# PMA BLOG

*ENJOY THE MATHEMATICAL MUSINGS OF OUR PMA COLLEAGUES AS THEY START A CONVERSATION ABOUT MATHEMATICAL LEARNING AND TEACHING ISSUES THAT MATTER TO THEM.*

*Kym currently works as an Education Consultant with his company “Futurity Learning” He has worked as a Principal, Teacher, Curriculum Consultant and Writer both here in the Department and overseas. He brings a passion for learning and the importance of creating “powerful learners”, as well as an outstanding breadth of knowledge about a broad range of learning research to any session he runs.*

**Four Tips for Developing Thinking Skills in the Mathematics Learning Space**

**Thinking that is productive, purposeful and intentional is at the centre of effective learning. By applying a sequence of thinking skills, students develop an increasingly sophisticated understanding of the processes they can use whenever they encounter problems, unfamiliar information and new ideas.**

**Australian Curriculum, General Capability: Critical and Creative Thinking, Introduction**

One of the challenges faced by Mathematics educators in the hustle and bustle of modern schooling is to ensure that all learners are developing as thinkers and creators of Mathematics, rather than mere consumers. Where there is an over-reliance on explicit teaching (in particular, the learning by repetition of mathematical facts and formulae), it is entirely possible that young people can spend their time learning Mathematics engaged in activities that require a lot of memory, but little critical and creative thought.

The team at Project Zero, based at the Harvard School of Education, have been documenting a wide range of ‘thinking routines’ that can be used to assist in the purposeful teaching of thinking in education sites at all levels. One of the routines, named MYST, is aimed at educators as a means of reflecting on practice in any area of education.

MYST is used here to provide four ‘tips’ – or more likely, reflection points for collegial discussion – for developing thinking skills in the Mathematics Learning Space:

**M – Me**

How do I make my own mathematical thinking ‘visible’ so that learners see me as a model and resource for their own thinking?

*Where I am using explicit instruction or individual or group coaching during mathematics learning time, am I explaining all my thinking, including how I self-correct and use inquiry skills to build my understanding of the mathematical concepts involved?*

**Y – You (the learners I am helping become thinking mathematicians)**

How do I provide opportunities for learners to make their own mathematical thinking visible to their peers and to me? Which listening and speaking skills will they need to be effective sharers of their mathematical learning?

*What thinking dispositions (inclinations to think and awareness of ways to think in a given situation) do I want to develop in learners of Mathematics? (These might include them being broad and adventurous, being able to question and be intellectually curious, being willing to seek clarity and understanding and continually demanding justification and evidence, to name a few).*

**S – Space**

How is the learning space we use as a base for Mathematics organised to facilitate the thinking of learners?

*The Sydney Centre for Innovation in Learning (SCIL) have put into practice some interesting and challenging ideas around flexible learning spaces, describing spaces like*

· *the campfire (a place for conversation, presentations and direct instruction),*

· *the cave (where learners can go to work individually on investigations, solving problems and consolidating understanding)*

· *the Mountain Top (a place to share ideas and publish and broadcast thinking to benefit others).*

*How might incorporating ideas like these to help make our mathematical learning spaces ore flexible support learners over time?*

**T – Time**

How do I provide time for thinking during our time learning Mathematics together? How do I see the mathematical thinking of each learner developing over time?

*Time is such a crucial resource. Even though educators now find themselves time poor in terms of the vast expectations others have of them, prioritising thinking time and providing opportunities for learners to collaborate and coach each other provides rich rewards in terms of developing thinking skills in the Mathematics Learning Space.*

**Follow-up Links**

www.visiblethinkingpz.org for more information about Project Zero and Thinking Routines.

https://www.linkinglearning.com.au/re-imagining-learning-spaces-to-inspire-contemporary-learning-part-one-models-for-change/ is an interesting blog by Kay Oddone, combining the ideas of Ewan McIntosh and David Thornburg (whose conception of spaces crossed over with those of SCIL).