-cube is a nifty 3D search engine in the Minority-Report vein.

Flaming Text allows the creation of nifty (though often annoying) animated headings

Screenhunter.com is a free screen grabber for those sick of the PrtScn and msPaint alternative.

Quick and free worksheet creator

Sometimes a student has a basic issue and directing them to MathsOnline or Matheletics is overkill. Other times you may just want a quick diagnostic tool prior to starting a course of work.

http://www.mathmaster.org/ is a great little resource as it freely generates random worksheets and answers for a wide range of simple number and measurement topics. It's tidy, quick and add free.

Being randomly generated generally creates a few sequencing errors but can be good if you are entering a test-retest-retest cycle and ensuring mastery has been gained.

Have a look!

Idiot Minister strikes again

Under the logic of "everyone is using it therefore it is good" our "Idiot of the year 2009" Julia Gillard has vowed to expand the myschool website - despite a raft of public opinion and advice from education circles to the contrary.

Given this logic I suggest the following (with a tongue firmly in cheek):

Everyone likes potato chips, therefore all schools should feed children potato chips.
A large part of the population find mathematics difficult, we should discontinue teaching mathematics.
Kids don't read anymore, we should stop enforcing reading programmes.
Everyone watches television, therefore television is good.
Everyone likes chocolate, therefore chocolate is good.
Everyone wants to be thin, we should all become anorexic.
Everyone prefers holidays to working, we should not work.

Furthermore her assertion that government couldn't have provided assistance to schools without myschool is blatantly false. The government has always had access to this information. It chose not to use it, until political gains could be made from publicising the assistance. This is very dirty politics as it uses children and their futures as pawns in political posturing. It is the publishing of this information, formalising and recognising educational elitism that is the issue.

Popularity, nor usage is a measure of the success of a project. Transparency of this sort has negative and positive effects. The negative effects in this case are not being adequately recognised. The failure of the myschool project will be measured by the negative impact on schools and students. This impact will not be seen in the short term.

Julia wake up!

Link to SMH article here.

Project scheduling "99" rule

The actual project scheduling rule goes like this:

"The first 90 percent of the task takes 10 percent of the time. The last 10 percent takes the other 90 percent."

The way we always said it was:

"The first 90 percent of the task takes 90 percent of the time. The last 10 percent takes the other 90 percent."

This is true of students. Often we can get them 90% of the way there but we don't have the time to get them the remaining 10%. That remaining 10% is found through practice and investigating the concept in a variety of contexts. I'm gaining an appreciation of the well written investigation that goes some of the way to assisting students gain this understanding.

For instance, we recently completed an investigation on radians. By the end of the investigation, students had worked through a variety of uses of radians, applied formula in a variety of ways and had to think about what the formula was comprised of and how it was derived.

This though is rarely done in lower classes - and is a real flaw in use of texts. If questions are presented in method-> practice exercise form, students rarely have to think about what is required to solve a problem. This causes a lack of retention and poor examination results (if examinations are done at all).

I've been thinking that a revision week may have their place in the programme, once a term where students are forced to reconsider earlier work with an element of training how to revise for exams.

I will think on this further.

Children are not clients

When in business, the client or customer always comes first. This makes sense as the customer requires a product or service and is paying to receive it. A client is "someone that a professional service is rendered for". To say a parent is a client makes some sense but a child is not a client. We do not render services for a child - they have no money to pay, are unable to contract and do not know what service they want. Children are not our clientele.

It makes even less sense to say a child is a client in a low socioeconomic school. The child is not a willing party to the transaction. They have no choice in choosing the vendor (school) or method to which they are taught as financially they have few options available. Generally, they would rather be somewhere else. Having few goals and little ability to see past the moment, someone else decides what is best for them and puts them on a pathway. This is usually the school itself, sometimes the parent has involvement.

A child in a low socioeconomic school has basic intrinsic motivation (of course there are exceptions, but they are not the norm). To use a child-centric model and increase student involvement in the process is to invite low performance as the happy child will focus on "the now" to the detriment of the rest of their lives. The prevalence of the child-centric model creates a struggle to interpret the needs of an immature mind and turn their attention to what they need to be done to interact successfully post school.

At present schooling is becoming more like product development. If we consider a child as a product, a school lives or dies by the products it produces and the reputation of these products in the marketplace. The quality of the product is important. The standard of the original materials gives us an idea of the products that can be produced, the unit cost of production to a reasonable standard and the time required to do so. The scope of the project (syllabus/curriculum) is important as it guides what is possible to do in the timeframe allowed. If we consider a child as a product, individual plans start to make sense. If a child is a product, we have decided what is possible and get on with the job.

