Students face a series of difficulties understanding the concept of variable when introduced to algebra. This study focuses on one of these difficulties namely students{\textquoteright} tendency to think of literal symbols, which stand for variables in algebraic expressions, to represent only natural numbers. The study tested the students{\textquoteright} understanding of the numerical values of variables in algebra, and its relation with the way they interpret the sign of the algebraic expressions. 110 10th graders were asked to assign numbers to the variables of two given functions, in order to make their graph, and also to determine the sign of algebraic expressions that appeared in inequalities and functions. The results supported the hypothesis of the study, that students have a strong tendency to interpret variables as standing for natural numbers only, and this tendency appeared to be related with their tendency to misinterpret the phenomenal sign of the algebraic expressions as always being identical with their actual one. The phenomenal sign is the sign an algebraic expression appears to have as a superficial characteristic of its form, i.e. students tended to think of -2x-1 as a negative quantity, and 4+3x as a positive one

}, keywords = {literal symbols, natural number bias, number concept, phenomenal sign, variables}, issn = {1792-8494}, author = {Konstantinos P. Christou} } @article {531, title = {{\"U}BERPRO {\textendash} A SEMINAR CONSTRUCTED TO CONFRONT THE TRANSITION PROBLEM FROM SCHOOL TO UNIVERSITY MATHEMATICS, BASED ON EPISTEMOLOGICAL AND HISTORICAL IDEAS OF MATHEMATICS}, journal = {MENON {\textcopyright}online Journal Of Educational Research, 2nd Thematic Issue}, year = {2016}, month = {05/2016}, pages = {27}, publisher = {University of Western Macedonia - Faculty of Education}, type = {Scientific paper}, chapter = {66}, address = {Florina, Greece}, abstract = {In spring 2015 the authors taught an intensive seminar for undergraduate mathematics students, which addressed the transition problem from school to university by bringing to the fore concept changes in mathematical history and the learning biographies of the participants. This article describes how the concepts of empirical and formalistic belief systems can be used to give an explanation for both transitions {\textendash} from school to university mathematics, and, for secondary mathematics teachers, back to school again. The usefulness of this approach is illustrated by outlining the historical sources and the participants{\textquoteright} activities with these sources on which the seminar is based, as well as some results of the qualitative data gathered during and after the seminar.

}, keywords = {genesis of geometry, higher education, mathematical belief systems, secondary school mathematics, transition problem}, issn = {1792-8494}, author = {Ingo Witzke and Horst Struve and Kathleen Clark and Gero Stoffels} } @article {536, title = {FACTORS CONTRIBUTING TO COMPUTATIONAL ESTIMATION ABILITY OF PRESERVICE PRIMARY SCHOOL TEACHERS}, journal = {MENON online Journal Of Educational Research, 1st Thematic Issue}, year = {2014}, month = {12/2014}, pages = {19}, publisher = {University of Western Macedonia - Faculty of Education}, type = {Scientific paper}, chapter = {90}, address = {Florina, Greece}, abstract = {This study focuses on the investigation of the factors that are related and contribute to computational estimation ability. We interviewed 69 students of the Department of Primary Education of the University of Crete. Moreover, these students had filled in a test. According to the analysis of the results, the factors that contribute to success at computational estimation are:

- good mathematical background and mainly good performance at exact mental computation and proportion problems,
- preference to mathematics at school,
- positive self-concept of computational estimation ability,
- positive self-concept of acquiring exact mental computation ability from the first grades of primary school
- positive self-concept of memory ability and particularly numerical data memory ability.