This paper presents the Mathematics Teacher’s Specialised Knowledge (MTSK) model. It acknowledges earlier contributions to understanding and structuring teachers’ knowledge, in particular, the special debt owed to Shulman’s notion of pedagogical content knowledge and to Ball and collaborators’ Mathematical Knowledge for Teaching (MKT), influential for the specialised nature of one of its sub-domains. The authors’ research with teachers has led them to explore the characteristics of MKT and to refine the descriptors relating to its sub-domains, a task which has underlined the difficulty involved in unambiguously delimiting the boundaries which separate these. As a result, and taking into consideration a broader view of the specialised nature of the teacher’s mathematical knowledge, the authors propose a framework which, whilst respecting the major domains of Content Knowledge and Pedagogical Content Knowledge, regards the specialisation in respect of mathematical knowledge as a property which is inherent to the model and extends across all sub-domains.

The coronavirus disease 2019 (COVID-19) pandemic caused a worldwide unexpected interruption of face-to-face teaching and a sudden conversion to emergency remote teaching (ERT). In this exploratory study, a sample of 244 secondary mathematics teachers was considered to analyze their perception of their readiness to ERT during the COVID-19 pandemic based on their technological pedagogical content knowledge (TPCK), their previous training in digital teaching tools, their level of digital competence for teaching mathematics, and their adaptation to ERT. An online questionnaire was applied, and the answers were quantitatively analyzed. Given the use of a large number of digital resources and the high percentage of self-developed materials using educational software, secondary mathematics teachers reflected adequate digital competence and TPCK for teaching mathematics. The sudden transition to ERT forced teachers to slow down the pace of teaching and to reduce the content taught. Significant differences were observed based on gender and age with respect to teachers’ perception of their adaptation to ERT. Despite the positive influence of previous training on their perception of readiness for ERT, in general, teachers recognized that they need more training. The demand for preparation for video editing and online quiz composition can be considered for the design of future training programs.

Este trabajo describe cómo establecer relaciones entre los subdominios del modelo de conocimiento especializado del profesor de matemáticas (MTSK) y las concepciones del profesorado de matemáticas, según el modelo concepciones de enseñanza-aprendizaje de las matemáticas (CEAM). Se presenta una metodología para identificar y analizar estas relaciones, que ha permitido comprender la práctica en el aula de una maestra de 5o grado de primaria. Se aporta la descripción del indicador “concepción de la matemática escolar” y las relaciones establecidas al aplicar este método. Finalmente, se discute la potencialidad de uso del instrumento propuesto.How to establish connections between specialized knowledge and mathematics teachers’ beliefs? This paper describes how to establish relationships between the subdomains of the Mathematics Teacher’s Specialised Knowledge model and the conceptions of the mathematics teaching, according to the Conceptions of Teaching-Learning Mathematics model. We present a methodology for identifying and analyzing these relationships, which has allowed to understand the practice in her classroom of one fifth grade primary teacher. As a result, the description of the indicator “conception of school mathematics” and the established relationships are provided. Finally, the potential use of the proposed instrument is discussed.Doi:10.30827/pna.v13i1.7944 Handle: http://hdl.handle.net/10481/53996Scopus record and citations

Previous research in mathematics education has explored teachers’ conceptions of mathematics and its teaching and learning, and how their instructional tendencies (e.g., “traditional”, “technological”, “spontaneous” and “investigative”) relate to these conceptions. However, empirical evidence on this topic from large samples of pre-service teachers is limited. This study adapts and validates an instrument originally designed for in-service teachers to analyse the conceptions of mathematics and mathematics teaching and learning. This was done in a sample of undergraduate students in several different degree programmes (primary education, mathematics, and the education itinerary in psychology) in a Spanish university. Existing theory about instructional tendencies and conceptions of mathematics teaching and learning that was developed in the context of in-service teachers is then re-examined in the context of empirical evidence from this sample of individuals (all potential future teachers) without teaching experience. Results show that items from the instrument can be separated into four factors focussed on investigative stances, the role of textbooks, the role of teachers and lesson planning. Individual participants are not characterised by single tendencies; rather, they can be described in terms of several combinations of tendencies, grouped into four clusters. In line with the previous literature on in-service teachers, results suggest that conceptions of mathematics and its teaching and learning are not best captured by rigid, sharply delineated profiles. Rather, individuals configure their own conceptions in terms of combinations of different characteristics of prototypical tendencies.

Statistical processes start with selecting the studied variable and collecting data. For organizing data, it is essential to carry out the tally of the observed values. In this paper, an approach based on the observed categories is considered, and different manipulative and pictorial strategies for the tally are analyzed, as well as their connection with frequency tables. Finally, an experience with pre-service teachers consisting of using manipulative charts of tallies as a previous step to statistical manipulative graphs is presented.