In a world of myschool, national curriculum, ratemyschool, performance management, social engineering, back to basics and independent schooling we need to consider what we are doing with children.

It's a chilling thought, as child-as-a-product seems to fly in the face of encouraging a pursuit of excellence.

Week two of action research cycle

1st report is due in this week and little to report. Students are settling into class and punitive measures for homework are starting to show results. Most students now know that not doing homework means being kept in.

Improving of teacher-student communication has also started with students realising that "I couldn't do it" is not an excuse and that they have to try and find a way to get the questions completed. They have a number of options from "finding me before/after school" to asking a friend, to copying someone else's answers.

For me, it's a way to quickly identify who is struggling.

Choral responses are improving, with students starting to use it as a way of communicating during class. Off-task communication is still a problem but there is slow improvement, with students completing a full exercise out of the book - something not done since the class changeover.

Student letters are taking a while to get out and I still haven't had a good look at the NAPLAN results for last year. I need to move on this soon.

First survey responses are in, I will need to examine these this week too and collate all the student/parent responses.

In class reward scheme has also kicked back in now that I have found the secret stash of rewards points. It will be interesting to see how that impacts on student responses.

First week in action research cycle

Finally approaching my first action research cycle. I've navigated the ethics hurdles, sent out permission slips and finally can get started.

I'm looking at ways of improving effective on task communication between the teacher and the student in order to improve performance.

Communication is set at six levels:

• School/Administration/Counsellor/Youthworker->Student
• Teacher->Student
• Mentor->Student
• Peer/Friend->Student
• Parent/Guardian->Student
• Student Introspection

My task is to identify ways a teacher can successfully add to each communication layer. I am looking at how to get students to communicate how far they are down a learning path for a particular topic. I'll measure success by examining the effects on student self esteem and enjoyment of mathematics. I am particularly interested in how student group dynamics can be manipulated to improve my performance.

To establish benchmarks I plan to run a motivation and career survey and then check their ability to work independently through a task observation. I will also need to speak to their yr 9 teacher about each student, identify student NAPLAN yr 7/9 results, student yr 10 entry exam results and student grades in year 8/9.

My first tool is aimed at student->teacher communication, re-introducing choral responses (Eg. "The answer is... I can't hear you... that's better!!). For the whole class to respond requires the whole class to be paying attention. It also makes it fairly easy to identify students that are not responding. By ensuring students are vocal (during on task behaviours) I hope to increase risk taking in the class. It's also a great tool for waking a class up!

My second tool will be at the Student->Parent level with a letter home to parents about homework and then setting online homework with MathsOnline and Matheletics. Homework is a teacher->student communication as it can inform the teacher about student motivation and their current performance level if it is closely tied to current classwork. Their completion and performance is easily monitored and I can bop a few students for not doing their homework, whilst reinforcing that upper school classes require homework done on a regular basis to ensure retention of materials for exams. It is also aimed at improving parent->teacher communication through regular email communications with parents (although out of scope of the research project).

Let's see how the week goes!

Dr Constable and the national curriculum

Dr Constable, our state education minister has been conspicuously absent from public education debates with the exception of this week when I read her reply regarding national curriculum impact on WA in The West newspaper.

It was a measured response that outlined the three years of implementation time being allowed, the need for an extended implementation (an extra year) in WA due to the variation between NSW, Vic syllabus and the current WA OBE based curriculum. She also raised issues with year 7 primary vs yr 7 high school, student entry ages in preschool/kindergarten, the lack of specialist teachers in primary and the need for training above normal 'PD' allocations requiring the sourcing of an additional budget for WA.

WA, with a smaller population and different educational requirements, will always have varied results and requirements to the eastern states. Competing with the Eastern seaboard is not statistically possible under the current measuring system.

It was encouraging to see an education minister that at least understood some of the issues faced by national curriculum and someone willing to make an attempt to avoid a head long rush into it. The challenge will be to address some of these issues and prevent these issues being swept under the table along with the children of Western Australia.

Absolute value

I spent a fair bit of time thinking about absolute value problems in the form |x+a| - |x-b| = c. Many students were struggling with visualising what these functions actually look like. What was happening when we try and solve them?

