Developing problem solving, reading and comprehension skills

My little challenging group of year 10's can be quite difficult to engage at times. A real issue with their maths is getting them to read the question effectively. Completely out of character, they have loved exercises in the book Logic Mysteries by Jane Molnar. Although it misleadingly states grade 3-5 on the cover, the year 10 students have loved the idea of reading these problems and solving them. When I first introduced it, I abandoned the rest of my normal planned lesson as I had not seen these students this enthused and engaged since the algebra topic.

Each mystery has a story and is solved by eradicating options that do not exist. A grid is set up to record the findings as they go through the mystery.

Many great mathematical concepts can be investigated. For instance complementary events become obvious, if she has a bird - all the options in the bird column that are boys can be eradicated. Inequalities can be investigated through clues like Jane's age is less than Mary's. Sets can be investigated through concepts like Mary's item fits in a school bag... and so on..

The main thing is that it requires the students to read the clues that are not necessarily in order, requiring reading and re-reading until they are all done.

A similar book Quizzles or More Quizzles by Wayne Williams has proven very successful with my upper class of year tens. These logic puzzles are multi dimensional and can be quite difficult so be warned!

For these to be successful I invited students to attempt them themselves for 5 minutes then modelled how to complete a problem. Then the following day I gave another problem at the start of class.

Either way, improving comprehension and reading ability is more and more important in mathematics (the temptation to enter into a diatribe as to why we need to teach English in maths here is near on irresistible - I shall try though!). These three books have been some of the more enjoyable methods of developing literacy skills thus far.

Ethical reasoning and streaming

Streaming is a difficult topic as it raises a number of questions regarding student capture, teacher judgement, assessment, and social justice.

Student capture for me is the most critical aspect of a classroom. Capturing a student's interest is a perpetual task, a combination of selling your subject and moving fast enough to keep their interest, yet slowly enough to allow them to fully grasp a subject. For some it can be done through connections with the teacher's personality, others through mathematics success, others through contribution to the class and others by connections with peers. If you can capture a student and get them to consistently have a positive attitude towards your subject then this is the first criteria met for a student to be placed into a difficult mathematics class. Streaming captured students into a class can greatly assist in improving possibility for success.

Teacher judgement is the next criteria. Does the student have the intellectual horsepower to complete the work? No amount of mathematics tutoring will assist a student that has extreme difficulty in reading a question, has too many holes in their skill base or takes too long to understand a new skill. A teacher needs to be able to identify that bit of extra practice that will move the student from being able to use a skill when directed, to be able to apply a skill undirected, to be able to identify the right skill from a range of available skills. It is possible that having to continuously assist a student on a continuous basis will destroy the flow of a class and disadvantage all within it especially in upper range classes.

Assessment is the next criteria. Assessment supports teacher judgement not the other way around. To stream purely on assessment is a recipe for disaster. This is especially true for students riding the end of their ability curve and coasting or loafing. These students, when they hit the wall and finally need to study can be hurt, confused and looking for those to blame for their lack of performance. If these students have not been properly coached before the 'big drop' in results, they can drop morale in a class at a rapid rate. Sometimes (especially in this case or the case where students are having external difficulties) it is best to ignore assessment and use the first two criteria to stream students.

Social justice is the final criteria and it has to be very carefully applied. An injudicious use of social justice to students when streaming will produce weak streams and deprecate the benefits of streaming. Just because a student has a legitimate reason for underperforming does not mean that in time a student will perform. Some say that streaming a class is a social justice issue in itself but watching students being unable to complete work that the rest of the class is working on and suffering self esteem issues or dumbing a class down to the lowest common denominator is not a solution to my mind.

The hardest part of establishing a stream is that it is not an exact science. A student performing at an optimum level with one teacher may not perform at all with another (this is especially true with boys). When creating a stream (especially in small class sizes) team dynamics play a large part - if you can create a team of peers and the teacher anything is possible. It's why I think traditionally the upper classes have been sought after - despite requiring the most skill to make work - they are the ones where there has been most flexibility in construction.

If that's culture.. you can have it.

Today I sat through Aida. Normally I can handle a little live Opera. I'm sorry, act three of Aida should be classified as grade A torture. Forty minutes to say the army is over there, get caught for treason and be sentenced to being buried alive. Three hours for the whole thing. It felt like forty years.

