Changes in 2022 and beyond in Upper School Mathematics

Five emerging themes in 2022 are of some concern in Mathematics and the severity will depend on the implementation by SCSA.  These are not new to 2022 but may be a surprise if you are not familiar with them.

- The requirement to embed design requirements (general capabilities) in classroom programmes

- The reduction in assesments per course to 8-10 assessments per year

- The requirement to follow the Mathematical Teaching Process, Statistical investigations or Theoretical investigations in ATAR

- Grading in Essential and ATAR courses

- Intended purpose of Applications and Methods

They are listed in order of prediction of impact from lowest to highest

General Capabilities  

<rant>General capabilities assist with the design aspects of a course.  A well designed syllabus has the general capabilities written in such that they flow naturally through the programmes of teachers.  If we are having a discussion (again) that general capabilities are not being implemented by teachers and displayed by students then the design of the course is the problem, not the application by teachers </rant over>.

Likely Impact: Minimal as teachers will ignore instructions about general capabilities as they can't be measured and have little/no positive impact on the course results.

Reduction in assessments per course to 8-10 in 2023

Statistically creating fewer data points, will reduce the reliability of results in mathematics.  This has the potential to reduce the correlation of class and external exam marks from the enviable position of Mathematics compared to other courses to among the same lines.  

Given the requirement of two of each type required

Year 11 (Four terms)

Investigation: 2 items

Response: 4-6 items

Exam: 2 items

Year 12 (Three terms)

Investigation: 2 items

Response: 4 items

Exam: 2 items

This is 1-2 response task per term.

The is not significantly different to current programmes albeit I prefer to have an additional investigation as the marks are more variable than response tasks and skew the distribution.

Suggestions made by SCSA to not assess dot points (which has always been done to some degree) or include assessment of content in investigations (I'm not even sure how assessment of content can work within an investigation as that is not the aim of an investigation) were put forward as good alternatives to response tasks.

Teachers are already talking about ways around the new requirements, specifically to combine recording of assesssments (one assessment with parts held two weeks apart).

The rationale for this by SCSA was to decrease the anxiety of students (using Physics as the example of 17 assessments) but I am not sure that creating more high stakes testing (as weighting is much higher with fewer assessments, likely to increase anxiety) will achieve this especially as encouragement was made to increase ungraded formative assessment through EPW style investigative learning practices.

The stated goal of reducing dot points in Unit 1 of Methods 11 is more likely to reduce student anxiety.

Likely impact: Reduction in reliability of Mathematical correlation between class and exam marks to level of other courses.  Reduction in number of investigative tasks given.  Lower SD in class marks in during investigative tasks to minimise impact (likely based on work ethic rather than capability). 

Mathematical Teaching Process

The ongoing faddish discussion about embedded critical thinking through Mathematical thinking processes continues with the encroachment of MTP in ATAR courses since 2018.  Until now the definition was fairly wishy washy and could be worked around.

Investigations have now been informally categorised as Statistical investigations, Practical Applications and Theoretical investigations each following a similar process to the old Mathematics in Practice (MIPS) approach.  Whilst I am a big supporter of the MIPS approach in a MIPS type course, imposing the time requirements of this approach on a student and the subsequent reduction in mathematical application during an investigation that it imposes is detrimental to an ATAR course.

Likely Impact: The watering down of theoretical style investigations continues in Methods.

Grading changes

The statement made by SCSA presenters was that in ATAR and General courses, the difference in an A, B and C style question is not content related but is related purely on how the question is asked and the amount of scaffolding given.

This makes a mockery of the differential in Mathematical ability required to complete each course particularly evident in the difference between Applications and Methods.

The rationale given was that scaling would compensate for this - but it doesn't if the gap between courses increases beyond the 5% mean + 5% of course total scaling given - Methods students are penalised for doing harder work (rather than rewarded).  

