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This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

The COVID-19 pandemic and the requirement for social distancing led to the closure of extracurricular activities that usually involve teamwork and collaboration, such as math clubs. Research on the design and effectiveness of extracurricular mathematical activities that aim to promote student interest and improve mathematical skills is limited, particularly in these challenging times. This exploratory case study examines an online after-school program, the Tecn@Mat Club, aimed at promoting middle grade students’ ability in solving mathematical problems with digital technologies during the pandemic. Based on document analysis, observation of the club sessions, questionnaires, and interviews with the participants (students and a mathematics education expert), this research documents the design and implementation of the Tecn@Mat Club, as well as its participants’ experiences and perspectives regarding the activity in which they engaged. The main results show the feasibility of adapting in-person, after-school math activities for an online setting, engaging middle grade students in mathematical problem-solving with technology by providing moderate mathematical challenges and promoting collaborative work. Results of a SWOT analysis (the acronym for strengths, weaknesses, opportunities, threats) allow for the identification of the key features to preserve and challenges to overcome in future replications of the club. Limitations of this study and future research directions are discussed.

When learning in a digital interactive mathematics learning environment (DIMLE) designed to foster the development of specific mathematics content, students come to express their ideas through different languages and representations. We devise a method based on the Theory of Instrumental Genesis (TIG) to analyse aspects of a middle school student's learning about algebraic generalisation in a DIMLE called "eXpresser". Our analytic scheme allows us to capture changes in her instrumented schemes when accomplishing a certain task repeatedly, gradually modifying her interactions with the system. The results concern both insights into a specific mathematics learning journey in a DIMLE, and methodological progress at a more general level. Indeed, the method we devised and explored in this specific case can be applied to infer students' schemes from their actions as they interact with other DIMLEs. This possibility yields great potential because more and more actions can now be recognized directly by software. This has important implications for computer-supported personalised learning, and AI in general. [ABSTRACT FROM AUTHOR]

This paper presents the results of an exploratory case study that examined a veteran secondary teacher's knowledge for teaching non-routine mathematical problem-solving with digital technologies. Data was collected through the observation of a veteran mathematics teacher, in real time, solving a mathematical problem with the digital tools of his choice. The descriptive model Mathematical Problem-Solving with Technology (MPST) was used to analyse the teacher's utterances and actions while solving a mathematical problem, with GeoGebra and a spreadsheet, and expressing his reasoning also with technology. Our findings reveal the complexity of expert problem-solving with technology, through regulation processes and several micro-cycles that mainly involve the processes integrate and explore. Mathematical problem solving with technology entails relevant mathematical knowledge as well as knowledge about the mathematical affordances of the digital tools available, and the ability to combine them to develop a conceptual model of the solution to the problem. Thus, the teacher's techno-mathematical fluency seems crucial to successfully solve the problem and express the reasoning with technology. Based on the findings, we discuss the teachers' knowledge for teaching mathematical problem-solving with technology as including a particular kind of proficiency, techno--mathematical fluency for solving-and-expressing problems with technology. The limitations of the study, further research topics and implications for professional development and teacher education programmes are discussed.

s t r i n g U t i l s. c o n v e r t A b s t r a c t M a t h H t m l (formulaUtilTools.convertMathHtml( s t r i n g U t i l s. c o n v e r t M m l (!article.abstractinfoEn))) Dynamic mathematics software, such as GeoGebra, is a kind of subject-specific digital tool used for enabling users to create mathematical objects and operate them dynamically and interactively, which is very suitable for mathematics teaching and learning at all school levels, especially at the secondary school level. However, limited research has focused on how multiple influencing factors of secondary school teachers' usage behavior of dynamic mathematics software work together. Based on the unified theory of acceptance and use of technology (UTAUT) model, combined with the concept of self-efficacy, this study proposed a conceptual model used to analyze the factors influencing secondary school teachers' usage behavior of dynamic mathematics software. Valid questionnaire data were provided by 393 secondary school mathematics teachers in the Hunan province of China and analyzed using a partial least squares structural equation modeling (PLS-SEM) method. The results showed that social influence, performance expectancy and effort expectancy significantly and positively affected secondary school teachers' behavioral intentions of dynamic mathematics software, and social influence was the greatest influential factor. In the meantime, facilitating conditions, self-efficacy and behavioral intention had significant and positive effects on secondary school teachers' usage behavior of dynamic mathematics software, and facilitating conditions were the greatest influential factor. Results from the multi-group analysis indicated that gender and teaching experience did not have significant moderating effects on all relationships in the dynamic mathematics software usage conceptual model. However, major had a moderating effect on the relationship between self-efficacy and usage behavior, as well as the relationship between behavioral intention and usage behavior. In addition, training had a moderating effect on the relationship between social influence and behavioral intention. This study has made a significant contribution to the development of a conceptual model that could be used to explore how multiple factors affected secondary school teachers' usage behavior of dynamic mathematics software. It also benefits the government, schools and universities in enhancing teachers' digital teaching competencies. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic and the requirement for social distancing led to the closure of extracurricular activities that usually involve teamwork and collaboration, such as math clubs. Research on the design and effectiveness of extracurricular mathematical activities that aim to promote student interest and improve mathematical skills is limited, particularly in these challenging times. This exploratory case study examines an online after-school program, the Tecn@Mat Club, aimed at promoting middle grade students' ability in solving mathematical problems with digital technologies during the pandemic. Based on document analysis, observation of the club sessions, questionnaires, and interviews with the participants (students and a mathematics education expert), this research documents the design and implementation of the Tecn@Mat Club, as well as its participants' experiences and perspectives regarding the activity in which they engaged. The main results show the feasibility of adapting in-person, after-school math activities for an online setting, engaging middle grade students in mathematical problem-solving with technology by providing moderate mathematical challenges and promoting collaborative work. Results of a SWOT analysis (the acronym for strengths, weaknesses, opportunities, threats) allow for the identification of the key features to preserve and challenges to overcome in future replications of the club. Limitations of this study and future research directions are discussed. [ABSTRACT FROM AUTHOR]

In this paper we propose STEAM practices that would foster mathematics learning through modelling architecture while connecting to culture and history. The architectural modelling process is applied by the teachers as participants of these practices from different countries allowing a broad cultural and historical connection to mathematics education. The modelling is implemented in GeoGebra platform as it is an open-source platform to allow teachers to model on a mathematics basis. The architectural modelling process does not provide participants with steps to follow but rather allows them to explore the architectural models' components and construct them with various approaches which may foster problem solving techniques. We aim to investigate how different phases of this approach (such as motivation, modeling, and printing process) reflect on opportunities of learning in STEAM education, with a particular lens in mathematical development from open tasks. This paper will show two use cases that took place in Upper Austria and the MENA region. [ABSTRACT FROM AUTHOR]