The aim of life is to live, and to live means to be aware, joyously, drunkenly, serenely, divinely aware.

Happy New Year to all! May we all venture forth into this new year with the resolution to be more ‘aware’ of things (this post’s title is a Henry Miller quote, one of my favourites). Despite the time pressures of the academic immediate – usually administratively based – and the things that anchor us in the everyday, I believe it is essential that we find the time and the headspace to be aware of knowledge, explore ideas and read and hear voices that influence our teaching and learning.


“And thus do we of wisdom and of reach

Find direction…”

(apologies to Polonius in Shakespeare’s Hamlet for modifying his speech to suit my own purposes!!)


“For classrooms to be cultures of thinking, schools have to be cultures of thinking for teachers”

Ron Ritchhart – at AISV’s Establishing and Sustaining Professional Learning Communities inservice February 29, 2008


I would like to start this year by reflecting on and reviewing a few books that helped increase and deepen my own awareness of things educational in 2008.


(1)  Exceptional Outcomes in Mathematics Education by John Pegg, Trevor Lynch and Debra Panizzon


This is a small publication I was introduced to at the Summer School for Teachers of Mathematics in early 2008. It is the result of a project conducted jointly by the University of New England, the University of Western Sydney and the New South Wales (NSW) Department of Education and Training. This project identified and explored the factors leading to exceptional outcomes in junior secondary classes in the Australian state of NSW. Primarily, it is of most interest to Heads of Mathematics Faculties but makes interesting reading for anyone involved in mathematics education within a secondary school setting. Chapters include Faculty Staff Characteristics, Faculty Practices, Teacher Practices and Identified Themes Contributing to Exceptional Mathematics Faculties. The stand-out of this book for me was the statement that individuals affect one class at a time. To have school-wide good results, it was necessary to move the whole team of teachers forward. Even ‘islands’ of good teachers weren’t particularly effective. A good school needed

*a mission of high educational outcomes

*a capable and supportive executive (at least one ‘legend’)

*sound organisational and administrational structures in place

*workable student welfare and support programs

It was mentioned that what we sometimes call ‘professional respect’ was actually a way of not scrutinising each other’s teaching and maintaining a protective layer around us that enabled us to get away with not authentically reflecting on our teaching and effectiveness. Interestingly, the research team discovered that the conversations in the science, maths and English classrooms they visited were remarkably similar – all focused on challenge, rigour and teaching for understanding.

Successful faculties were the ones that could align themselves with the school policies better than others.

Aspects of faculties that were high-performing:

*strong sense of team

*high standards expected of colleagues

*faculty seen as ‘family’

*stable staff

*enculturation of new staff

*capable faculty leadership

*high expectations of student performance

*adequate programs and resources

*ongoing mentorship and sharing of resources and ideas by colleagues

*ongoing reflective, informal practice

*professional development occurred regularly

*physical infrastructure promotes teamwork

*disagreements resolved professionally

In many of these faculties, assessment procedures were the catalyst for the above to occur. There was collaborative setting and marking, quick and effective feedback given to students, grading was a focus and assessment used as motivation for students. The most important feature seems to be that teachers are not resting on past laurels and always looking for ways in which to improve.

“Outside show is a poor substitute for inner worth”


(2)  Understanding by Design and Schooling by Design by Grant Wiggins and Jay McTighe


The Understanding by Design (UbD) book has been around for some time and impressed me greatly. The UbD framework allows us to create a curriculum that enables and supports thinking and understanding. Learning is a product of thinking. Curriculum should also be a product of thinking. Can teachers articulate the reasons for why certain content is to be included in the syllabus? What are the ‘big ideas’ we want our students to understand? What questions could we ask that develop these understandings in our students? How will we know if students have developed these understandings? These are important constructs on which to base a curriculum. This curriculum should focus on challenge, complexity, opportunities for discussion and analysis, no set approach for solution, going beyond the straightforward and stretching students’ thinking to develop understanding.



Well-documented curriculum is important because it sets the agenda and articulates the vision and provides an enforceable structure, on which improvements to teachers’ practice can be based and referred back to, but we have to simultaneously and continuously work on changing our beliefs about teaching, pedagogy and methodology otherwise the curriculum design will be largely ignored. Teachers ultimately determine how any curriculum will be interpreted and our beliefs and ways of thinking will consequently determine the extent and success of any change. It is the teacher and his/her pedagogical beliefs about how the learning should be shaped that will ultimately determine whether or not learning will occur, how authentic that learning will be and the quality of the learning that happens in our classes.


