Benefits of 4tφ

As you will well know from your own experience, teachers of Scholarship Calculus have an extremely difficult job. 
For starters, even though in most cases you are just normal mathematics teachers and have limited exposure to and knowledge of Scholarship-style problems and ways to answer them, you are somehow expected to instil this knowledge in your students. The exam, while intended to be able to be sat by students of NCEA Level 3 using only the knowledge they have learned in NCEA, far surpasses the scope of Level 3 work and, unfortunately, also that of the help many teachers are able to give their students in preparation. Furthermore, any specific Scholarship teaching is typically done outside of the classroom, so any time you as teachers devote to it is additional to that required by your standard teaching responsibilities. Because of this, it is often the case that you are only really able to start small-scale tutorials in the third or fourth school term, using only past exam questions as a basis of learning – there are almost no other resources out there, and teachers don’t get enough free time to find what little is available. This is too little too late, and students are liable to go into the exam unprepared for what they will come up against, resulting in the brightest mathematics students feeling like they have failed.

I want to make life easier for teachers and improve the learning of students so that they are able to succeed.

The 4tφ package does this by providing a structured 2-year supplementary course intended to take just 1-2 hours a week of commitment from both students and teachers. The content is fully explained by notes and worked examples, there are exercises for students to do to cement their learning, and (best of all) there are complete worked answers available in a style which students can aim to model in their exams, so that “I don’t know” is never a problem.

The benefit to teachers of using the text is that you have something structured to rely on, so don’t have to feel limited by just using past exam questions and don’t have to take extended amounts of time to prepare your own resources. Though past problems provide good preparation for students, they are only really accessible once they have covered the majority of the year’s work, so it is left to teachers to deal with any necessary extension of NCEA material on your own in the first three terms of the year. For this purpose, there needs to be something to teach, not just a goal in the form of a problem to be answered. Because of the lack of teaching resources available at Scholarship level, you as teachers are left to fend for yourselves, resulting in a stressful environment which could be damaging to your teaching abilities. With the 4tφ package, however, the hard work of building and structuring resources has already been done, leaving you free to focus on the most important part – your teaching.

As a flow-on from this, students will benefit from less stressed teachers who have more time to focus on their teaching, as it will be easier for difficult aspects to be explained fully and more time will be made available to cement learning. In addition, they will also benefit from extension to a degree that they would probably not have received otherwise, since the package is intended to be used in a two-year programme instead of all the Scholarship material being crammed into just one term. Such extension is more likely to result in their understanding mathematics than simply answering questions, and is also more likely to excite a passion for mathematics within them which result in greater success and will carry through to tertiary education. This is particularly relevant as Scholarship exams to date have included topics beyond the scope of Level Three, with some students underperforming not necessarily because they didn’t have the required mathematical skills, but moreso because they just had not met a particular technique or application before and therefore didn’t understand how to apply their skills. The extra exposure and understanding supplied by a structured programme of extension ranging over two years will give students the benefit of confidence in understanding what to do in the event of being faced with such problems. This confidence will result in them feeling mathematically successful, independent of any exams. Furthermore, the introduction to topics traditionally covered in the first year of tertiary-level mathematics will be helpful for those particularly high-flying students who choose to pursue direct entry into second-year courses at university. 

There are also benefits to the New Zealand mathematics community in general which follow on from this – better-prepared teachers will enable bright students to be extended and feel successful at high-school level, which will make them more likely to pursue, enjoy and connect with mathematics at a tertiary level and beyond. The students who sit the Scholarship Calculus exam are the best mathematicians of their age in the country, and it is precisely those students who should be encouraged to join the wider mathematical community through tertiary education. The 4tφ package will enable such encouragement to be presented more easily, with potential impacts which extend beyond the years of secondary school and may even be important on a national or international scale.