1-on-1 Mastery-Based IB Mathematics · Taipei

IB Mathematics, from algorithms to abstraction.

IB Mathematics rewards recognizing structure, not procedure recall alone. Lessons build from the algebraic and computational fluency students bring toward the abstract reasoning, route-specific depth, and Mathematical Exploration the IB Paper questions, and university coursework, will demand.

Audience
IB Mathematics AA and AI content at HL and SL, international school students
Format
1-on-1, 1 to 1.5 hours per lesson
Duration
Typically across the 2-year IB Diploma cadence
Begin
Complimentary consultation & assessment class

What Students Learn

Mastery-based IB Mathematics at the level your child's school actually requires.

IB Mathematics is for students working through the IB Diploma Programme who want to move past procedure execution toward the abstract reasoning, route-specific depth, and Mathematical Exploration the IB assessment tests. The program covers the full IB Mathematics Subject Guides for both Analysis and Approaches and Applications and Interpretation, at HL and SL. Reasoning from algebra and functions to predict and prove how mathematical structures behave. Working through geometry and trigonometry, including the unit circle, vectors, and the spatial relationships the IB assessment expects. Tracing calculus from limits and continuity through differentiation, integration, and applications, with depth varying by course route. Building reasoning across statistics and probability, including descriptive statistics, distributions, hypothesis testing, and the inference work both AA and AI rely on. Connecting modeling and applications to real-world data the AI route emphasizes and the AA route applies to specific contexts. Designing and writing the Mathematical Exploration that the IB assessment requires. These are the topics the IB Paper 1, Paper 2, and Paper 3 questions test, and the foundation any university mathematics, engineering, economics, computer science, statistics, or quantitative-research course will assume.

IB Mathematics is not advanced calculation. The shift is from algorithms to abstraction. Students move from executing procedures correctly to recognizing the abstract structure underlying a problem and choosing the right approach without being told which to use. A student who can apply a procedure when told to apply it is doing the algorithmic work. A student who can look at an unfamiliar problem, recognize what mathematical structure the situation maps to, choose the technique the structure invites, and justify why that technique is correct is doing the abstraction the IB assessment rewards across topics. The program closes the gap between the two.

Lessons follow Harland's IB Mathematics curriculum, built to bring students to mastery of IB Mathematics content as defined by the IB Diploma Programme Subject Guides for both Analysis and Approaches and Applications and Interpretation. The program runs ten units across the 2-year IB Diploma cadence, with each unit closing in an assessment that mirrors IB Paper formats and includes the analytical work the Mathematical Exploration requires. Each student is matched with faculty who teach their specific course route, whether Analysis and Approaches at HL or SL with its emphasis on calculus, proof, and analytical methods, or Applications and Interpretation at HL or SL with its emphasis on modeling, statistics, and applied mathematics. Lessons calibrate to your child's individual gaps and the topics they're working through at school. If a student is working through differential calculus at school, the teacher works through it with the student, applying the unit's analytical structure to the questions their Paper 2 will eventually ask.

Progress shows up in places parents can see. Where your child once memorized which procedure applies to which problem type, they now reason from the underlying mathematical structure to choose the technique the situation invites. Where your child once produced an answer with no clear justification, they now construct an argument, name the theorems and assumptions the argument uses, and check whether the result is reasonable. Where the Mathematical Exploration once felt like an open-ended task, it now feels like a structured investigation your child can plan, execute, and write against the IB rubric.

How We Teach It

IB Mathematics taught for understanding, with the score arriving as a consequence.

Harland's pedagogy is content-based learning. Mathematical abstraction, structural recognition, and the analytical depth the IB Paper 2 and Paper 3 questions reward develop through the topics, problem sets, and past papers your child is already working with. Assessments check whether the thinking holds up when the student moves to new material alone.

A student working through calculus works on it with their teacher, building the reasoning that connects limits, differentiation, integration, and applications to the multi-step problems the IB Paper 1 and Paper 2 questions require. A student moving into statistics and probability works on it with their teacher, applying the unit's analytical structure to distributions, hypothesis testing, and the inference work the IB data-response questions test. A student working through modeling and applications, particularly on the AI route, works on it with their teacher, building the scaffolding that lets them translate real-world data into mathematical structures, derive predictions from those structures, and explain the mathematics with the rigor the IB rubric expects.

IB Mathematics students arrive with two layers under the surface. The score pressure is real. The May or November exam matters for university plans, particularly for students aiming at engineering, mathematics, economics, computer science, or quantitative-research paths, and most students know it. But beneath the score pressure is a specific cognitive challenge that defines the IB Mathematics assessment. Procedure execution is not the hard part. The hard part is reading an unfamiliar problem, recognizing which mathematical structure the situation invites, choosing the technique the structure calls for, and justifying the choice with the abstraction the IB rubric expects. The 1-on-1 format gives teachers room to slow down where the abstract reasoning is unfamiliar, and to keep the work rigorous without losing the student's engagement with mathematics itself. Skill and abstraction develop together. Neither moves far in isolation.

