Mathematics Education as a Science and a Profession

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six chapters. In the first chapter, the author studies the relation between the surface approach and the strategic approach to learning outcomes according to the results of research conducted with a group of university students in Denmark. This chapter presents the results of research carried out with the students who were required to recognise and interpret mathematical concepts that could be interpreted from the graphs in different contexts. It also provides an insight into a detailed analysis of the tasks of the Croatian State Matura exam related to the functions. In the second chapter, the authors discuss the topic of the importance of spatial reasoning and the effect of computer technology on geometry education. They study regular and semiregular polyhedrons in Euclidean space and compare geometric properties of Euclidean and hyperbolic planes. In the third chapter, the authors examine teachers' classroom practices and beliefs about mathematics and the use of textbooks as curriculum resources. The results of textbook analysis on an asymptote and the asymptotic behaviour in the two most common series of high-school mathematics textbooks in Croatia are presented. The language of mathematics textbooks is analysed in the third paper. In the fourth chapter, the author investigates the impact of using the proposed computer-guided discovery learning model on students' conceptual and procedural knowledge of mathematics. The application of the computer program Graph is illustrated. The advantages of introducing software to the teaching process are considered. In the fifth chapter, the author examines whether there is a connection between the attitudes towards mathematics and the performance in mathematics exams. In the second paper, the authors describe a method for selecting a group of students that is supposed to receive additional teacher attention in order to improve their performance in the course. This chapter presents research results on the relations between the use of mathematics tutoring services at the university level and building student profiles. The problem of mathematical anxiety is also researched. An inclusive approach to mathematics curriculum can be revealed through the presence of curriculum accommodations for pupils with disabilities. The author of the last paper in this chapter provides content analysis of national curricula of five European countries: Great Britain, Finland, Germany, France and Croatia. In the last chapter of the monograph, the authors suggest some useful approaches to teaching mathematics. Learning through games increases student motivation and encourages positive attitudes towards mathematics. The characteristics of problem solving in mathematics education are listed in the last paper of this monograph. Papers in Chapter 1 include: (1) The study approaches of university students in a calculus class (Bettina Dahl); (2) Searching for a common ground in mathematics and physics education: The case of integral (Zeljka Milin Sipus, Maja Planinic, Ana Susac, and Lana Ivanjek); and (3) Functions in the 2015 and 2016 Croatian State Matura in higher level Mathematics (Matea Gusic). Papers in Chapter 2 include: (4) Spatial reasoning in mathematics (Nikolina Kovacevic); (5) The football {5, 6, 6} and its geometries: from a sport tool to fullerens and further (Emil Molnar, Istvan Prok, and Jeno Szirmai); and (6) Holes in alien quilts (A. S. Leeds, Natasa Macura, and Zachary Moring). Papers in Chapter 3 include: (7) Teachers' beliefs on mathematics as a background for their teaching practice (Ljerka Jukic Matic and Dubravka Glasnovic Gracin); (8) Asymptote as a body of knowledge to be taught in textbooks for Croatian secondary education (Aleksandra Cizmesija, Ana Katalenic, and Zeljka Milin Sipus); and (9) Language of Croatian mathematical textbooks (Goran Trupcevic and Anda Valent). Papers in Chapter 4 include: (10) The impact of using GeoGebra interactive applets on conceptual and procedural knowledge (Zeljka Dijanic and Goran Trupcevic); (11) The use of the computer program "Graph" in teaching application of differential calculus (Bojan Kovacic and Mirela Katic Zlepalo); and (12) Applications of free computational software in math courses at Zagreb University of Applied Sciences (Luka Marohnic and Mandi Orlic Bachler). Papers in Chapter 5 include: (13) Mathematics attitudes among students of Civil Engineering (Josipa Matotek); (14) Targeting additional effort for students' success improvement: The highest effect group selection method (Dusan Mundar and Damira Kecek); (15) Discovering student profiles with regard to the use of mathematics tutoring services at university level (Ivana Durdevic Babic, Ana Kozic, and Tomislav Milic); (16) Identifying mathematical anxiety with MLP and RBF neural networks (Ivana Durdevic Babic, Tomislav Milic, and Ana Kozic); (17) Standardization of learning outcomes in teaching mathematics (Zoran Horvat); and (18) Teaching and learning mathematics in inclusive settings: Analysis of curriculum of compulsory education in five European countries (Ksenija Romstein and Ljiljana Pintaric Mlinar). Papers in the Chapter 6 include: (19) Enhancing positive attitude towards mathematics through introducing Escape Room games (Amanda Glavas and Azra Stascik); (20) The presence of mathematical games in primary school (Ruzica Kolar-Super, Andrea Sadric, Zdenka Kolar-Begovic, and Petra Abicic); and (21) Problem solving in elementary mathematics education (Edith Debrenti). An index is included. Individual papers contain references. Abstracts are provided in both English and Croatian. [Abstract modified to meet ERIC guidelines.]