Knowledge
Mathematics Education: Moving Beyond the Idea of Abstraction
The current syllabus-based approach to teaching mathematics often focuses on abstract concepts without providing students with a clear understanding of how these concepts fit into the larger picture
For many years, mathematics has been viewed as an abstract subject, one that is only accessible to a select few. However, this perception is flawed, and it is time to move beyond the idea of abstraction in mathematics education.
To begin with, it is essential to acknowledge that mathematics deals with concepts that are not inherently abstract. Numbers, functions, and geometric shapes are all tangible objects that we encounter in our daily lives. It is only when we begin to delve deeper into these concepts that they may become a little bit abstract. However, this does not mean that mathematics, as a whole, is an abstract subject.
Furthermore, the idea that mathematical concepts may not have a direct connection to real-life scenarios is also flawed. The opposite is true. To make mathematics more accessible to students, we should use real-life scenarios and examples to help students understand the mathematical concepts they are learning. By doing so, we can help students connect abstract concepts to concrete, tangible examples.
For instance, consider the following example: a carpenter needs to determine the length of a diagonal brace for a structure. By using the Pythagorean theorem, the carpenter can calculate the length of the brace based on the measurements of the other sides of the structure. This demonstrates how mathematical concepts can be applied to real-world scenarios.
It is also important to note that mathematical concepts do not exist in isolation. Instead, they are part of a larger system of interconnected ideas. By showing students how these concepts fit into a larger framework, we can help them understand the relevance and importance of what they are learning. This can help to break down the perception of mathematics as an abstract subject and make it more approachable for all students.
Another significant factor contributing to the perception of mathematics as an abstract subject is the existing mathematics education system. The current syllabus-based approach to teaching mathematics often focuses on abstract concepts without providing students with a clear understanding of how these concepts fit into the larger picture. Instead, we should adopt a more modelling and animation-based approach that can explain any known mathematical concept through models and animations.
In response to these challenges, we have developed a novel approach to teaching mathematics – DassMath. The new technique comprises a few tools that can convert any mathematical concept into geometrical shapes. Three broad tools/steps comprise the “DassMath”: Plotting graphs in MS Excel, Matrix Multiplication for Transformations, and Creating Animation. These common tools can be used in solving any problems in any sphere of life. By utilizing these tools, we can show students how mathematical concepts fit into real-world scenarios and make mathematics more approachable.
As an example, consider the image which demonstrates how a transformation matrix can be used to reflect a geometric shape across a line. This not only shows the practical application of matrix multiplication but also helps students understand how mathematical concepts can be used to solve real-world problems.
In conclusion, it is time to move beyond the idea of abstraction in mathematics education. By using real-life scenarios and examples, showing students how mathematical concepts fit into a larger framework, and adopting a more modelling and animation-based approach to teaching, we can help to break down the perception of mathematics as an abstract subject and make it more approachable for all students. It is time to shift the narrative and recognize that mathematics is a tangible subject that can be understood and enjoyed by everyone.
Author – Chanchal Dass, FIE, Founder and Chairman, Dass Scientific Research Labs Private Limited Ahmedabad, Gujarat
