Mathematics is a language of numbers, equations, shapes, functions and theories. A vast field of study that continues to evolve with new discoveries, mathematics forms the foundation of education and is used in everyday life. For students looking to become math whizzes, understanding the order in which mathematics should be learnt is essential to success.
To this end, this article will outline the order one should generally learn mathematics, from basic principles up to high-level concepts.
1 – Understanding Basic Maths:
The journey of learning mathematics begins with understanding the fundamentals. This includes the four basic arithmetic operators (addition, subtraction, multiplication and division), numerical systems (decimals, fractions and percentages) and other fundamental operations such as order of operations and solving equations. At this point of learning, it is important to understand these elementary concepts deeply, as they form the building blocks of further mathematics such as algebra and trigonometry.
2 – Developing an Appreciation for Algebra:
Algebra is a powerful tool used to figure out unknown values using equations. Although the concept may appear difficult at first, its utility – when used properly – can be invaluable for solving a wide variety of problems.
Students should begin with basic algebra such as understanding and working with variables, simplifying expressions, simplifying equations and graphing linear equations. It is also beneficial to learn the basics of linear inequalities, fractions, exponents and roots. Doing so provides students a good grasp of algebraic concepts and procedures.
3 – Applying Techniques to Solve Advanced Problems:
As students dive deeper into mathematics, they should focus on solving advanced problems. Common techniques such as logarithms and series can aid students in solving problems with more ease. Factoring and polynomial equations can also be learnt at this stage.
Students should also focus on learning and understanding the techniques used in solving linear and quadratic equations, and how to plot and solve linear inequalities. Finally, looking at how advanced functions, such as exponential, inverse, sine and cosine, can be graphed and used to solve problems should be done.
4 – Exploring the World of Geometry:
Geometry, which deals with the properties of shapes, points and surfaces, is a fun and challenging field of study. Initially, one should look into basic concepts such as understanding the relationships between angles and sides of shapes, constructing triangles and circles based on certain criteria, as well as exploring lines and points in the plane. As understanding develops, students should look into measuring the area and volume of shapes, bisecting lines, constructing polygons and solving equations and inequations involving geometric figures.
Scale drawing and working with 3D shapes should also be part of the learning process at this level.
5 – Introducing Higher Maths Concepts:
At this stage, one should focus on more advanced mathematical topics. Trigonometry, which deals with right triangles as well as studies angles based on circles, covers techniques of measuring distances, angles and areas. Probability, which is the study of how likely an event is to occur, deals with concepts such as independent and dependent events, permutations and combinations.
Finally, calculus helps to study continuous change, allowing students to apply mathematical principles to problems with the aim of understanding, predicting and explaining physical processes.
6 – Leveraging Concepts in Physics and Chemistry:
As students gain a more thorough understanding of mathematics, they can apply concepts from other domains such as physics and chemistry. Although it is not essential to have knowledge of these fields for learning mathematics, doing so enables students to better understand and interpret mathematical problems.
By understanding the principles of forces, motion, work and power, students can gain a better insight into the mathematical problems posed. This can become especially useful for those looking to pursue a career in either physics or chemistry.
7 – Investigating Mathematics Further:
Multiple technologies, such as computer programming, also form a significant part of mathematics. Students should explore various technologies, as there are a wide variety of options available.
Working through tutorials and creating basic programs can help to increase one’s understanding of the fields of mathematics. One should also look into more advanced topics, such as Database Management Systems and Artifical Intelligence, to understand how mathematics is used in the modern world.
8 – Practicing Sample Problems:
Mathematics is a subject that requires a great deal of practice and consistency. Practicing through sample problems not only helps to gain an understanding of the concepts learnt, but also allows for the identification and rectification of errors. Moreover, practicing through sample problems will aid in evaluating one’s abilities and understanding concerning the concepts learnt.
An easy way to do this is to work through sets of exam papers, which usually come with solutions as well as explanations.
9 – Working with a Partner:
Working with a partner is an effective way to apply the concepts learnt. By discussing various techniques and strategies, two can gain a better understanding of the concepts and come to a solution quicker.
Working with a partner also aids in discussing complex topics and allows for a more effective division of labour.
10 – Making Use of Educational Resources:
Educational resources are essential for students learning mathematics. Apart from working through textbooks, students should explore tutorials and videos related to the topics studied. Doing so provides students with a more immersive experience, allowing them to understand the topics discussed in a more practical manner.
11 – Joining a Mathematics Club:
Mathematics clubs provide a great opportunity for students to further their understanding of mathematics. Apart from giving students access to teachers and tutors who can guide them in further understanding of difficult concepts, they also provide resources, such as worksheets and practice problems. Furthermore, mathematics clubs can help to foster an appreciation for other mathematical fields and aid in developing a passion for mathematics.
12 – Participating in Mathematics Contests:
Participating in international and national mathematics contests not only provides an opportunity to test one’s understanding of mathematics, but also offers an excellent chance to meet and collaborate with students from across the globe. Such competitions also aid students to develop a good understanding of problem solving and learn a variety of topics relating to mathematics.
13 – Seeking Guidance from Professionals:
Finally, it is wise for students to seek help from experienced professionals in order to gain a better understanding of the field. Professional tutors and mentors can help students to identify weaknesses and improve upon them in a quick and timely manner.
Furthermore, receiving support from professionals also provides students with the opportunity to get direct and constructive feedback on mathematical solutions and strategies.
Conclusion
Mathematics is a subject that requires patience, diligence and consistent practice. To this end, it is important to understand the gradual order in which one should learn mathematics. Starting with the fundamentals and working towards more advanced concepts, the order discussed in this article provides a clear and comprehensive guide of how to learn mathematics.
Finally, making use of available resources, practising problems and getting guidance from professionals are all necessary steps that should be taken to gain a better understanding of mathematics.