By: Debbie Wong, Founder and Teacher, Debbie’s Learning Cove (The following article is based on my opinion and observations as a tutor over the past decade.)

What is IP and IP Math?

The Integrated Programme (IP) in Singapore is a specialised educational programme that spans six years (from Secondary 1 to Junior College 2), designed for students who have performed well in Primary School. It allows selected students to bypass the traditional GCE O-Level examinations and proceed directly to the GCE A-Levels or other equivalent qualifications, such as the International Baccalaureate (IB) Diploma or the NUS High School Diploma. With no O-Level exams, the programme is designed to give these students more space for intellectual exploration, leadership development, and enrichment activities. This includes a greater focus on critical thinking, independent learning, and interdisciplinary studies. The programme is tailored for students who are academically strong and can benefit from a less exam-centric environment during their secondary school years. The IP programme is available in certain elite schools in Singapore, such as Raffles Institution, Hwa Chong Institution, Nanyang Girls' High School, and National Junior College, among others. IP Math is the specialised mathematics curriculum tailored for students enrolled in the Integrated Programme. The IP Math curriculum has a broader scope compared to the mainstream secondary school math syllabus. It is designed to prepare students directly for the GCE A-Levels, the International Baccalaureate (IB) Diploma, or other equivalent qualifications like the NUS High School Diploma. As the vast majority of IP students sit for A-level exams at the end of six years, my discussion here is focused on IP Math learning for the A-level pathway, not the IB or the NUS High School Diploma. By the term ‘mainstream’ school, I am referring to secondary schools that are geared towards the O-level exams. The first two years of IP Math consist of lower secondary math of mainstream schools, as well as selected topics from the upper secondary mathematics (E Math) of mainstream schools.   Years 3 and 4 of IP Math expand into two subjects, often called Math 1 and Math 2. Some schools use different terms like Intermediate Math and Advanced Math. IP Math includes upper secondary E Math and Additional Math (A Math) of mainstream schools, as well as a few selected topics from JC H2 Math (A-level Math). Since IP students are academically strong, independent learning is a key feature of IP education. Math concepts are often introduced in an exploratory manner in school. For example, a new formula might be derived through a classroom activity or group work rather than direct instruction from teacher to student. Students are expected to be self-directed and use available resources to strengthen their understanding of math concepts. Schools often provide students with a large repository of practice questions, which the self-directed student is expected to use for revision. Interdisciplinary learning is also encouraged, often through projects that involve Math alongside other subjects like Physics and Economics. For more guidance and structure in their Math learning, many IP students and their parents seek out-of-school tuition support in Mathematics. My discussion today focuses on supporting the learning of Math for IP Years 3 and 4, which correspond to the upper secondary years. At Debbie’s Learning Cove, we begin our support programme for IP students starting in Year 3. Based on my many years of teaching students from all the IP schools, and from conversations with parents of IP students, here are some myths I would like to debunk so that you, the reader, can make a more informed choice when selecting support for your child.

Myth 1: IP students cannot join mainstream A Math tuition.

Many tuition centres market their IP Math tuition classes as exclusively for IP students to attract them. However, this exclusivity is unnecessary due to one key fact: No two IP schools have the same syllabus. Let me explain. Within each IP school, the syllabus is determined internally. The syllabus generally covers three areas: all the O-level A Math syllabus, nearly all the E Math syllabus, and a few JC Math topics. The differences lie in the few JC Math topics that each IP school decides to include in the IP Math syllabus. Each IP school teaches different JC topics. Some teach Functions, others Linear Transformation, some teach Sequences and Series, and some teach the use of Graphing Calculators, etc. A few IP schools do not include JC topics at all. Furthermore, within the IP syllabus, the coverage of each JC topic is less extensive than what actual JC students learn. For example, an IP school might teach JC Permutation and Combination but omit circular permutation. Questions on these topics are also much easier than those faced by actual JC students It is not feasible for an IP Math tuition class to cover ALL the topics from various IP schools in a single class. It is also not advisable to teach all the JC topics to IP students, whether they need them or not, as this could lead to unnecessary time being wasted and confusion. To complicate matters further, each IP school follows a different order of topics. An IP Math tuition class cannot cater to the specific order of topics for each IP school at the same time. The exception to this is when the IP Math tuition caters to only one particular IP school and excludes students from other IP schools. However, this is rare due to the small cohort size from each IP school. As a result, IP Math tuition classes often focus on teaching A Math to IP students. The so-called IP Math tuition is actually an Additional Math tuition class. There is nothing wrong with this. In fact, the largest, most challenging, and most important part of IP Math is the Additional Math component. If a student can manage all the Additional Math topics well, they will have the skills to manage the watered-down JC Math topics as well. Ultimately, the JC Math component comprises less than 10% of the syllabus, while A Math makes up about 60%. The remaining 30% consists of E Math topics, which are often very manageable without tuition support. It is a myth that IP students cannot join mainstream A Math tuition. A Math tuition is beneficial and relevant for every IP student. It provides the structure and extra practice needed to reinforce what is learned in school. Therefore, when selecting a suitable tuition centre for your child, you do not need to limit your choices to those that market a purely IP Math class. You can consider A Math tuition for your child.