The format also lets teachers calibrate within the program's structure. A student fluent with procedural mathematics but uncomfortable with IB structural-recognition questions gets pushed toward the Paper 2-style scenarios the assessment will ask. What kind of problem is this. What technique does the structure invite. What additional information would change the choice of approach. A student strong on technique but weak on the Mathematical Exploration's writing and justification gets work calibrated to the rubric's expectations. That means refining the Exploration topic and research question, justifying methodological choices, presenting mathematical work with attention to the rubric criteria, and writing the Exploration against the standards the IB assessment uses.

Mathematics also has an exploratory dimension. The IB Mathematics Diploma Programme requires every student to complete a Mathematical Exploration as Internal Assessment, worth around 20 percent of the final grade across all four routes. The Exploration is an independent research paper of roughly 12 to 20 pages where students investigate a topic of personal mathematical interest, applying the techniques their course route covers to questions that engage them. Harland's 1-on-1 IB Mathematics program supports the Exploration through every stage. Teachers help students choose a topic that fits both the rubric criteria and the student's actual mathematical interests, develop the research question, work through the mathematical content with rigor appropriate to the rubric's expectations, and structure the writing against the IB assessment criteria. The Exploration matters as much as exam preparation, and the program treats it accordingly.

Curriculum and Alignment

A structured curriculum keyed to the IB Mathematics Subject Guide.

IB Mathematics at Harland follows a structured curriculum keyed to the IB Mathematics Diploma Programme Subject Guide for HL and SL. A student who completes the program has demonstrated mastery of IB Mathematics content as the IB Subject Guide defines it.

Harland's IB Mathematics runs ten units across the 2-year IB Diploma cadence, with Mathematical Exploration preparation integrated rather than appended. Most school IB Mathematics courses spread the same content across more class time, with Exploration work happening alongside or after class. 1-on-1 lessons don't lose time to group pacing or mixed-ability instruction, so the same core content fits in more substantive units. The time saved goes into the abstraction the IB Diploma assessment rewards.

Standards
IB Mathematics Diploma Programme Subject Guide (HL and SL), with the Internal Assessment criteria as the cross-cutting skill framework
Materials
Harland curriculum materials and IB-aligned textbooks, with past IB papers and IA exemplars integrated as ongoing input
Assessment
End-of-unit assessments aligned with IB Paper 1, Paper 2, Paper 3, and the Internal Assessment rubric
Reporting
Skill-level tracking against Harland's internal rubrics, mapped to IB assessment criteria

Prerequisites and What Comes Next

Where IB Mathematics fits in your child's learning.

Before starting

IB Mathematics assumes prior coursework in mathematics, typically built through pre-IB or MYP mathematics, and the algebraic fluency, basic trigonometry, and function manipulation those courses develop. Pre-calculus content provides the strongest foundation, particularly for students entering Analysis and Approaches. Students arriving from a different curriculum or with uneven foundations work through gaps in foundational pre-calculus before or alongside IB Mathematics proper, and the assessment class identifies which IB Mathematics route best fits the student's school program and goals.

One thing to know about scope. The IB Mathematics Internal Assessment, the Mathematical Exploration, is an independent research paper worth around 20 percent of the final grade. IB schools provide formal supervision for the Exploration, including checkpoint deadlines and final submission. Harland's 1-on-1 tutoring focuses on the mathematical content, the research question development, and the writing the IB rubric directly tests. The Exploration itself is submitted at school under supervisor oversight per IB requirements, and Harland's role is the planning, mathematical, and writing work that turns an interest into a strong Exploration.

The consultation and assessment class establishes whether IB Mathematics is the right starting point, which route fits best, and whether parallel work in foundational mathematics or Academic English would help. Some students arrive needing both algebra-foundation reinforcement and IB-specific support, and the lesson plan covers what's most urgent first.

What comes after

Most students complete IB Mathematics across the 2-year IB Diploma cadence, sitting either the May or November exam. Cadence varies by entry point and exam timing, with most students attending one to three sessions per week.

IB Mathematics does not have a direct successor course in the IB sequence. After the exam, the abstraction and analytical reasoning the course develops carries directly into university mathematics, engineering, economics, computer science, statistics, finance, and any quantitative-research degree. Students choosing Mathematics as their Extended Essay subject work with their primary teacher across the research-question, methodology, and writing stages on the Extended Essay program.

The longer-term aim of IB Mathematics is to make itself unnecessary. The program brings students to mastery of IB Mathematics content. Students sit the May or November exam, submit their IA, and the program's role ends. A parent who's no longer worried about their child's IB Mathematics work is the point of all of it.

Common Questions

Common questions about IB Mathematics at Harland.