For example:

|x+5| - |x - 2| = 6

How could I display this equation graphically to give students an understanding of the underlying algebra to solve it?

I tried graphing y = |x+5| - |x - 2| and y=6 to find the intersection but was unsatisfied with the result as y = |x+5| - |x - 2| is not something easily tied to the absolute value concept or 'v' shaped absolute value graphs.

I was eventually satisfied with graphing y= |x+5| and y = |x-2| and then examining each part of the graph until I found a section of the graph that was 6 units apart.

For those wondering how to put it into a graphics calculator while exploring the concept

Go Menu -> Graph & Tab

Edit -> Clear All -> ok

at "Y1:" ->Softkeyboard->mth tab->select 'x'->type "x+5)" (it will change from abs(x+5) to |x+5|)

at "Y2:"->select 'x'->type "x-2)"

ensure that the boxes next to "Y1" and "Y2" are ticked

Now the temptation is to assume the answer is the intersection point.

but if we look at the equation |x+5| - |x - 2| = 6, it is asking "for what value of x is the value of |x+5| (the dotted line) subtract the value of |x-2| (the solid line) equal to 6". When is the gap between the two functions +6.

We can ignore values of x<= -5 as y=|x+5| is below y=|x-2| and the subtraction will only give negative values (we are looking for a gap of +6 which is a positive value).

We can also ignore values up to the intersection point as this also will only result in negative values.

The next place I looked is at x>=2 as the gap is constant and positive after this point (both functions have the same gradient).

at x=2, |x+5| is equal to 7 and |x-2| is equal to 0. |2+5| - |2-2| = 7. We can ignore values where x>=2 as the answer is not +6.

In fact the only possible solution has to lie between the intersection point (x~-1.5) and 2 and is probably closer to 2.

For y=|x+5| all values are positive between -1.5 < x < 2

For y=|x-2| all values are negative between -1.5 < x < 2

To ensure positive values for x-2 in the range -1.5< x < 2 we need to take the negative of (x-2) when solving the equation |x+5| - |x - 2| = 6.

x+5 - (-(x-2)) = 6
2x+3 = 6
x=1.5

Check answer:

|x+5| - |x - 2| = 6
Let x=1.5
|1.5+5| - |1.5-2| = 6
LHS =| 6.5| -| -.5|

= 6.5 - 0.5
= 6.0
= RHS

Viola.

It would also be interesting to explore |x+a| + |x-b| = c,  |x+a| = |x-b| and -|x+a| = c in a similar way.

Here is a link to other CAS calculator posts.

Keeping up and reducing doubt.

It's a hard ask keeping up sometimes. It's my first year teaching year 12 Calculus, Probability and Statistics. Your focus slips from your good year 12 kids, to the lower classes where your interest lies and all of us sudden you are faced with a crisis of confidence.

Are you good enough? Have you done enough? In a subject like maths, students need you to always be on the ball, or their confidence also suffers.

It's times like that you have to go back to basics. Do each exercise. Talk to a staff member that you trust. Get your confidence back. Maybe put some things aside for awhile.

I remember when I found out that I was on a pathway to take these classes, I wondered if I was up to the challenge, if my mathematics had risen back to that level. I argued that these kids needed the best teacher available. I still believe this should happen, but will fall in line with department wishes.

Maybe I have to rekindle some doubt in myself and do some real work to improve. It's a shame, because I'm really making some ground putting effort into my teaching capability with the lower classes. My masters research is teaching me a lot about myself and my teaching style - a teaching style that is much harder to work on with a good bunch of kids that will respond to a simple instruction.

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Limited trial of National Curriculum.

Again, on a rushed timetable, the government pushes out information that a trial is to be done this year (5 weeks into term). Teachers will be given programmes (at the 11th hour) and the kids will have to deal with a poorly understood curriculum by teachers through no fault of the teachers themselves.

Successful project management is not rushed and has an understanding of as many factors as possible. Head-in-the-sand management is a recipe for disaster. Success becomes a factor of luck rather than good management. Children's futures should not be a part of a recipe for the re-election of the Labor party at the next election. It should be a bipartisan agreement implemented with long term planning and proven methods.

Regardless of any issues with the trial, the national curriculum will be rolled out next year. What is of bigger concern is that senior school curriculum will be rolled out later this year. I really hope senior school curriculum will be given more consideration than the lower school programme as the consequences for university entrance and TAFE integration are far more severe than upper school teachers coping with students who have suffered a partial implementation with gaps in learning.

