The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra.

This paper provides a longitudinal analysis of the understanding of repetition patterns by 24 Spanish children ages 3, 4 and 5, through representation and the type of justification. A mixed quantitative and qualitative study is conducted to establish bridges between algebraic thinking and computational thinking by teaching repetition patterns in technological contexts. The data are obtained using: a) participant observations; b) audio-visual and photographic records; and c) written representations, in drawing format, from the students. The analysis involves, on the one hand, a statistical analysis of the representations of patterns, and on the other, an interpretive analysis to describe the type of justification that children use in technological contexts: “elaboration”, “validation”, “inference” and “prediction or decision-making”. The results show that: a) with respect to the representation of patterns, errors decreased by 27.3% in 3-to-5-year-olds, with understanding and correct representation of repetition patterns gaining prominence in more than 50% of the sample from the age of 4; b) on the type of justification used, it is evident that in 3-and-4-year-olds, “elaboration” predominates, and at 5, progress is made towards “validation”. We conclude that it is necessary to design learning sequences connected with theory and upheld through practice, and that foster the active role of the teacher as a promoter of teaching situations that help spur the beginning of computational and algebraic thinking.

At a time when more student-centred teaching methodologies are being introduced, it is essential to investigate how educational research in teacher professional development has progressed. In this study, we focus especially on mathematics teaching to promote responsive teaching and noticing since both practices place students in the foreground in the teaching and learning processes. To this end, we carried out a systematic review of research articles published between 2010 and 2023 in the Web of Science and Scopus databases on responsive teaching and noticing in mathematics teacher education programmes of early childhood and primary school levels. Using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement, 40 articles were identified. The general results show that the most productive countries were the United States, Spain and Australia; that the most addressed mathematical contents were those related to the teaching of numbers, operations and their properties; that there are more studies focused on primary school than on preschool; and that most studies used qualitative methodologies. The specific results show that the research topics focus on three aspects: teachers’ decision-making in relation to culturally responsive mathematics teaching; the identification of general characteristics of the noticing competence in mathematics teaching; and the specific development of professional noticing skills.

Resumen En este trabajo se analiza la demanda cognitiva de las tareas matemáticas propuestas para el aprendizaje de la estadística y la probabilidad en libros de texto escolar chilenos. Los resultados muestran una variedad de tareas matemáticas, con fuerte predominio de aquellas tareas vinculadas a procedimientos con conexión. Por otro lado, evidencian la necesidad de enriquecer el tipo de tareas que buscan promover el aprendizaje de la estadística y la probabilidad en la Educación Primaria, sobre todo en el caso de la probabilidad, pues a la luz de los datos de este estudio, se observa que el tipo de tareas propuestas para el aprendizaje de la probabilidad es poco variado lo que resta valor a su aplicabilidad, y por ende, limita su comprensión.

En este estudio se analizan las tareas matemáticas sobre álgebra temprana en una colección de ocho libros de texto chilenos de Educación Infantil (4 a 6 años). La investigación siguió una metodología cualitativa, de carácter exploratorio-descriptivo, utilizando la técnica de análisis de contenido. Los resultados muestran una presencia de tareas algebraicas en todos los libros de texto analizados, predominando las tareas vinculadas con establecer relaciones a partir del reconocimiento de atributos, seguidas de tareas que requieren de la seriación a partir de patrones de repetición y una escasa presencia de tareas que implican la descripción de cambios.