Choy, Ban Heng

When mathematics teachers plan lessons, they interact with curriculum materials in various ways. In this paper, we draw on Brown’s (2009) Design Capacity for Enactment framework to explore the practice of adapting curriculum materials in the case of a Singapore secondary mathematics teacher. Problems from the textbook used and the worksheets she crafted were compared to determine how she adapted the content. Video-recordings of the lessons and post-lesson interviews were used to clarify how her personal teacher resources contributed to her design decisions. The findings suggest that her seemingly casual use of problems from the textbook are in fact unique variations of adapting curriculum materials.

The urgency of teaching diverse learners is aptly demonstrated in many parts of the world as the ethnic, racial, class, and linguistic diversity grows rapidly. Such diversity not only brings about opportunities for creative teaching, but also challenges for ensuring educational equity and providing high-quality teaching for all students from diverse backgrounds, especially those presently underserved by the educational system (Buehl, & Beck, 2014; Civitillo, Juang, & Schachner, 2018). Researchers have found that teachers prepared for working with students from diverse cultural backgrounds need to embrace beliefs that recognize the strengths of cultural diversity (Anagnostopoulos, 2006; Banks et al., 2005; Fives & Buehl, 2014; Gay, 2010). Thus, exploring and challenging teachers’ beliefs about cultural diversity should constitute a major objective in teacher professional learning. However, only a few studies have examined how in-service teachers’ beliefs are enacted and shaped in professional learning community practices (Little, 2003; Tam, 2015; Turner, 2011), and focused even less on teachers’ beliefs about cultural diversity (Pang, 2005; Sleeter, 1992). There are a few studies examining teachers’ cultural beliefs about diversity in Singapore, and found that Singaporean teachers are influenced by prevailing political ideologies, and have ambiguous perceptions towards students from less advantaged backgrounds (Anderson, 2015; Alviar-Martin & Ho, 2011; Dixon & Liang, 2009; Ho & Alviar-Martin, 2010; Ho et al., 2014; Lim & Tan, 2018). However, these studies discussed teachers’ individual perceptions of disadvantaged learners without further exploring how these perceptions are mediated by influences from professional development practices, where teachers’ cultural beliefs about diversity issues are in (inter)action as ideas emerge, clash, change, and (dis)agree with each other when teachers work together.

In this paper, we re-examine the commonly-held notion that typical problems, such as textbook exercises and examination questions, are not useful for orchestrating mathematically-rich learning experiences. Drawing from a larger design-based research project, we present a case study of Alice, a secondary school teacher, who orchestrated a productive discussion by using examination questions. We describe how she perceived and harnessed the affordances of such typical problems before and during her lesson. Findings suggest teacher noticing as a key mechanism to enable teachers to unlock the mathematical potential of such problems.

We study some essential ideas of Banach spaces which provide n framework for mathematical analysis, and investigate the smoothness of norms and their impact on the topological properties of these spaces. We also take a first look at rough norms and give some equivalent conditions for a norm on a Banach space to be rough.

Typical mathematics problems, such as examination-type questions, are often used in classrooms to develop students' procedural fluency. In this article, we describe and analyse what a secondary school mathematics teacher noticed about the affordances of such a problem, as well as how she orchestrated a mathematically productive discussion using the adapted problem in class. The findings suggest that a teacher's productive noticing of the affordances offered by typical problems can enhance the learning experiences of mathematics students.

Teacher-designed notes and worksheets are common instructional materials used in Singapore mathematics classrooms that are critical to guiding the flow of a lesson. However, making sense of how teachers design these materials is complex and research that reports on their creation is only just emerging. In this paper, we propose a tri-lens approach for capturing teachers’ design processes by using notions of pedagogical reasoning and action, curricular noticing, and resources, orientations and goals. We demonstrate how these frameworks combine to form a tri-lens for unpacking important aspects of teachers’ design work using the example of Mrs Fung, an experienced secondary mathematics teacher. We further illustrate how a tri-lens approach can provide a more comprehensive portrait of the teacher and argue that this approach can potentially address the complexity of teachers’ design processes when crafting instructional materials.

In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic cross-multiplication method. Analysis of Isaac’s introduction and use of the cross-multiplication method suggest his key considerations were linked demonstrating the efficiency of the cross-multiplication method, while also helping students to make making meaning from the cross-multiplication method.

Despite recent calls to adopt practice-embedded approaches to teacher professional learning, how teachers learn from their practice is not clear. What really matters is not the type of professional learning activities, but how teachers engage with them. In this paper, we position learning from teaching as a dialogic process involving teachers’ pedagogical reasoning and actions. In particular, we present a case of an experienced teacher, Mr. Robert, who was part of a primary school’s mathematics professional learning team (PLT) to describe how he learned to teach differently, and how he taught differently to learn for a series of lessons on division. The findings reiterate the complexity of teacher learning and suggest possible implications for mathematics teacher professional development.