Pozivamo Vas na 37. Fakultetski seminar Prirodoslovno-matematičkog fakulteta, 17. rujna 2019. godine u 12:00 sati, u amfiteatru A1-1, u sklopu kojeg će prof. Tatjana Hodnik (Faculty of Education, University of Ljubljana) održati predavanje pod naslovom:
Mathematical problem solving in theory and practice
Problem solving is a leading mathematical activity which stimulates mathematical thinking. From the theoretical point of view this activity is very complex due to different issues which describe what problem solving is and what is its role in the process of teaching and learning mathematics. Our interest regarding these issues mainly focuses on the following: what are basic characteristic of a mathematical problem, the nature (conceptual, procedural) and the role of representation (interplay between internal and external) of a mathematical problem, mental schemas for problem solving, heuristics as principles, methods and (cognitive) tools for solving problems, types of generalisations and reasoning (abductive, narrative, naïve, arithmetic, algebraic), problem solving as a challenging activity for mathematically gifted students and role of teacher’s guiding of problem solving as a way of implementing students’ problem solving in the classroom. Studies we carried out on problem solving in Slovenian context, which we believe are relevant also to other country contexts, include different groups of students at all levels (from elementary school, secondary school, prospective teachers) are presented aiming to encourage our thinking about prospects of problem solving in the process of teaching and learning mathematics in relation to reality of mathematics classrooms. We believe that problem solving has different roles and benefits for the learners (beside the activity of problem solving itself), namely (we are presenting those we have investigated): students can through problem solving demonstrate their pre-knowledge about a certain mathematical concept, problem solving activities provoke students’ creativity, problem solving is challenging for gifted students, because they are interested in complex problems, which lead to different solutions, problems encourage them to take decisions, include uncertainty…, problems solving enables diagnosis of students’ misconceptions about mathematical concepts, an analysis of students’ problem solving activity provides us knowledge about students’ mental schemas for problem solving, the role of the context of a problem: how students recognise a mathematical concept in a contextual problem. Research has proven and it was confirmed many times that there is a great potential of (mathematical) problem solving for the learners but the reality in terms of teaching practice, external examinations, teaching material, mathematics curriculum seems not to be in tune with the research findings. We are going to present some possible reasons why we are facing this gap and give some ideas for improvement the situation (arguing that problem solving must take place in the mathematics classroom). Among others we claim that going back to heuristics, teach and guide students’ problems solving (meaning developing systematic approach to problems solving), as a complement to constructivist ideas (where students are encouraged to develop problem solving strategies themselves, using the knowledge they possess and developing new) might be a good ‘start’ to put forward problem solving activities in the classroom.
Prof. Tatjana Hodnik obtained her master degree Master of Education – Mathematical Education at the University of Leeds, after which she completed her PhD at the University of Ljubljana, Faculty of Arts with the thesis ‘The role of different representations of arithmetic algorithms in primary school’. At the moment she is in a position of the full professor at the University of Ljubljana Faculty of Education where she runs different courses at all levels (1st, 2nd and 3rd cycle studies) and supervises undergraduate, master and PhD students at their thesis. She runs courses also in English and is regularly in touch with international researchers. Her main fields of interests are exploring problem solving strategies of different age group students, investigating students’ meaning and understanding of different representations, understanding in mathematics, anthropological theory of didactics of mathematics. She was involved in different international projects; recently she is a coordinator for the EPTE program (European Primary Teacher Education) and involved in an international TEMPUS project MedUP (Kosovo) as well as in some regional research projects (didactics in higher education, mathematical literacy). Her research, scientific and professional contribution is available on the SICRIS webpage: izumbib.izum.si/bibliografije/Y20181203195850-17009.html