The progress achieved in the models used by future Spanish primary school teachers on the phenomenon of tides is analysed after implementing a modelling-based didactic sequence. It was implemented throughout ten sessions in two classes (N = 88). An open-ended questionnaire was used as a data collecting instrument. Based on prior studies and the…

The objective of the study was to characterise how pre-service kindergarten teachers used a Hypothetical Learning Trajectory on length and its measurement to notice children's mathematical thinking. A total of 64 pre-service kindergarten teachers enrolled in an Early Years Education mathematics teaching course were asked to notice teaching…

Because of their brief nature, vignettes are a strategic way to highlight or explore complex instructional practices. Using a qualitative approach, we examined how the use of vignettes in a Vignette Activity Sequence contributed to secondary mathematics preservice teachers' understanding of the Mathematical Practices and the Mathematics Teaching…

This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

In this paper a teaching-learning sequence (TLS) introducing pre-service elementary teachers (PET) to weather map reading, with emphasis on wind assignment, is presented. The TLS includes activities about recognition of wind symbols, assignment of wind direction and wind speed on a weather map and identification of wind characteristics in a…

In this work, we present a teaching-learning sequence on colour intended to a pre-service elementary teacher programme informed by History and Philosophy of Science. Working in a socio-constructivist framework, we made an excursion on the history of colour. Our excursion through history of colour, as well as the reported misconception on colour…

Throughout the time of my teaching career, the tide has exposed changes in the nature of music, students and music education. This paper discusses teaching and learning in contemporary music at seven critical stages of 21st century music education: i) diverse types of undergraduate learners; ii) teaching traditional classical repertoire and skills…

In this paper we present how the redesign of professional tasks in the teachers' formation of Secondary Mathematics Teachers influences changes in didactical analysis competency of future secondary school teachers. We draw on data collected from 3 groups of prospective teachers, using qualitative methods. We discuss how the training on the use of…

This study reports on targeted science courses for undergraduate childhood education majors. We describe an inquiry-oriented, three-course sequence spanning physical, life, and environmental science. All three courses are hands-on and are designed to reflect the content and pedagogy most important to future elementary school teachers.

We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which…