Ljerka Jukić Matić
Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests
 Mathematics Education
 Popularization of Mathematics
 History of Mathematics
Degrees
 PhD in Mathematics, Department of Mathematics, University of Zagreb , 2011.
 BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2005.
Publications
 Lj. Jukić Matić, M. Karavakou, M. Grizioti , Is digital gamebased learning possible in mathematics classrooms?: A study of teachers' beliefs, International Journal of GameBased Learning 13/1 (2023), 118The literature reports that while digital educational games are used in the elementary classroom, they are rarely, if ever, used in the upper secondary mathematics classroom. In order to investigate this situation, a survey was conducted to determine what upper secondary school mathematics teachers think about digital games and what obstacles and limitations they perceive in using DGBL as a teaching approach. The results indicate that mathematics teachers view digital games as a useful teaching tool; however, the lack of knowledge about teaching with digital games and shortage of appropriate games for teaching upper secondary mathematics seems to discourage them from using them as a main teaching tool. These findings imply that professional development should be designed with a focus on teacher training. Furthermore, the development of constructionistbased games should be considered, where games are based on meaningmaking rather than practicing mathematical content, as has previously been the case.
 Lj. Jukić Matić, J. Sliško, Empirical Study of Mathematical Creativity and Students' Opinions on Multiple Solution Tasks, International Journal of Mathematical Education in Science and Technology 10 (2022)Creativity and problem solving are considered to be 21st century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilisation of multiple solution tasks (MSTs) to investigate students’ creativity. Multiple solution tasks are mathematical tasks with an explicit requirement to be solved with different methods. For the purpose of the study, we used a common textbook question which allows multiple solution pathways as our research instrument. This MST was administered to firstyear mathematics students along with additional questions related to their experience in school mathematics. The results of the study showed that students had difficulties complying with the demands of the task, but generally have positive disposition toward MSTs. Moreover, the results underline the necessity of incorporating MSTs in mathematics classroom teaching to create a more coherent corpus of mathematical knowledge. The study also provides an example of how a regular textbook task can be used as an MST.
 Lj. Jukić Matić, G. KehlerPoljak, S. Rukavina, The Influence of Curriculum on the Concept of Function: An Empirical Study of PreService Teachers, European journal of science and mathematics education 10/3 (2022), 380395This article reports on the understanding of the function concept by preservice mathematics teachers from two countries (Germany and Croatia). We focused on investigating students’ concept definition and concept image of the function in relation to their curriculum experiences. Data were collected using a questionnaire in the form of openended questions followed by interviews. The results indicate that the curriculum has a great influence on the development of the concept definition and concept image. The curriculum strongly influenced the theoretical background of the function concept and thus the gap between the formal and the personal definition of function. Later and more intensive work with the formal definition of function led to a better development of the function concept in general. The curriculum also had an influence on the range of the concept image developed by the preservice mathematics teachers, with no proportional dependence in relation to the better developed understanding of the concept of function.
 Lj. Jukić Matić, Croatian Mathematics Teachers and Remote Education During Covid19: What did They Learn?, Center for Educational Policy Studies Journal 11 (2021), 361382The study reported in this paper aims to show how Croatian lowersecondary mathematics teachers coped with remote education during the lockdown necessitated by the Covid19 pandemic. The research design refers to the case study of six teachers. On five occasions, the teachers were interviewed about the organisation of their virtual classrooms, forms of assessment, and utilisation of (digital) teaching resources from the beginning of March until the end of June 2020. The study results showed that social parameters were prominent factors in the decisionmaking of many teachers regarding teaching remotely. For example, the teachers always put students’ needs first: they were accessible almost all day to their students, they tried not to overload students and provided daily feedback on their work. In addition, the teachers in the study raised the issue of academic dishonesty in remote education – the digital environment made cheating easier and meant that the usual assessment formats became unfeasible. Although the findings provide insight into the work of teachers during a pandemic, a larger sample would provide generalisations about the changes in workload that mathematics teachers experienced during remote education.
 Lj. Jukić Matić, D. Glasnović Gracin, How do teacher guides give support to mathematics teachers? Analysis of a teacher guide and exploration of its use in teachers’ practice, Research in mathematics education 23/1 (2021), 120The materials and artefacts used by teachers and students for learning mathematics have always had an important role in mathematics education. Key among such materials are textbooks and teacher guides. The study presented in this paper attempts to investigate the interaction between mathematics teachers and the teacher guide as well as its influence on textbook use in the classroom. The qualitative approach involved a case study with two mathematics teachers from Croatia. The results showed that the participants used different types of textbook and teacher guide mobilization in a dynamic way. The analysis of the teacher guide showed that it contains little educative support, but the results obtained from the observations and interviews suggest that the teacher guide had an educative impact on teachers, supporting their use of active teaching methods in their classroom practice.
 A. Glavaš, Lj. Jukić Matić, S. Prša, Uppersecondary teachers' perceptions of the Matura exam in mathematics, Metodički ogledi 28/1 (2021), 217242This paper reports a study on mathematics teachers' perceptions of the Matura mathematics exam in Croatia. The study focuses on the suitability of mathematics school textbooks for students' preparation for the exams, the complexity of the tasks in the exams, the grading and scoring of the exams, and teachers’ level of satisfaction with student achievement. The study used a convenience sampling method. It was conducted through a questionnaire administered to 308 upper secondary mathematics teachers. The findings showed that teachers do not perceive school textbooks as suitable resources to prepare for the higher level exam. Furthermore, the teachers believe that the test length is not appropriate i.e., the time given to students for the higher level exam is insufficient. On average they are satisfied with their students’ results, but are undecided about the criteria and scoring of the Matura. Vocational school teachers showed more dissatisfaction with the requirements and outcomes of the Matura exam compared to grammar school teachers. The results of this empirical study can be taken as a good starting point for reassessing the requirements of the Matura exam in mathematics.
