There are 4 gems in the Australian Curriculum for Mathematics! Officially they are called the proficiency strands, I like to think of them as the gems that add sparkle and magic to my mathematics lessons. They help me take my mathematics teaching and my students’ learning to higher levels.
The proficiency strands are Understanding, Reasoning, Fluency and Problem Solving. They describe the actions students should engage in when learning and using the content of each year level. They indicate the breadth of mathematical actions teachers might emphasise as they teach lessons and programs of work. There are some examples given at the beginning of every year level for how the proficiency strands might interact with the content. When I am planning I use these suggestions as a starting point, and then think of more ways to incorporate the 4 strands into each lesson and program of work.
The Understanding strand focuses on the connections students make within and between the content they have learned and the new things they are learning. I want my students to make connections between related concepts and apply what they know to support their development of new ideas. Encouraging students to develop mathematical understanding enables them to explore the relationship between the ‘why’ and the ‘how’ of mathematics. I really want my students to see mathematics as a web of connected ideas and skills, rather than each topic being a whole new separate set of knowledge. Some ways I encourage my students to develop mathematical understanding is to seek similarities and differences in the ideas we explore. It can be also be strengthened by having students represent concepts in different ways, in varied contexts and to describe their thinking.
The Problem Solving strand is the one I struggle with the most in my mathematics program. The actions in this strand go beyond posing the usual problems for students to solve, it is more complex. Problem solving situations should provide students with genuine opportunities to make choices (even when it will lead to a wrong answer!), interpret, formulate, model, investigate and communicate solutions. The curriculum materials say students should represent unfamiliar and meaningful situations as well as design investigations. i think the main difference in this approach to problem solving is that the maths content can be taught through problem solving. Setting up situations for students to solve problems using unfamiliar math concepts can be a challenge, but the understanding and reasoning that comes from working through an inquiry is worth it.
Fluency is the strand I am most familiar with from my childhood experiences of mathematics! All my teachers encouraged fluency, often at the expense of understanding and reasoning. The Australian Curriculum says students need to develop skills in choosing appropriate procedures, carrying out procedures flexibly, accurately, efficiently and appropriately, and recalling factual knowledge and concepts readily. Students are fluent when they can calculate efficiently and can make estimations when appropriate. Knowing the meanings of mathematical vocabulary and the facts of mathematics are also examples of fluency that I think are important parts of a mathematics program. I like to think of fluency as the end-game for the content I am teaching. Once my students understand why and how to do something, we work on their fluency. I don’t expect fluency until students have experienced the content across many lessons.
Reasoning is my favourite gem! When I was a child I struggled with mathematics, I always wanted to know the the ‘why’ of what we were learning. My teachers rarely encouraged us finding those answers and many times were unable to answer the questions themselves. As a teacher, I try hard to help students reason with the maths they are experiencing. The Australian Curriculum for Mathematics (ACARA, 2014) puts it best, “Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices.” Reasoning is a powerful force in the mathematics classroom, when students work on and with the skills listed above, the other 3 proficiencies are well supported.
The proficiency strands are well worth devoting more time to developing as we cover the content of the curriculum because they will help us to grow well-rounded mathematicians. Stay tuned, I will look at ways to plan with the gems of Understanding, Problem Solving, Fluency and Reasoning in a future post.
P.S You can download a copy of the posters I have used in this post here Proficiency Strand Posters