Given an A, B or C in Methods is significantly harder to achieve (due to content continuing to be learned at a faster pace than Applications requiring a more difficult sequence of learning), it is hard to fathom how the way a question is asked and subsequently answered, fairly and adequately assesses the level of a student.  To reduce it to this does not replicate the alignment currently required by ATAR assessment via understanding displayed in the external exam and the assessment completed to achieve similar class marks.

Likely Impact: This will need to be rethought.  It is not a good idea and will not be replicable under exam conditions without a blowout in Methods marks.  Students in 50-57 Methods range (exam and class) in Year 11 are achieving 80% (65% after scaling) in Applications - and this is being told to students by course counsellors, reducing retention in Methods courses.

Rationale of Methods and Applications

Universities have knobbled interest in Specialist courses (there is little desire during mining slumps) by reducing pre-requisites outside of engineering (or even in engineering in some cases) and now are doing similar to Methods courses.  Students are discouraged from attempting ATAR Methods by counsellors as it is not required for their courses and complete the easier ATAR Applications instead.

Intended level of difficulty (increasing to left)

Foundations            Essentials                    Applications/Methods                   Specialist

In a discussion with SCSA staff post meeting it was stated (and themed throughout the presentation) that Applications and Methods are aimed to be delivered at the same level (and the grade related descriptors show this) but for different purposes (eg Applications for biological sciences/humanities students, Methods for Physical Sciences, Specialist for Engineering students).

If this is the case Methods and Applications require a significant re-write (and I don't believe this is the intent as this was stated in the presentation) as they do not meet this purpose.  Whether Methods needs to come to the level of Applications or the Applications course requires a complete rethink (this is my belief) is not clear.

Likely impact: This will need to be rethought.  Scaling will negatively impact students whilst this is poorly understood and implemented as per 2020.  Return to a hierarchy of Foundation -> Essentials -> Applications -> Methods -> Specialist in a future iteration of courses is likely.

Maths as a Mixed Martial art

 Entering a Year 7 classroom can be quite daunting for a student. I'm reading a few dystopian dramas and imagined a parallel universe with traditional classes mixed with mixed martial arts (MMA) bouts - a child entering a high school classroom for the first time.  It's all a bit dramatic but typical of my sense of humour.

“Jonny enters the Octagon being unable to count the sides, knowing that he is about to take a beating.  He hasn’t done the work required to be at this level.  Every previous outing he has failed. He seeks to distract his opponent by avoiding work set, breaking the rules and getting thrown out before his lack of competence can be identified and ridiculed.  Against all odds he attempts to answer the first question and it beats him to a pulp.”

“Mary enters the Octagon full of confidence.  She struts around the room announcing to everyone how this is too easy, she has the answer for every problem, being well prepared through her summer programme and her University educated parents.  She sees others in the room similarly confident – is she really the best in the room anymore? Her confidence falls.  Her first answer is wrong and now she is no longer the no.1 contender.”

“Harry walks into the Octagon.  He has worked hard but never found the success that warrants the work that he has put in.  Every step forward is difficult and he envies those that make it easy.  He timidly lifts his hand to give an answer.  He is ignored for a student that is actively seeking to give theirs.  His answer is correct but nobody knows.  He fails again.”

“Jill enters and listens to the instruction before the match.  She has heard it all before and could recite it before it is said.  She drifts off and starts thinking about fairies and unicorns.  The match starts, the test given and it is all over in a moment.  She has defeated each question and can return to the unicorns, with no idea of what she is capable of.”

“The teacher stands in the middle of the ring again as referee, coach, mentor, instructor.  Full of enthusiasm at the start, waning over the course of the match as the level of focus required and the challenges faced start to wear her down.  Will she do a good job or will the commentators attack her for not being all that is required?”

“The crowd stand on the edge of the ring, each encouraging their contender despite all odds.  Every parent is different – some on phones watching Netflix, others actively denouncing the referee despite all evidence, others taking notes of what needs to be done in the next match, others confused unable to comprehend what is happening.” 

In hindsight after writing this in the shoes of each participant, I realised learning should not be treated as a combat sport but often has elements of it.   I think I traumatised some of my staff when I read it to them.  We need to be mindful of what we are expecting of students,  making it into something that is wonderful to experience and not what is written above.