Myth 2: IP Math is harder and more fast-paced than O-level A Math.

Most IP schools cover the syllabus at a slower pace than mainstream schools. This is because mainstream schools are preparing students for the national exams in October and November of the Sec 4 year. Thus, the syllabus for A Math, and all other subjects, is completed by early July of the Sec 4 year, in time for preliminary exams in August. In contrast, IP schools have their students sit for the school’s internal year-end exam in late September to early October. The syllabus is usually completed by the end of August. IP schools teach A Math topics at a slower pace than mainstream schools. Another reason for the slower pace is that key features of the IP programme include exploratory learning and projects, which inevitably slow down the pace of syllabus coverage. It is not a key feature of the IP programme for students to learn at an accelerated pace. It is also not true that IP Math is more difficult than O-level A Math. As IP Math exam papers are set internally, compared to the standardised nationwide GCE O-level exam papers, the difficulty level of IP Math exams can vary greatly. It is not true that IP Math exams are always more difficult than O-level exams. Additionally, the O-level exams have been gradually increasing in difficulty over the years, with an increasing emphasis on testing candidates' critical thinking abilities. It is dangerous for some IP students and parents to assume that underperforming in IP Math is acceptable because it is supposedly harder and faster-paced than mainstream math. This assumption can lead to a false sense of security. When I review IP exam scripts, it often becomes clear that the questions are not more demanding than those in mainstream exams and that the student is weak in math concepts. During the COVID years, a very worried parent inquired about my tuition services. His son was in Year 3 of an IP school and scored a meagre 17% for the end-of-year IP Math exam. During our initial meeting, the boy told me that the school exam was extremely difficult and that his class average was well below the passing score. To test this assumption, I invited a mainstream A Math student of the same age to attempt the same exam questions under a mock exam setting. She was a consistent A1 student in her mainstream school’s A Math tests and exams. I marked her script, and she scored 89%. Of course, factors such as exam pressure and differences in assessors may cause her score to be lower if she had taken the actual exam. Even so, the difference in scores was too significant to be ignored. The IP student and his classmates likely had a poor school learning experience during the months of lockdown and home-based learning. Subsequently, that IP student enrolled in my A Math tuition class. By the end of his IP Year 4, he scored an A in IP Math. A student who has a solid understanding of A Math concepts will perform well in exams, whether in an IP school or a mainstream school. At Debbie’s Learning Cove, IP and mainstream students learn A Math together. I teach with the goal of preparing my students for the A-level exams. As such, I prioritise building a strong foundation in A Math concepts. If a student’s understanding is superficial and only sufficient for managing common types of O-level A Math questions, they will struggle with JC H2 Math when they move on to JC. For example, when teaching trigonometry ratios, I ensure that every student understands the concept of the principal value range of inverse trigonometric functions. This is something that many O-level students simply memorise, leading to inadequate comprehension when they proceed to JC. I use graphs and examples to explain why and how we obtain the principal value range, as well as how to perform accurate calculations of trigonometric ratios and angles to present exact values. This knowledge is assumed when students proceed to JC but is often not emphasised in mainstream schools. As such, my lessons are highly beneficial for both IP and mainstream students. I design my notes and worksheets with IP learning in mind. My questions enable students to use higher-order thinking skills and critical analysis. The questions in each worksheet gradually increase in difficulty, from structured to less structured, to challenge students to think critically about the strategy and procedure needed to solve the problems. Having taught in IP schools previously, I am familiar with the difficulty level and format of IP questions. I guide my students in developing the skills necessary to manage such questions. These skills also benefit my mainstream students, as the O-level exams have been getting increasingly difficult over the years.

Myth 3: IP students must have one-to-one tuition to cater specifically to the syllabus.

Some parents seek one-to-one tuition to fully cater to the unique syllabus and order of topics in the IP school. While this arrangement has many advantages, parents should check with the tutor to ensure that they are equipped to guide the child in JC topics as well. Many one-to-one secondary math home tutors are well-versed in A Math and E Math, but not in JC H2 Math topics. In such cases, the tutor may be unable to guide the child on the JC Math component, leaving a gap in the one-to-one guidance arrangement. A parent can seek a qualified JC Math tutor for one-to-one tuition. However, JC Math tutors often charge higher fees than secondary math tutors.

Recommendation

The IP Math teaching and learning culture in schools requires students to learn independently and be self-driven. However, it is not uncommon for IP students to require out-of-school support in Math to provide more structure, guidance, and practice. In my opinion, an A Math tuition class provides adequate help for the child to prepare for IP Math exams. Parents do not need to limit themselves to specialised IP centres or one-to-one tuition. I also recommend that the child enrols in A Math tuition at the start of Year 3. This is because, due to the slower pace of IP lessons, it is very beneficial for the child to get a head start in A Math learning, allowing more time to practice Math before exams. IP Math is primarily A Math, and a child who excels in A Math will also do well in IP Math.