Mathematics

At the beginning of Term 2, we welcomed Ms Cattanach back from maternity leave and it very quickly seemed like she’d never been away. It’s been great to see her continued enthusiasm in the classroom.

Also in Term 2, Mr Udy-Bothwell was finally able to enjoy the prestigious ten week sabbatical he was awarded in 2020. This fully-funded sabbatical reflected his outstanding contribution to mathematics education and his long service at Rangitoto College and previous schools. He was originally intending to spend the time attending a range of international mathematics education conferences, but Covid-19 meant that instead he spent his time in New Zealand participating in virtual conferences. Ms McDonald did an excellent job of looking after the leadership of Level 3 in his absence. Sadly, Mr Bissett left the department at the end of Term 2, ending his daily commute from over the Harbour Bridge. Mr Bissett was a valued member of the department’s leadership team and an excellent teacher who will be missed by his colleagues and students. He had been working for Rangitoto College for five years, his second period at Rangitoto, and he had contributed a great deal to the department and the wider school. Mr Bissett’s departure led to some leadership opportunities within the department, with Ms Walles, Ms Sanderson, and Ms Curtis all taking on acting leadership roles until the end of the year while we consider the leadership structure. All three are making significant contributions to the success of our department and ākonga.

Over the last 12 months, it has been really pleasing to see some of our senior students take an active role in fostering and developing the next generation of mathematical talent. In particular, students from the International Baccalaureate Creativity, Action, and Service group, and students from Year 12 and 13 Calculus have been training and supporting junior students every Tuesday lunchtime for challenges including the Otago Junior Maths, Canterbury Kiwi Maths, and the Australian Mathematics Competition. The students, led by Ethan Lu and Mason Liu, recently planned and hosted the Rangitoto Mathex selection rounds, Rangimathex. Over 20 teams and 100 students were pitted against each other in a fast-paced chain game with four top sides selected to represent the College in the upcoming Auckland Mathex Championships.

Another exciting development was the hosting of the North Auckland branch of the national Maths Olympiad workshops and the setting up of a junior group that attracts, not only Rangitoto students, but also students from Westlake Girls’ High and Kristin College. It is hoped that these developments will flourish in their new home in the school library after school on alternate Wednesdays.

With our best ever success in the Calculus Scholarships, 15 Scholarships including two Outstanding Scholars, the extension programme is growing with more and more opportunities and content being offered to all our extension students. It has been unfortunate that delays due to pandemic effects mean that any more results from this year’s efforts will have to wait until Panorama 2022 for publication.

Finally, next year will see even more developments with our new senior student team of Alex Kang, Jessica Wang, and Rihoko Suzuki taking over the leadership roles under the guidance of Mr Craik.

This year, our juniors have been exploring all strands of the New Zealand Curriculum. Our teachers this year have made a huge effort to develop students’ mathematical vocabulary and retrieval strength—two of the college’s teaching principles. We believe that a focus on mathematical language will give students confidence and allow them to access material needed to be successful in this subject area. Retrieval practice will equip students with the capability to recall learning and apply knowledge in a variety of contexts throughout their mathematical journey.

Year 9 students have been focusing on building a solid foundation in number, measurement, algebra, graphs, geometry and probability. As well as developing the key mathematical skills, students have been working on applying these in order to solve a range of unfamiliar problems.

Year 10 students have been focusing on solidifying and furthering their understanding of Mathematics in the areas started in Year 9. They have also had the opportunity to sit two NCEA internal assessments and gain up to seven Level 1 credits. The first assessment involved applying numeric reasoning to solve a problem and the second involved interpreting statistical bivariate data. After two years our junior students are well prepared for senior mathematics, having been exposed to both mathematical and statistical concepts.

Our Level 1 students were grateful that they were able to focus on their studies fully in 2021 without the worldwide disruptions prevalent in 2020. Teachers were able to plug the possible gaps in student knowledge to enable the cohort to stride forwards to enjoy and shine in their mathematics. The various teachers approached the teaching and learning of the content in a myriad of ways which helps and encourages the students to see their way through the problems before them.

One major adjustment in our approach to assessment was to allow our students to produce two of their statistical NCEA internal Achievement Standards digitally. This allowed the students to demonstrate their deeper understanding and knowledge of the content in a more accurate and analytical way. The results were, therefore, a better reflection of the talents of our students. As always, the teachers will be hoping that their students will have been able to display their true abilities in the NCEA November external examinations. With success on the challenges of the Level 1 content, we can welcome our students on the pathways to higher levels of success in their mathematics. These differing pathways are carefully selected for each individual student depending where their strengths lie. In an Olympic year, we are sure that many students will have achieved gold and many others will have attained “personal best” scores!

This year the Mathematics and Statistics Department introduced a new course at Level 2: 12MAT. This course was designed to allow students who were unlikely to succeed in our mainstream Statistics or Calculus courses to continue with Mathematics, by successfully completing a mixture of Level 2 standards. These students have had a positive year and many of them are planning to continue their Mathematics journey into Year 13 and beyond. Our Mathematics Applied students have also had a successful year, earning Level 2 unit standards in topics such as construction and finance.

Our Level 2 Statistics students have enjoyed a year filled with data collection and analysis. The course allows students to earn NCEA credits while exploring new statistical knowledge and skills which will provide them opportunities in their future studies and careers. We are excited that, next year, students will be able to take courses in both statistics and calculus at Level 2.

Our Calculus students at Year 12 have had a successful year focusing on their skills in algebra, computation, and problem-solving. The 12MCA and 12MTX courses provide the opportunity to earn NCEA credits, and the 12MTX course also builds a strong foundation of knowledge in preparation for the scholarship course at Year 13. We are happy that from next year, students will be able to broaden their knowledge further by taking one of these calculus courses in conjunction with a Level 2 statistics course.

Students taking this course were lucky enough to study both mathematical and statistical concepts during the year. While studying the maths standards, students learnt how to solve problems that required finding optimal solutions. During the statistics standards, they learnt how to construct a report that required them to further develop their literacy skills. Students that had the most success in this course had high attendance and displayed good time management skills.

Approximately half of all Year 13 students choose to study this very valuable course where they learned to select and analyse statistical data to make informed recommendations which they presented in written reports. They also designed and ran randomised statistical experiments to test causal hypotheses. For example, one group of students, inspired by the Economics Day, tested Year 9 and Year 13 students to discover whether an increase in the quality of packaging causes students to think that the product enclosed is of better quality; their results were conclusive for the experimental group tested and gave us all something to think about. Students ended the year by learning a rigorous approach to critiquing media reports to help them to make informed choices in life.

Students who gained entry into a Scholarship Statistics class further developed their logical thinking skills. Many attended the regular afterschool sessions which helped them to fully prepare for the rigour of the Scholarship examination.

Many of the students that take this course enter a career in engineering; others simply chose it for the intellectual stimulation it provides. Students begin to build more complicated models of the real world that can be used to make informed decisions. This includes situations that require optimal values, like analysing maximum and minimum profit. The trigonometry standard requires them to build mathematical models that can be combined to find and compare all possible solutions in a given real-life situation. These students also delve into the mysteries of the imaginary world too and see how this can help them solve real problems.

Students selected for the Scholarship Calculus course were often pushed outside their comfort zones. Those that attended the optional lunchtime sessions had the opportunity to work with other students to solve more challenging problems in a group.