Mathematics Education Abstracts of Presentations

Jumping Tasks: Not too High, not too Low, but Just Nice

Ast/P Choy Ban Heng

Tasks are important for developing competencies in mathematics and language classrooms. Particularly, in lesson study, a well-designed jumping task provides students opportunities to solve problems, discuss ideas, and reason together. Consequently, teachers have to spend time to think about how tasks can be used to facilitate and encourage student thinking during lesson study discussions. However, designing such tasks is challenging and teachers often find it difficult to connect the task with the concept they are teaching. In this presentation, we will present some of the tasks designed by the teachers in our study, and examine the design of these tasks in terms of three principles: the content principle, the activity principle, and the documentation principle (Choy, 2018). In addition, we will highlight the challenges our teachers face, and suggest how teachers can be supported as they design jumping tasks as part of the lesson study discussions using these three principles. Last but not least, we will discuss our insights into the teachers’ pedagogical reasoning as they design tasks to facilitate collaborative learning and listening in Math classrooms, as well as the implications for lesson study practitioners.

Reference: Choy, B. H. (2018). From Task to Activity: Noticing Affordances, Design, and Orchestration. In P. C. Toh & B. L. Chua (Eds.), Mathematics Instruction: Goals, Tasks and Activities (pp. 11-31). Singapore: World Scientific.

Proof and Proving in the Singapore School Mathematics Curriculum

Navinesh

Research on proof and proving in schools has been mainly researched in the US. There is a general belief that proof and proving is inaccessible to students in primary and secondary schools and hence not prioritised as much in the syllabus. Teachers do also face problems in the teaching of proofs. How then can we facilitate the teaching of proofs in the curriculum? Proofs are the foundations of mathematics and involve multiple modes of reasoning which are advocated in the Singapore Mathematics Curriculum Framework. In this presentation, we will look at three types of reasoning commonly cited in literature related to proofs in particular, and, how we can attempt to structure such reasoning into a model. The presentation concludes with a short group activity on proof and proving at the secondary level.

Differentiated Instruction in a Secondary Mathematics Classroom

Vinnie Goh and Toh Tin Lam

This presentation provides a literature review of the theories underlying differentiated instruction. Based on the literature review, we will suggest strategies to design differentiated instruction in Secondary Mathematics classrooms. Our literature review shows that various theories, including Dunn and Dunn’s Learning Styles Model, Gardner’s Multiple Intelligence Theory and Constructivism theories by Piaget and Vygotsky, are the basis for developing differentiated instruction in classrooms. Suggestions to enact differentiated instruction in the mathematics classroom include differentiation based on content, process and product in order to accommodate students’ readiness, interest level and learning profiles.

Seeding Māori and Pasifika Success in Tertiary Mathematics

Chin Sze Looi

In New Zealand, Māori and Pacific Island (MPI) students are underrepresented in tertiary mathematics courses and achieve significantly lower results. The project focuses on enhancing MPI achievement through creating culturally-meaningful resources which will better prepare MPI students for tertiary mathematics and plant seeds of success. In this presentation, I will share some of the tasks which were co-created with MPI students.

Talk in a Mathematics Lesson

Wong Lai Fong

A wide variety of talk occur within a mathematics lesson. However, the mere presence of talk does not ensure that understanding follows – only meaningful math talk can enhance learning. We can examine math talk from the perspectives of the teacher (teaching talk) and the students (learning talk) according to Alexander’s (2017) dialogic teaching framework. In this presentation, teaching episodes enacted in the interactions between a competent and experienced teacher and his students will be shared to illustrate the kinds of math talk (univocal and dialogic) and how the teacher uses the students’ talk to generate meaning and creates the learning moment where students construct their own knowledge.