Mathematics Education Abstracts of Presentations

Productive Teacher Noticing: An Untapped Resource in Mathematics Education

Dindyal Jaguthsing

During the past few years interest in Teacher Noticing has considerably increased. The idea that teachers attend to, interpret and respond to significant events in the classroom ¬¬(Jacobs, Lamb, & Philipp, 2002; Van Es & Sherin, 2008) is a prominent aspect that has been highlighted in the literature. In this presentation, we highlight the related idea of Productive Teacher Noticing (PTN) that has the potential to enhance classroom instruction even further. We describe the case of Alice, a teacher from our project, who through her practice that involved the use of typical problems, was influential in our re-conceptualisation of PTN in the teaching of mathematics.

Students’ Errors and Misconceptions in Quadratic Inequalities

Hng Choon Keong

This qualitative study set out to identify the errors which secondary students commonly make when studying quadratic inequalities; understand what misconceptions students have; and investigate why students make these errors and end up having these misconceptions. Data were collected from 58 students coming from five different classes. The students had to complete a test with 11 items and twelve of them from different ability ranges were selected for one-to-one interviews. The five teachers who taught these students were also interviewed. It was found in this study that students made four main categories of errors aligned with the framework proposed in a study by Godden et al. (2004) – careless errors, procedural errors, calculation errors and application errors. Results also showed that students routinely applied their prior knowledge about equations incorrectly when solving quadratic inequalities.

The title of my talk is Development and Field-Testing of an Instrument for Rating Cognitive Demands of Mathematical Assessment Items

Ng Wee Leng

Teachers’ judgements of the cognitive demand of assessment items have implications for the nature of students’ learning experiences. However, existing taxonomies for classifying cognitive demand are often not customised for A-level mathematics teachers to use. This talk reports on the development and field-testing of a cognitive demand instrument specifically for helping A-level mathematics teachers sharpen their judgements of the cognitive demand of A-level mathematical assessment items.

Making a Teacher’s Thinking Visible through the lenses of Commognition and Teacher Noticing

Chia Su Ngin

Learning Mathematics in Primary Schools is often mediated through the use of multiple representations. However, teachers may not pay enough attention to the way they use these representations. Given that the translations between representations and language may not always be smooth, it may be insightful to examine how teachers mediate learning through the use of multiple representations and language. In this presentation, I will share key ideas in commognition and teacher noticing before I present a case study of how Hannah, a teacher, mediate learning of percentages in her class. I will also introduce the idea of a ‘Mediation Flowchart’ and demonstrate how these flowcharts can be used to describe and analyse a teacher’s use of language and multiple representations.

The Changes of Four Thai Primary 6 Mathematics Teachers’ Reflections on Their Teaching

Muanfun Yaowiwat

This session will report the experiences of conducting a 4-month video-based professional development programme to a group of Primary 6 mathematics teachers in Thailand and some preliminary findings related to the teachers’ changes of their reflections on teaching. Four primary 6 mathematics teachers participated in the study. They attended a 3-day workshop to become familiar with the mediation strategies framework, after which each of the teacher was video-recorded during mathematics lessons where mediation strategies were used. Stimulated recall interviews were conducted for the teachers to reflect on their teaching. During the presentation, the research methods will be also discussed.