Frequently Asked Questions

You can take several courses of action:

We want to help students to become better thinkers by teaching them about most impenetrable form of reasoning available to humankind: mathematics. We believe in uncovering their creativity and extending that intuition with the help of logical rigour. In you are interested in reading more about our philosophy, please visit our About page!

We are enthusiastic to work with school-age students who are motivated to learn about mathematics. Check out our free YouTube videos if you identify with one of the following groups!

  • Middle school or high school students who want to excel at math in an Ontario school
  • School students who wish to go beyond the standard school curriculum, including those preparing for mathematical contests and competitions, or preparing for standardized exams
  • First-year undergraduate students in math, computer science, or physics programs who wish to bolster their learning experience with a primer in mathematical proofs

We teach in two streams:

  • School Curriculum: The Government of Ontario has outlined clear mathematical expectations of students in middle school and high school. We teach concepts from these courses, ranging from Grade 8 Mathematics to Grade 9/10 Principles of Mathematics, Grade 11 Functions, Grade 12 Advanced Functions, to Grade 12 Calculus and Vectors. We also teach in the International Baccalaureate (IB) and Advanced Placement (AP) streams. We do not offer official credit, but our students generally find that working with us allows them to excel in school in ways they could not have done independently.
  • Enriched Curriculum: We present ideas that are helpful for solving “thinking-level” problems in school, and that are broadly applicable in middle and high school mathematical competitions in Canada and the USA. Activities include solving our original problems in algebra, geometry, combinatorics, and number theory. Many of these concepts will benefit the student far beyond obtaining a good score on an annual contest. For students preparing for university, we show how to prove mathematical statements rigorously using logic and axioms. We cover logical arguments, sets and other structures, proof techniques like induction, and properties of functions and relations.

When developing educational materials, we take a “first principles” approach by asking ourselves what is possible instead of repeating the status quo. This means that we are always surprising ourselves with original approaches to presenting mathematics. Here are some examples:

  • A general approach that we have taken is to point out ideas that underlie many arguments but are usually not mentioned explicitly enough. Examples are the discrete Fubini’s principle, equivalence classes, and antisymmetry.
  • The ordinary proof of the quadratic formula needs some casework on signs in the final step, whereas we prefer a less-known method of completing the square that avoids any casework.
  • In geometry, we do not shy away from the underused “explementary angles” (two angles that make a whole circle!), or from using complex numbers for proving classical geometric results.
  • We like to generalize divisibility rules in number theory to all bases instead of just applying them to base-10 (imagine counting with 12 fingers instead of 10!).
  • We approach combinatorics from the perspective of sets and functions, thereby providing insight into where the topic falls within the mathematical universe, instead of it seeming to stand on its own.
  • We do not hesitate to create new terminology for temporary usage if the appropriate nomenclature does not appear in the literature to the best of our knowledge.
  • Ideas that are a part of higher mathematics, such as the matrix multiplication of small matrices or the Jordan curve theorem, occasionally play a role on our curriculum if they help in simplifying concepts and are accessible to students.

We are distinguishable from other on-curriculum or enrichment programs because of our emphasis on the quality of the learning environment instead of the quantity of students. Students who choose our tutoring services receive individual attention, or occasionally learn in small cohorts when they sign up together. On the other hand, there are online schools where each class has too many students. We have seen first hand what happens in such cases: students fall behind, resulting in slowed teaching, more homework extension requests, and students looking up answers on the internet. Our focus is not unrestrained growth, but to ensure our students’ achievement. The instructor is also experienced and qualified.