This began as part of a course called the Middle Leadership Development Project. For my project I chose to focus on aligning and improving the relationship between physics and maths at our school. My school had two physics teachers. In the following year the other one would move onto her next school while I remained. For the first time it was down to me to decide who would progress to IB Physics and who would be denied.

Not entirely true. The teachers never had the final say. That was someone in senior management. This person would take our advice but balance them against the wishes of the students, pressure from parents, class sizes and the IB Diploma requirements.

This left a tension within the science department. The cohort needed to be split between biology and physics. Chemistry was available but timetabling and staff restrictions meant that everyone has to take one of these two.

My solution to this process was a maths aptitude test (available here). From my perspective it was a success. I will talk more about the issues and how I set about addressing them before delving into why I think it worked.

## The least worst forced option

From this point onward, when I say physics or biology, or indeed any subject I will be referring to the courses rather than the discipline for simplicity’s sake. I will also note that my school does IGCSE and IB. I will also ignore their IGCSE performance in science. A good grade is a great indicator for continued study of a particular subject and for that reason we will ignore it. This is about other considerations and complications in deciding an IB course for study.

It is normal for all subjects to struggle with eligibility and potential. With science there is the question of mathematical aptitude to consider. While biology may not be as intertwined as physics, the students still need to be able to carry out 7 statistical tests. It is not a refuge from the spectre of maths.

The reasons students reach the age of 16 lacking confidence in their mathematical ability are abundant. Until my school manages to secure a grades for** all** students above the global average there will always be this question of “Where should those who achieved low grades go?” They have to make a choice between physics or biology, higher or standard level. It would be a disservice to encourage them onto courses counter to their affinities. I also cannot be dispassionate about the needs of the biology teachers who will take up the dissuaded.

## Imperfect judgements

Physics as designed by the IB is a curious thing. It does not assume continued parallel mathematical study by the students. There is no calculus. There are no matrices. If you take the Relativity option then we need the Lorentz transformations. The only three new skills I have to teach my students are radians, logs and surds. Radians is only taught because I teach it slightly earlier than it is taught in maths. Logs because a second round is helpful. Surds just pop up from time to time and I remember verifying that there was one specific selection of IGCSE options and IB options that could mean a student would not encounter it. Log graphs has come up precisely once and is taught in the final revision scramble.

The majority of the skills needed are the skills encountered during the IGCSE. We still set a requirement for all physics student to achieve a minimum of B in IGCSE Maths. There are a few major flaws in this system. Firstly with intense studying, tutoring and a dose of luck a student may perform very well and achieve that B grade. This threshold shifts but is generally requires between 120 and 130 out of a total of 200 marks. Those marks may not be in the skills necessary for physics. So without knowing the make up of the questions that lead to that B grade I know very little.

Also a single instance of achievement under intense focus with a great deal of permissible oversights does not translate into continuous performance.

I often tell the students who inquire about the maths requirements for the IB course. “There isn’t that much new maths. But the Maths you do know, you have to do that almost perfectly. And they don’t design the course with time for me to give extra maths lessons.” Then I also push them go talk to the Biology teachers about the statistical tests so that they have a full picture.

Another requirement we set is that they take at minimum the *Mathematics: analysis and approaches SL* course. Either that or take the Higher level version of either maths course. This is purely to do with trends. The other course *“Mathematics: Applications and Interpretations SL”* is the least difficult maths course offered by the IB. It is uncommon for a student to chooses HL physics alongside the easiest maths option, but I have already taught several to varying degrees of success.

Our requirements are not strict however. We place them to help steer students based on experience. Going against our advice requires some meetings with the student and Parents. All a school should do is present the honest picture of the course and attempt to guide the parent and child to take and honest look at themselves. They have commitments to their other five subjects (Three equivalent to first year university courses), civic duty, a local curriculum and their own personal development. Time is a limited resource. They can do physics. The maths is not hard and I can teach them in my spare time, but they need committed to putting the time in. The aforementioned aptitude test has that commitment designed into it.

Ultimately a person who prefers physics to biology should be in physics rather than biology. Just perhaps not at the Higher Level.

## A survey

All good ideas should start from research. Admittedly this was not rigorous, but I knew that my experience drew heavily from biases, speculation and half-remembered conversations so some measure of diligence was warranted. These students were surveyed in May or June towards the end of their first year on the IB physics course. 14 HL students and 15 SL.

So while the responses were mostly encouraging I need to make the number of unprepared students clear. 4/29, 6/29, 5/29, 6/29 4/29 and 6/29. So between 14% to 21% have been under served by us teachers. I consider these numbers damning.

The survey also asked them how to improve support. Responses had three basic themes. More *practice in contex*t, more *practice of pure maths* and most of all *coordination with the maths department*.

