Why Fractions Are More Convenient Than Decimals in Math Education
Despite the prevalence of decimal notation in everyday life, fractions remain a fundamental and indispensable tool in advanced mathematics and practical applications. This article explores the advantages of using fractions over decimals in arithmetic and algebra, and argues why fractions should continue to be a cornerstone of math education.
Why Fractions Are Preferable in Advanced Math Courses
Throughout my advanced undergraduate and master's level math courses, I rarely, if ever, used decimal notation. Fractions were the foundation upon which complex mathematical concepts were built. Understanding and working with fractions was crucial for almost every mathematical discipline, from linear algebra to calculus.
Challenges in Teaching Fractions in Elementary School
When I taught Basic Algebra, many students initially preferred using decimals because they were afraid and uncomfortable with fractions. This resistance often hindered their progress in the course, as basic arithmetic with fractions is necessary for mastering more advanced topics. Key concepts like rational expressions, equations, and functions rely heavily on the ability to manipulate fractions effectively.
Take, for example, the rational expression (frac{x^2 - 7x 12}{x - 4}). To simplify and solve this expression, one must have a solid understanding of fractions. Decimals, while useful in certain contexts, do not provide the precision and flexibility required for algebraic manipulations.
Advantages of Fractions Over Decimals
Compared to decimals, fractions offer several advantages. Firstly, they enhance precision and accuracy in calculations, especially when dealing with ratios, proportions, and fractions of integers. Secondly, fractions enable more straightforward division and multiplication, without the need for long division or complex decimal operations.
Historical Context and Practical Applications
The ancient Romans recognized the importance of fractions in their daily lives and commerce. They used fractions in the form of twelfths, with a fraction as small as 1/234. This system allowed for more precise measurements, particularly in construction and other practical fields. The use of twelfths (uncia) influenced modern terms like inch and ounce, derived from the Roman "uncia."
Despite the practicality of decimals in everyday calculations, such as financial transactions and measuring tools, knowledge of fractions remains essential for deeper mathematical understanding and problem-solving. Mastering fractions not only aids in algebra but also in higher mathematics, where the ability to manipulate rational expressions is a critical skill.
Conclusion
While decimal notation is widely used in everyday life, fractions are a fundamental tool that students must learn to succeed in advanced mathematics. Emphasizing fractions in elementary and middle school education ensures a solid foundation for future mathematical challenges. The mantra that “fractions fractions fractions!” should guide math education, as the mastery of fractions opens the door to more advanced mathematical concepts and applications.