Besides the five areas of study (Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, and Calculus) in the IB Diploma Programme (DP) subject Mathematics, we also study Theory of Knowledge (TOK). TOK is an essential ingredient that underpins the philosophical and ideological framework of the IB DP in Mathematics. It explores the different ways of knowing across many academic disciplines. TOK poses the central question: How do we know?
To assist students in exploring the implications of TOK in various contexts, Mathematics teachers at Preshil have prepared inspiring prompts related to the five main areas of study. Besides the final examination, IB DP has a unique Internal Assessment (IA). The maths IA is all about exploring the math behind a topic of interest, and then presenting the whole thing in the form of a short, thorough report. It offers students an opportunity to demonstrate they have a firm grasp of mathematical concepts, principles and knowledge.
At Preshil, a variety of IA topics are explored in class to help students explore their interests in the beautiful language of mathematics.
YEAR 11 MATHEMATICS: APPLICATIONS AND INTERPRETATIONS
The Year 11 Mathematics Applications and Interpretations students have been digging into the memory banks to recall all we know about trigonometry. Words like ‘sin’, ‘cos’, ‘tan’ and ‘Pythagoras’ came flying back as they refreshed their skills at finding missing side lengths and angles of right-angled triangles.
However, that happy familiar feeling hasn’t lasted long as we move beyond right-angle trigonometry and learn the Sine and Cosine rules for non-right triangles. This will lead to the application of trigonometry in using triangulation to find distances to far-off locations and Voronoi diagrams to navigate, path-find and establish an optimum position on a graph.
YEAR 11 MATHEMATICS: ANALYSIS AND APPROACHES (STANDARD LEVEL)
In the Year 11 Mathematics Analysis and Approached (SL) class, students investigated different trigonometric models and open problems in class including a Ferris wheel problem, cycloid question and DC motor. Students learned the relation between electric current and the RPM of coils. Different sound waves were also created in the class from various frequencies. Through these activities, students found the initiative to study trigonometric functions.
YEAR 11 MATHEMATICS: ANALYSIS AND APPROACHES (HIGHER LEVEL)
Guillaume de l’Hôpital also known as Guillaume-François-Antoine Marquis de l’Hôpital, Marquis de Sainte-Mesme, Comte d’Entremont and Seigneur d’Ouques-la-Chaise was a French mathematician. His name is firmly associated (though he did not invent it) with l’Hôpital’s rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. While the rule did not originate with l’Hôpital, it first appeared in print in his 1696 treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes. In class, we are using l’Hôpital’s rule to find stubborn limits which would be otherwise impossible to resolve!
YEAR 12 MATHEMATICS: APPLICATIONS AND INTERPRETATIONS (STANDARD LEVEL)
In Year 12 Mathematics Applications and Interpretations, our students have been introduced to the world of calculus. They entered the unit having a solid grasp of linear equations and were comfortable with explaining the gradient of straight lines. In calculus, we explore the gradients of curved lines. In these lines, the gradient is constantly changing. It could be measured by drawing the line perfectly, then drawing a perfect tangent (a straight line touching the curve at only one point that is moving in the same direction as the curve at that point) and finally measuring the gradient of that line…
But that is slow, difficult and prone to error. So instead the students learned how to differentiate (as seen in Diagram 1). By differentiating we derive a function that will tell us the gradient of a curve at any point on that curve. No need to draw it. Just substitute an X value and we have it!
Once the students were comfortable with differentiation we went one step further. We moved on to antidifferentiation. By performing the exact opposite of differentiating we can discover another function called an integral. This function has its own special quality. It can generate the area under a curve between two points.
YEAR 12 MATHEMATICS: ANALYSIS AND APPROACHES (STANDARD LEVEL)
Probability and Statistics is our final topic in the lead-up to the all-important October / November examinations. And no, you aren’t seeing double… Venn Diagrams are guiding the way!
YEAR 12 MATHEMATICS: ANALYSIS AND APPROACHES (HIGHER LEVEL)
Students read the History of Euler’s beautiful equation. They discussed one of the mathematician’s comments on it: “That is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth.”
Through these discussions, students find the beauty of mathematical abstraction. Students also studied the connection between complex numbers and engineering by researching conformal mapping and Fourier transform.