 Lj. Jukić Matić, D. Glasnović Gracin, Use of textbooks and other resources in curriculum reform. A longitudinal case study, ZDM – Mathematics Education (2021), 13731385Curriculum reform brings new approaches to classroom practice. As changes to the curriculum are implemented, teachers need to receive additional support from textbooks and other materials. In the study presented in this paper, we explored the use of resources during the process of educational reform in Croatia. The focus was on the use of a mathematics textbook set as the main resource, but the use of other material and nonmaterial resources was also examined. The study also dealt with the social factors that influenced the use of these resources. It was designed as a case study of one mathematics teacher and her students, examined at three time points, before the reform, in the preparation period, and subsequent to the implementation of the reform. The results showed that the textbook set is a stable resource over the time periods, although it did undergo some changes towards digitalization. The teacher’s professional development was shown to be an important nonmaterial resource during the period of change. The research also revealed that the participants’ decisions concerning the use of resources depended on some social issues, such as norms concerned with being a teacher or a student. The study showed that longitudinal monitoring of the use of resources in the period of curricular change may contribute to a better understanding of the processes of instructional transformation and development.
 Lj. Jukić Matić, D. Moslavac Bičvić, M. Filipov, Characteristics of effective teaching of mathematics, Didactica Slovenica  Pedagoška Obzorja 35/34 (2020), 1937When referring to effective mathematics teaching, the terms good teaching and quality teaching are often used. There is no universal definition of what constitutes good or effective teaching of mathematics, and views on these concepts are largely dependent on the educational traditions and values in different countries, as well as on the beliefs of mathematics teachers. The notion of effective teaching is important because it significantly influences educational policies and teaching design decisions. The aim of this paper is to problematize the issue of effective mathematics teaching, to determine the features of effective mathematics teaching and how teachers perceive effective mathematics teaching. The way a mathematics teacher teaches is an indication of what he or she considers to be most important. Teachers are critical determinants of students’ learning and educational progress, so they must be trained to deliver quality and effective lessons. Mathematics teaching is effective when it promotes students’ performance as best as possible. Nevertheless, cultural norms influence the way effective features are implemented.
 Lj. Jukić Matić, D. Glasnović Gracin, Mathematics textbook in the hands of the lower secondary students: how, when and why they use it. /Matematički udžbenik u rukama učenika viših razreda osnovne škole: kako, kada i zašto ga koriste., Croatian Journal of Education 22/1 (2020), 940Textbooks play a very important role in education; their content and practice exercises may have an influence on the students' opportunities to learn. Although many studies have focused on the teachers' use of textbooks, studies on students' textbook use are sparse. The aim of the study presented in this paper is to examine how, when, and why students utilize textbooks for learning mathematics. The data was obtained by combining quantitative and qualitative methods (triangulation of questionnaire results, interviews, and students' diaries). To that purpose, the model of a sociodidactical tetrahedron was used, where the dynamic relationship among textbook, mathematics, teacher and student was observed. The results show that students regularly use the textbook for practice exercises and homework. The social component of textbook use points to: (1) teacher as a mediator between the textbook and students; (2) the important role of the textbook in terms of help at home given by parents or siblings if the student did not understand the subject matter in school. Therefore, the utilization of the textbook is a complex and dynamic process which includes various parameters and participants, not just teachers and students
 Lj. Jukić Matić, Pedagogical design capacity of lowersecondary mathematics teacher and her interaction with curriculum resources, Revista de Investigación en Didáctica de las Matemáticas 8/1 (2019), 5375Various curriculum resources emerged in the last decades, but the textbook still remains the most used teaching and learning resource in mathematics classrooms. In this paper, we use a case study to analyze teaching practice of one math teacher. The aim of the study is to examine how math teacher interacts with the textbook and teacher guide, especially when teacher offloads on those resources, adapts them or improvises in the classroom. The study was conducted using lessons observations and semistructured interviews. The results showed that teacher does not favour particular type of resource mobilization. Her interaction with resources can be characterized as a dynamic interplay, where type of resource mobilization exchange between the lessons and within a lesson as well. Moreover, teacher’s mobilization of textbook and teacher guide depends on teacher’s goals and assessment of the most pedagogically beneficial instruction for students.
 Lj. Jukić Matić, The Teacher as a Lesson Designer, Center for Educational Policy Studies Journal 9/2 (2019), 136160Teachers’ pedagogical design capacity is their ability to perceive and mobilise existing resources to create productive instructional episodes in the classroom. To a certain extent, this ability is dependent on the curricular resource used. As the textbook remains the most commonly used curricular resource in mathematics classrooms, the study reported in this paper investigates how and why one experienced mathematics teacher utilises the textbook. Data were gathered using lesson observations, as well as prelesson and postlesson interviews. The teacher used offloading on the textbook, adapting the textbook content and improvising in the lessons to varying degrees, being aware of the affordances and constraints that the textbook has for her teaching practice. That approach to the textbook enabled the teacher to create various opportunities that enhance learning. The results of the study indicate that the mathematics teacher’s awareness of what a particular resource offers for teaching practice, and what constraints could be encountered on this journey are significant in terms of the teacher’s design capacity.
 Lj. Jukić Matić, The Effect of Problem Solving Course on PreService Teachers’ Beliefs about Problem Solving in School Mathematics and Themselves as Problem Solvers, Magistra Iadertina 12 (2017), 141159Problem solving in schools begins with mathematics teachers. The degree to which mathematics teachers are prepared to teach for, about and through problem solving influences on their implementation of problem solving in school. We conducted a small scale study where we examined the effect of implementation of heuristic strategies and Polya’s steps in mathematics method course. We assessed preservice teachers’ knowledge and attitudes about them as problem solvers before and after the course. Moreover we assessed their beliefs of problem solving in school mathematics. Those beliefs were assessed in two occasions: right after the course and after finished teaching practice. Although students’ knowledge on problem solving was improved, the results of students’ beliefs show that it is important that preservice teachers, and consequently inservice teachers, are constantly reminded on the positive effect of constructivist and inquirybased approach on teaching mathematics.
