Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

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This paper deals with the construction of noncommutative phase spaces as coadjoint orbits of noncentral extensions of Galilei and Para-Galilei groups in two-dimensional space. The noncommutativity is due to the presence of a dual magnetic field B * in the Galilei case and of a magnetic field B in the Para-Galilei case.

This paper presents the findings of a convergent parallel mixed methods research that was carried out to explore the views of student-teachers on how geometry was taught and the confidence of those student-teachers in teaching geometry to secondary school learners when they will become professionally qualified. Respondents were randomly selected from two Colleges of Education in Burundi. Although the study was predominantly quantitative, some qualitative data were also collected to gain deeper insights into the prevailing situation. Ninety-seven pre-service teachers of Mathematics from the said institutions completed the questionnaire whose items were closedended except for one that was open-ended. Results show that the teacher-centered approach had dominated geometry classes in their respective secondary schools. Nevertheless, studentteachers exhibited higher confidence in teaching geometry. These findings provide evidence on the need for teacher education programs to consider embedding instructional and assessment approaches designed for specific branches of mathematics.