Singstar Competition

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

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

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

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

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

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

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

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

Welfare and schooling

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

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

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

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

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

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

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

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

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

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

Hello out there!

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

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

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

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

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


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

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

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

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

I'll try and keep a more open mind.

Outstanding Teacher... Nonsense.

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

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

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

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

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

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

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

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

Quick and easy game to promote retention

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

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

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

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

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

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

Teaching Linear Equations and Functions

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

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

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

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

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

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

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

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

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

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

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

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

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

Developing deeper understanding

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

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

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

Problem: Find 50% of 50.

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

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

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


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

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


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

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


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

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




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

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

Review of material written

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

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

Writing lasting material

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

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

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

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

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

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

CAS calculators

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

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

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

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

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

Calm before the storm

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

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

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

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

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

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

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

A profession that consumes the individual

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

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

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

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

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

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

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

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

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

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

Good Day

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

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

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

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

A nice change from Friday.

Russ.

Making mistakes

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

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

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

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

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

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

Solving Venn diagrams where the intersection is unknown

n=40

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

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

n=40











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

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

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

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

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

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


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

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

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

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

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

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

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

Further exploring the properties of one

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

eg 0.123

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

therefore:

0.123 = 123/1000


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

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

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

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

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

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

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

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

Viola.

PD Days & Collegiality

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

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

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

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

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

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

Drawing the first derivative

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

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

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

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

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

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

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

<- It looked like this.

















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



















We then repeated the process for a quartic.

yay!

School Fights

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

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

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

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

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

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

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

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

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

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

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

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

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

Harry the goat

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

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

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

Catering for gifted students

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

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

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

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

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

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

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

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

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

Fractions

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

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

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

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

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

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

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

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

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

1/2 x 1 = 1/2

3/3 = 1

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

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

We also looked at cancelling and why it works..

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

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

2m/3m

as

2/3 x m/m

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

Therefore we can simplify to

2/3 x 1

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

Quite a fun little lesson.

Russ.

Moderation - advice for new players.

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

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

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

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

Have Fun.

Russ.

Bullying

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

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

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

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

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

NAPLAN preparation

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

Here's something to try with your child.

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

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

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

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

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

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

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

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

Fractions and year 10

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

PARENTS NOTE: TEACH YOUR CHILDREN TABLES.

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

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

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

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

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

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

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

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

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

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

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

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

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

Russ.

Attacking a subject

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

Students that are attacking a course:

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

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

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

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

Multiplying and dividing by powers of 10

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

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

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

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

25 ÷ 10 = ...

This time students considered the position of the decimal point:

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

We then looked at the case

2.5 x 10 =

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

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

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

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

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

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

National Curriculum confusion reigns

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

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

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

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

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

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

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

Being proud of those making a difference

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

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

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

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

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

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

Cheers to that!

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

Board games in high school

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

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

Simple Games:

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

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

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

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

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

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

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

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

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

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

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

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

More complex games (require multiple sessions):

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

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

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

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

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

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

Russ.

(Updated 24/4/2011)

Promotion to incompetence

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

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

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

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

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

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

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

Russ.

Summer School Day 4

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

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

Russ.

Summer school day 1

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

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

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

A productive day!

Summer School 2010/2011

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

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

I wish I could find our slides from last year!

IOTY 2010 Winner

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

... (drum roll please) ...



.... Julia Gillard .....




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

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

Congratulations Julia!

Funny Quote.

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

Visitors Poll

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

Russ.