 D. Glasnović Gracin, Lj. Jukić Matić, The Role of Mathematics Textbooks in Lower Secondary Education in Croatia: An Empirical Study, The Mathematics Educator (Singapore) 16/2 (2016), 2956This paper reports a study on the use of mathematics textbooks as curriculum resources in lower secondary education in Croatia. The focus of the study is placed on how and why the textbook is used during the teaching of new content and the practicing phase in classrooms. The aim of the study was also to investigate the influence of a textbook on the teaching instructions. The study was conducted using classroom observations supplemented with interviews with mathematics teachers from observed classrooms. The findings showed that the textbook played a central role in teachers' lesson preparation, as well as in the selection of worked examples and practice exercises for the students. They turned out to be also very important as a source for homework. The interviews revealed an influence of a social dimension on the utilization of mathematics textbooks in the classroom.
 Lj. Jukić Matić, D. Glasnović Gracin, The use of the textbook as an artefact in the classroom: A case study in the light of a sociodidactical tetrahedron, Journal für MathematikDidaktik 37/2 (2016), 349374Mathematics textbooks have long been used as an educational tool for teaching and learning. They play an important role in various didactical situations both within and outside the classroom. After the previous largescale quantitative research on the use of mathematics textbooks in lower secondary education in Croatia, a new study with a qualitative approach was conducted. The new study encompasses classroom observations and an indepth interview with one mathematics teacher. The results of this study are explained using the sociodidactical tetrahedron and are compared with previous survey results on the extent to which mathematics textbooks are used in Croatian classrooms. The findings of this study indicate that the textbook has a significant role in mathematics lessons in which the aims of the teacher and the textbook are aligned. The study also offers some explanation as to why teachers rely on the textbook for preparation, teaching and practicing. Here the extension of the didactical tetrahedron to a sociodidactical tetrahedron proved to be very valuable due to the social factors involved in textbook use which cannot be neglected.
 Lj. Jukić Matić, Nonmathematics Students’ Reasoning in Calculus Tasks, International Journal of Research in Education and Science 1/1 (2015), 5163This paper investigates the reasoning of first year nonmathematics students in nonroutine calculus tasks. The students in this study were accustomed to imitative reasoning from their primary and secondary education. In order to move from imitative reasoning toward more creative reasoning, nonroutine tasks were implemented as an explicit part of the students’ calculus course. We examined the reasoning of six students in the middle of the calculus course and at the end of the course. The analyzed data showed that the students’ reasoning differed in the middle of the course and after having passed the course, in terms of having more characteristics of creative reasoning. In addition, we found several negative metbefores and metafters affecting the students’ knowledge and interfering with their reasoning
 Lj. Jukić Matić, Mathematical Knowledge of Nonmathematics Students and Their Beliefs About Mathematics, Mathematics Education (a.k.a International Electronic Journal of Mathematics Education) 9/1 (2014), 1323Mathematics is tightly interwoven with science and engineering, where it has numerous applications. In the educational context, there is an ongoing debate who should teach mathematics to non mathematicians and how this mathematics should be taught. The knowledge gained in mathematics course is used in another course (mathematics, science or engineering), hence students should retain core concepts some time after learning. Beliefs that students have about mathematics significantly influence on their learning, and consequently on the retained knowledge. We investigated retained calculus knowledge and beliefs about mathematics in two groups of first year students coming from the science and engineering study programs. The results showed that both groups of students showed better procedural knowledge than conceptual. Also they showed positive beliefs about mathematics in their study program, but were not certain where this knowledge will be used later. However they differed in the perception of mathematics as being exciting discipline. The educational implications of these findings are also discussed.
 Lj. Jukić Matić, On D(w)quadruples in the rings of integers of certain pure number fields, Glasnik Matematički 49/1 (2014), 3746The purpose of this paper is to show the non existence of D(w)quadruples in number fields of odd degree whose rings of integers are of the special form. We derive some elements which can not be represented as difference of squares in such rings and comment the nonexistence of corresponding Diophantine quadruples. This relies on the nonsolvability of system of congruences which we prove in some lowdegree cases.
 Lj. Jukić Matić, Recalling calculus knowledge, Teaching mathematics and computer science 12 (2014), 5570The main purpose of educational system is not only that the students perform well at the exam, but to remember the learnt material to some degree some time after the learning. This paper investigates students' retained knowledge, focusing mainly on topics concerning derivatives and differentiation, and examines the effect of relearning in a short period of time. Results indicate that retained knowledge should be taken into consideration in instructional design and curriculum planning for the sequencing courses.
 Lj. Jukić Matić, B. Dahl Soendergaard, Retention of Differential and Integral Calculus: A Case Study of a University Student in Physical Chemistry, International Journal of Mathematical Education in Science and Technology 8/45 (2014), 11671187This paper reports a study on retention of differential and integral calculus concepts of a secondyear student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly reconstruct the knowledge, given a few hints, this is just as good as retention. The study was conducted using a mixed method approach investigating students’ knowledge in three worlds of mathematics. The results showed that the student had a very low retention of concepts, even after hints. However, after completing the calculus course, the student had successfully used calculus in a physical chemistry study programme. Hence, using calculus in new contexts does not in itself strengthen the original calculus learnt ; they appeared as disjoint bodies of knowledge.
 Lj. Jukić Matić, F.M. Brueckler, What do Croatian preservice teachers remember from their calculus course, Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal 1 (2014), 115This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two preservice mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of the concepts in the conceptual embodied world can reflect on the longterm retention of mathematical knowledge in the proceptualsymbolic and formalaxiomatic world as well.
 Lj. Jukić Matić, Nonexistence of certain Diophantine quadruples in rings of integers of pure cubic fields, Proceedings of the Japan Academy. Series A Mathematical sciences 88/10 (2012), 163167In this paper we derive some elements of the rings of integers in the cubic fields of the form $mathbf{;Q};(sqrt[3]{;d};)$, where $d$ is even, which cannot be written as a difference of two squares in the considered ring. We show that corresponding Diophantine quadruples do not exist for such elements, what supports the hypothesis mainly proved for the ring of integers and for certain quadratic fields.
