Does Mathematics Education need a re-think?

Once upon a time Mathematics was easy to teach. A typical lesson would begin with a direction towards a particular page of the text book and would conclude with the ceremonial marking of the answers. This process was repeated over and over, year after year and in the end students would be able to repeat the required method with a satisfactory degree of accuracy. Understanding was not a requirement and as such the teacher needed to know only a little more than the student or perhaps only have ready access to the answer page. But times change and today Mathematics is an area of study that requires a deeper level of understanding from both the student and the teacher. - Read More

Rethinking Mathematics Education

Mathematics holds an important place at the core of all curriculum models for good reason. The traditional focus on Literacy and Numeracy reinforces the special place that Mathematics holds in our educational thinking. The importance of Mathematical thinking to our daily lives is arguably increasing as we rely on computational models and large data sets. Industry, according to multiple reports requires more graduates with a STEM (Science, Technology, Engineering & Mathematics) background and the M in STEM is seen by many as providing the glue which holds the model together. Despite the importance of Mathematics and the high esteem it holds as a discipline too few students are pursuing it as a pathway beyond school and many people report a fear of Mathematics. - Read More

Mathematical thinking presents teachers and students with new challenges

Mathematics is a discipline that is central to all national and state curriculum models. It is one of the core subjects studied by students across the world, and an understanding of mathematics is considered an essential skill for success beyond school. Mathematics is broadly acknowledged as playing an essential role in our lives and its importance in modern times is amplified rather than diminished by our ever-increasing reliance on technology. As is the norm across education, questions are being debated about the nature of mathematical learning and how we might ensure our students leave school with the skills, knowledge and dispositions they need. What does it mean to be a mathematical thinker? - Read More

A Conceptual approach to Big Understandings and Mathematical Confidence

Contemplating the effects of traditional mathematics in "A Mathematicians Lament", Paul Lockhart wrote

"If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done - I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

The traditional pedagogy of Mathematics encourages students to see the discipline as one that requires them to memorise and recall on demand a set of procedures and isolated facts. Speed and correct answers are overemphasised at the expense of understanding and genuine number fluency. As students focus on learning the procedures they fail to make a connection with the logic behind the methods they are using. They develop fundamental misconceptions and develop a narrow and shallow mathematical knowledge. A conceptual approach can change this. - Read More

Number Talks for Number Sense

"Number Talks" is an approach to the teaching and learning of Number Sense. Rather than relying on the rote-memorisation of isolated number facts achieved through drills of "table-facts", Number Talks aim to build confident, number fluency, where learners recognise patterns within and between numbers and understand the properties of numbers and operations. Number Talks are a "mind on" learning task that engages students in an active learning process as they search for patterns, decompose and recompose numbers and develop a flexible understanding. It is achieved through direct instruction methods and facilitative dialogue with the teacher or between groups of peers who have had experience with the number talks methodology. It becomes one of the routines of a classroom focused on mathematical reasoning. - Read More

Teaching mathematicians shouldn't be like programming a computer

Traditional methods of teaching maths have more in common with how we programme a computer than what we might do if we wanted to engage our students in mathematical thinking. We shouldn’t be overly surprised then when our students consider mathematics to be all about learning a set of rules that they need to apply in the right order so as to output the correct response. But is there a better way? - Read More

Bringing Mathematical Reasoning into our Classrooms

Reasoning is at the heart of mathematical thinking. It is what mathematicians do. The importance of reasoning is acknowledged in most if not all mathematical curriculums. In New South Wales it is a part of working mathematically which is described as the thinking and doing of mathematics. Mathematical reasoning is defined by the writers of the Australian Curriculum as follows:

Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. They are reasoning mathematically when they explain their thinking, deduce and justify strategies used and conclusions reached, adapt the known to the unknown, transfer learning from one context to another, prove that something is true or false, and compare and contrast related ideas and explain their choices. - ACARA

With this in mind and a desire to build the capacity of our students to reason, we do well to ask how this might be achieved. How do we teach our students to bring such high order cognitive dispositions to their mathematics? - Read More

Supporting Mathematical Thinking through the Eight Cultural Forces

At the heart of mathematics are a set of connected thinking dispositions. The mathematician uses these dispositions as the cognitive tools of their trade. While the traditional imagining of mathematics might be all about the accurate application of well-rehearsed algorithms and processes, in the real world of mathematics, it is all about the thinking. As we consider what our students need from their mathematical education, we should not overlook the importance of these dispositions. - Read More