Theory and practical application are two completely different beasts. To quote that 900 people have been involved in the theoretical design of the curriculum (with little coalface application) is not going to impress. Are these the same 900 people that designed and implemented OBE in WA? I really hope not.

The media release is found here.

Politicians... What a zoo!

I wrote to the zoo to send me a politician and they sent me a

.. Julia Gillard

.. but she is an idiot, I sent her back.


so they sent me a

.. Kevin Rudd

.. but he kept apologising in Chinese, when I finally caught him in Australia, I sent him back.


so they sent me a

.. Wayne Swan

.. but he spent the postage and gifted my savings to inflation, I sent him back.


so they sent me a

.. Brendon Abbott

.. but he was too busy kissing babies, I sent him back.


so they sent me a

.. Penny Wong

.. but who cares about climate change anymore? I sent her back.


so they sent me a

.. Peter Garrett

.. but he set my house on fire and speared the whales, I sent him back.


so they sent me a

.. Wilson Tuckey

.. I tried to send him back, but he was returned to sender.


so the zoo thought really hard and sent me a banana.

.. it fit right in at parliament house.

Julia Gillard and the national curriculum

Yes, schools can change their whole curriculum focus, understand, resource and ensure that assessment is in place for a draft curriculum that will change five times before the end of the 2010. We obviously have learnt very little from the OBE implementation fiasco.

Dear, oh dear. I hope no-one buys her "it'll be all right mate" routine.

Here comes another round of teacher bashing when poor direction from government is the issue. I heard Kevin Rudd accept personal responsibility for the performance of his government. I hope he is willing to take the legal liability for rushing something through that affects so many.

Julia Gillard is again doing something in a political timeframe not appropriate to schools. Again, the children of Australia will suffer the consequences.

Where is the testing and ensuring that it is applicable in states where it is to be implemented? The issues will only become apparent under application, it needs a limited application/trial before rollout. Cynically, this won't be done due to the poor polling results of the Labor party and political necessity rather than good practice.

The sheer arrogance of the rush approach is astounding.

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

3896
4321
------

and tried to subtract..

3896
4321
------
?575

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.

4321
3896
------
*425

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!

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.

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.

Eg

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.

Eg.

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.

yay!

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.

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.

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.

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.

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.

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.

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.

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.

First Day of school tomorrow

All fired up.. lessons planned.. preparation done.. Let's go!

Rubrics

I sat through another round of someone extolling the benefits of rubrics/analytic marking keys/explicit marking keys. There was no doubt a lot of effort went into constructing them, but the usual issues were there amongst the generic template.

Assessment is supposed to be Fair, Explicit, Comprehensive, Educative, Valid

Rubrics vary between too vague to be of benefit (fails the explicit test - makes marking easy but cannot be easily connected to assignment without 'dejargoning') or so explicit that most students can get an A if they put some effort in (fails the comprehensive/valid test - can a student do it without the rubric??).

The position put forward was that marking should be quick. I'm afraid I can't see how this is true. The only comments students read, are ones in red pen. If you circle where students lie in a marking key, they normally just skip to where the final grade is. Students will read every line written in red pen and ask for clarification of it.

This is where investigations today fall down a little. Typically we guide students through the investigation (so that it becomes more like self teaching than investigating) - but the other side of the coin is that students can't be expected to rediscover what mathematicians took millenia on their own. We need to find a middleground.

We have collected a wide range of investigations, categorised and standardised them. I must admit I have struggled with selecting, generating, marking and guiding students with regard to investigations and marking keys. It needs more work and thought.

And the 2009 IOTY winner is...

Julia Gillard, Federal minister for education.

Julia is awarded the Idiot Of The Year 2009 for her potential to damage confidence in public schooling, her flip flop on league tables and her continued faith in the face of all evidence and public opinion that NAPLAN information should be made public.

Today her media release finally acknowledged that it was likely that the myschool website and NAPLAN data would be used for league tables.

"I’m not a newspaper editor but I’m a reader of our media and a watcher of our media and what I know is that in the past, media outlets have sometimes decided to do a big story on an individual school and call it a bad school. That’s happened already; it’s happened five years ago, ten years ago, 15 years ago, 20 years ago. If an editor makes decisions to do that, that’s nothing to do with the My School website. " - Julia Gillard

Sorry Julia, if you provide the ammunition for producing misleading information, it is your fault. Media is renowned for producing sensationalist data and you are well aware of it - the potential for damaging schools rebuilding their reputations after poor government curriculum policy over many years far outweighs perceived benefits. State schools will close, pressure on parents to put students in independent schools will rise (for no academic benefit putting further stress on financially struggling families) and it will be the fault of your policy when the majority of people are saying this was a stupid idea.

