Elementary Mathematics: Manual Calculations

Abstract

The student is introduced to numerical calculations at the initial stages of studying mathematics. The student masters the execution of four arithmetic operations (addition, subtraction, multiplication, division) manually. For calculating trigonometric and exponential functions, square and cubic roots, arithmetic calculators or tables are usually used; this also applies to logarithms. At the same time, confident proficiency in mathematics necessarily involves the ability to perform calculations manually, with at least some accuracy (2–3 significant figures), for any task in natural sciences and mathematics within the school curriculum. This competence enables the student not to perceive computer computations or calculator-based calculations as something incomprehensible — like a trick or a "black box," where input data is provided and output results are obtained. It is understood that the authors do not advocate abandoning calculators when solving school tasks. However, the student should not become entirely dependent on this tool. The article demonstrates methods for calculating the values of exponential, logarithmic, and trigonometric functions, extends the set of exact values of trigonometric functions beyond what is known from the school curriculum (for arguments , , , , ), and illustrates methods for finding square and cubic roots of a number.