The aim of this paper is to examine whether the use of a hypothetical learning trajectory as a guide to notice students' mathematical thinking could improve pre-service teachers professional discourse and enhance pre-service teachers' noticing. Twentynine pre-service primary school teachers participated in a learning environment in which they had to interpret students' thinking about the fraction concept using a hypothetical learning trajectory as a guide. Results suggest that using a hypothetical learning trajectory as a guide helped pre-service teachers develop a more detailed discourse when interpreting students' mathematical thinking, enhancing their noticing skill. The enhancement of the skill of noticing, however, was linked to pre-service teachers' mathematical content knowledge. This research provides teacher educators with resources to help pre-service teachers produce a more detailed professional discourse to attend to the details of students' answers and their different mathematical levels of thinking in mathematics teacher education programs.

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The issue of integrated STEM curriculum design and evaluation requires a more consistent understanding and clarity among STEM educators. In this paper, we propose an instructional framework of STEM integration based on the theoretical notions of disciplinarity and problem-centred learning. The proposed S-T-E-M Quartet instructional framework utilises complex, persistent and extended problems at its core, and the problem solving process as the overarching frame. The key difference between the proposed S-T-E-M Quartet instructional framework and models such as the STEM road map and the Cubic model for STEAM education is the emphasis on the connections between different disciplines. Similar to the STEM road map, the application of the S-T-E-M Quartet framework begins with a single lead discipline as the focus and subsequently examines how knowledge and skills of the lead discipline are connected and related to the other three disciplines. As an instructional framework, the S-T-E-M Quartet requires description of learning outcomes for each discipline when students work with the problem. The learning outcomes within individual disciplines constitute the vertical learning within a discipline. Depending on the problem described, the learning outcomes for some disciplines might be more in-depth than others. As the S-T-E-M Quartet foregrounds connections between disciplines, attention is also paid to the strength of connections, whether they are weak, moderate or strong. A case example of application of the S-T-E-M Quartet instructional framework is presented as an illustration of how the S-T-E-M Quartet instructional framework can be used to design and reflect on STEM tasks.