"This has been worked on by experts and experts have looked at the Australian Bureau of Statistics information that’s relevant to that school and relevant to educational achievement. And through looking at that information, they’ve created an index and it’s the first time we’ve had an index than enables us to compare schools right around the country. " - Julia Gillard

A school's level of disadvantage is notorious to define (see the issues that occurred using bureau statistics for the ghetto allowances in WA). More-so the ability of a school to produce true generational change takes generations to measure. Where gentrification in an area is occurring, four years of lag will exist between when the census occurs and when SEI is measured. Furthermore it will take 13+ years for these students to start entering the system (although it is more likely the struggling school will be closed and sold) and it's likely the new students won't have a nearby public school to go to anyway. With data at least four years old, principals have changed, teachers moved on, the school is different to the index. This statement is one big furphy.

"Now we’ve got to be clear about this: being from a poor household doesn’t mean that you are somehow destined to go badly at school. Kids from the most disadvantaged circumstances can get great educational results but we do need to give them an extra helping hand to get there and that’s why this index is so valuable." - Julia Gillard

Ok, myschool statistics could identify some schools that need more help for disadvantaged students but why does this information need to be public (unless the idea is to use student results for political gain)? Why stigmatise students, teachers and schools? I have no argument that NAPLAN results could be used to help identify struggling schools, but why compromise the results by discouraging good students from entering the school whilst positive change is occurring and extra funding is available. Julia, you are creating a self defeating system.

Yet, has anyone considered that low SES students test poorly anyway and their actual understanding is usually higher than their scores. This is due to the averaged nature of NAPLAN scores. Many things effect the scores. Students "throw" the test as they do not value the results, have performance anxiety generally passed on by poor performing parents. In general, a lower weighting of importance is put on tests by schools due to a whole range of factors. Furthermore, test results are skewed by teachers wasting whole terms coaching students on how to answer NAPLAN questions. Topics are introduced out of sequence (to the detriment of students) to maximise NAPLAN results. The NAPLAN scores (if they are meant to identify low performing schools and help low performing students) are a poor measure of their actual performance!

Even when schools become earmarked for change, in many cases it simply will not occur no matter how much money is thrown at the school (and subsequent stress placed on teachers to perform miracles) due to dietary issues, birth defects, difficult circumstance, limited positive adult (especially male) role models, limited parental support, refugee cohorts, additional needs students, behavioural issues, alcohol and drug abuse, gang involvement, criminal behaviour, difficulties in identifying, attracting and retaining good teachers/administration, financial issues at home, generational endemic poor attendance, domestic violence and other such issues that cannot be changed by a school alone. A bigger picture approach must be taken in many cases.

Issues with current league tables (measuring student scores rather than career success, issued by The West newspaper in WA) is further proof that the myschool website is built on a flawed premise. A school can have near 100% of their aspirant university students achieve their dream (being the first in their family history to attend university) yet still be last on their league tables due to the cutoffs assigned to presenting scores (see current issues with 75+ TER recording in WA).

If the Liberal party said they would dump league tables, I would urge teachers to vote for them and I'm guessing so would many others. It would be a foolish Labor party that ignores this sentiment. WA was lost due to the teacher vote. Teaching voter backlash is not something to be ignored.

When public opinion becomes a tool for government intervention (and not the other way around) it indicates a government unable to control. Releasing NAPLAN information to stir public support for government intervention rather than just identifying issues and solving them, speaks of a government more interested in polls than doing good in the community.

Julia, if you fail to see the issues with this idea or are only going through with it for political reasons - you have to be an idiot.

You are a worthy winner of the IOTY for 2009. There was no competition.


Media release here.

Julia taking another potshot at teachers here (have a giggle at the stretched neck photo of Julia).

Myschool website here (but don't say I didn't warn you!)

What mathematics do students need before high school?

I was at my master's summer school unit and caught up with my high school mathematics teacher. We started talking about what was needed before starting high school in mathematics.

I knew the year 7 teachers from her feeder schools (albeit a few years ago I had done my practicums at both schools). The year 7 teachers were proactive teachers, and had started topics like volume and Pythagoras' theorem. In my naievity, I had thought this a good thing.

