Thursday, October 30, 2008

Measuring Teacher Performance

I stumbled upon this article from 1999 stating clearly issues raised by teachers regarding student performance in primary and secondary schools. It is just as relevant today as it was then. This shows a number of areas of difficulty measuring teacher performance. I have highlighted some of the areas of student performance impacted by teachers. Many carry through to high school from primary.

I grouped the results into behavioural (primarily learned behaviours brought to the classroom), genetics, environmental (factors with limited control by the teacher), structural (constraints imposed on a classroom) and societal factors to isolate factors solely controlled by teachers within the classroom. Pedagogy(teaching methods), content knowledge are the two major factors teachers contributing to teaching students.

  • students who are not doing well tend to give up, refuse to try, and this makes the problem worse - this behaviour gets worse as they get older and they start to compare their work with those of other students (behavioural)
  • high achieving students can taunt low achievers and this makes the problems worse
    students with psychological problems (eg, trauma experienced in the home) have trouble learning (behavioural)
  • sometimes teachers can’t work out why students can’t learn - it can be the problem of the teacher who hasn’t worked out how to engage students (getting inside the walnut) (pedagogy)
  • parents refuse to have their children placed in classes for students who have intellectual disabilities (structural)
  • students lack academic ability (genetics/environmental)
  • teachers don’t explain concepts clearly (pedagogy/content knowledge)
  • parents indulge their children so they won’t pay attention in class (societal)
  • parents don’t take an interest in children’s school work (societal)
  • students are transient and so miss a lot of school (societal)
  • it’s more difficult these days to get students placed in classes for students with intellectual disabilities there are children with attention deficit disorder who have difficulty concentrating in class (structural)


  • students haven’t been well taught in earlier years at school (historical)
  • students don’t value school work (behavioural/societal)
  • parents don’t value their children’s school work (societal)
  • students lack ability (genetics/environmental)
  • the system allows students to progress through grades without passing subjects (structural)
  • maturational level - students mature at different rates - they may not be able to grasp concepts now but they could in a couple of years’ time (genetic/environmental)
  • poor teaching (pedagogy/content knowledge)
  • teachers blame the students for poor performance when it’s the teachers’ fault (pedagogy)
  • students have psychological problems because of unhappy home lives (environmental)
  • teachers don’t have a good mathematics background (pedagogy/content knowledge/structural)
  • students’ poor behaviour in class means they don’t pay attention to the work - discipline problems in schools are on the rise - it’s part of wider societal problems (behavioural/structural/societal)
  • students lack self discipline - they’re not prepared to work (behavioural)

It is clear to see that student performance is a poor measure of teaching ability as many other factors exist to influence this criteria. To blame teachers for poor performance of students based purely on teacher pedagogy (teaching methods) or lack of knowledge of content ignores a host of other possible reasons.

Creating an 'unAustralian' education system

An article in the Australian discusses the challenge of improving schooling in Australia. Another article with opinion and without supporting facts to back them up. What has happened to our media? Why can they not develop a position and then report with supporting or refuting evidence!

The main points were:
  1. Development of a national curriculum (supported).
  2. Minimising or even abandoning plans for national testing programs (supported).
  3. Funding private and public schools on the same basis (?).
  4. Auditing the intellectual capital -- that is, teacher quality -- in all schools (?).
  5. Greater autonomy for schools and principals (?).
  6. Creating a federation of schools, in line with the British model (?).
  7. Refurbishing or replacing most school buildings constructed in the 20th century (supported).
  8. Increasing the business sector's involvement in education, including private funding of schools through foundations and trusts (supported with reservations).
Part three: By doing this we are accepting that we will have a two+ tier society. Those that can afford private schooling and those that can't. Public schools cannot compete with schools that have equal funding with private schools and are supplemented through school fees. Those students that cannot pay fees in private schools will be disadvantaged (students in private schools schools already have the advantage of rapid exit of undesirable students, this is their USP). Public schooling should be given more of the public purse than private schools. Our disadvantaged kids need our support. How is further disadvantaging them going to prepare them to compete equally in the workforce - it just creates an underclass. The funding ethos put forward is grossly capitalist and American. It is decidedly unAustralian.

Part four: Sure, let's audit teachers, how and who shall do it? What makes a good teacher? What happens if a teacher fails the audit? How do we re-educate them? Who plans and pays for the implementation? Who is to blame for poorly performing students - the teacher, past teachers? It's nonsense.

Part five: Where is the research that greater autonomy for schools leads to better student outcomes? The idea is counter intuitive. Surely re-inventing administration currently centralised cannot be cheaper, as flexible to change or as easily monitored than decentralised at a school level. All decentralisation does is decentralise blame for a system that isn't working very efficiently. Today is a time of centralisation as information technology closes the efficiency gains once found through decentralisation. Analysis and change coordinated at one location is far more efficient than directing responsibility to islands of learning.

