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The Strands of Mathematical Proficiency

Updated: Feb 8, 2021

One of the most frequently heard buzzwords in Education circles today is the acronym STEM. Needless to say, the subject areas of Science, Technology, Engineering and Mathematics (STEM) make up the pillars of a progressive and productive society in the 21st century.


For us, one particular subject area across the STEM group stands out in the context of its magnitude in everyday life and the very world we live in.


Mathematics: dating back to the very history of our universe, mathematics is the underpinning body that fuels the progress of science, technology and engineering. Without mathematics, we wouldn’t be able to even know how long it takes to get ready in the morning, or what time we should be going to sleep to stay healthy. It is a crucial part of our everyday lives and is the backbone of our understanding of the world around us.

Education authorities understand this and emphasise this discipline across a multitude of skill levels, with varying strands of mathematical proficiency.


Today, we will cover the NAPLAN strands of mathematical proficiency and explain to you why they’re important and how we apply these concepts to our own framework for teaching mathematics.


The purpose of NAPLAN’s document is to “capture what they believe is necessary for anyone to learn mathematics successfully” in the context of an education system.


The five strands of mathematics:



Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with a strong conceptual understanding are more advanced than just knowing the facts and methods. They understand concepts in the context in which it is supposed to be used and how they can be applied in solving a problem. This is crucial to a student’s ability to tackle surprise questions in a testing environment and also builds their foundation to be able to think more laterally for other problems they may encounter. Our lesson delivery framework supports the development of this strand as it pivots from the traditional rote-learning, high-repetition style of tutoring.


Procedural Fluency refers to the knowledge of mathematical procedures, its applications and the skill in performing them flexibly, accurately and efficiently. Students with procedural fluency are able to quickly and accurately perform basic computation of whole numbers without referring to other aids.


The importance of procedural fluency is underpinned by the education system’s need to test ability in a limited time frame. Having this fluency will help a student solve mathematical equations, allowing them to ultimately prioritise their efforts on solving the more complex steps. Our lessons focus on empowering students with a framework to solve number problems quickly and accurately, giving them the edge in test performance.


Strategic Competence refers to the ability to formulate mathematical problems, represent and solve them. Having such a skill is important, not only for students but also all of us in everyday life. Strategic competence gives students an advantage outside of the school environment, including university scholarship applications, internship applications or more generally, their preparedness for the obscurity of adult life. It is the strand crucial to mastering the art of lateral and critical thinking, which applies to all facets of our lives; in or out of an education context. This strand is an area of study that is now receiving significant attention in light of the changes to the OC and Selective entry test, which focuses on a student’s capacity to think creatively and critically. Our programs, developed on our ethos of nurturing life-long learners, help support and challenge students to ensure they develop the strategic competence to embrace and conquer any obstacles they may encounter..


Adaptive Reasoning refers to the capacity to think logically about the relationship between concepts and situations. It is a strand which allows students to piece different parts of problems together, and draw connections between them. In mathematics, adaptive reasoning is the glue that binds everything and encourages students to navigate through many different facts, procedures and concepts.


Adaptive reasoning is, in some ways, a concatenation of all of the strands coming together. It allows students who can grasp a multitude of mathematical concepts to bring these together and create something special. Our programs not only teach our students concepts, but also explore how they relate to one another and the different applications they have for solving real-world problems.


Productive Disposition refers to our habitual inclination to see mathematics as a sensible, useful and worthwhile topic paired with a belief in diligence and one’s own efficacy. In some ways, it is the advocacy of mathematics and a student’s confidence in their own ability.


Having a passion for mathematics can lead to an increased confidence in a student’s ability to solve problems confidently and accurately, which aids the overall development of any student’s academic arsenal. Our teaching style is grounded on positive reinforcement and intrinsic motivation, to cultivate confident and passionate learners. .


With rapidly developing technology, no one can anticipate all the skills that the students will need to face the complexities ahead. The strands of mathematics is a crucial part of a students’ learning journey as it provides them with the foundation of mathematical proficiency. Through our programs, we provide students with opportunities to acquire the knowledge and skills required to grow mathematically proficient; ready to face the challenges of the modern world.

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