Academic journal article Australian Primary Mathematics Classroom

From Routine to Rich: Developing an Algebraic Reasoning Task for a Middle/upper Primary Class

Academic journal article Australian Primary Mathematics Classroom

From Routine to Rich: Developing an Algebraic Reasoning Task for a Middle/upper Primary Class

Article excerpt

Read how one pre-service teacher, with the right support, was able to adapt standard textbook questions to create rich tasks. In the process, many of the big ideas of algebra were employed and three essential cogs of effective classroom teaching meshed together to create a meaningful learning experience. Read on to find how all of this was achieved.

In many classrooms where mathematics is driven through the demand of having to use a prescribed text book, it can sometimes be difficult for some teachers to see how they can create an engaging lesson. Thinking with and about the mathematics and the learning experiences embedded in good tasks are skills that move beyond the learning of set procedures and the solution of routine problems often seen in text books (Booker, Bond, Sparrow & Swan, 2004). There are also the competing tensions of that lesson being able to be mapped against the prevailing curriculum documents and using to best advantage the limited amount of time given over to teaching mathematics in a busy working week.

As part of one of the undergraduate Bachelor of Education units offered as a specialisation unit in primary mathematics education at The University of Notre Dame Australia, the pre-service teachers were asked to complete an assignment. In this assignment they were given 12 typical algebra text book problems which they were asked to solve and then to take one of these problems and work extensively with it, to turn it into what was referred to as a 'rich' learning experience. Working through the process of solving many problems provides experience to allow the identification of what constitutes a good task (Siemon, Beswick, Brady, Clark, Faragher & Warren, 2011).

The main body of this article is the journey undertaken by one of the pre-service teachers, Courtney, in completing this assessment task and his reflections about the task. It should be noted that this assignment was preceded by much in the way of discussion and modelling of current best practice with an emphasis on developing sound pedagogy backed by current research. In answering the task requirements, Courtney drew the many strands of understanding together to create what was considered to be a cogent and thoughtful reflection which illustrates how a relatively trivial and context-free question can be teased out to provide not just an answer but a series of activities that can lead to developing some key understandings in the area of algebra.

At the conclusion of this article is a small section which outlines some of the Australian Curriculum proficiencies and content links which have been addressed in the completion of this set of activities.

The pre-service teacher's journey

I knew how important rich mathematical tasks were for students within the classroom but I did not know where this would lead me. I believed most students given an algebra question would begin with the idea of completing the questions by following the patterns and initially this was how I approached it. Having been asked to choose a question and reframe it to engage students in deep mathematical thought was a new challenge. I had to put myself in my students' shoes and walk myself through each stage of the question, using concrete materials, representations and ultimately abstract thought to extend the ideas further.

The typical textbook question chosen to use as a stimulus for the development of a useful classroom task was: If the pattern bellow continued in the same way and you used 188 matchsticks to build it, how many fish would there be?

Number of fish      1   2    3    4    5    6    7     ?

Number of matches   8   14   20   26   32   38   44   188

Students within a classroom are regularly confronted with the same style of mathematical questions. This can often lead them to getting the right answer for the wrong reasons. The main focus was to choose a question that could be reframed in such a way as to contextualise it in a meaningful manner. …

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