Part six: I have no idea yet what this idea is of federated schools in the UK but I haven't heard the UK system as a model system for eons. I must investigate this further.

Passion, student behaviour and being fiery

One of the issues in classes today that stems from the home is that students have trouble accepting that a teacher has authority in the classroom. At home they argue with parents in a very democratic fashion. Students believe (wholeheartedly) that they have a right of reply to any misconception that they face.

I must admit this gets me fired up especially in my 'A' class. Any student willing to take responsibility for the care, nurture, learning needs and welfare of thirty students, get a degree as a minimum requirement for teaching can have my job if they can prove they would do it better. Until they do this, if I ask a student to be quiet or stand in the hall, see the team leader, copy off the board or attempt a question they may believe they can't do, I expect them to attempt to follow my expectation.

They will fail sometimes, and this is ok. This does not give them a right to argue and waste teaching time. It should prompt some introspection as to why they didn't understand how to do it and hopefully seek assistance from friends, pay more attention when solutions are put on the board or seek assistance at an opportune moment during class or after class. Maybe it would be a good idea to get them to journal why they have had such trouble understanding a concept and identify ways they could better understand a topic. Bringing the correct materials to class (eg. CAS calculators, pens, paper, texts), paying attention during instruction, fostering friendships with those that do understand, reading their notes (and keeping them in a place they can be used) - attending school regularly (my favourite) and catching up after sickness may be a good start.

These students do not have a right to insist on help at a time that suits them. To use a claim for help to justify poor or avoidant behaviour is not acceptable. I would love to be able to provide just-in-time intervention to every student all of the time. In a class of thirty it just is not possible. The belief that getting instant help is a right is infuriating and I don't know where it is being fostered. Maybe I should enquire into how many are only children (and thus do not have to compete for attention) and also examine my own methods of helping during practice time (maybe I am a contributer to the problem!).

When instructed on where their actions are errant I expect nothing less than silence especially with those talking during teaching time - this is done in the hall outside my room. Try my patience and half the school hears. It's fun watching them open their mouth and then hear them "but you won't let me talk to explain". If you talk during my teaching time and I have to stop the only thing I wish to hear is I'm sorry and then see an end to that behavior. Woebetide the student that interupts me again. My other students have the right to learn and it must be protected.

There must be a line between teacher expectation and student behaviour. There must be a consequence if this is crossed. A lecture, for many of my kids is enough to get the message. If they get the message, no further consequence. If it continues -they start the path to BMIS.

The argumentative nature of students at correct times needs to be fostered (we don't want meek students) - but it must be cultivated with manners and knowledge that there is a time and place to discuss the finer points of an issue. I always offer time after class for extra assistance and am happy to discuss any issues or problems from a class at this time. Funnily enough rarely is this offer taken up by these students during lunch or their own time.

Tuesday, October 28, 2008

Creating inspirational students

Students aren't born inspirational. They're born rather podgy blobs that whinge a lot... Some never change...

This week I spent a bit of time reminding my year 10's that they are inspirational. Lower school students look to them for cues on how to behave, on determining what is important and setting the tone within the school. If they want a happy school - be happy. If they want a school with a million rules - do stupid things. If they want a school based on success of students, show the lower years that our school can perform at a high level.

For this I think it is important that we create opportunities for them to be successful and protect those that foster these activities. It might be taking an interest in a student that is doing an afterschool ESL class, or not getting grumpy with the dance teacher that is taking students out of class for a recital, being supportive of the physical education staff and their events, supporting SOSE excursions by providing extra supervisor bodies or helping out with relief classes.

I think it also means looking for information that might help inspire kids. I recently found two books by the actress that played Winnie on the Wonder Years (Kevin's girlfriend for those of you ancient enough to remember). One is called 'Math doesn't suck' and the other is 'Kiss my Math'. The books themselves may be just the thing to get a student going and get them to believe that you care about how they think. The maths is a bit dodgy in places ('Highest common factor' becomes 'greatest crush factor') but it has a go at making maths pop culture ready and that's a good thing.

Another bit of success I've had is to let them into my life a little. Last class we created tally tables on the best baby name that we had selected. Next time I'll have a silent poll as it was a case of many just following the leader. Maybe this is a discussion in itself. We've also used my history to investigate stocks, examine salary ranges and evaluate priorities on what is important in life.

Another opportunity has been with my guitar. I am worse than hopeless, but the kids see that I am still learning well beyond school.