She quickly set me straight and said that these were easy things to teach if the basics were in place. Without the basics they were quickly forgotten.

So I started thinking to myself, what were the basics?

1. Did they have one-to-one number correspondence (could the children identify 1 with one of something, 2 as two of something so on and so forth)?
2. Could the children read the time?
3. Did children understand their four operations?
4. Did they know their tables?
5. Could they add and subtract one and two digits without a calculator?
6. Could they recognise basic units of measure?
7. Could they manage small amounts of money?
8. Did they understand place value?
9. Were students aware of order of operations?
10. Can they recognise basic shapes?
11. Can they identify uses of maths in their environment?

By the time I arrived at 8, I quickly understood her meaning. If students were able to do pythagoras, but were unable to recognise 4 lots of something was a multiplication sum then time was probably better spent sorting out operations.

These topics are easily tested by parents and school instruction can be complemented by a number of readily available books and websites.

BST - Bloody Stupid Transparency

There's a new acronym in town. We have the GST, the tax we had to have. Now we have the BST. The Bloody Stupid Transparency we had to have.

I noticed an article in the West that TISC had released statistics describing schools percentages of students that achieved their first preferences for university. The West (in typical media fashion) has then released this information with a bit of spin and gloss.

In this age of the BST, the inference is that if students are getting their first preference then schools are obviously superior in their counselling processes.

It is of course a load of complete nonsense. Students have an expectation of a TER score based on their school scores, outside of the top 5% their actual TER can vary substantially due to scaling (how their class does in comparison to the state) and a host of performance issues. Having a range of scores is a sensible solution to a variable situation.

If high percentages are getting their first preferences (outside of the top 5% where students typically are in courses where none more difficult exist), it actually indicates poor student counselling. Students should be aiming to reach for the sky, not just set their goals on the safe options.

The main issue analysing 1st preference data is that this form of transparency in a competitive market encourages schools to dumb down student expectations to promote the school "1st preference" success and subsequent positive publicity (or prevent negative publicity).

Again the statistics are being presented in a primitive fashion with no real causal effect established indicating whether students are better prepared or should have actually aimed higher.

Smacking is good for children under 6

Here's a non-PC article quoting research that smacking (not abuse of) young children is beneficial. 2600 children were sampled and it showed that smacked children under 6 were more likely to perform well at school, perform volunteer work and aspire to university.

To all those from the smacking generation, finally some research that shows smacking might be ok after all.

Being a dad with an eleven month old, I think I still have some serious reservations :-)

Advice for kids in a new year

Ok,

So it's a new year.. new teachers.. new situations.

What can a student do to fare well in a new year.

1. Come with a great attitude.

I don't mean suck up. Mainly I mean come ready to work. A new teacher has no expectations of you, even if you have had them in a previous year or have known another sibling. If you are willing to work, you will be noticed. If a teacher sees that you are working hard, and need some extra help, they will always be more willing if they can see if you have tried.

2. Follow instructions and come prepared.

This seems obvious, but a faster way is not always the better way in mathematics. If you can lay your work out properly from an early age, it's a skill you don't have to learn in year 11. Neatness is something people attribute to braininess (don't ask me why) - but don't let this be an excuse to be slow! ..and don't waste time asking for materials that could be spent working!

3. Sit with people you can work with

If you get to seat yourself, then stay with people you can work with. It can be hard, and sometimes you will need to have a quiet word with the teacher to move you elsewhere. Good students are the people that can help you when you are stuck and the teacher is with someone else that needs help. Remember to help others as what goes around...

4. The teacher is on your side unless..

Teachers are not in it for the money. They get a buzz out of seeing you learn. If you prevent others from learning you are killing their buzz. Expect to get squashed.

5. Be on time and prepared

Being on time is more than being at class when the bell goes. Homework arrives on time. Assignments arrive on time. If you know multiple assignments are due at the same time, spend some time in the library and miss that of so important TV show or MSN.

6. Do your best

Don't loaf. Ability will only take you so far, at some point you need to learn a good work ethic. It's easy to coast. Find ways to stay motivated. Race yourself. Try and get more correct answers next time. See how far you can get without asking the teacher a question. Use notes and worked examples given by the teacher. Make your next test the best result ever.

7. Failure is the path to success.

If you fail, don't give up, see it as learning what not to do. When you fail you learn about what you do not know. This is important. Identify what it is you need to learn and when you get an opportunity find out how to do it. Always, always, always do your corrections after assessment.

