Academic journal article Australian Primary Mathematics Classroom

Tools of the Trade: Kathy Arnold Describes Her Experience Using the Assessment for Common Misunderstandings Tools with Her Students. as with Any Tool, She Explains, It Is How You Use the Tool That Makes the Difference

Academic journal article Australian Primary Mathematics Classroom

Tools of the Trade: Kathy Arnold Describes Her Experience Using the Assessment for Common Misunderstandings Tools with Her Students. as with Any Tool, She Explains, It Is How You Use the Tool That Makes the Difference

Article excerpt

This article outlines one teacher's efforts to build her knowledge of students' understandings of mathematics whilst catering for different abilities within a Year 1 classroom, using the freely available Assessment for Common Misunderstandings tools (Department of Education and Early Childhood Development [DEECD], 2007).

It was whilst undertaking postgraduate study in primary mathematics teaching that I began a journey which focussed on improving my own understanding of how children learned mathematics and what constituted best practice in assessing children's understanding of mathematics. As the DEECD (2007, para. 1) points out, "scaffolding student learning is the primary task of teachers of mathematics, but this cannot be achieved without accurate information about what each student knows already and what might be within the student's grasp with some support from the teacher and/or peers." It was at an early stage of my studies that I first became aware of these tools, which were to become the most important 'tools' of my trade.

Charles (2005) makes reference to key features of effective mathematics teachers which include "the grounding of a teacher's mathematics content knowledge and their teaching practices around a set of Big Mathematical Ideas" (p. 9). The Assessment for Common Misunderstandings materials have been "designed to assist teachers identify student learning needs in relation to a small set of big ideas in Number without which students' progress in mathematics is likely to be seriously impacted" (DEECD, 2007, para. 1). The tools provide diagnostic tasks that assess these big ideas from Prep to Year 10, Victorian Essential LearningStandards levels one to six inclusive (Victorian Curriculum and Assessment Authority, 2007). All of the tasks are short, quick and easy to administer.

Getting started

I first used the tools by implementing the Level 1.1 Subitising tool with my whole class during March. No training and minimal preparation was necessary: I read the relevant page, printed the cards and off I went. I was pleased with how little time this actually took--probably about a 100 minute block of administrative planning time to rotate through the whole class. However, after deciding to address the issue of subitising 'whole class', I quickly moved onto the Level 1.2 Mental Objects tool. This particular assessment comes in two parts: the first one uses four counters in a small, non-transparent container with an additional five counters; the second is a small card covered by two flaps, one half has nine dots, the other half has seven dots. The second part of the task is only undertaken if the student is successful at the first part. Again, the tool was quick to implement, with minimal preparation and gave me very clear direction for teaching. The advice helped me to group the students into three stages of development--perceptual, figural or conceptual counters--and gave specific advice as to what sort of activities were required at each stage in order to move these students forward.

Creating student activities

Following this first round of assessment, the advice for teaching enabled me to form three groups of students based on like needs. The first group (six students deemed to be perceptual counters) was given the task of counting on from a given number using number cards and 6 sided dice. This activity came straight from the teaching advice with no modification whatsoever. The second group (figural counters) worked in pairs using subitising cards and dominoes, explaining to their partner what they saw and how they saw it. The third group consisted of two students (conceptual counters) who worked with tens frames solving mental addition problems and playing games like Place Value Path (Siemon, 2000.) The activities were repeated for periods of about ten minutes at the start of our mathematics sessions for about two weeks. The children seemed to enjoy the familiarity of the activities and I was able to roam from group to group, intervening when necessary. …

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