Long term improvement in Mathematics classes through an evidence based approach.

The health of a faculty can be measured in a number of ways:

- Student Behaviour

- Staff Morale

- Student Achievement / Student Progress

- Engagement

Measuring these is a complex and time consuming task.

- Student Behaviour (no. of behaviour reports)

- Staff and Community Perception (perception surveys, anecdotal evidence)

- Student Achievement / Student Progress (student class results, standardised testing)

- Engagement (student perception, participation rates, student success)

Each term, we focus on one of the measures and identify where focus areas are, possible measures for improvement and where success has been found.  Currently we are working on engagement in classrooms.  The chosen metric is success that a student is experiencing.

For instance, a class with an average of 50 under assessment conditions has half of the students in the class feeling unsuccessful as they have not been able to complete half of the assessment set.  Given that 50% is a common indicator of where minimum performance is expected, it is a fair indicator that engagement rates are poor and/or declining.

To drive improvement and increase engagement, a target of 85% of students achieving at least 50% on assessment tasks was set for the team.  Classes and teachers reaching this target were identified and then examined for practices that could be developed across the team.

Eyebrows were raised that such a high percentage was set as the target off a relatively low base.  Students entering high school experience success in Year 7 & 8, as work becomes more difficult and adolescence in Year 9, engagement can fall if not attended to and then lead to Senior school where students are placed in courses doing work predominantly covered in Years 7-10 and engagement rates rise.  Achievement of WACE is a siginificant motivator for staff and students given it is a highly monitored metric.

The forgotten middle is another area to target as often high achieving (and motivated) students and low ability students are given additional attention.  Students at a C level are often banded together and reinforce average performance with lower expectations (and subsequent class averages) experienced.  By encouraging higher levels of success (by increasing expectation and modifying grade cutoffs/assessment difficulty) it is hypothesized that higher overall achievement can be achieved (a concept at the heart of pathway grades in public schools).

Classes averages of 65, with SD of 12 indicate success levels commonly experienced in Methods and Specialist classes.  Averages of 60 with SD of 10 indicate levels similar to Applications classes.  Low SD indicate that assessments or instruction may be too narrow and skills based, pedagogy change may be required, wider may indicate that sections of the class require additional attention. Both cases may indicate that streaming processes need review.

Given 85% of students achieving passing grades is difficult to achieve, it requires attention at a student level, analysing individual student performance/underperformance, how it can be measured and how it can be improved. This can be done vs standardised testing or class averages longitudinally by teachers to identify students that require additional attention.

Where students experience legitimate, well explained succcess, senior school Mathematics participation, retention in courses and course achievement should improve.  The cycle of improvement is long, with 5-7 years to see significant change in results and culture of achievement.  Short term gains at a year or class level need to be celebrated to maintain the focus on improvement.

Nearly end of term

 It's nearly end of Term 3.  Time to thank everyone that has helped get this far.

Students that are looking forward to the holidays but are tired and ratty.

Teachers that are dragging their feet into work and are looking forward to the recharge that is coming.

Principals and admin that are dealing with all the complaints and grizzlies that are occurring.

Student services that are just trying to hold it all together.

It's not a nice time but if we are all understanding we can make the most of it.  Not everything that happens in the next few days will be rational - put decisions off, understand that people can be emotional and these next few days will be fairly painless.  

Get the last bit of content and marking done and we are on our way.

High School Board Games 2021 edition

 My most recent plastic box filled with boardgames in the high school classroom (in no order):

Anomia (party) - 4 players
For Sale (auction) - 6-8 players
Citadels (strategy) - 6 players
Hamsterrolle (dexterity) - 4 players
Five Minute Marvel (action) - 4 players
Dixit (party/deduction) - 6-8 players
Rhino Hero (dexterity) - 4 players
Turing Tumble (problem solving) - 1 player
Murder in Hong Kong (deduction) - 6 players
Santorini (strategy) - 4 players
SET (trick taking) - 6-8 players
Blockus (abstract) - 4 players

With the exception of Hamsterrolle (out of print) and Turing tumble (expensive), they are all usually readily available, most fairly cheaply.  I try and keep 6-8 games going concurrently thus it is important to have games of 6-8+ players for larger classes.

