There are five components of mathematical proficiency. The first strand of mathematical proficiency will help you develop a conceptual understanding of what you are doing. You will have knowledge, as well as the ability to comprehend the major ideas that you may be exploring. For instance, conceptual understanding will make it clear that 4X8 is the same as 8X4.
If students are familiar with procedural fluency, they will be able to perform simple mathematical operations, but may not understand the concept behind it. For instance, you may be able to regroup, but may not entirely comprehend place value as you are only proficient with “carrying the one.”
Flexibility with numbers can be achieved through strategic competence. For instance, you can easily tell that 6+9 = 15, 8+6+1 = 15, or 8+9-2 = 15. Strategic competence helps you think of numbers in various ways.
Math becomes more logical with adaptive reasoning. You will be able to justify and explain what you are doing. For instance, students will be able to provide a logical explanation as to how they reached at a particular result or solution, thereby justifying your answers through mathematical talk.
If you have a strong professional disposition, you will be able to persevere in the hardest of environments. Your mathematical outlook will be confident and you will know your capabilities. For instance, you may say that a certain problem is tricky, or that you may have to resort to another method to solve it, or request explanations until you thoroughly understand it. But once understood, the problem can be solved with relative ease. With maths help from a maths tutor, Mathematical Proficiency can be attained by understanding how to use all these aspects together.