Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

I present my perspective on the design process in this article, arguing for a focus on student learning and "slow design" that stems from knowledge of mathematics and their support system in the learning process. I have a question about the design process academization and task design research direction. Numerous examples from my work at…

In this study, the teacher candidates who learnt to find the algebraic equation corresponding to geometric structure of the ellipse in analytic geometry classes were requested to find the algebraic representations corresponding to the structures that contained ellipses in different positions. Thus, it would be possible to determine higher order…

The present study examined the ability of content domain (algebra, geometry, rational number, probability) to classify mathematics misconceptions. The study was conducted with 1,133 students in 53 algebra and geometry classes taught by 17 teachers from three high schools and one middle school across three school districts in a Midwestern state.…

This study examined the identity resources used and the subject positions taken by secondary students in autobiographical narratives of their experiences with mathematics (mathographies). Data consisted of mathographies from 54 students in two differently tracked math courses at a large, diverse public high school in Brooklyn, NY. The study asked…

A growing body of research suggests that accounting for student specific variability in educational data can improve modeling accuracy and may have implications for individualizing instruction. The Additive Factors Model (AFM), a logistic regression model used to fit educational data and discover/refine skill models of learning, contains a…

This study was conducted to compare two grade-ten mathematics textbooks according to Bloom's Taxonomies. In the Arabic version, 37 out of 70 periods (55.29%) were given to plane geometry and trigonometry, whereas 29 out of 70 periods (41.41%) were allocated for geometry and trigonometry. Also, 12 periods (17.14%) were allocated for algebra in the…

In this work we examined the content of approximately 950 mathematics questions used in measuring achievement among 4th, 5th and 6th graders in the US in an attempt to determine how the current standardized examinations, which were developed to reflect new national curricular mandates, compared to the old measures used for the same purpose. Using…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

The present study tries to identify the "picture in mind" that students' have about defining, proving and modelling. We access to it through external representations of their mental representations; in particular, from the way in which these representations are expressed in written form (sentences and situations). In the study we have…

This study surveyed 82 preservice elementary teachers using items from an instrument designed to predict student achievement based on a teacher's mathematics knowledge for teaching (MKT) in numbers and operations concepts. Additional mathematics beliefs items asked participants to rate their level of agreement with math myths and math anxiety…

The results from a year-long study to investigate the technical features of easyCBM mathematics screening measures for first grade are presented. Measures were designed based on the National Council of Teachers of Mathematics Curriculum Focal Point standards, which for Grade 1 include (a) Number and Operations and Algebra, (b) Number and…

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…

Purpose: The purpose of this scientific monograph is to show new and creative approaches to different school subjects in primary and secondary level. Methodology: Interdisciplinary and international comparative approaches were used. Now according to the 7th Framework Program, the preferred form of Science Education (www.scientix.eu) is preferred…