Are Calculators Essential in High School Education?
The debate surrounding the use of calculators in high school is a contentious one. While some educators and students advocate for their indispensability, others, like myself, argue that they serve as a crutch that impairs the development of fundamental arithmetic skills. In this article, we will explore the importance and potential drawbacks of using calculators in high school, focusing on their impact on arithmetic skills and the development of estimation abilities.
Why Calculators Might Not Be Essential
Firstly, using calculators can be seen as a crutch that allows students to bypass the process of simple arithmetic, which is essential for building a strong foundational understanding of mathematics. This reliance can stifle the development of mental computation skills and the ability to perform quick and accurate calculations without technological aid.
A Case Study: Cashier's Misstep
A common example that illustrates this issue is when a cashier makes a mistake because a calculator input error led to an incorrect total. For instance, if a student orders a coffee at $1.25, two donuts at $0.50 each, and a newspaper for $1.00, the correct total should be $3.25. However, if a cashier rings up a total of $12.75, it's clear that a button was accidentally pressed multiple times. The issue here is that the student, who used the calculator, did not catch this error, indicating a reliance on the device rather than a sense of arithmetic intuition. This example demonstrates how calculators can lead to a lack of vigilance in performing basic calculations.
The Importance of Estimation Skills
Arithmetic skills, particularly the ability to estimate orders of magnitude, are crucial for developing a strong intuition in mathematics. Estimation skills help students understand the relative size of numbers and make quick and informed judgments. This is essential not only in everyday life but also in more complex mathematical concepts and real-world applications.
Historical Context: Pre-Calculator Era
Reflecting on my time in high school before the widespread use of calculators, I remember learning to use a slide rule. This analog tool was not only a fascinating tool to work with but also instilled in me a sense of computational precision and estimation. The slide rule required students to perform calculations mentally and visually estimate results, fostering a deeper understanding of numerical relationships and improving our ability to estimate magnitudes.
Impact on University-Level Math
These skills proved invaluable during my first-year university courses in chemistry and physics, where a strong grasp of arithmetic and estimation was necessary for solving problems and understanding concepts. While these skills were less critical as I progressed through my studies, the foundation laid during early education remained crucial for advanced mathematical and scientific pursuits.
The Disruption of Learning Fractions
Another significant drawback of calculator usage in high school is its potential to interfere with the learning of fractions. While decimal representations can be used to approximate fractions, it is crucial to understand the inherent differences between the two. For instance, the fraction 5/7 cannot be precisely represented as a decimal, as it is a repeating decimal. Similarly, 1/3 is a non-repeating, infinitely long decimal. Relying solely on calculators can hinder students' understanding of the exact values of fractions and their relationships.
The Limitations of Decimal Approximations
Using calculators can lead to a reliance on numerical approximations, which may not always be sufficient for precise mathematical reasoning. Students who are comfortable with fractions have a better grasp of mathematical concepts that involve ratios, proportions, and algebraic expressions, which are fundamental in higher-level mathematics. Without a solid understanding of fractions, students may struggle with more advanced algebraic problems and scientific calculations.
A Failed Suggestion: Dropping Fractions from Curricula
Interestingly, a senior member of the Ontario Ministry of Education once suggested dropping fractions from the school curriculum because students could perform all of their calculations with calculators. This idea, however, was met with immediate opposition. The fact that calculators can provide approximate results does not negate the importance of teaching students to understand and manipulate fractions precisely.
Moreover, the ability to perform mental calculations and understand the nuances of mathematical concepts is crucial for developing critical thinking and problem-solving skills. These skills are not just limited to mathematics but are transferable to other subjects and real-world scenarios, making them a valuable asset throughout a student's academic journey.
In conclusion, while calculators undoubtedly have their place in modern education, they should not be seen as a replacement for the development of fundamental arithmetic skills and estimation abilities. By fostering a balance between technological aids and traditional methods of computation, educators can help students develop a deeper understanding of mathematics and its practical applications.