All can be taught or learned from the instructions, played and packed up in less than an hour.  I have a second box of different games I use for younger or less mature classes.

Previous success has been found with but have been replaced by the games above:

Ticket to Ride (trick taking)
Carcassonne (tiles)
Coup/Resistance/Avalon (strategy)
Spyfall (deduction)
Apples to Apples (party)
Kingdomino (tiles)
Splendor (strategy)
7 Wonders (strategy)
Love Letter (strategy)
Pitchcar (dexterity)
Lupus in Tabula/Werewolf (party)
Azul (tiles/strategy)
Dominion (deckbuilding)
Machi Koro (dice)

There are many games I enjoy more, but won't work within the hour constraint common in a school period.

Support vs intervention

Mainstream and extension classes are able to access the  year level curriculum as set by the Curriculum and Standards Authority (SCSA).  Some students for a range of reasons are unable to access this curriculum.  To assist them requires a level of differentiation either through ongoing additional support or intervention.

Reasons for requiring differentiation are extensive.  Gaps in conceptual understanding happen for many reasons - illness, teaching quality, taking holidays during term, sporting commitments, lack of ability, mental health, lack of cultural support, lack of confidence, peer conflict, family conflict.  

Whether a child requires ongoing additional support or intervention requires careful analysis to see if it is feasible to bridge the student back to the year level curriculum or if they will require ongoing additional support throughout schooling.

Support classes acknowledge that students are unlikely to access the year level curriculum and are typically assessed against what they can do through procedures such as SEN reporting.  This allows the  student to achieve success in the classroom and promotes engagement.  Parents need to be informed and on board with the decision if students are moved to supported environments.  It is not a decision that can be made lightly.

Intervention is different, is less frequently done during normal classroom time and typically done through tutoring and outside of the classroom.  When done in the classroom, interventions are measures introduced that assist students learn the behaviours and techniques known by mainstream students whilst preventing the student from falling further behind.  This means that students that are behind, have to work harder in class than students on syllabus, to catch up, something difficult to achieve with struggling students.  EALD students and highly motivated students are groups where catchup is possible, particularly where literacy is the inhibitor.

Streams encounter the issues solved through intervention frequently as behaviours required in higher streams need to be taught to students in lower streams to increase the chances of success prior to transition.  Where this is not done effectively, students are less likely to find success in classes that they are moved to and transition takes longer to achieve.  Typically intervention during transition is required in the form of encouragement, academic assistance and peer alignment to bridge students to the requirements of the new stream.

Working hours

The common perception is that teachers are overworked and underpaid.  There are times  when this is still  true.  The first three years as a graduate teacher is a slog.  Exam marking.  Designing investigations.  Managing 30 adolescents is hard.

.. but.. are teachers actually doing the quoted average 60 hours per week? Possible reasons for working these hours are lack of organisation, failure to collaborate, capacity building, reinventing the wheel, "recovery time", carrying unproductive staff, behaviour management and allocation of duties beyond the classroom. At face value it appears to be a misconception that isn't really happening and is based on historical/aged evidence.

Today we buy exams, work across schools to share assessments, mark formally less frequently, have programmes that describe what to teach, when to assess and what to assess that are trialled and tested over multiple years (the last full syllabus refresh was 2016ish), have IT to assist reusing of resources, have significant item banks to draw assessment from.  It is not clear what the majority of teachers are doing that takes increased working hours beyond the 37.5 normal working week.

Teachers have 20ish hours of contact time - that leaves an additional 40 hours (according to the average) of time doing DOTT tasks (of which traditionally 20 hours are unpaid, recompensed through additional holidays and flexible time outside of school hours).  The lack of auditing of what teachers are doing to ensure that time is being efficiently used talks to systemic management inefficency and appears to be an area that can be investigated for more productive use of public monies.

