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A part of students learning in the classroom depends on how the teacher responds to their thinking. The literature has separately addressed teachers' feedback responses to errors and unexpected strategies that students put into play when solving tasks. We propose a framework to analyze these responses together based on three criteria: the focus of the answers (teacher or student), the type of knowledge (conceptual or procedural) that the teacher puts into play in the teacher-centered answers, and the types of actions (asking and proposing) involved in student-centered responses. We codified and analyzed the feedback responses of a group of mathematics teachers to a questionnaire that inquired about their curricular practices. We found similarities in their reports of responses to students' errors and unexpected strategies: two-thirds of teachers have a teacher-centered response. For the student-centered answers, the number of responses of the teacher in which he/she proposes activities is three times the number of responses in which he/she asks students questions. Furthermore, responses to unexpected strategies differ from responses to errors because teachers evaluate, correct, and accept those strategies.

We characterize the thematic trends of the "Geometry and its Applications Meeting." This meeting is held periodically in Colombia, country in which our study was carried out. We used a taxonomy of key terms specific to mathematics education to code the proceedings of this meeting. The study variables are purpose, educational level, pedagogical notions, and topics. We establish the thematic trends in terms of the values of the variables. We describe their evolution over time and, using a normalization process, we compare the extent to which geometry topics are treated with respect to the other variables. The meeting has disseminated activities and curricular innovations to a lesser extent. The community that attends the meeting is focused on the theoretical development associated with geometry and on higher educational levels. The papers that address pedagogical notions focus on learning and the classroom. The topics with the highest percentage of research are geometry in three dimensions and Euclidean geometry. We suggest that the meeting should promote the dissemination of curricular innovations and give more attention to the notions of teaching, curriculum and assessment in both research and innovations. We perceive the need to address learning and teaching in preschool and primary education.

In this paper, we propose a model to explore how teachers learn pedagogical concepts in teacher education programs that expect them to become competent in lesson planning. In this context, we view pedagogical concepts as conceptual and methodological tools that help teachers to design a lesson plan on a topic, implement this lesson plan and assess its results. Concepts such as the notions of learning goals, errors, conceptual structure, representation systems, resources, grouping, interaction or assessment strategies are examples of such pedagogical concepts. We propose a model that involves three types of knowledge of a pedagogical concept--theoretical, technical and practical--for describing teachers' learning of it. The knowledge classification proposed by this model assumes that a teacher should know the theory about the pedagogical concept (theoretical knowledge), be able to use it for analysing the topic and producing information about it (technical knowledge), and be able to use this information for making decisions in the planning process (practical knowledge). We present examples of the development and enactment of those types of knowledge by a group of mathematics future teachers in a teacher education program we have worked on.

The professional development for teachers is an important component of the quality of education. However, few systems for monitoring and analysing the quality and impact of teacher professional development programmes have been created. In this article, we present the effects on classroom practices of a Colombian professional development programme for in-service secondary mathematics teachers. We compare the teachers' classroom practices of planning, implementation, and assessment, before and after participating in the programme. We found that the professional development programme shows a statistically significant and positive effect on planning, implementing and assessment practices. These results serve as evidence of teacher training policy in terms of changes in classroom practices. [ABSTRACT FROM AUTHOR]

In this article, we make a curricular review on topics included in statistics in primary school in Colombia and in the 56 countries that participated in TIMSS 2015. We describe the topics based on the concepts and procedures, representations and phenomenology related to statistics in primary education. We identify differences and similarities between the topics considered in Colombia and the topics from the countries participating in TIMSS 2015. We found that statistics is included in the curricula of most countries and in Colombia. The topics focus on graphical and tabular representations, on the concept of mean, and reference is made in phenomenology to statistics to organize information. These results may generate curricular discussions and motivate similar studies in other countries. [ABSTRACT FROM AUTHOR]

Copyright of REICE. Ibero-American Journal on Quality, Effectiveness & Change in Education / REICE. Revista Iberoamericana Sobre Calidad, Eficacia y Cambio en Educación is the property of Red Iberoamericana de Investigacion sobre Cambio y Eficacia en Educacion and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Procesos Historicos is the property of Universidad de Los Andes (Venezuela) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on a curricular framework, this article presents a critical review of the document "Derechos básicos de aprendizaje en el área de matemáticas" published by the Ministry of Education of Colombia. Following this analysis, we make a proposal to adjust it in a new document that meets the need to educate citizens in mathematical competence. [ABSTRACT FROM AUTHOR]