Academic journal article Australian Primary Mathematics Classroom

# Promoting Reasoning through the Magic V Task

Academic journal article Australian Primary Mathematics Classroom

# Promoting Reasoning through the Magic V Task

## Article excerpt

Reasoning in mathematics plays a critical role in developing mathematical understandings. In this article, Bragg, Loong, Widjaja, Vale & Herbert explore an adaptation of the Magic V Task and how it was used in several classrooms to promote and develop reasoning skills.

The importance of reasoning

Mathematical reasoning is the foundation of deep understanding (Bragg, et al., 2013). Adaptive reasoning is viewed as "the glue that holds everything together, the lodestar that guides learning" (National Research Council, 2001, p. 129). The importance of reasoning is noticeable in its inclusion as an explicit learning requirement of many nations' curriculum documents (Loong, Vale, Bragg & Herbert, 2013) including the Australian Curriculum: Mathematics (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2013) where it is one of four designated proficiency strands defined as:

Students develop an increasingly sophisticated
capacity for logical thought and actions,
such as analysing, proving, evaluating,
explaining, inferring, justifying and generalising.
Students are reasoning mathematically
when they explain their thinking, when
they deduce and justify strategies used and
conclusions reached, when they adapt the
known to the unknown, when they transfer
learning from one context to another, when
they prove that something is true or false and
when they compare and contrast related ideas
and explain their choices. (p. 5).

Opportunities to reason should commence at the earliest opportunity for children and as they progress, their reasoning should become more sophisticated when supported by teachers through a systematic approach (Stacey, 2013). The Mathematics Reasoning Research Group at Deakin University developed the Mathematical Reasoning Professional Learning Research Program [MRPLRP] to support and further teachers' knowledge of reasoning to foster the critical engagement of their students in mathematical reasoning. In this article, we describe our adaptation of the Magic V task (http://nrich. maths.org/6274), in the second of two reasoning lessons demonstrated in three Victorian primary schools and one Canadian elementary school in our project to assist primary teachers to promote and support mathematical reasoning in middle and upper primary classes. See Bragg, et al. (2013) for a full description of the first reasoning lesson called "What else belongs?"