Math

In order to truly engage with math, students must be furnished with opportunities to connect it to something meaningful to them. Concentration cannot be forced but it can be directed toward a point of interest where it will be actively seized by the student. Whether the seed of the idea is a soccer ball, a found object, a building in Singapore or a sound wave doesn’t really matter. The guide’s role is to stand by, equipped to journey student enquiry and facilitate their ability to sink deeply into the work.

Lyceum students are privately tutored in math by Rizwan Kassamally. Riz’s unique approach blends group lessons followed up with applied math problems and supported by individual study and presentations in theoretical math. This year, our younger students covered fractional numbers, basic algebra and geometry of plane figures and soilds. The older group studied calculus and trigonometry. Students graduating from our grade eight program are working at the equivalent of grade 11 in the Ontario curriculum. Their final year individual assignment and presentation was a 60 page paper on theoretical mathematics. Topics included Fermat’s Conjecture, String Number Theory, Euclid’s Elements, Cantor’s Theorem and the Origins of AI.

Last year, our students showed their ability toward apply math to architecture, modelling and massing a famous world landmark. Next year, they will work with RIz, Holly and Sam under the guidance of Architect Raymond Chow. These projects spark energy and enthusiasm for studies in mathematics.

In February 2023, students exhibited their work in math in The Lyceum Gallery. Math Lab showed the artistic manifestation of studies in math and geometry featuring mod diagrams, building models, vellum curtains made of massing arithmetic, a tessellation wall, a giant origami truncated icosahedron and a monster long division that spills down one wall of the gallery and across the floor. Check out the story here https://thelyceumgallery.com/exhibition/math-lab/

Students arrive in grade six to review fractional numbers, Over the past year, our grade eight students have studied functions and relations, force and energy and quadratic equations. These in-class studies are augmented by real-world problem scenarios and case studies such as building massing, hydrolics budgeting and investing and planetary orbits. Our grade six and seven students are learning fractions and decimals, graphing and linear equations by applying their lessons to real world problems such as nutritional analysis and budgeting. Our small class sizes allow for the flexibility and resources to work on individualized plans tailored to each student’s needs.

Scaling Equivalencies in the Table of Pythagorus

A Math Story

The Table of Pythagoras (Decanomial Square) is a beautiful manifestation of the power of Montessori’s math. It introduces the decanomial: the concept that all numbers are organized by decades (tens). Children are usually given the sensorial presentation of this material around the age of four or five in casa. When it re-emerges early in Elementary, it is used to situate and reinforce multiplication facts before charting a course into new understandings of the commutative law, squaring, and binomials. It lays the foundation for algebraic determination and eventually, for the cubing material that follows in upper elementary. Interestingly, this material is visually resolved to the pink tower they are first introduced to sensorially at the age of two and a half. We discovered that none of this is by accident.

Every step of the way, the materials pluck strings laid deep in the child’s absorbent mind years prior. Materials are auto-didactic, not just to correct errors made as they work with it but also to lead them to the next place of discovery. Midway through the year, some of our students deduced the great reveal hidden within the decanomial square. At its diagonal centre, sits a magnificent secret: the sum of the units of the bissected square divided as a right angled triangle are identical to the sum of the cubed material that takes the square into a third dimension. This is a cool math fact to be sure but the days the children spent solving it were breathtaking. They will remember what they “learned” because they experienced and discovered it, not because they memorized it for a test. They worked together to test different theories and approaches. They got a little frustrated and in the end, they came together and found a solution.