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The research project presented here is a natural continuation of the lines of research that the team members have developed in recent years. Previous research projects studied the thought processes involved in the knowledge and development of mathematical concepts, as well as the difficulties, obstacles, and errors that emerged in the treatment of these concepts. Research was conducted on numerical and algebraic concepts with primary and secondary school students, as well as on mathematical analysis, algebra, and statistics, and on the understanding of the decimal number system in students with Down syndrome (PI 2001/064, PIDIT 200/05, PCI 2007). In a subsequent stage, the projects evolved toward the evaluation of experiences with the incorporation of studies on the mathematical and professional competence of mathematics teachers. This project aims to integrate, under a single theoretical framework, the research carried out with different groups of students (future mathematics teachers, secondary school students, and students with special educational needs). This common framework has a guiding thread based on Problem Solving as a means for developing mathematical competence. Mathematical competence is understood as the relationship between the following components: conceptual understanding, procedural fluency, strategic competence, adaptable reasoning, and productive disposition (Kilpatrick et al. 2001). The aim is to identify how these components of mathematical competence are used and related in teaching and learning processes when solving problems that promote them. In Project EDU2015-65270-R, mathematical and didactic aspects were addressed from a threefold dimension: epistemological, semiotic, and phenomenological, in teacher training. Now, a different perspective will be used. Mathematical competence (Kilpatrick et al. 2001) will be complemented by the MUST model (Heid, Wilson, and Blume 2015), which includes Mathematical Activity and Mathematical Context for Teaching as components. One of our specific objectives is to incorporate technological aspects derived from the TPACK model (Mishra and Koehler, 2006) into this framework. We will analyze the strategies used by primary, secondary, and pre-service secondary teachers during the problem-solving process, observing difficulties, their possible origins, and changes in the different phases. The ultimate goal is to establish methodological and didactic implications. Each group of students has its own object of study. With pre-service teachers, we will analyze the use of digital technologies in problem-solving with dynamic geometry software. With secondary school students, we will examine how they model mathematical phenomena of variation using interactive books and how they evaluate responses to numerical problems. With students with special educational needs (SEN), we will study how to foster their arithmetic problem-solving skills so that this leads to a better conceptual understanding of basic operations and improves their knowledge about their mathematical learning. This is considered an important approach to the use of technology by secondary school students, and especially by pre-service teachers, which, in the medium term, can have a significant impact. in the classrooms. [/vc_column_text][/vc_tta_section][vc_tta_section title=»Abstract» tab_id=»abstract»][vc_column_text] The proposed research project is a natural continuation of the research lines that the team members have been developing in the last few years. The previous research projects studied the thought processes involved in the knowledge and development of mathematical concepts, as well as the difficulties, obstacles and errors that emerged in the treatment of these concepts. Research was conducted about numerical and algebraic concepts with primary and secondary school pupils, as well as about mathematical analysis, algebra and statistics in the field and on the understanding of the decimal number system in students with Down Syndrome (PI 2001/064, PIDIT 200/05, PCI 2007). In the following stage, the projects evolved towards the evaluation of experiences with the incorporation of studies on the mathematical and professional competence of the mathematics teachers. The aim of the present project is to integrate the research carried out with different groups of students (future mathematics teachers, secondary school pupils and specific educational support needs) into the same theoretical framework. This common framework has a common thread based on Problem Solving as a medium for the development of mathematical competence. Mathematical competence is understood as the relationship between the following components: conceptual comprehension, procedural fluency, strategic competence, adaptive reasoning and productive disposition (Kilpatrick et al., 2001). The objective is to identify «»how they use»» and «»in which way they relate»» these components of mathematical competence in teaching and learning processes when solving problems that promote them. In the Project EDU2015-65270-R, mathematical and didactic aspects in teacher training were approached from three dimensions: epistemological, semiotic and phenomenological. A different perspective will now be used. Mathematical competence (Kilpatrick et al., 2001) will be complemented by the MUST model (Heid, Wilson and Blume 2015), which includes Mathematical Activity and Mathematical Context as components for Teaching. One of the specific objectives in the project is to incorporate technological aspects arising from the TPACK model (Mishra and Koelhler (2006) to the said framework). The strategies used by primary and secondary school pupils and secondary school trainee teachers will be analyzed during the problem solving process, observing difficulties, their possible origins and changes in the different phases. The final objective is to establish methodological and didactic implications. Each group of students has its own object of study. In the case of the future professors, the use of digital technologies in problem solving with dynamic geometry software will be analyzed. There will be a study about how secondary school pupils model mathematical phenomena of variation using interactive books and how they evaluate responses to numerical problems. In the case of special students needs, there will be an analysis of how to enhance their ability to solve arithmetical problems in such a way that gives them a better conceptual understanding of basic operations and will improve knowledge about their mathematical learning. The use of technology by secondary school pupils and especially by future teachers is considered an important approach and could prove to be beneficial in the classroom in the medium term.
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