Unpacking the complexities of Singapore secondary mathematics teachers' design of instructional materials
Authors:   , Chin Sze Looi 
Published: October 2024

Lesson planning plays a critical role in teachers facilitating meaningful lessons and achieving their instructional goals. Research on how teachers think about lesson planning has generally examined the lesson plans they produce, which include their learning objectives, the activities they might use, and how they will evaluate if students have achieved the learning objectives. In this study, I propose an alternative site for making sense of teachers’ lesson planning thinking: teacher-designed instructional materials. In general, the materials that mathematics teachers use in instruction tend to be curriculum materials, such as textbooks and workbooks. However, in Singapore, it is common for mathematics teachers to use these curriculum materials as base materials to form the foundation for designing their own instructional materials (IMs). These teacher-designed IMs contain the items the teacher intends to cover in their lessons, sequenced to reflect how the teacher will sequence their teaching, and are given directly to students to use as the main resource during the lesson. Due to their important role in teachers’ lesson planning and in the classroom, studying how they are designed can provide insights into the complexities of teachers’ thinking. This study examined the prominent design principles employed by two Singapore secondary mathematics teachers, Tanya and Mary (pseudonyms), that could characterise how they designed IMs for the topic of ratio with an emphasis on proportionality. Using a case study approach, this study unpacked the complexities of their design through documenting the design process from the preparation of their IMs through to the final implementation. A flexible frame size analysis was adopted to examine teachers’ goals and design principles across the item, set, and interset levels, as well as across the iterative design cycles, capturing the nuanced nature of their design. Four prominent design principles were determined from Tanya’s and Mary’s design process. For Tanya, her design principles were determined from the item-level and set-level of her IM, which were: T-DP1: Create opportunities for students to make mistakes in order to highlight implicit features of concepts. T-DP2: Sequencing items within a set to catch mistakes by changing the momentum. As for Mary, her design distinguished a separation between investigation tasks and practice problem sets, and the set-level and interset-level analysis frames were used to determine Mary’s two prominent design principles: M-DP1: Engendering students’ reasoning through comparative contexts. M-DP2: Balancing coverage and highlighting important ideas in order to maximise students’ engagement. The notion of a catch task was introduced to describe the types of items that both Tanya and Mary employed that were directly aimed at targeting students’ errors and surfacing them during instruction. A comparison of the extent to which Tanya’s and Mary’s IMs concretised their intentions for the lesson, and a characterisation of how they used base materials to prepare their IMs and how they used their IMs to inform their instruction, demonstrated that a two-step process occurs, contrary to previous research. The application of a flexible frame size to the context of teacher-designed IMs was shown to be valuable in developing a comprehensive portrait of Tanya’s and Mary’s design that captured the nuances in their design thinking.