Problem-posing is recognized as an important component in the nature of mathematical thinking (Kilpatrick, 1987). More recently, there is an increased emphasis on giving students opportunities with problem posing in mathematics classroom (English& Grove, 1998). These research has shown that instructional activities as having students generate problems as a means of improving ability of problem solving and their attitude toward mathematics (Winograd, 1991). In this study, teaching Taxicab Geometry which is a non-Euclidean geometry is aimed to mathematics teacher candidates by means of computer game-Simcity- using real life problems posing. This studies’ participants are forty mathematics teacher candidates taking geometry course. Because of using Simcity computer game, this game is based on Taxicab Geometry. Firstly, students had been given Taxicab geometry theory for two weeks and then seperated six each of groups. Each of groups is wanted to posing problem and solving from real life problems at Taxicab geometry. In addition to, students applied to problem solving at Simcity computer game. Studens were model into Simcity game. They founded ideal city, healty village, university campus, holiday village, etc. interesting of each others.

Many countries are reporting of difficulties in exact education at schools: mathematics, informatics, physics etc. Various methods are proposed to awaken and preserve students’ interest in these disciplines. Among them, the simplification, accent on applications, avoiding of argumentation (especially in mathematics) etc. must be mentioned. As one of reasons for these approaches the growing amount of knowledge/skills to be acquired at school is often mentioned. In this paper we consider one of the possibilities to integrate partially teaching of important chapters of discrete mathematics and informatics not reducing the high educational standards. The approach is based on the identification and mastering general combinatorial principles underlying many topics in both disciplines. A special attention in the paper is given to the so-called “pigeonhole principle” and its generalizations. In folklore, this principle is usually formulated in the following way: “if there are n + 1 rabbits in n cages, you can find a cage with at least two rabbits in it“. Examples of appearances of this principle both in mathematics and in computer science are considered.

Working with problems and making investigations is an activity one has to learn already very early. Therefore in primary school children should not only learn concepts and solve given tasks. They also should find out knowledge and reasons by themselves. Here you will find some problem fields in elementary arithmetic within children of primary school can make different investigations and find as well as give reasons for special statements. The topics concerned are partitions of numbers, sums of consecutive numbers, figured numbers, sequences and chains, table of hundred and numberwalls.

Central to this article is networking in math lessons, whereby concentration is placed on the construction of a student-focused teaching method for the networking of mathematical knowledge in the lower secondary. Firstly, normative standards and descriptive results will be compared. Secondly, several already existing teaching methods for networking in math lessons will be added to the method of „chapter-spanning task variation“. Using this method, attention is be placed on the integration of mathematical content and specific social netowrk-form (e.g. teacher led classes, group-work etc.). This paper will be concluded with the presentation of the testing of the method in the school context).

Visual modeling concept of integrated constructs (essence) of mathematical objects in teacher training of humanistic area is presented as technology of education in problem solving. The main goal of innovative approach is student’s activity in mathematics on generating of concrete essence manifestations on concepts, methods, theorems, algorithms, procedures and so on. Such student’s activity should be: · Success in an area of actual interests and person’s experience and reached by perception; · Have high level of variability in visual modeling; · Success in domain of reflection process stimulation. Similar creative behavior of persons is typical for actors, dancing, and figure skating and so on. Now we show that such technology will be fruitful for teacher training in mathematics for humanistic specialties.

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Fehlende Kompetenzen in Mathematik und Naturwissenschaften werden von Studierenden als ein Grund für den Studienabbruch in Ingenieurwissenschaften angegeben (Heublein et al., 2017). Welche Kompetenzen für Studierende zu Beginn des Ingenieurstudiums relevant sind, ist jedoch bisher wenig empirisch untersucht. Das Ziel der vorliegenden Studie ist, relevante mathematische Kompetenzen von Ingenieurstudierenden zu analysieren und dabei sowohl Wissensbestände als auch die Anwendung von Wissen und die Zusammenhänge zwischen beiden Bereichen zu berücksichtigen. Dazu wurde eine Studie im Mixed-Methods Design entwickelt. In dieser werden die Studierenden hinsichtlich ihrer Dispositionen in Mathematik und Physik zu Beginn des Studiums und am Ende des ersten Studienjahres mit quantitativen Methoden getestet. Zu diesen beiden und einem weiteren Zeitpunkt am Ende des ersten Semesters wurden zudem die situationsspezifischen Fähigkeiten bei der Bearbeitung von Mathematik- und Physikaufgaben mit Hilfe eines theoretischen Rahmens zum mathematischen Problemlösen mit qualitativen Methoden untersucht. Dieser Theorierahmen umfasste für die Mathematikaufgaben die Aspekte Heurismen (Bruder & Collet, 2011; Schoenfeld, 1980) und Problemlösephasen (Polya, 1957) sowie das Modell der Epistemic Games (Tuminaro, 2004) zur Analyse der Bearbeitung von Physikaufgaben. Die Ergebnisse zeigen Zusammenhänge zwischen mathematischen und physikali-schen Dispositionen. Zusätzlich wird die Bedeutung von Aspekten des Problemlösens deutlich, um die Prozesse bei den Bearbeitungen von Mathematik und Physikaufgaben im ersten Studienjahr zu analysieren. Auf Grundlage der qualitativen Beschreibungen konnten Cluster von Fällen von Studierenden gebildet werden. Mit Hilfe dieser Cluster zeigen sich Zusammenhänge zwischen den Dispositionen und situationsspezifischen Fähigkeiten bei den besonders leistungsstarken und leistungsschwachen Studierenden. / Missing competences in mathematics and sciences are cited by students as a reason for the drop-out in engineering sciences (Heublein et al., 2017). However, the competences that are relevant for students at the beginning of their engineering studies have so far not been investigated in an empirical way. The aim of this study is to analyse relevant mathematical competences of engineering students, taking into account both knowledge and the application of knowledge and the interrelationships between the two. A study in mixed method design was developed for this purpose. In this study, students are tested with regard to their dispositions in mathematics and physics at the beginning of their studies and at the end of the first year of their studies using quantitative methods. At these two points in time and a further time at the end of the first semester, the situation-specific skills in processing math and physics tasks were examined with the help of a theoretical framework for solving mathematical problems, using qualitative methods. This theoretical framework included for the mathematical tasks the aspects heuristics (Bruder & Collet, 2011; Schoenfeld, 1980) and problem solving phases (Polya, 1957) as well as the model of Epistemic Games (Tuminaro, 2004) for the analysis of the processing of physical tasks. The results show interrelationships between mathematical and physical dispositions. In addition, it became clear that there is a need of problem solving aspects in order to analyse the processes involved in the working on maths and physics tasks in the first year of studies. Based on the qualitative descriptions, clusters of student cases could be formed. These clusters show the interrelationships between dispositions and situation-specific skills of particularly high-performing and underperforming students.