 Lj. Jukić Matić, B. Dahl Soendergaard, University students’ retention of derivative concepts 14 months after the course: influence of ‘metbefores’ and ‘metafters’., International Journal of Mathematical Education in Science and Technology 43/6 (2012), 749764This paper reports the concluding part of a larger study on retention of key procedural and conceptual concepts in differential and integral calculus among Croatian and Danish university students in nonmathematics study programmes. The first parts of the study examined the retention of the students’ knowledge through a questionnaire testing core calculus concepts in derivative and integration given two and six months after the students had passed an exam testing those concepts. In the present article we continue to explore the retention of core concepts in derivative through a mixed method approach examining the knowledge of 10 secondyear nonmathematics students 14 months after they took the course. The result showed that there were several negative metbefores and metafters affecting the students’ retention
 Lj. Jukić Matić, Differences in remembering calculus concepts in university science study programmes, Aplimat  Journal of applied mathematics 3/3 (2010), 137146This study examines a retained university level of conceptual and procedural knowledge focusing mainly on derivatives and differentiation. A questionnaire, given two months after students were taught certain concepts from differential calculus, investigated whether the students are able to solve elementary tasks. Results are compared for five nonmathematics study programmes at one university in Croatia.
 Lj. Jukić Matić, Longitudinal Study on The Textbook Use: A Student’s Perspective , 44th Conference of the International Group for the Psychology of Mathematics Education, Thailand, 2021, 164165
 Lj. Jukić Matić, D. Glasnović Gracin, Curriculum Noticing: A Case of Lower Secondary Teacher, 44th Conference of the International Group for the Psychology of Mathematics Education, Thailand, 2021, 219220
 D. Glasnović Gracin, Lj. Jukić Matić, Same textbook, different points of view: students and teachers as textbook users, Third International Conference on Mathematics Textbook Research and Development., Paderborn, 2019, 173178The utilization of textbooks by mathematics teachers has been the subject of many recent studies; students’ opinions, however, have not received such attention. The study presented in this paper aims to investigate both students’ and their teacher’s ways of and reasons for using the textbook, with an emphasis on the vertices of the SocioDidactical Tetrahedron. The findings indicate that the beliefs about being a teacher and about being a student strongly influence textbook utilization. Also, the students’ use of the textbook is influenced by the teacher’s intentions. Here the extension of the didactical tetrahedron to a sociodidactical tetrahedron proved to be very valuable due to the social factors involved in textbook use.
 Lj. Jukić Matić, B. Bognar, Systematic Review as a Research Method: A Case of Professional Development of Mathematics Teachers, Suvremene teme u odgoju i obrazovanju, Zagreb, 2019, 7879This study utilized a systematic review of literature as the main research method. The systematic review consists of precisely defined steps to ensure research rigor. First, we formulated appropriate research questions. Second, we defined the search terms and selected databases. Third, we used inclusion and exclusion criteria, which guided us in the further literature search. Fourth, we evaluated the scientific quality of the obtained publications using predefined quality criteria. Only studies that met the quality requirements were included in this review. Finally, data answering the research questions were extracted. Our aim was to identify studies that examined the professional development of mathematics teachers with an influence on student achievements. In this process, we identified 22 studies connected with our research question. In the reviewed studies, we examined whether professional development influenced student achievements, the effect size of achievement, and we classified the models used in professional development according to the autonomy given to the teacher in the professional development. Most professional development models were transmissive, some combined features of malleable and transmissive models, while characteristics of only malleable models were present in few studies. Half of the studies described professional development that did not impact student achievements. Our review showed that many studies had small effect size on student achievements in comparison with the effect size of 0.40, Hattie’s “hinge point” for educational interventions.
 D. Glasnović Gracin, Lj. Jukić Matić, The dynamic interactions between teacher and resources in the use of the textbook and teacher guide, Re(s)sources 2018, Lyon, 2018, 159162Textbooks and the accompanying teacher guides are recognized as important resources in mathematics education. They can be used in different ways by teachers in the planning phase: teachers may closely follow the textbook or guide content, they may adapt it or improvise. This study focuses on investigating the interrelationship between teachers and the mobilization of textbooks and teacher guides. The two participants used the textbook as the basis for lesson planning, consulted the teacher guide as an additional resource for activities and ideas, and then went back to the textbook to finalize their lesson plans. The results suggest that the process of teachers’ lesson planning cannot be described as linear, but rather as a dynamic and complex process.
 Lj. Jukić Matić, Teacher’s pedagogical design capacity and mobilization of textbook, 10th Congress of the European Society for Research in Mathematics Education, Dublin, 2017, 37623763
 Lj. Jukić Matić, D. Glasnović Gracin, Teacher Offloading, Adapting And Improvising With The Textbook – A Case Study, 40th Conf. of the International Group for the Psychology of Mathematics Education, Szeged, 2016, 5966The study presented in this paper investigates how two mathematics teachers utilize textbook in a traditional curricular environment. Using Design Capacity for Enactment framework, we analysed four lessons, observed in each teacher classrooms. The results of the study showed that teachers used the textbook extensively in their teaching practice. Most of the time teachers offloaded lessons from the textbook for various activities: teaching a new content, practice exercises or homework. The teachers offloaded lessons on the textbook because the textbook supported their current teaching goals and was aligned with their beliefs for particular lessons. Other types of textbook utilization such as adapting and improvising were present but to a lesser extent. They were used when textbook did not satisfy teacher’s goals and beliefs.
