Conference synopsis 20240805 - Flipbook - Page 105
G28 CALCULUS WITHOUT ALGEBRA USING
PRIMARY SCHOOL ARITHMETIC AND EXCEL.
Subtheme: Pedagogy
Enzo Vozzo, Mentone Grammar
(Year 11 to Year 12)
The fundamental theorem of calculus that connects the
two branches of differential and integral calculus is one
of the greatest milestones and discoveries in the history
of mathematics. Although algebra is used to prove this
important theorem, students who struggle with algebra
miss out on appreciating how derivatives and integrals are
intimately related. However, without any algebra, we can
show the fact of this theorem using only the four operations of
arithmetic (primary school maths!) and Excel. We will analyse
functions such as polynomials, trigonometric, exponential,
logarithmic and others by dividing them into 100 (or more)
rectangles. Then calculating dy/dx (using subtractions and
divisions) and areas (using multiplications and additions), the
original function can be reconstructed after differentiation
and integration, hence showing the inverse nature of these
two branches of calculus.
KEY TAKEAWAYS:
1. A non-algebraic demonstration of the fundamental
theorem of calculus.
2. Use of primary school arithmetic (addition, subtraction,
multiplication and division) to demonstrate the fundamental
theorem of calculus.
3. Use of simple operations in Excel to demonstrate the
fundamental theorem of calculus.
Remember: Delegates should be familiar with the
fundamental theorem of calculus and have a basic working
knowledge of Excel. You are invited to bring you laptop with
Excel installed so you can implement the demonstration of
this theorem.
THE MATHEMATICAL
ASSOCIATION OF VICTORIA
105
