Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students’ higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a more comprehensive perspective, especially in the curriculum. We therefore ask two questions: What characteristics should problem solving have at each stage of the curriculum enactment process to ensure successful implementation? What role should problem solving have from a global curriculum perspective? To answer these questions, we perform a literature review to identify the roles and characteristics of problem solving that facilitate its successful implementation. Based on qualitative analysis of the data, we organize the results into the following categories: conditions of the education system, curriculum structure, characteristics of the planned curriculum and instructional design, types of problems in the intended curriculum and instructional materials, characteristics of the tasks implemented, classroom management, evaluation, student-related considerations, and teachers’ roles during problem solving. We also identify five principles to implement problem solving in teaching mathematics: understanding, reasoning, autonomy, collaboration and affective factors.

The emergence of STEM (Science, Technology, Engineering, and Mathematics) in research and the practice of science, technology, engineering, and mathematics education is today an unquestionable fact at international level. Despite the importance attached to STEM education, there is a lack of synthesized approaches to teaching the interdisciplinarity of STEM. This lack of synthesis can hinder a strong theoretical foundation for STEM education and possible new contributions. The purpose of this position paper is to contribute a theoretical framework for STEM education that enables the unification of criteria regarding disciplinary integration and associated teaching methods. The authors discuss disciplinary integration in STEM activities, the implication of STEM literacy, educational stage, and teaching method, and provide suggestions for future research.

La noción de trayectoria hipotética de aprendizaje ha despertado recientemente interés en la literatura de investigación en educación matemática. Sin embargo, el papel que esta noción puede jugar en la formación inicial de profesores de matemáticas de secundaria no es claro. En este artículo, revisamos las diferentes interpretaciones de esta noción y proponemos una adaptación de la misma con la que el futuro profesor de matemáticas de secundaria puede recoger y organizar información para el diseño de unidades didácticas. Hypothetical Learning Trajectories in Preservice Mathematics Teachers TrainingThe notion of hypothetical learning trajectory has arisen interest in recent research literature in mathematics education. Nevertheless, the role that this notion can play in preservice secondary mathematics teachers training is not clear. In this article, we review some of the interpretations of this notion and propose an adaptation that can be used by preservice secondary mathematics teachers in order to collect and organize information for the design of didactical units.Handle: http://hdl.handle.net/10481/4708Nº de citas en WOS (2017): 3 (citas de 2º orden, 0)Nº de citas en SCOPUS (2017): 3 (citas de 2º orden, 0)

The decisions that teachers make in transforming the curriculum into specific lesson plans determine the real enactment or otherwise of curricular ideals. These decisions are shaped by the resources available and by each teacher’s goals and orientations. This exploratory study employs Schoenfeld’s decision-making model to examine how resources, goals and orientations influence lesson planning for mathematics problem solving, for different profiles of primary teachers in Chile. To this purpose, a survey was conducted among 40 teachers of varying degrees of ability and experience: some were beginning teachers, others were experienced but had no further training in teaching problem solving and a third group was composed of experienced teachers with specific training in this question. Interviews with two teachers from each profile revealed important differences between the three groups. Beginning teachers relied more heavily on official resources such as the official curriculum and standard textbooks, aligning themselves with school requirements. Experienced teachers with problem solving training demonstrated a strong inclination towards teaching through a problem solving approach. While beginning teachers acknowledged the importance of promoting problem solving strategies, they did not usually adapt problems to the mathematical content or to the age/competence of their students. Interestingly, all three groups under-utilised sections of curricular resources that emphasise the present curricular focus on problem solving. Finally, the study found that experience alone is not enough to develop a problem solving approach and that focused professional development programmes are needed to equip teachers with the necessary skills. In addition, a diagnostic teaching approach should be incorporated into initial teacher training.

This article proposes a theoretical framework for STEM education. It begins by determining the epistemological (based on the Model of Educational Reconstruction and General Systems Theory) and pedagogical (grounded in Situated Learning Theory and co-teaching) alignments. Once these issues are established, a pedagogical model is proposed to facilitate the implementation of the STEM approach in the classroom. This is the IDEARR model, consisting of six phases (Initial, Deconstruction, Explanation, Application, Review, and Reporting) to address an ill-defined problem. This article concludes with a reflection on the educational implications that arise from adopting this theoretical framework for working on STEM education in classrooms, particularly those related to the organization and operation of educational institutions and the initial and ongoing training of teachers.