 Lj. Jukić Matić, M. Kristek, A. Mirković Moguš, Preservice teachers and statistics: an empirical study about attitudes and reasoning, Mathematics and Children, The 5th International Scientific Colloquium, Osijek, 2015In the paper a preservice elementary teachers’ attitudes were examined using the Scale of Attitudes Towards Statistics and the analysis of results showed preservice elementary teachers’ neutral attitude toward statistics. Their statistical reasoning in measures of center was also examined using several items from Quantitative Reasoning Quotient Test. This analysis showed that preservice teachers’ statistical reasoning is inconsistent from item to item, or topic to topic, depending on the context of the problem. Results of both assessment instruments indicate that preservice teachers lack awareness of the usefulness of statistics in everyday life and lack of experience in solving everyday problems. Since the attitudes have a significant effect on the learning process, we believe that not knowing where, why and when statistics can or will be used, influenced on preservice elementary teachers’ statistical reasoning.
 Lj. Jukić Matić, D. Glasnović Gracin, Teacher and textbook: Reflection on the SDTmodel, 9th Congress of the European Society for Research in Mathematics Education, Prag, 2015, 30723078This study investigates indepth how two teachers use the textbook in mathematics classrooms. Their use of the textbook was analysed in the light of a sociodidactical tetrahedron (SDT) which proved to be a powerful model to describe many aspects of textbook use that we encountered. Our results showed that the teacher acted as the mediator between the textbook and students, but the lower part of the SDT helped us to detect the influence of social factors on textbook use which cannot be disregarded.
 Lj. Jukić Matić, M. Kristek, Attitudes of prospective teachers towards statistics, Education vision & challenge for future 2014, Ljubljana, 2014, 2062013he goal of research was to examine the attitudes of prospective mathematics teachers towards statistics and possible differences in their approach to learning. Participants were prospective mathematics teachers who filled out two questionnaires via computer: Scale of Attitudes Towards Statistics and Approaches and Study Skills Inventory for Students. The results have shown that, ultimately, students have moderate positive attitude toward statistics. They see the importance of statistics and statistical literacy in the real life, but are indifferent toward learning it and do not have a clear perception of its use in other fields. When examined connections between students approaches to learning, results have shown a high correlation between strategic and deep approach. In relation with their attitude toward statistics, the positive correlation was found with a deep approach. Taking in consideration that the attitudes of teachers have an important role in satisfaction, success and students' choice of learning approaches, this study contains important implications for further research in this field
 D. Glasnović Gracin, Lj. Jukić Matić, Schulbuch als Teil des implementierten Curriculums, 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Koblenz, 2014, 431435Diese Studien umfassen qualitative Forschungen (Interviews und Unterrichtsbeobachtungen) die das Ziel hatten, die Rolle der Mathematikschulbücher in der Praxis zu erforschen. Die Ergebnisse können helfen, ein besseres Bild über die Rolle der Schulbücher zu bekommen.
 A. Katalenić, Lj. Jukić Matić, I. Matić, Approaches to learning mathematics in engineering study program, Mathematics and children, 4th International Scientific Colloquium, Osijek, Hrvatska, 2013, 186195
 Lj. Jukić Matić, K. Dobi Barišić, I. Đeri, The influence of formal education and personal initiatives on the willingness to use ICT in teaching mathematics, Mathematics and children, 4th International Scientific Colloquium, Osijek, Hrvatska, 2013, 261270Application of computer technology in the classroom is a challenge for every teacher who wants to follow the development of the information society. Teacher’s competence to work with computer technology certainly depends on formal education but also on personal initiatives. This paper presents the results of study on the willingness of mathematics teachers to use ICT in teaching mathematics in the different educational cycles with respect to their competences. Teachers are aware of the need to use ICT, but point out the shortcomings of their formal education, that shows progress, and emphasize a great need for personal initiatives and further education
 Lj. Jukić Matić, I. Matić, Educating future mathematics teachers: Repeating mathematics from primary and secondary school, Mathematics and children, 3rd International Scientific Colloquium, Osijek, Hrvatska, 2011, 2734
 B. Dahl Soendergaard, Lj. Jukić Matić, University students’ concept image and retention of the definite integral, 35th Conf. of the Int. Group for the Psychology of Mathematics Education, Ankara, Trukey, 2011This paper reports a part of a larger study researching the retention of key derivative and integration concepts months after the calculus course exam at a Croatian and Danish university. In this paper we focus on the students’ longterm retention and concept image of the definite integral. 18 students in nonmathematics science study programmes were interviewed in pairs and presented with four tasks on the definite integral in order to expose their concept definition and concept image. No student had a coherent concept definition which caused problems solving the tasks. However, some of these students appeared to have more coherent concept image, and solved some of the tasks, while others did not. We argue that the relation between concept definition and concept image varies from student to student.
 Lj. Jukić Matić, B. Dahl Soendergaard, What Affects Retention of Core Calculus Concepts Among University Students? A Study of Different Teaching Approaches in Croatia and Denmark, 7th Congress of the European Society for Research in Mathematics Education, Rzeszow, Poljska, 2011This paper reports a parallel study of two university calculus courses in Croatia and Denmark using different teaching approaches. Both have lectures to a large group of students but they use different types of exercises. In Denmark, the exercises are studentcentred, while the Croatian university uses a teachercentred approach. The content of the courses are similar regarding the concepts we study in this paper. The students‘ retention was tested two months after the course exam on these concepts. Our statistical data analysis shows that the Danish students of our sample performed significantly better than the Croatian students of our sample on the conceptual questions, and vice versa for the procedural ones.