Want to get someone to talk? Need to know where that bomb has been hidden? Easy peasy.. Stick them in front of that dull as dishwater, repetitive, boring Verde nightmare. By the end of it they would be trying to poke their own eyes out and have their arm buried to the elbows in both ears.

I'd rather eat my own leg off than see it again.

Teacher turnover, teamwork and classes for 2009

The generation of school spirit comes from the school, focuses through teachers and into students. Harmony between teachers is a key component to the generation of that aura of success in a school.

Part of this is ensuring that there is balance between the needs of students and the needs of teachers. At this time of year tension arises between staff regarding the classes teachers would like to teach to further their careers and what is in the best interests of students. What is in the best interest of students is not always the best option. This takes some courage to say, as it has always been my position that students come first - but I think it is naive to think this is always the case.

In the real world, knowledge management issues of a revolving staff are well documented. When staff leave it does not only cost in terms of vetting and rehiring staff but also in the content knowledge loss, training investment and organisational understanding that is only gained through experience with customers.

Teaching is no different. Reduce turnover and the school benefits. An organisation that considers the needs of staff to progress successfully in their careers is an organisation that cares for its staff. To do this staff members needs to have their progress clearly illustrated and documented.

In mathematics, this means careful consideration of the new level 3 MAT and MAS courses. If there are a number of teachers vying for these classes it may be a number of years before teachers are given access to them. Being offered these classes (or knowing that a course has your name on it two years hence) can be a clear motivating factor in staying with the school and fully embracing PD opportunities until that time.

Conversely not being offered these courses or seeing the courses offered to those 'less worthy' can be a demotivational factor. Similarly being continuously asked to take lower school or low ability senior school classes can be disheartening for those seeking to enhance their skill base or for those seeking rapid promotion.

This ties very close to timetabling as many promotional opportunities rely on staff having access to senior school classes. Timetabling can often make or break the way a teacher sees their classes. Teaching out of area, sharing classes with other teachers, large class sizes, behaviourally 'difficult' classes can all be contributors to negative staff morale.

For a maths team to be successful they have to work as a team, support each other and find new and innovative solutions to student behavioural, content delivery and motivational issues. When class distribution for the following year is being considered, it means that careful thought has to be made as to what will satisfy the majority of the team, motivate members and ultimately prevent turnover.

Union president and lack of representative integrity

Anne Gisborne, president of the SSTUWA, is again out whoring the latest EBA attempt. Her actions are disgraceful.

A person in a representative capacity should not have made this comment in the media:

"Teachers union president Anne Gisborne admitted its members were running out of reasons to end the long-running pay dispute with the Government after the in-principle pay agreement."

Who is she to decide what her members should think? That is why members have a vote. She has been elected to represent members views even when member views are not her own (the last vote proved that members do not share her voice and thus she should keep it reserved until she again has member support). If she does cannot represent members and put her own views aside when it disagrees with members then she should step down.

It doesn't take blind Freddy to see that this union faces extinction if it continues to not heed the mandate given by its own State council and continue to act irresponsibly towards its members. The acts of the genuine few believers will not be enough to stem the tide of those leaving the union. Unfortunately the outcome will be no true public school system (other than a safety net), pay per use education and further movement to a multiple class society.

EBA4 Teacher pay rise and the new offer

Here is a link to the DET summary of EBA4

General opinion seems to be to accept the offer which is around 20% over three years (including the 6% we already have) with the next pay increase scheduled for October 09. No back pay to the last agreement. No 15 hrs unpaid overtime (eg. compulsory PD).

I can't say that I am excited - but will be glad when I can focus on teaching and all the fuss about wages and conditions stops.

I suppose I think back to the original questions posed at the start of the campaign.

• Has the new EBA created a profession with salary and conditions that will attract new teachers? No.
• Does the new EBA create conditions that will keep existing teachers within the system? No.
• Has the new EBA energised teachers within classrooms by making a statement that they are a valued part of the community? No.
• Should we fight further? No. In an economic downturn we should lick our wounds and stand aside.

To my mind the whole EBA process has been a lost opportunity, but now is not the time to resume this fight, it is a time to regroup, accept the small gains and prepare as one (DET, teachers, union, community, media, government) to create a feeling that education is the most critical element of our society.

When we better appreciate, evaluate and express publicly the positive contribution education makes to the community, then and only then will large increases to teaching budgets and salaries be justified.

