Editorial.

Day, Lorraine

Welcome to the first issue of Australian Primary Mathematics Classroom for 2016!

With the beginning of a new school year comes an excitement for planning even better learning experiences for our students. We try to remember all of those great ideas we had last year (and forgot to write down!) about how learning could be enhanced within our classrooms. The articles in this issue provide food for thought as planning for the year ahead progresses.

McDonough, shares classroom stories in early years' classrooms, providing three main messages for teachers planning to use concrete materials. Importantly, she makes it very clear that it is how the teacher sets up the learning opportunities, asks key questions and encourages students to explain their thinking that makes the learning with concrete materials so powerful, not the materials themselves.

Hurst and Hurrell share some examples from a current research project with Year 6 students to illustrate how a combination of conceptual understanding and procedural fluency is necessary to develop multiplicative thinkers.

They investigate the understanding of the vertical algorithm used by most of the children in the study and how it links to the children's understanding of place value.

Khosroshahi and Asghari use the case of the associative rule to demonstrate methods for encouraging students to use a range of efficient mental and written strategies for addition and subtraction problems. They stress the importance of learning activities that assist students to recognise and use numerical structures that can be easily translated for understanding of algebraic structures at a later time.

West provides an example of how the problem solving strategies of 'looking for patterns' and 'solving a simpler problem' can be used as the basis to improve student understanding and mathematical reasoning. He provides an example of how an investigation based on the study of patterns and relationships may be scaffolded for students to investigate powers, place value and indices.

Referring to the joint AAMT/Australian Industry Group report that identified estimation as an essential skill in the workplace, Mildenhall's article focuses attention on the importance of estimation, as a tool for mathematics and as a transferable life skill. There are many opportunities for estimation within each school day, which are often overlooked by busy teachers. Mildenhall asserts that if students can learn to estimate confidently within meaningful contexts during their primary school years this confidence may be transferable for use outside of the classroom.

A framework for assisting teachers to choose both concrete and digital materials to promote student learning at various experiential stages is developed in Larkin's article. The framework's use is demonstrated as well as using it to evaluate the quality of two notionally similar apps. Tucker, Moyer-Packenham, Shumway and Jordan look at four case studies of Year 2 students demonstrating how mathematical applications may help to reveal or develop mathematical understanding, but may also conceal mathematical understanding. They makes suggestions about aspects teachers should consider when selecting apps for particular students.

Bronwyn Welch shares vignettes of partnerships between primary classrooms and practising mathematicians as part of the CSIRO Mathematicians in Schools program. The Proficiency Strands of Problem Solving and Reasoning are at the forefront of these partnerships and students are able to see that mathematics is a human endeavour embedded in much of what we do and in the way problems are solved.

This issue provides many ideas and opportunities for teachers to reflect on their teaching and the learning experiences they provide their students. Wishing you a wonderful school year ahead!