 Lj. Jukić Matić, K. Dobi Barišić, I. Đeri, What Is the Future of the Integration of ICT in Teaching Mathematics, Mathematics and children, 3rd International Scientific Colloquium, Osijek, Hrvatska, 2011, 128140n recent years the need for introducing information and communication technology into the teaching process has posed one of the unavoidable changes in the educational system. Present generation of students are so proficient in usage of the information and communication technologies in their daily lives, that this change in the educational system can not be viewed as an investment in a better future, but as a necessity in order to keep pace with technology and students. Considering the integration of ICT in teaching mathematics, it is clear that the replacement of board and chalk with digital presentation material does not cover all the aspects that technology and mathematics can improve when working hand in hand. One of the important prerequisites for quality integration of ICT in teaching mathematics is the teacher’s personality, i.e. his knowledge, willingness and desire to improve his lessons bringing mathematics closer to the present generations of pupils. The aim of this paper was to investigate the readiness of the future mathematics teachers at the elementary and high school levels to integrate ICT into their teaching of mathematics. Factors influencing described readiness that are considered in this paper are teacher’s university education and initiative with regard to personal digital competence and infrastructure. We conducted the survey research on the samples of individuals from the population of students enrolled in final years of a fiveyear Master of Arts in Teaching Primary Education programme at the Faculty of Teacher Education in Osijek, Croatia (n = 196), and Master of Arts in Teaching Mathematics and Computer Science programme at the Department of Mathematics in Osijek, Croatia (n = 36). The obtained results indicate that identified aspects have impact on considered readiness and that teacher’s university education causes the differences in the attitudes towards his digital competencies necessary for quality integration of ICT in mathematics lessons.
 F.M. Brueckler, Lj. Jukić Matić, How science students understand, remember and use mathematics, 4th International Conference on Research in Didactics of the Sciences, Krakow, Poljska, 2010Practically all science study programmes contain mathematical courses. They are meant to give the students mathematical tools they should be able to apply later in applyed contexts of their specific study area. This can only be attained if the students remember the concepts after they have completed the corresponding courses. It is often noted that students who have succesfully completed their mathematics courses, often containing quite sophisticated mathematical topics, are in many cases unable to correctly apply them in a concrete context. One of the reasons could be that students tend to learn their mathematics courses as separate entities, and are thus often unaible to apply a mathematical technique learned (and successfully tested on in the mathematics course) in the real applied context. Another, and the authors conjecture that this is the main one, are overloaded syllabusses, particularly characteristic for the Croatian educational system, which facilitate the retainment of procedural, and less of conceptual knowledge. As both types of knowledge are necessary to succesfully a mathematical concept, an affirmation of this conjecture would explain the noted problems, and suggestions for improvement could be made. As the content of mathematics courses varies from study to study, the authors decided on testing the retainment of knowledge in basic calculus (derivatives and integrals), as this topic is covered in all of the mathematics courses for science students. The authors have made several surveys testing the retained level of knowledge about derivatives and integrals at two Croatian and one Danish university. Also, the firstnamed author, teaching the mathematics courses for chemistry students in Zagreb, has tried to incorporate more applications of derivatives and less mathematical formalism in the mathematics course, thus making it less a separate identity in the learning process. The outcomes of this approach are still to be tested.After statistical analysis of the surveys, the results support our conjectures.
 Lj. Jukić Matić, B. Dahl Soendergaard, The retention of key derivative concepts by university students on calculus courses at a Croatian and Danish university, 34th Conference of the International Group for the Psychology of Mathematics Education, Belo Monte, Brazil, 2010his paper reports a part of a larger study investigating the calculus teaching at a Croatian and Danish university. It concerns the students’ retention of key procedural and conceptual concepts of derivative two months after having passed similar Calculus 1 courses, and while being taught a Calculus 2 course. The results showed that for both countries, a large portion was forgotten and the passing grades of the Calculus 1 course did not predict the results in the test two months later. In fact, often students with the lowest passing grades had the better results two month later.
 M. Jukić Bokun, Lj. Jukić Matić, D. Marković, Projekt GAMMA, Osječki matematički list 22/2 (2022), 161170Projekt GAMMA je Erasmus+ projekt na kojemu je Odjel za matematiku Sveučilišta u Osijeku koordinator. U radu predstavljamo projekt i njegove rezultate, opisujemo aktivnosti važne za razvoj rezultata i najavljujemo službene diseminacijske aktivnosti.
 Lj. Jukić Matić, I. Kladušić, Mateamtičke dijagnostičke probe, Osječki matematički list 21/2 (2021), 137149Dijagnostičko vrednovanje provodi se kako bi se utvrdila kvaliteta i razina učeničkih predznanja i vještina prije početka procesa poučavanja. Ovaj oblik vrednovanja može se koristiti i za određivanje prikladnoga oblika odgojnoobrazovne podrške pojedinim učenicima. Matematičke dijagnostičke probe kratki su zadaci koji pomažu učiteljima prikupiti informacije o predznanju učenika, kao i o kolektivnim miskoncepcijama te individualnim poteškoćama učenika. Mogu se primijeniti u svim domenama matematike kako u osnovnoj tako i srednjoj školi.
 Lj. Jukić Matić, M. Filipov, I. Šustek, Učinkovita povratna informacija u nastavi matematike, Matematika i škola 23/112 (2021), 5156U radu je opisano što čini učinkovitu povratnu informaciju i razine na kojima se povratna informacija upućuje. Davanje povratne infromacije usmjereno na učenikov daljnji razvoj ilustriran je na matematičkim primjerima.
 Lj. Jukić Matić, J. Alilović, Zadatci više i niže kognitivne razine, Matematika i škola 23/110 (2021), 195200Zadatak je osnova nastave matematike. Kakvim zadatcima izlažemo učenike, takvo znanje im i razvijamo. Ne samo znanje, već i shvaćanje o samoj prirodi matematike. Doživljavaju li učenici matematiku kao skup nepovezanih definicija, pravila i postupaka pokazuje da su često bili izloženi zadatcima u kojima se ne povezuju znanja različitih matematičkih domena. Ili da ne postoji veza između konceptualnog značenja nekog postupka i samog postupka.
 D. Novački, Lj. Jukić Matić, Formativno vrednovanje s pomoću kognitivnog konflikta, Matematika i škola 21/104 (2020), 147153U ovom radu opisujemo kognitivni konflikt i njegovu upotrebu u nastavi matematike.
 Lj. Jukić Matić, Produktivni neuspjeh, Matematika i škola 21/102 (2019), 5155
 I. Matić, Lj. Jukić Matić, Rođak Miško, Osječki matematički list 19 (2019), 4972
 Lj. Jukić Matić, Učenje otkrivanjem i produktivni neuspjeh u nastavi matematike (2019)U radu je opisano učenje otkrivanjem i produktivni neuspjeh u nastavi matematike.