Lastly whenever a leadership event occurs I draw their attention to it and suggest that they pay heed to things done well or poorly as they will soon be in that position. If they can learn good leadership habits now, they will be in better stead going forward.

Saturday, October 25, 2008

Year 12 leaving ceremony

It was interesting to watch the leaving ceremony for the year 12's. It gives you a lot to think about for times where you are helping set up such an event and things that kids really need to do to make these events successful.

Firstly all kids need to feel included in the ceremony - not just the popular kids. Photo montages need to include everyone, memorable events need to cover the full spectrum of students academic, sporting, VET; dominant personalities need to celebrate and value the achievements of all, not just the popular few.

Perhaps we need to consider how we could create photo libraries for all years, mini yearbooks documenting events as they occur as part of the various handshaking ceremonies throughout the year.

There was a clear lack of thanks from the current year group. There was a brief thanks to all our teachers and then a celebration of all the events where misbehaviour had occurred and had perhaps caused embarrassment to students, the school or disrupted classes. This left a sour taste in the mouths of the senior teachers as a lot of effort had gone into getting this cohort over the line. Many have decided to give the graduation ceremony and dinner a miss. Maybe this is an indication that we need to focus on those that appreciate our efforts and that the efforts at 'inclusive' education have gone too far. Maybe students beliefs are right and we are not doing enough! I don't know but somehow I doubt that our efforts are best spent on students that perform at a very low level (even with all the help in the world) and take away time from students that could really use extra help. There needs to be further authority given to schools to move students that will not respond to learning opportunities to free up time for those ready. Perhaps it is just my utilitarian tendencies showing through.

When all graduate there is a clear diminishing of value placed on secondary graduation. With graduation rates of 80-100% and all students needing to continue school to year 12, graduation for many has limited worth. Many leave with little more knowledge than they had at year 10. It has diminished the achievements of those attempting TEE courses, there is little recognition of the difference in effort required. I feel for those that attempt TEE courses and get fails on their certificates due to external circumstance instead of taking the easy option and doing VET or alternate education courses.

Another clear transformation is the knowledge that these kids will probably communicate with their cohort for some time unlike any cohort from my time. The advent of Facebook and mySpace will mean that they can have instant communication with their cohort and an instant network to resolve issues and celebrate success. I don't know if this is a good thing as coming of age was about new times and new people, the removal of negative reinforcers and a new beginning.

The lack of concern of students for their TEE exams and the haphazard attitude to study borne through portfolio entry and low TEE scores is definitely to their detriment. The baptism of fire is now more dip in a warm pool. These students have managed to leave school without any anxiety of security and self worth - how will I support myself, what occupation can I do, how will I be worthy of my life partner, how will I be a valid contributor to society? Resilience is something borne of experience and these students lack any real concept of the difficulty of gaining true independence.

Casio Classpad 330, Finding the mean and missing values

I posed the following question to my year 10's in order to continue our learning of the new calculator. It is an example of solving a problem where the mean is known but a value in the sample is not.

"Q: A class had 5 students. Student results in the last test was {50,56,64,72,81}. Isabella joined the class and the new mean became 68. Did Isabella score higher than the old mean and what was her score?"
H: If the mean of {50,56,64,72,81} is less than 68 then Isabella has scored higher as a higher score by Isabella will raise the mean. Since we know the new mean (68) we can work out Isabella's score by working backwards.
Set up a working pane with a main application and a list editor. Title a column 'list1'. Add the 5 student results to the list editor.

Click in the main application and type mean(list1) using the soft keyboard. Hit the blue exe button. The answer is 64.6 .
A: The old mean 64.6 is less than 68 therefore Isabella has scored higher.

To find Isabella's score click in the list editor and tap the next empty cell in list1. Press the x button. Click in the main application pane on the line that says mean(list1). Press the blue exe button.

This will return a sum to work out the mean of the list for values of and value of x i.e. (x+323)/6.

As we know the new mean alter the first line to read mean(list1)=68. Highlight the solution sum and tap Edit in the menu bar and then Copy. Paste the sum on the next line in the main application pane. Highlight the sum, tap Interactive on the menu bar, then tap Advanced on the sub menu and then tap solve. Tap ok at the base of the dialog box. The answer is x=85.
A: Isabella's test score was 85.

Click here for other CAS calculator articles

Revisiting fractions

My 10D class has revisited fractions over the last week. For many fractions is like another language others have managed it in the past but have forgotten basic principles. The sequence I have used leading up to percentages of amounts is as follows

Drawing and identifying numerators and denominators
First exercise was identifying a variety of numerical fractions from pictorial form and then constructing pictorial fractions from numerical forms. We spent a lot of time looking at mixed numerals and converting between mixed numerals and improper fractions using pictorial means.
eg. for 3 2/3: draw 3 lots of 3 boxes with all boxes coloured and 1 lot of 3 boxes with two boxes coloured. When students counted the coloured boxes they had 11/3.