8. Read ahead.

Read the text book before school starts. Understand as much as you can. Know what you need to ask the teacher about. If you already know the basic stuff, it will give you time to learn it in more depth during class and with the help of the teacher.

9. Leave the playground in the playground.

Get used to putting your mind in work mode when you enter a classroom. Walking into a classroom high fiving and calling out to friends as you walk in (normally late) is a sure way to get on the wrong side of a class and teacher.

That's it!

Misleading league tables

Today is a sad day. A whole year's effort that can be summed up by a parent saying our results based on league tabled published in the West are in the bottom four in the state. This will discourage parents from entering kids in our school, in a year where getting kids is tough due to the half cohort.

Yet, if I go on last years experience, each of the kids listed as sitting four or more TEE subjects, that wanted university entry, will be in university next year or will have deferred for the following year.

For some they will go through the front door and it is a fantastic achievement whether it is with a 60 TER or 99.5 TER. Students reaching their goals is where our focus should be. They have made it with little parental support, limited schooling, some with ESL backgrounds and with a host of social issues.

For some, they are the first students to graduate year 12 in their families. For others, just the opportunity to try for university is an achievement for this generation - a goal which may still eventuate through a uni entrance programme or other 'back door' programme.

At least the independent schools stood up and said the publishing of these tables was wrong.. It's a pity the department and our politicians still don't accept that these tables give a false representation of what is happening post school.

Misleading and a poor use of statistics.

Here is our state Minister's recent comment on the topic. It credits teachers with using a range of assessment to assist in teaching a child and recognises that change is required but does not recognise the damage caused by releasing data that ignores this information!

Headlines rather than journalism

The poor journalism at Channel 7 continues with a sensationalist report aimed at placing doubt on teacher quality by drawing conclusions from statements that were not causal.

The headline stated that teacher quality was the main reason for state school improvement, whereas Neil Hunt (the principal of Churchlands SHS) stated that teacher improvement programmes were a major factor. A poor quality teacher cannot improve, teacher quality has little to do with the quality of improvement programmes.

Sharon ONeil called for schools to closely examine student statistics. This also is not a statement about teacher quality. Underlying this statement is the fact that lower student input in year 7/8 means that lower student output in year 12 is also likely. Where state schools competed outside of the big five with competitive entry (Perth Mod, Churchlands, Rossmoyne, Shenton, Willeton) then there is something very good going on in those schools and they should get a pat on the back (Belridge, Duncraig etc.).

Should we fire a new teacher because they are gaining experience? Should only teachers with experience teach at higher levels? Is a C result for a class of disaffected kids worse than an A result in a talented and motivated class in a green leafy? How do we measure quality and their results? Teacher quality is not a quantifiable measure of a school.

Furthermore, I suppose the media thinks that saying it's the best achievement in years is help but it is disingenuous if you then immediately show that state schools are performing worse than private and independent schools - they have re-inforced the gap especially if connections to catholic and SES status are not also drawn. Sensationalist, with little purpose and damaging to the sector. A report completely lacking journalistic integrity.

If the media continues to bash state schools then we can't expect to close the gap to the private sector. We ask a lot of low SES kids, when they compete with kids with strong educational backgrounds. To compete effectively we need to attract more middle class kids that have clear examples of the benefits of an education.

I understand that some level of criticism and improvement must be publicised for parents to again get confidence in the public system, but we have to be careful in its implementation and remember that the core of the issues faced are as a result of poor government management, planning and implementation over a long period of time (especially during the OBE implementation). To scapegoat teachers as requiring "quality" improvement (inferring that teachers in general lack quality without stating whom, what or how it will be fixed), damages the integrity of the system and does not attempt to address the underlying issues causing the fall in standards.

For state schools to improve they need to attract the full range of students, not just those that can't afford private education. If the current trend continues, most state schools will become part of a safety net, ending in continued inequity for low SES families.

For the profession to increase in status and output, we need to acknowledge the good work done, manage improvement where necessary and ensure applicants have the capability and training to do a good job. I'll leave it to the experts to manage how these changes can be brought into effect.

Combinations & Permutations on the CAS Classpad330

The factorial(!) button is found in the soft keyboard under the abc tab (hit the up arrow next to 'z' and the '1' turns into a '!' (like with a computer keyboard). It's probably worth looking for (or making) an eActivity to speed it up a little.