Changing role of senior school

Senior school, years 10,11,12 have traditionally been the home of the most experienced teachers. These teachers generally have a vast amount of experience that is tapped from time to time by other teachers when need arises, either in behaviour management, content knowledge and generally are aware of how things work, what has been tried before and how to get things done. They have the experience to guide our students through to TEE, university entry or into VET pathways where necessary.

Now I say this as an observer (as I am neither experienced, nor the most capable in senior school). I have no ambitions for a HoD role and actively promote the idea that the HoD should teach the most capable class and other senior school teachers should do an apprenticeship of sorts with mid range classes to hone technique and pedagogy first. ... and I enjoy classroom teaching too much to get involved with the admin required to do the job properly.

Somewhere along the line I think we have lost track of what senior school teachers bring to the school. We have lost our heads of department in Mathematics/English/SoSE/Science to other areas such as literacy experts and careers guidance, L3 adminstrative roles. Responsibility now for the performance of learning areas has fallen to those incapable of measuring success or failure as they may not have ever taught the subject.

An issue that is currently rising is the lack of time to complete yr 12 COS in time for the TEE exams. With 1 term lost to the exam process, it leaves only 16 weeks per semester to complete the course. A possible way to increase the amount of teaching time for COS is to use term 4 year 10 to start the COS process and to start the year 12 course a term early.

Staffing of this is a real issue because if a unit starts in term four, few teachers are willing to take on an overloaded teaching schedule to make this happen. At this time of year the temptation arises to utilise senior school staff to fulfil this role as in many cases they will be teaching these students in the following years anyway.

I think we need to resist this happening especially for our HoD's. If our best and most capable are not given unallocated time to identify and remedy issues within learning areas it is only likely that over time things will get worse. The time that they put into improving staff ability and student output is clearly underestimated and is not being adequately nurtured. It would be good to see the complete opposite occur and HoD's given the time, recognition, responsibility and pay to make things happen.

Class size & the concept of 'Intervention Time'

I have heard many times that reduced class size is not a factor in learning or that it has minimal effect. Reduced class sizes is not the panacea to improved student learning but it is a handy tool when used correctly. To have an early intervention strategy there must be adequate class time for intervention.

If you have a high performing class of motivated students (with 3 levels between the top and bottom performing students), class sizes of around thirty in year ten can be managed. You would need to use a fair amount of skill to keep them motivated as after instruction and settling time (say 30 mins per class, two blocks of instruction, h/w and pack up) it would be hard to get to every student every class to identify issues, correct them (say 1 minute of intervention time per student per class) and maintain their learning inertia. You would more reliant on picking up issues during the homework, quiz, revision, assessment and corrections teaching cycle and complete more marking out of class.

In a mid performing class (with four levels between the top and bottom performing students) with around 20 students and 20 minutes of instruction and settling time you could get to each student twice (eg. average of 2 mins of intervention time per lesson). This seems feasible.

If you have a low performing student group in mathematics (with five levels between the top and bottom performing students), I would say that a class of 30 is lunacy (there are usually valid and disparate reasons why students are this far behind) and would send the best teachers barmy. Under normal circumstances in these types of classes there are not enough corners in the room to separate disruptive students. Each student in a class of that type requires constant attention to fully enjoy and appreciate mathematics. For example in my class, one student required behavioural attention once every 3 minutes (I timed him), each time requiring further attention to settle him. In a class of thirty that would make teaching nigh near impossible. For a class of this type it is preferable to have intervention time around 3-4 minutes per student, limiting class sizes to 13-16 students. This size of class would also promote more collaborative work, especially if other teachers are willing to assist during their DOTT or if a T/A is available.

In practice each student does not need (or get) an individual minute of your time and is normally able to do their work without individual intervention through the teacher identifying classwide issues and modifying instructional techniques (eg. more modelling), by using peer assistance, having effective instructional notes, by increasing participation in after class discussion or by bringing groups of students back to the board. What the intervention time model does is provide a benchmark of performance and can help identify structural issues vs teaching issues with classes that are clearly not working.

Using a model of this nature we could measure the learning capacity of student groups (by creating class sizes and monitoring teaching/intervention/disruption time) and the approximate class sizes required to teach them optimally. This has the potential to greatly assist in designing and justifying appropriate class sizes for our students.