I liked the simple (but not simplistic) three-step plan to designing curriculum and exploring understandings within the discipline. This three-stage approach of the framework referred to as ‘backward design’ involves planning with ‘the end in mind’ by first clarifying the understandings one seeks then thinking about the evidence needed to certify that students have achieved those understandings then planning the means by which those understandings will be attained. It not only provides a well-articulated, coherent and comprehensive structure for curriculum, it also compels those designing the curriculum to explore their own constructs of their knowledge of mathematics and pedagogical practices.


The Schooling by Design book explores the wider perspective of the whole school in the quest for teaching for understanding. It is my belief that, for a professional learning team to be involved in productive decision-making that can positively influence the direction taken by a school, its membership needs to include those who have the capacity to do so. Any initiative involving curriculum will need to be actively supported by Heads of Faculty. These people have much influence over the curriculum direction of their areas of responsibility. They are generally very experienced and respected practitioners within their discipline areas. They co-ordinate the content, articulate the vision for the methodology employed and have responsibility for the documentation of the curriculum. They bring knowledge to the group and ‘reach’ to the school. They can ‘seed’ the impetus and drive any reform. Knowledgeable members of staff who are open-minded about their practice and who continually seek to improve what they do in order to provide rich and authentic learning experiences for our students can extend their own reach as well as that of others within their sphere of influence, through their involvement in professional learning teams. In order for the whole school to move forward, it is necessary, in my view, to involve as many members of staff in the process as possible. This book provides leaders of learning with a strong theoretical background and ideas as to how to accomplish this in schools.


(3)  Teaching Secondary School Mathematics by Merrilyn Goos, Gloria Stillman and Colleen Vale.


Teachers make a difference to the quality of student learning. This book attempts to ‘untangle the complex relationships that exist between teaching practices, teacher characteristics and student achievement’ (taken from p3).

Sections include Mathematics Pedagogy, Curriculum & Assessment, Teaching and Learning Mathematical Content, Equity and Diversity in Mathematics Education and Professional and Community engagement. It is clearly written and easy to read and understand. It contains up-to-date research findings, multiple examples that can be used in the classroom and examples of performance tasks that target specific big ideas. It also has many ‘Review and Reflect’ sections throughout chapters, in which teachers are given tasks that help us to identify our own beliefs, design assessments, think about the whys and hows and extend our own professional knowledge bases. These would make excellent discussion starters in faculty meetings.

Highly recommended.


(4)  Improving Student Achievement – A Practical Guide to Assessment for Learning by Toni Glasson


From the Introduction: ‘ an era in which curriculum documents describe specific standards, the teacher’s role is one in which they are asked to make sure that increasingly greater numbers of their students are able to demonstrate the ability to meet those standards. How is this to be done? The answer lies, to a significant extent, in changing the way in which we regard and use assessment in the classroom. In itself, this sounds quite simple, but in reality it requires a major shift in thinking and, indeed, in the very essence of our attitudes to teaching’


This book looks at Learning Intentions, Success Criteria, Strategic Questioning, Effective Teacher Feedback, Peer Feedback, Student Self-Assessment & Making Formative use of Summative Assessment. It is based on the seminal research into assessment of Black and Wiliam. It has a firm classroom-based approach and, like the previous book mentioned, it has sections at the end of each chapter headed Professional Learning Focus  that could be used to develop teacher learning during staff meetings or other teacher learning situations.

Also highly recommended.


(5)  The Brain that Changes Itself by Norman Doidge


I’m only about two-thirds through this book at the time of writing this post, but it has already impressed me greatly.

From the Preface: ‘This book is about the revolutionary discovery that the human brain can change itself…children are not always stuck with the mental abilities they are born with…thinking, learning and acting can turn our genes on or off, thus shaping our brain anatomy and our behaviour…people [can] rewire their brains with their thoughts. The neuroplastic revolution has implications for our understanding of..learning. While the human brain has apparently underestimated itself, neuroplasticity isn’t all good news; it renders our brains not only more resourceful but also more vulnerable to outside influences. Neuroplasticity has the power to produce more flexible but also more rigid behaviours. Once a particular plastic change occurs in the brain and becomes well-established, it can prevent other changes from occurring’


As educators, we can help our students (and ourselves!) formulate and strengthen connections that are of benefit to present and future learning and assist them to break free of others that might not be so beneficial for their learning. What teaching and learning strategies and practices can support this? Which ones hinder this? We know that teachers are at the centre of student learning. We have a tremendous responsibility and, although not directly aimed at education, I think that every teacher should read this book as changing the brain is surely what we do for a living!




Best wishes for an informed, productive, joyful year of teaching.


About Linda

I have been involved in secondary mathematics education in Victoria, Australia for over 25 years.
This entry was posted in Ideas for teaching & learning, Pedagogy, Students, The discipline, The profession, Things that engage, Vision. Bookmark the permalink.

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