Going through the first two 3C exercises in Saddler, the easiest way I've found to use the calculator is to open the softkeyboard, press cat tab, scroll to N (using the alphabet at the base of the softkeyboard), highlight nCr, press INPUT and seperate the n & r values with a comma from the hard keyboard.

(Update 1/2/2009): One of my students found another way via softkeyboard->mth tab-> calc->nCr which is a lot simpler and nPr is also there!

When you need to use multiple functions just rehit the INPUT button with nCr still highlighted. Completed the whole of 3C Ex 1A & B with a combination of no calculator and this function.

viola!

I don't have my calculator books here, so this will have to do until I get back to school.

Here's a link to an index of other CAS calculator posts.

Expectations of low SES students

Low expectation is something that can be easily reinforced. It can be environmental (like praising effort instead of achievement), it can be by omission (such as not making information public that would promote academic behaviour), it can be through antisocial behaviour (such as allowing bullying of academic kids) or peer associated pressures (such as girls not wanting to appear smart).

The challenge for the community, schools, teachers and parents is to prevent these negative re-enforcers.

I ask parents of friends how their students are doing and they have no idea whether they are good enough to attempt university. I get comments like - "they're getting level 'x' whatever that means - the comments from teachers are always very positive!". Parents can help motivate students without accurate information about their student. Our PC reports are doing them a disservice.

I asked lower school students how many of our students make it to university each year. The predominant response was zero to four students. The actual number is between 20 and thirty or nearly 2/5 of the cohort that stays until year 12.

The majority of students, at year 8/9, actually think that university is unobtainable. The scarier fact was in a middle school environment middle school teachers rarely teach upper school classes and can't recognise the students that need to be informed, coached and supported into university pathways.

When I asked yr 10/11 students, "What classroom scores were needed to enter university?", they answered 80+. This is not only an unrealistic target for many students but also plainly wrong, it is far lower for the majority of courses.

When I sat with teachers and we looked at standardised testing scores and sought to identify potential yr 9 students for university pathways, no-one (including me) had any idea what we could call a benchmark score before considering student attitude, school results and work ethic to start the process of identifying university bound students. We will figure it out more accurately over a number of years (if tests are kept standard) because we are interested but what of the teachers that are classroom cohort focused instead. They will rediscover similar information by the end of the year.

I start my masters this week (all going well) and the broad topic I have chosen to investigate is: "What tools are available to identify university bound students, what programmes are available to guide students into university and how effective are they for low socio-economic students?"

If you have any ideas, I would love to hear about them and include them in my research. I look forward to hearing from you!

New Games in 2010

I've been playing a few new games this year that have been great fun.

Twilight Struggle is a great two player game that focuses on the events of the cold war. The US and the USSR fight for influence throughout the world in order to gain supremacy. Each game takes about two hours, so I'm not sure about implementation in the classroom, but we're addicted and have been playing for a couple of hours each night. Twilight Struggle is published every couple of years by GMT games and was about $60 pre-ordered over the web.

Three quick games that are great for the classroom are from Fantasy Flight games Silver Line series - Citadels, Condotierre and Colossal Arena. Citadels is a great game for up to 5 (after five it becomes a bit slow), easy to learn and has a great element of backstab and competition. Condotierre is a game about medieval/crusader Italy, where players fight for control of emerging city states. It has a really dinky board but has some real meat in the gameplay that is accessable to students. Colossal Arena is the surprise of the three as the betting mechanic and card flow develops as the game is played. All three of these games can be taught in minutes and promote consideration of strategy for future games. They have a real magnetic quality. Each can be picked up for under $40 online.

Anyone that has played 500 and #$%hole knows that trick and bluff based paired card games can be engaging, strategic and addictive. Tichu (supposedly played by 600 million chinese players every day) is no exception. It has a weird flow and is seemingly random until new strategies emerge the more it is played. I played it with 500 players that were very critical, but I would love to play this more with people that have a more open mind to exploring this game. A tichu deck can be created from a normal deck (and marking up four special cards mahjong, phoenix, dog and dragon). The rules can be found online.

I had a quick game of Sorry Sliders ($15 at Toys r Us) which is a great little dexterity game. Similar to the ending in ludo, players try to reach the end of their target and other players try to eliminate them. It's a great game for the end of a small class or for kids 7-12 on a rainy day.

I found a great new online store - http://www.unhalfbricking.com/. A weird name but he does have a lot of unusual and hard to get games. Ordering was simple and delivery was fast. I was impressed.