LUMAT: International Journal on Math, Science and Technology Education https://journals.helsinki.fi/lumat <p>LUMAT publishes peer-reviewed research articles on math, science and technology education. Articles include research papers and perspective papers.</p> en-US editor@lumat.fi (Johannes Pernaa) editor@lumat.fi (Johannes Pernaa) Fri, 20 Dec 2019 00:00:00 +0200 OJS 3.1.2.0 http://blogs.law.harvard.edu/tech/rss 60 Editorial https://journals.helsinki.fi/lumat/article/view/1241 <p>During the past few decades, several interconnected research traditions have paid more and more attention to the process of educational design. Educational design research and other design-oriented methods seek solutions for complex educational problems through systematic, iterative, and continuing process of design, development, and evaluation of educational practices. This special issue presents six articles including research on educational design research methodology as well as research utilizing educational design research methods.</p> Johannes Pernaa, Veli-Matti Vesterinen Copyright (c) 2019 Johannes Pernaa, Veli-Matti Vesterinen https://creativecommons.org/licenses/by-nc/4.0/ https://journals.helsinki.fi/lumat/article/view/1241 Fri, 20 Dec 2019 00:00:00 +0200 Teachers as actors in an educational design research: What is behind the generalized formula? https://journals.helsinki.fi/lumat/article/view/1242 <p>Educational design research provides opportunities for both the theoretical understanding and practical explanations of teaching. In educational design research, mathematics teachers’ learning is essential. However, research shows that little consideration is given to teachers and the participation of teachers throughout the entire design process as well as in continued learning. With this in mind, an educational teacher-focused design research was used to explore the challenges teachers face and the opportunities teachers are given when they participate as actors in all the phases of educational design research - designing, teaching, and refining theoretical concepts within the teaching. In this study, the mathematics focus of the design research was generalizations in patterns with Design Principles as the theoretical frame. The results show that the participation of teachers in all the phases of a design process is central for the teachers’ learning. Moreover, challenges that the teachers encounter in the classroom provide opportunities and consequences for the continued design process and lead to changes in the teachers’ understanding of generalizations. The results also indicate that functional thinking and linear equations contributed to both the teachers’ and students’ learning about generalizations in patterns.</p> Helén Elisabeth, Kristina Sterner Copyright (c) 2019 Helén Elisabeth, Kristina Sterner https://creativecommons.org/licenses/by-nc/4.0/ https://journals.helsinki.fi/lumat/article/view/1242 Mon, 16 Dec 2019 00:00:00 +0200 Design and evaluation of practice-oriented materials fostering students’ development of problem-solving competence https://journals.helsinki.fi/lumat/article/view/1243 <p>In a design-research project on problem-solving, theory-based and practice-oriented materials were developed with the goal of fostering systematical development of students’ problem-solving competence in a targeted manner by learning heuristics. Special attention was given to working backward strategy, which has been shown difficult for students to learn and use. In the study, 14 Grade 5 students participated in explicit heuristic training. The results show that even though the students intuitively reversed their thought processes before the explicit training, they experienced difficulties when solving complex reversing tasks, which improved considerably after explicit heuristic training. Thus, the study results showed that the developed materials using design-based research-approach promoted the development of students’ flexibility of thought when problem-solving by working backward. At the end of the paper, the results are discussed with regard to their theoretical and practical implications.</p> Ana Kuzle Copyright (c) 2019 Ana Kuzle https://creativecommons.org/licenses/by-nc/4.0 https://journals.helsinki.fi/lumat/article/view/1243 Wed, 11 Dec 2019 00:00:00 +0200 Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning https://journals.helsinki.fi/lumat/article/view/1244 <p>One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper, I present a case study, conducted within the education course, in which I analyse the characteristics of teacher knowledge produced by five small groups of pre-service teachers in an open-ended problem-based learning task. The results indicate the problem-based learning approach has the potential for enhancing specialised content knowledge such as knowledge of different representations of and applications of mathematical concepts. The results also highlight the challenges in using this approach for enhancing horizon content knowledge such as knowledge about the relationships between mathematical concepts. The findings in this case study suggest that problem-based learning can be used to develop mathematics teacher education, although further research is needed to design instructional practices that enhance pre-service teachers’ horizon content knowledge.