This, therefore, is Mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth.
-Proclus (410-485)
Mr. Guan is a distinguished mathematics educator in the Sydney area, renowned for his expertise in cultivating analytical minds. A former faculty member of the James Ruse Agricultural High school mathematics department, he not only instructed classes but also played a pivotal role in coaching and coordinating students for high-level mathematics competitions. His approach goes beyond rote learning—he treats mathematics as a mental discipline, training students to develop logical reasoning and problem-solving skills through a diverse range of strategic methods.
While many educators perceive HSC standards as excessively challenging, university faculty often find them insufficient preparation for the rigorous demands of mathematics, engineering, and the sciences. Mr. Guan bridges this gap by equipping his dedicated students with the tools to surpass HSC benchmarks, ensuring they are well-prepared for advanced academic pursuits.
A firm advocate of traditional yet highly effective teaching methods, Mr. Guan’s instruction is systematic, engaging, and results-driven. His 30-year track record speaks for itself: dozens of his students have ranked in the top 10 in 4-Unit HSC Mathematics, and three have earned medals in the prestigious International Mathematical Olympiad.
Mr. Guan takes immense pride in the success of his students, many of whom have gone on to secure esteemed positions in society. He believes in a holistic educational philosophy—one that not only fosters mathematical excellence but also instills intellectual resilience, preparing young minds to excel in academia and beyond.
The Current Classes:
MathGym 1 (Starts from Term 2 each year)
This class is designed to introduce Year 6 to Year 8 newcomers to the beauty of mathematics through Algebra and Geometry, providing them with essential strategies to think mathematically and solve problems effectively. With a balance of challenge and enjoyment, the course draws inspiration from math competitions and engaging Chinese mathematical puzzles, making learning both stimulating and rewarding. Students will build a strong foundation for formal Algebra and Geometry, focusing on two critical yet often overlooked skills: setting up equations for problem-solving and articulating logical reasoning in their mathematical work. These areas are common weak points among high school students, and this course aims to address them early, equipping learners with the clarity and confidence needed for future mathematical success.
Base 1 (Sunday 4-6:30pm)
This course lays the groundwork for high school mathematics, covering key topics such as Algebra, Mensuration in 2D and 3D, and Geometric Reasoning. A strong emphasis is placed on symbolic computation and its applications in Geometry, equipping students with essential problem-solving skills. Students will also be introduced to the principles of Euclidean Geometry, developing a deeper understanding of logical deduction and geometric proof—fundamental skills for higher-level mathematics. This course provides a solid foundation, preparing students for advanced studies with confidence and precision.
MathGym 2 (Please call for details)
This class requires completion of Base 1 or an equivalent foundation. It is designed to elevate students’ algebraic transformation skills and Euclidean geometry reasoning to a master level.
Featuring an exciting selection of challenging and intricate problems sourced from various Chinese high school mathematics competitions, this course offers young mathematicians a space for imagination, creativity, and a deep appreciation for mathematical treasures passed down through generations. These invaluable aspects—once the pride of mathematical education—have been unwisely ignored, mindlessly devalued, and long forgotten in today’s Western education systems.
All well-educated minds understand the importance of Euclidean Geometry and the power of logical reasoning. This class is an opportunity for:
- Math-gifted students seeking challenge
- Math lovers eager to explore beyond the rigid school curriculum
- Future scientists, engineers, and thinkers who need a solid mathematical foundation
Above all, this is a place for students to contribute, inspire one another, and sharpen their reasoning through diverse approaches to problem-solving—an environment sought after by students and parents who can no longer tolerate the pointlessness of school math activities.
🚫 Warning: If you’re simply looking for better school grades, this is absolutely the wrong place for you. The uselessness to schoolwork is a core feature of this class—because true mathematical mastery extends far beyond the confines of standardized tests.
Base 2 (Thursday 6:30-9pm)
This class focuses on Coordinate Geometry, Linear and Quadratic Functions, and Polynomials, providing students with a solid understanding of Functions as a whole. Through structured exploration, students develop the ability to analyze and manipulate algebraic relationships with confidence. In addition, the course introduces fundamental counting techniques, including Combinations and Permutations, equipping students with essential problem-solving tools for probability and advanced mathematics. This class serves as a crucial stepping stone for students aiming to deepen their mathematical reasoning and prepare for higher-level studies.
Base 3 (Saturday 1:00 – 3:30pm)
This class provides a comprehensive study of high school Trigonometry, along with Exponential and Logarithmic Functions, Sequences and Series, Inequalities, and Absolute Values.
