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This traditional pedagogy results in students developing a negative attitude towards mathematics. Many develop a mathematical phobia and believe that they are not a "maths person". When confronted by challenging mathematics they retreat and have no or only poor strategies with which to approach new ideas. This all leads to a decline in the number of students pursuing mathematical learning beyond the years where it is compulsory. Fortunately there is a growing body of research that shows there is a better way. 

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. 

Our beliefs about mathematics play a significant role in how we approach learning within the discipline. These beliefs are established by the nature of our early engagement with mathematics and are difficult to change once established. For many people mathematics is viewed as a subject that is not for them. Indeed the situation is so bad that many people will say that they are not a maths person and approach mathematics with fear and anxiety. 

What becomes clear, as you dive further into the emerging research that connects what we know about learning, mindsets, dispositions for learning and the development of mathematical understandings, is that a new approach is required. We need to move away from memorisation and rule based simplifications of mathematics and embrace a model of learning that is challenging and exciting. We can and should be emerging all our students in the beauty and power of mathematics in learning environments full of multiple representations, rich dialogue and collaborative learning. 

The landing of the Perseverance rover on Mars is an excellent catalyst for a discussion with students about the nature of Mathematics. It is a chance to inspire curiosity and wonderment and to do so through a mathematical lens.

Of all the subjects that our students engage in, mathematics is the one most requiring an injection of learner agency. What is it about mathematics that engenders it to modes of teaching that are so heavily teacher-directed? How might this change if we seek to understand the place that learner agency plays in producing learners who will emerge from our classrooms with a love of mathematics and a deep understanding of its beauty?

The shift away from teaching for the rote memorisation of prescribed methods requires teachers to rethink their approach to the discipline. With this new pedagogy comes a need to understand the processes of mathematical thinking in ways not previously required. When we require our students to be able to reason and problem-solve through unique challenges we also require our teachers to have an understanding of the mathematical moves that their learners are likely to call upon.

I have just had the opportunity to spend the weekend learning alongside a large group of mathematics teachers. After a day and a half of talking and thinking about mathematics teaching, I am excited to get back to school and try out some new ideas. There were also some key takeaways for me that I share below. These are the questions or wonderings that my mind wandered to while listening to the numerous talented speakers over the past two days.

Number Talks are a wonderful way to see where our students are with their mathematical thinking. As a part of a daily routine, a Number Talk promotes number sense and mathematical reasoning. In this post, I revisit what a Number Talk can reveal about our students' understanding of mathematics, and how they might be used to promote a fresh perspective. In addition, I examine a success criteria for Number Talks that is more expansive and recognises their true power.

How do move from an emphasis on rote learning of procedures in mathematics towards a focus on mathematical reasoning?

Traditional methods of teaching maths have more in common with how we programme a computer that 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?

Videos of mathematics in the movies. Engaging for kids to see!

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.

Reasoning is at the heart of mathematical thinking. It is what mathematicians do. But how do we teach it?

Looking at the New Directions for school leadership and the teaching profession discussion paper, the only evidence presented to support the assertion that Victoria's education outcomes are not improving is the report "Challenges in Australian Education: results from PISA 2009: the PISA 2009 assessment of students' reading, mathematical and scientific literacy" Specifically the New Directions paper focuses on reading literacy, where in 2009, 14,251 students were given a two-hour pen and paper comprehension test. To get an idea of what types of competencies the reading test is assessing we can look at the sample test , with questions range from comprehension about a letter in a newspaper, the ability to interpret a receipt, comprehension around a short story, an informational text, and interpreting a table. While it doesn't seem unreasonable to want our students to be able to accurately perform these kind of tasks, these tests are not a true or accurate representation of the skills and competencies our students need in today's technology driven world.

"So, we now have an elegantly mathematical approach to mowing the lawn. But, alas, that analysis took a while, and it seems to be getting dark. The mowing will just have to wait until next weekend."

A fascinating and detailed mathematical discussion about how best to cut the front lawn.

In times when we taught face-to-face, some of these challenges would be overcome through the use of concrete materials, at least with younger students. Unfortunately, it is common for the use of concrete materials to decline as students grow older. Fortunately, this pattern, and the prejudiced beliefs on which it is founded, are today being questioned.

Microsoft has some great Teacher Guides available. The guides have teaching tips and step-by-step instructions on a variety of topics and tools and technologies. The guides are all free and downloadable in PDF form. Topics include: Critical Thinking in web searches, Windows Movie Maker, Free tools from Microsoft, Digital Storytelling, Microsoft Office, web apps, OneNote, Bing and Mathematics, and Accessibility in the Classroom. The guides are easy to use and read and a great resource

My thought for this site is that you could use it to generate an interdisciplinary writing task with students. They select a starting location then find its opposite; the writing task is that they narrate the journey from the starting point to its opposite. They could research the different places they pass through and choose their own line of travel (making it either more realistic or fanciful). Integrated activities might include geography (different environments); mathematics (distance and measurement); science/physics (distance & displacement).

A collection of math posters that outline key elementary mathematics concepts - addition, subtraction, multiplication, division, quotient, difference, product

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