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., 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?"

The Magic V task

The Magic V is a task which affords children an opportunity to develop and test conjectures and form generalisations (Widjaja, 2014). The Magic V explores mathematical reasoning giving children the opportunity to, "Investigate and use the properties of odd and even numbers (ACMNA071)" (ACARA, 2013, p. 30). Specific learning objectives addressing reasoning for this demonstration lesson within the MRPLRP included but were not exclusive to: use oral language for equivalence and equivalent number sentences to record, explain and justify solutions; compare and contrast to generalise and develop ideas (conjectures); test ideas (justifying and proving); trial to form conjectures (inductive reasoning); develop a logical argument based on an understanding of equivalence and properties of odd and even numbers (deductive reasoning). There was also an emphasis on developing mathematical language, such as "equals" and "does not equal", as the children explored and explained properties of odd and even numbers. Skills associated with problem-solving, such as applying systematic trial and error to seek solutions, were also supported in this lesson.

The lesson commences with the teacher referring to the two Vs on the board (see Figure 1a and 1b) and inviting the children to share what is the same about the Vs.

Typical responses are "Number 1 to 5 are used in both Vs", "5, 3 and 2 are in the same spots" and "All the numbers add up to 15." Once the sameness of the two Vs is exhausted, the teacher invites the children to share what is different about the two Vs. …

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