</p> Jani Hannula Copyright (c) 2019 Jani Hannula https://creativecommons.org/licenses/by-nc/4.0 https://journals.helsinki.fi/lumat/article/view/1244 Wed, 11 Dec 2019 00:00:00 +0200 Pedagogical experiments with MathCheck in university teaching https://journals.helsinki.fi/lumat/article/view/1245 <p>MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if the step is incorrect. It has been in student use since the autumn of 2015 and under design-based research from the first online day. The main research questions of this study are the following. 1) How can the usage of MathCheck support the aspects of conceptual understanding and procedural fluency of constructivism learning? 2) How can MathCheck empower both students and teachers in the education of mathematics? This paper presents the results of five pedagogical experiments considering both students’ and teachers’ point of views. In each experiment, the students have suggested improvements, which have affected the further development of MathCheck. In general, both students and teachers have given positive feedback on MathCheck. MathCheck seems to support learning better than tools that only provide the “incorrect”/“correct” verdict after checking the answer. MathCheck is suitable for independent studying as well as an addition to traditional lectures. In the best case, it can reduce teachers’ workload during courses.</p> Terhi Kaarakka, Kirsi Helkala, Antti Valmari, Marjukka Joutsenlahti Copyright (c) 2019 Terhi Kaarakka, Kirsi Helkala, Antti Valmari, Marjukka Joutsenlahti https://creativecommons.org/licenses/by-nc/4.0 https://journals.helsinki.fi/lumat/article/view/1245 Mon, 16 Dec 2019 00:00:00 +0200 Towards student-centred solutions and pedagogical innovations in science education through co-design approach within design-based research https://journals.helsinki.fi/lumat/article/view/1246 <p>The aim of this case study is to demonstrate how a co-design approach could be used within design-based research (DBR) with diverse multi-stakeholders in the LUMA ecosystem to promote social creativity towards novel student-based solutions and pedagogical innovations. As a case, a national LUMA2020 development program (2019–2020), organized by the national LUMA Centre Finland and funded by the Finnish Ministry of Education and Culture, was studied in detail. The different data sources (e.g. an action plan, written observations) were analysed through qualitative content analysis. The Edelson’s design-based research model used in the program offered a systematic framework or a map for co-designing both the action plan and its implementation. The co-design approach within the model was organised through three stages to engage all multi-stakeholders (altogether about three hundred participants) for it: (i) a research and societally oriented framework stage, (ii) a practical stage and (iii) a “bottom-up” stage in which teachers from 160 schools were active participants and professional key contributors. The co-design approach and the design decisions were facilitated by using guided face-to-face communication in small group work and digital creative learning spaces as a medium for social creative thinking. The co-designers were teachers, teacher educators, scientists or industry specialists in different stages. The co-design model used could be a way to bridge the newest research and innovations into praxis for supporting the curriculum at the school level and for promoting teachers’ professional development by forming creative and diverse learning communities, in which all partners can learn from each other through sharing.</p> Maija Aksela Copyright (c) 2019 Maija Aksela https://creativecommons.org/licenses/by-nc/4.0 https://journals.helsinki.fi/lumat/article/view/1246 Wed, 11 Dec 2019 00:00:00 +0200 A systematic review of educational design research in Finnish doctoral dissertations on mathematics, science, and technology education https://journals.helsinki.fi/lumat/article/view/1247 <p>Since educational design research (EDR) was introduced to educational research at the beginning of the 1990s, it has gained recognition as a promising research approach that bridges the gap between research and practice in education. This paper aims to investigate how EDR has been utilised and developed and which challenges it has faced by systematically reviewing 21 Finnish EDR doctoral dissertations on mathematics, science, and technology education published between January 2000 and October 2018. The findings indicate that all dissertations yielded practical and theoretical contributions. Moreover, common EDR characteristics, including the use of educational problems in practice as a point of departure, research in real-world settings, evolution through an iterative process, development of practical interventions, and refinement of theoretical knowledge, were found in all dissertations. Most of the doctoral researchers were confronted with challenges, such as high demand for EDR with limited resources and difficulties associated with multidisciplinary teamwork. However, the dissertations were diverse in terms of research contexts, practical educational problems, research outcomes, research methodologies, scale, and collaboration. This systematic review not only enhances the understanding of the utilisation, development, and challenges of EDR but also provides implications for future EDR.</p> Daranee Lehtonen, Anne Jyrkiäinen, Jorma Joutsenlahti Copyright (c) 2019 Daranee Lehtonen, Anne Jyrkiäinen, Jorma Joutsenlahti https://creativecommons.org/licenses/by-nc/4.0 https://journals.helsinki.fi/lumat/article/view/1247 Mon, 16 Dec 2019 00:00:00 +0200