## The skills

The survey also questioned the students about their familiarity with the required maths skills in physics. I took some guidance from page 22 of the syllabus.

In retrospect I should have set the survey to require all to respond as there is a clear gap with line graphs. The trend is weak but it can be seen that most student recall that they learned a skill at IGCSE and that skills learned at IB have a lower level of confidence.

Following from this I sat down to complete the May 2019 Time Zone 1 Higher level Exam in full and documented the proportion of marks awarded to each skills needed to answer the questions.

65% of the marks had a mathematical component to them. The top 3 skills needed were building expressions, transpositions and ratios. Post-IGCSE topic were not as critical the most basic parts of algebra.

## Designing an assessment

It was obvious that when designing the aptitude test that it would be smart to apportion the marks to match the distribution I discovered. I removed anything trivial or post-IGCSE since they would not provide me or the students with any useful information.

More subtle would be defining and delivering the goals of the assessment and assessment procedure. I wanted to:

- communicate the necessary topics to students
- gauge competence in pure maths skills
- observe creativity with said maths skills in unfamiliar contexts
- avoid the physics context
- justify my decisions to management
- aid student self-reflection and self-selection
- give students the opportunity to demonstrate that they will persevere in their effort into making up a shortfall

To provide that feeling non-familiarity I chose to draw from question from a different examination board. I settled on a 40 mark paper designed to take 50 minutes. A few volunteers from the class surveyed as well as a few maths teachers took the test to verify that the skills in the papers had been covered in the IGCSE, were representative of the course from a student perspective but were also different enough from the typical presentation so that we could observe understanding rather than algorithmic application.

Before giving in to the prospective physicists I also showed it to the school director who was a maths specialist. He suggested being flexible on the time limit that I add the following message to the front page of the test. I also verbally stressed the goals to the students several times.

Other guidance that was not printed but was heavily communicated was that this simply informs our recommendation and was not a hard pass/fail, acceptance/rejection test. There was also another opportunity to do the test after the summer holidays and change our recommendation for those who still wished to do physics.

These all came together for the key purpose of this whole project.

*Anyone can take the course.* *To succeed you will need a base level of maths skills. If you are unsure we will give you a chance to see the skills you need. If we are unsure based on past performance we will give you the chance to show us that you will work on missing maths skills. *

## The resulting cohort

I will only compare Figure 1 and 2 as the rest appears to be broadly the same. It should also be noted that this survey was done remotely during the pandemic and did not have as high a compliance rate and thus the data will probably skew higher as the respondent are more likely to draw from the more studious members.

I will once again make the number of unprepared students clear. 3/16, 4/16, 0/16, 4/16 2/16 and 3/16. So between 0% to 25%. Still far to high. I draw hope from the 3rd question “I am now ready for the level of maths in Physics at the end of the year.” Despite similar number feeling a lack of support they are all more confidence in their own ability.

So no strong numerical evidence. I will not be able to use the IB results either as the first cohort was assessed algorithmically. My impression however is the current cohort is far more adept at maths. I have had far fewer tangents to recap mathematical principal and have been able to focus on the science. Student no longer treat every formula as a new entity that require individual exploration and are instead part of the tool kit. This has freed me up to focus on the quirks of such formulae and interaction with other topics rather than demonstrating simple use. Perhaps this increased base level expectation has left them feeling equally challenged but at more advanced level. Also this higher level of adeptness has definitely helped in the pandemic and remote teaching.

## The third cohort.

The third cohort made their choices during a period of lockdown. Since it was unfeasible to run the exam its use was far more targeting. Anyone who had personal qualms, or who drew reservation from staff were asked to complete it. This seems to have caused a similar level of self selection as a few changed their mind during the process. Experientially the teaching is far closer to Cohort 2 than Cohort 1. I will ask them their opinion once again the end of their first year of physic teaching. The data will of course be compromised due to remote teaching.

## A note on mindsets

Some may ask “Why dissuade students?” This whole process seems counter to the goals of growth mindset, continual improvement, addressing failure and constant encouragement. Why am I being exclusionary with my course? My duty should be to support these students with their endeavours rather than write them off.

The simple answer of extra support sessions and teacher time is not a simple answer. Time spent on any addressing shortcoming is come at the expense of time spent on other skills. Many students also need support with literacy. This is a massive focus in our multilingual school. There are missing IT skills as many have not used a spreadsheet in any depth. There are also other complementary competencies that other subject rely on that they also need to work on. These are not skills that the course designers planned into the timings. I am naming these above the normal holistic load of meta-cognition, time management, research, note taking, critical thinking and stress management.

Students can always improve. They need to be ready to improve in so many ways. Everything is only little extra until it becomes too much. My subject should not have an out-sized mental burden. Honestly, openness, guidance and support all come together to make sure the students have the chance to succeed in all of their courses.