By mastering these topics, students will develop a deep understanding of all major function types, ensuring they are fully equipped for the next step—Calculus. This course bridges the gap between foundational algebraic concepts and the advanced mathematical thinking required for higher studies.
Base 4 (Saturday 4-6:30pm)
This class delves into the art of mathematical proof and advanced problem-solving techniques, covering:
- Mathematical Induction
- Inequality Proofs
- Max-Min Problems (without Calculus)
- Proof by Contradiction & General Proof Strategies
- Pigeonhole Principle
- Binomial Theorem & Related Identity Proofs
- Binomial Probability & Classical Probability
Designed for students ready to engage in rigorous logical reasoning, this course strengthens their ability to construct and analyze mathematical arguments—essential for higher mathematics, competitions, and beyond.
HSC 1 (Sunday 9:30am-12pm)
This class provides a systematic and rigorous study of Calculus, covering both its logical foundations and major applications. Students will master the differentiation-integration process and apply it to a wide range of mathematical problems, including:
- Curve sketching for all fundamental function types
- Max-min optimization problems
- Area and volume calculations in space
- Differential equations and rate of change applications
- Advanced integration techniques at the 4-Unit level
Additionally, the course explores Complex Numbers and their applications in Polynomials, equipping students with essential tools for higher-level mathematics and problem-solving.
This class is designed for students who seek a deep understanding of Calculus, preparing them for university-level studies.
HSC 2 (Sunday 1-3:30pm)
This class serves as an intensive final revision for students preparing for the HSC examination, focusing on advanced problem-solving through harder questions. It systematically reinforces all major concepts while addressing the most challenging topics to ensure students are exam-ready.
Additionally, this course fills in any remaining gaps, covering smaller areas that may have been left unattended in previous studies. Designed for students aiming for top performance, this class sharpens problem-solving skills and builds the confidence needed for the final exam.
About the homework
Unlike school teachers, who have daily contact with students and can provide immediate feedback, our academy meets once a week for 2.5 hours. To surpass the depth and quality of school instruction, we design homework assignments that integrate questions from the following week’s content. This approach allows students to become familiar with new concepts in advance, formulating questions to bring to the next class.
We do not expect students to complete every question flawlessly each week. In fact, our homework is intentionally challenging, designed to stretch even the strongest students beyond their comfort zones—a crucial part of the learning process. Students may find certain weeks more difficult, especially when they are new to the class, when we are midway through a complex topic, or when we are tackling extension questions at the end of a unit. Approximately 20% of each term’s homework consists of higher-level problems, ensuring a balance between reinforcement and challenge.
Encouraging Consistency & Growth
We recommend that students establish a structured study routine:
- Allocate dedicated time daily for current homework.
- Reserve extra time for reviewing previous extension questions.
For example, a student may spend three hours per week on new homework and complete 75% of the material. During class, they can ask about the remaining 25% they struggled with. The following week, they should dedicate an additional hour to revisiting those difficult problems while progressing with new content.
Some concepts may take several weeks to fully grasp. The key is to persist, ask questions, and keep working through difficulties. We support students learning at their own pace and accept late homework submissions as long as they are handed in within the current term.
How parents can help students
To foster independent mathematical thinking, we strongly encourage parents to allow students to attempt and complete their homework on their own. While your intentions to assist are appreciated, excessive input from parents or home tutors can be counterproductive. Struggling through challenges is an essential part of the learning process, and homework is designed for students to solve—by themselves, sooner or later.
The best way to support your child’s progress is to:
- Identify and circle unsolved problems each week.
- Encourage them to revisit these questions repeatedly until they can solve most, if not all, on their own.
Every student learns at their own pace, and some concepts take longer to master. Patience and encouragement are key, especially as your child is learning among peers of exceptionally high calibre.
Mathematics Beyond the HSC
We uphold traditional, rigorous mathematical standards, far exceeding the bare minimum required for a good HSC score. If your child’s primary goal is a high HSC mark but they do not intend to pursue university studies in mathematics, engineering, or the sciences, completing about 80% of the homework each term will be sufficient. Our curriculum ensures that all diligent students can secure a score of 95 or above in the HSC.
However, our mission extends beyond exam preparation. We strive to nurture and motivate students to reach their maximum potential. In an ever-changing and complex world, the challenges ahead are unpredictable. We firmly believe that mathematics is the keystone of education, forming the foundation for success in university and beyond.
The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
-Bertrand Russell