Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers' ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences…

One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that…

We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil…

Currently Australian pre-service teachers' levels of personal numeracy are under a great deal of scrutiny. There are calls for universities to raise entry standards into teaching degrees and counter-calls that the output of universities should be gauged rather than inputs. In 2015, doubts about the ability of graduate teachers to convey the…

This study reveals the transformation of prospective science teachers into knowledgeable individuals through classical, combination, and information theories. It distinguishes between knowledge and success, and between knowledge levels and success levels calculated each through three theories. The relation between the knowledge of prospective…

Prospective secondary mathematics teachers' pedagogical knowledge for teaching the estimation of length measurements was investigated by examining their personal benchmarks for measurement estimation. Benchmarks for measurement estimation are the meaningful representations of units that serve to increase one's understanding of…

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and…