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.