 Lj. Jukić Matić, I. Matić, Crtice iz tramvaja zvanog ludara, Osječki matematički list 18/1 (2018), 5969Matematički zadatci uz priču
 Lj. Jukić Matić, I. Matić, Obitelj Medić u dizalu, Osječki matematički list 18 (2018), 159177
 Lj. Jukić Matić, I. Širić, Singapurska metoda modela, Matematika i škola 19/95 (2018), 195199
 I. Matić, Lj. Jukić Matić, Dnevnik malog Medića, Osječki matematički list 17/1 (2017), 8994
 Lj. Jukić Matić, M. Štivić, Konačno ili beskonačno? Kako učenici i studenti shvaćaju pojam beskonačnosti, Poučak 18/70 (2017), 1927
 Lj. Jukić Matić, I. Matić, Tri Medića i beba, Osječki matematički list 17/2 (2017), 171176
 Lj. Jukić Matić, Zašto je ta proporcionalnost tako teška?, Matematika i škola 18/89 (2017), 147154
 Lj. Jukić Matić, I. Matić, Obitelj Medić u posjetu zoološkom vrtu, Osječki matematički list 16/1 (2016), 9398
 I. Matić, Lj. Jukić Matić, Shopping, Osječki matematički list 16/2 (2016), 9194
 Lj. Jukić Matić, I. Matić, Ključevi, Osječki matematički list 15/2 (2015), 6067
 Lj. Jukić Matić, I. Matić, Lov na blago, Osječki matematički list 15/1 (2015), 9598
 Lj. Jukić Matić, D. Zucić, Realistic mathematics education: primjena na eksponencijalnu i logaritamsku funkciju, Matematika i škola 79 (2015), 147153Rad daje opis nizozemske matematičke edukacije poznate kao Realistična matematička edukacija (RME).
 Lj. Jukić Matić, I. Matić, M. Pavlović, Geometrija i Sherlock Holmes, Matematika i škola 75 (2014), 195201
 Lj. Jukić Matić, I. Matić, Obitelj Medić se priprema za odlazak u svatove, Osječki matematički list 14 (2014), 169174Zanimljivi zadatci uklopljeni u priču o obitelji Medić.
 Lj. Jukić Matić, I. Matić, Priprema za državnu maturu obitelji Medić, Osječki matematički list 14/1 (2014), 7781
 Lj. Jukić Matić, V. Tutnjević, Algebarski koncepti u nastavi matematike, Poučak 14 (2013), 3138Uvođenje algebre u nastavu matematike počinje u višim razredima osnovnih škola, a posebno je istaknuto u prvoj godini srednjoškolskog obrazovanja. Ovdje govorimo o osnovnim algebarskim konceptima.
 Lj. Jukić Matić, I. Matić, Gozba obitelji Medić, Osječki matematički list 13/2 (2013), 191194
 Lj. Jukić Matić, I. Matić, Ljetovanje obitelji Medić, Osječki matematički list 13/1 (2013), 8490
 Lj. Jukić Matić, I. Matić, Put djeda mraza, Osječki matematički list 13/1 (2013), 101105
 Lj. Jukić Matić, V. Tutnjević, Razvijanje matematičkog razumijevanja, Matematika i škola 70 (2013), 196200U radu se opisuju metode za razvoj matematičkog razumijevanja kod učenika kroz istraživačku matematiku.
 Lj. Jukić Matić, I. Matić, Role of the competitions in the curricula of teaching computer science, Croatian Journal of Education 13/3 (2011), 201231
 Lj. Jukić Matić, H. Velić, Fibonaccijev brojevni sustav, Math.e : hrvatski matematički elektronski časopis 16 (2010), 110U ovom članku prikazujemo kako pomoću Fibonaccijevih brojeva izgraditi brojevni sustav
 Lj. Jukić Matić, I. Hartmann, Od rimskih brojeva do chisanbopa, Matematika i škola 54 (2010), 161166Članak opisuje opisuje vezu između rimskih brojeva i metode računanja na prste koja se zova chisanbop (chisonbop).
 Lj. Jukić Matić, Matematičke slagalice, Osječki matematički list 9/1 (2009), 1320Čak i kad mislimo da je igra samo igra, ona je zapravo više od toga. Kroz igru se možemo zabaviti, ali i dosta toga naučiti. Takve su i slagalice tangram i IZZI 2. S jedne strane razvijaju logičko rezoniranje i kombiniranje, a s druge strane su neiscrpan izvor zabave
 Lj. Jukić Matić, Matematika i origami, Osječki matematički list 7/1 (2007), 2332Origami je japanska umjetnost savijanja papira u zanimljive modele, bez korištenja škara i ljepila. U ovom članku dajemo nekoliko primjera “ origami geometrije” .
 Lj. Jukić Matić, Matematika kroz igru domino, Osječki matematički list 7/2 (2007), 6979Domino pločice nisu namijenjene samo za igru. One se mogu koristiti kao sredstvo za savladavanje raznih matematičkih pojmova i razvoj logičkog mišljenja.
 Lj. Jukić Matić, I. Matić, Priče obitelji Medić, Odjel za matematiku, Sveučilište J.J. Strossmayera u Osijeku, Osijek, 2021.
 Z. KolarBegović, R. KolarŠuper, Lj. Jukić Matić, Towards new perspectives on mathematics education, Fakultet za odgojne i obrazovne znanosti i Odjel za matematiku, Sveučilište u Osijeku, Osijek, 2019.
 Z. KolarBegović, R. KolarŠuper, Lj. Jukić Matić, Mathematics Education as a Science and a Profession, Odjel za matematiku i Fakultet za odgojne i obrazovne znanosti, Osijek, 2017.
 Lj. Jukić Matić, I. Matić, Priručnik za nastavu matematike, Odjel za matematiku, Sveučilište J.J. Strossmayera, Osijek, 2017.