Who is IB Mathematics at Harland for? +
IB Mathematics at Harland is for high school students working through the IB Diploma Programme. Most of our students fall into one of two patterns. Some are taking IB Mathematics at school and come to us for support alongside the school program, building the abstract reasoning and the structural-recognition depth the IB assessment tests differently from typical mathematics coursework. Some are preparing for the May or November exam in an intensive run-up, working through past papers, IA refinement, and targeted weakness review in the weeks or months before the assessment. Students whose situation falls outside these two patterns, including students transitioning curricula mid-DP, students at schools without strong IB programs, or students who need a more flexible curriculum than the standard IB Mathematics program provides, work with us through Harland's Academic Coaching framework, where the curriculum is calibrated to the individual situation rather than the IB Subject Guide alone.
My child can execute the procedures but struggles with choosing the right approach when the problem isn't framed for them. Can the program help with that kind of thinking? +
This is a familiar situation. The IB Mathematics assessment tests a kind of thinking that the textbook doesn't always practice directly. Reading an unfamiliar problem and recognizing which mathematical structure the situation maps to. Choosing the technique the structure invites, when the problem doesn't tell the student which technique to use. Constructing arguments grounded in mathematical reasoning, with the abstraction the IB rubric rewards. We work directly on these skills, slowing down on the structural-recognition work the Paper 2 questions require, on the writing the Mathematical Exploration tests, and on the rubric criteria that distinguish a strong response from a vague one. Most students who come to us strong on procedure execution but struggling on the structural-recognition prompts close that gap by working through the rubric explicitly, with sample questions and practice under time constraint.
What does the IB Mathematics program cover? +
The program follows the IB Mathematics Diploma Programme Subject Guides for both Analysis and Approaches and Applications and Interpretation, at HL and SL. Content covers algebra and functions, geometry and trigonometry, calculus, statistics and probability, and modeling and applications, with the Mathematical Exploration threaded through as an independent research paper. The four routes have meaningfully different content emphases. Analysis and Approaches emphasizes calculus, proof, and analytical methods. Applications and Interpretation emphasizes modeling, statistics, and applied mathematics. Harland's program runs ten units across the 2-year IB Diploma cadence, calibrated to the framework your child's specific course route requires.
How long is each lesson and how often does my child attend? +
Lessons are 1-on-1 sessions of 1 to 1.5 hours, in person at our head office in Da'an or online. Most students attend one to three lessons per week. Harland's IB Mathematics program runs ten units across the 2-year IB Diploma cadence. At one or two lessons per week alongside a school IB course, the program runs through the DP cycle and concludes with the May or November exam. At three lessons per week, the program covers the same content at faster pace. For students preparing in an intensive run-up to the exam, the cadence increases as the test approaches, typically two to four months at higher frequency. The Student Coordinator helps you choose the cadence that fits.
How are lessons scheduled, and what if we need to reschedule? +
Lessons happen on a fixed weekly slot reserved with your child's primary teacher. This protects the teacher's time and keeps a consistent rhythm for your child. If you need to reschedule, give us at least 24 hours of notice and we'll find another time when your teacher is available. Many families add classes during summer or winter vacation, either to accelerate progress or to make up for a slower term. Once a unit has started, it should be completed within a defined window. The Student Coordinator walks through the details when you enroll.
Can my child begin IB Mathematics over the summer? +
Yes. Summer enrollment is available across Harland's IB Diploma programs, with two patterns. Students preparing for the upcoming May or November exam in an intensive run-up sometimes begin or accelerate in summer at higher cadence (typically two to three sessions per week), particularly when their school IB course pacing has fallen behind, when their Internal Assessment is at draft stage, or when the run-up to the exam needs concentrated time. Students preparing for an exam sitting further out (i.e., entering or partway through the 2-year DP) often use summer for a head-start block, working through current-year content or building the prerequisite foundation before the next school year begins. The Student Coordinator helps you choose the right summer pattern based on which exam sitting your child is preparing for and where their IA work currently stands.
How do you measure progress? +
Progress is measured through unit assessments aligned with the IB Mathematics Subject Guide. Harland's IB Mathematics program is organized into ten units across the 2-year IB Diploma cadence. Each unit closes with an assessment that mirrors IB Paper formats, including the calculator-free items of Paper 1, the calculator-allowed items of Paper 2, and the Internal Assessment rubric, and measures conceptual understanding, structural recognition, technical accuracy, and the abstraction that connects techniques to problems across the unit's content. Parents receive updates after every lesson and formal progress reports when each unit ends. Skill-level tracking uses Harland's internal rubrics, which map to IB assessment criteria. Where helpful, the Student Coordinator translates this into the expectations of your child's school.
How do we begin? +
Every Harland relationship begins with a consultation, followed by a 1-on-1 assessment class. The consultation is about your goals and your child's situation. The assessment class is about how your child works in the subject. Together they tell us where to start and what kind of teacher will fit best.

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