Yet the perception is that teachers are overworked and underpaid.  This perception shift needs to occur towards that we are in a priviledged situation and have a profession that is well staffed, conditioned, paid and catered to.  It is an unpopular postulate that we are not overworked/underpaid but one that needs to be considered and marketed.

Streaming - not as simple as moving a student.

I spend considerable time each term dealing with streaming issues.  The issues in each stream are significant and relate to the perceptions of how streams should work by stakeholders.  Some of the issues faced below occur each term and relate to students wishing to move streams.

1. Stream sniping: A disengaging student in the bottom third of a class seeks access to a lower stream to find success and claims demotivation/anxiety as primary reason for lack of success.  Where a large gap exists between streams, by allowing a high ability student into a lower ability class, it has the potential to demotivate current students finding success in the lower stream.  The preferred solution is to use engagement strategies to again make the student competitive in the higher stream.

2. Teacher pedagogy: A student is struggling to adapt to teaching methods of a teacher compared to a teacher in a previous year. This is most evident when moving from an inexperienced teacher that teaches a narrow directed course to a more experienced teacher that drives a conceptual course in middle secondary years.  Issues can also relate to over or under expectation of students, particularly late maturing boys or over emotional girls.   The preferred solution is recognise the issue and to develop the capacity for independent learning whilst providing additional support for students struggling in transition.

3. Performance Anxiety: A student who has experienced significant failure over time may be unable to function optimally under assessment conditions.  The preferred solution is to focus on what has been learned from each assessment and provide alternate assessment feedback to the student to indicate their learning.  

4. Restreaming resistance: Teachers can provide significant resistance to restreaming students as it can cause considerable disruption to stable environments to continue to have students introduced to a class.  Popular teachers able to cater with difficult students can often have classes swell in size if not observed carefully. Where restreaming has been successful, the temptation is to introduce more students that are also struggling to see if a similar result can be obtained.  The solution here in most cases is to resist re-streaming outside of defined streaming times during the year in all but extreme cases and limit transition issues to defined periods during the year to maximise learning for all students in each class.  

5. Parent nag: A student can nag their parent into continuous follow up with the school where no evidence exists that a student warrants moving.  This can often follow when a student is allowed to move for legitimate reasons and friends or students with lower results see it as a path to lower work expectations.  The solution for this is a clear understanding of the evidence base for the student (current ranking, standardised testing, prior grades) and re-presenting this nicely back to the parent.  Often this is as simple as replying with their ranking and indicating that others would be considered first.

6. Disengagement: Where students disengage on mass, as issue exists for the teacher to re-engage the class.   The solution requires examining pedagogy, engagement strategies, expectations, content and audience to identify strategies that may work.  This can require questioning teaching philosophies and compromising principles to get students to a position where learning recommences.

7. Isolation: This is a hard one.  Where a student is an isolate in a class and friendship groups are elsewhere, especially students with limited social skills, the requirement to move class can be legitimate.  The performance of a student in this situation where a student is on their own or where a class has turned on them (girls in particular can be mean in this situation), moving the student can be required.  This should be done in conjunction with student services to ensure that the teacher isn't then nagged by a wider range of students.

8. Transition: A student transitioning from a lower to a higher pathway needs time to transition as there will be considerable gaps in understanding, particularly closer to Year 10.  Students in this situation need constant care and encouragement to find success.  To promote success, students should be primed as to the expected behaviours of the new class and be preloaded with material prior to movement to support their success in the new class.

Streaming is not a simple solution to drive learning - it is a blunt instrument that is used at specific  times of the year to ability group students.  After it is done, time is needed to assess the requirements for the next streaming point - constant change will result in making it difficult to settle the streams and get them right - it is better to use differentiation between streaming points and make better streams than to use streams as diagnostic tools to provide students opportunities and disrupt the learning of many, constantly.  Those involved with streaming know this intuitively, as they have to deal constantly with the demands of restreaming otherwise.