Open Mathematical Education Notes

1-7

Authors: Milica Videnovic

One of the most striking differences between the Canadian educational system and most European educational systems is the importance given to oral examinations, particularly in mathematics courses. In this paper, seven mathematics professors share their views on mathematics assessment, and their thoughts about the types of knowledge and understanding in mathematics that can be assessed on written and oral exams. Four out of seven professors were born and educated in Bosnia, Poland, Romania, and Ukraine, and they are currently teaching in Canada. The other three professors were born and educated in Canada, the United States, and Germany, and they are all currently teaching in Germany. With the increased emphasis on closed book written examinations, the results in this study show that written exams alone are not sufficient to assess students‟ conceptual knowledge and relational understanding, and therefore, there is a critical need for implementing the oral assessments in mathematics courses.

29--42

Authors: Daniel A. Romano

This study describes the mathematical proficiency of pre-service elementary school teachers in geometry within the paradigm: mathematical and methodical types of knowledge are necessary for teachers understanding of teaching and students’ learning of the basic geometric concepts. In order to define the parameters that allow us to consider students’ skills is mentioned paradigm, we tested 63 students of the third and fourth years of studies at two pedagogical faculties for teacher education in Bosnia and Herzegovina on a few questions about the relationship between the basic geometric objects - points, lines and planes. We analyzed students’ reflections on these questions using quantitative and qualitative methods. Although the tested students have solid intuitive understanding of basic geometric objects (the 'level 0' by van Hiele’s classification), their understanding of the process with these geometric objects is much lower. This paper is written to formulate the hypothesis that the difficulties that have been observed in the tested population were not the result of students' intellectual deficiency but, to a significantly greater extent, of insignificantly built components of geometric thinking during the previous school education.