 Lj. Jukić Matić, D. Glasnović Gracin, How Croatian mathematics teachers organize their teaching: differences according to the initial education, Element, Osijek, 2015.Initial education of mathematics teachers is important for teaching and learning mathematics in school classrooms. Some studies showed that there exists a relation between students’ achievement and teachers’ mathematical and pedagogical content knowledge. In Croatian lower secondary education, there are mathematics teachers who significantly differ in their initial education. In this paper, we examine teaching practices of two groups of mathematics teachers ; those who finished former pedagogical academies and those who obtained their degrees from departments of mathematics. Using qualitative methods as observations and interviews, we investigated the teaching practice of 12 lower secondary mathematics teachers with special reference to the utilization of the textbook. Results showed that these two groups of teachers differ in the use of textbooks, but also in some other parts of teaching practice.
Projects

Kreativna STEM revolucija u Slavoniji (20212022)
 ERASMUS + KA201 "GAMMA"
The project GAMMA aims to direct students' knowledge of digital games and their connection thereto to enhance their mathematical skills. Since teachers should have a leading role in this process, the project aims to develop educational materials that will be useful to all mathematics teachers who want to use gamebased learning (GBL) founded on digital technology (20202022)

Researcher in the project SURFPRIMA Professional development of teachers in the function of improving the learning outcomes of primary school students in science and mathematics (https://surfprima.net) funded by the Croatian Science Foundation from 20182022.

"STEMp"  Development of modern study programs for the education of IT teachers, technology teachers biology, chemistry, physics and math teachers using the Croatian Qualifications Framework . Project ran 2015/2016.

"Discrete series in generalized principal series ". Project ran in 2013/14, supported by University of Osijek.

"Teaching and learning outcomes in undergraduate calculus courses for students of technical and science studies in Croatia and Denmark" . Project ran in 2010/11 in collaboration with professor Bettina Dahl Soendergaard from University of Aarhus, Denmark. Project was supported by National Foundation for Science, Higher Education and Technological Development of the Republic of Croatia.

"Teaching for quality learning of mathematics in technical and science study programs" Project run in 2008/09 in collaboration with professor Bettina Dahl Soendergaard from University of Aarhus, Denmark. Project was supported by National Foundation for Science, Higher Education and Technological Development of the Republic of Croatia

"Matematički temelji prirodnih i društvenih spoznaja" Project ran from 20072014 in collaboration with professor Franka Miriam Brueckler from University of Zagreb, Croatia. Project was supported by Ministry of Education, Science and Sports.
Professional Activities
Editorial BoardsOsječki matematički list
Committee Memberships
Udruga Matematičara Osijek secretary (20132017), vice president (2017 ...)
HMD (Hrvatsko matematičko društvo)
ERME (European Society for Research in Mathematics Education)
PME (International Group for Psychology of Mathematics Education)
Refereeing/Reviewing
Service Activities
 August, 2020 organiser at Inovativna nastava matematike (Teaching mathematics innovatively)
 August, 2022 lecture Active learning of mathematics for qualification exam
 February, 2021 lecture Qualitative feedbcak in mathematics teaching at National confres of mathematics teachers
 December, 2020 lecture How to write esay for Mathematics teacher qualification exam
 August 2020 organiser and speaker at Inovativna nastava matematike (Teaching mathematics innovatively)
 August 2016, organiser and speaker at Inovativna nastava matematike (Teaching mathematics innovatively)
 January 2015, lecture at National conference for mathematics teachers "Mathematics in context" (Singapore math)
 November 2014. lecture at Teacher professional development meeting (ŽSV učitelja matematike Learning outcomes)
 2013 .... member of committee for teacher credentialing, appointed by Education and Teacher Training Agency
 December 2014. Večer Matematike (Night of Mathematics)Kako sakriti poruku od ostatka Zemlje
 May October 2013. Nacionalni centar za vanjsko vrednovanje obrazovanja (NCVVO) member of expert group for developing the guide for the state graduation exam in mathematics in 2014./2015.
 October 2010. participating in workshop "Matematičko područje u nacionalnom okvirnom kurikulumu za predškolski odgoj i obrazovanje te opće obvezno i srednjoškolsko obrazovanje"
 October 2010. lecture at 2. stručnometodičkom skupu Udruge Normala with topic “Nastava matematike i izazovi moderne tehnologije“  tema "Dokazivanje i softveri dinamičke geometrije"
 June 2010. Nacionalni centar za vanjsko vrednovanje obrazovanja (NCVVO)
member of expert group who determined rank of passing the state graduation exam in mathematics in 2009./2010.
FESTIVAL ZNANOSTI (Science Fair)
2017. organizing
2016. workshop Svijet origamija
2015. workshop Sunčana matematika, Magični Kvadrati
2014. workshop MathCraftOrigami
2013. workshop Pogled u budućnost
2012. organizing
2011. workshop Pobjedničke strategije
2010. workshop Kako sakriti poruku od ostatka Zemlje
2009. workshop Kako računati na prste  ručni kalkulator
2008. workshop Matematičke slagalice
2007. workshop Matematika kroz igru domino
Zimska škola matematike za srednju školu (Winter math school for high school) organizing and participating
2010. lecture Teorija grafova
2009. lecture Matematička indukcija i Goodsteinov teorem
2006. lecture Funkcijske jednadžbe
Zimska škola matematike za osnovnu školu (Winter math school for secondary school)
2011. workshop Pascalov trokut
2010. workshop Malo o grafovima
2009. workshop Sudoku
Teaching
Methods of teaching mathematics 1
Methods of teaching mathematics 2
Teme diplomskih radova
 Formativno vrednovanje u nastavi matematike.
 Izometrije u nastavi matematike.
 Razlomci: koncepti i procesi.
 Grunvorstellungen (osnovne ideje u nastavi) i diferencijalni račun
Personal
2 children
Currently married to Ivan Matić