Investigating fractions of amounts
It seemed strange to do this here, but funnily enough it worked well as it established relevancy of the topic for many students. We started with a problem 3/4 of $24 is to be given to John and 1/4 to Mary.
I explained it as:
3/4 of 24 is: $6 per part (24/4)
I drew a box and split it into 4 equal parts (drawing attention to the denominator)
I put $6 in each box.
I coloured in three sections that represented John's portion
then counted $6 x 3 parts = $18 for John

I then repeated the same steps for Mary
1/4 of 24 is: $6 per part (24/4) then $6 x 1 part = $6 for Mary

We checked our answer to ensure all the money had been accounted for ($18+$6=$24). Students then completed a number of examples.

Investigating multiples and factors & Equivalent fractions
Next day we looked at multiples and factors. I explained this through examples, showing them examples of multiples and factors, then getting them to find the first five multiples for 2,3,4,7 and then the first five multiples for 2,3,5,7 over 100. After this they found factors of 10, 15, 24 and 42. We investigated patterns in factors (none greater than 1/2 the original valure other than itself, how it helped knowing your tables, factor pairs, 2 is always a factor for even numbers)

Students were then given a fraction wall and identified equivalent fractions in preparation for adding and subtracting fractions. The idea was put forward that fractions rely on parts to be equal otherwise the idea of equivalency would not be able to be used.

Adding and subtracting fractions
In the third lesson we looked at the problem of 1/3 + 1/2 using paper strips. The aim was to establish why equal parts is essential to an understanding of fractions. We used our fraction wall to look for equivalent fractions that allow us to add equal parts. After a few pictorial examples I started to show students how to use multiples and factors to assist in finding common denominators.

Next lesson we look at multiplying fractions...

Thursday, October 23, 2008

Recharging students for success in mathematics

Being in a low socio-economic school sometimes is disheartening. The students don't believe that they are able to achieve academically. This is reinforced by parents, teachers and the school in subtle ways throughout the year.

A parent complains that the student is only doing lower maths and does not need a $175 calculator. The timetable allows many non-TEE subject to run, but only a few TEE subject selections are available. Portfolio entry is seen as a primary pathway to university rather than a backdoor entry for extreme cases. Lower school programmes lack the rigour of programmes in more academic schools. A single student or groups of students can disrupt classrooms for an entire year, but little coordinated effort can be made to limit the damage being caused. The idea of secondary graduation is diminished by the idea that 'anyone' can graduate. Cohorts of students are labelled challenging and good students lose opportunities as classes are aimed to manage the lower students and keep them engaged to detriment of academic achievement by top students.

Charging academic students for success is a mentality that must be driven - it doesn't just happen. Kids need to be told that they have the ability to succeed, shown possible outcomes, be given opportunity to try/fail/succeed and be mentored as they go along. Setting clear standards sets the groundwork for success.

Things that I consider serious issues in my A class:
  • Not being quiet and ready to start work within 2 minutes of entering the room
  • Being late for class and not entering the room quietly
  • Complaining, whining and whinging before attempting work
  • Not paying attention when instruction is given
  • Relying on friends or personal attention of the teacher for instruction rather than some level of personal investigation
  • Not attempting homework
  • Failing a test or assignment ( lower than 1 standard deviation from mean)
  • Not seeking assistance when required
Students that continuously fall into these issues risk demotion to BCD classes. For some, demotion is the right option, for others the motivation to be moved down is enough for them to alter negative behaviours. For a relative few, it identifies students with ability but are unlikely to succeed at TEE level. This year, boys in particular have been a real issue and a focus for the course next year (I think this is the most significant issue at our school).

Things that I do to promote positive attitudes towards mathematics and address issues:
  • Look for opportunities to congratulate students on achievement
  • Attempt to talk to each student each class
  • Allow friendship groups to remain together only when learning is occurring
  • Ensure that new topics include new material
  • Promote the A class as being a privilege and a responsibility
  • Reinforce that attitude is as important as aptitude
  • Change the difficulty level regularly to allow for opportunities for success/failure and stretching of the mind.
  • Question their own beliefs of their ability and remind them of progress made
  • Use personal experiences to enhance class material
  • Focus the basis of enjoyment in mathematics in achievement rather than entertainment by the teacher (though the converse may be more important in lower classes)
  • Encourage students to self monitor behaviour and provide peer feedback
  • Create opportunities for students to see the different rapport with yr 11/12 TEE students than with yr 10 students