This text aims to present new research perspectives on teacher training. In particular, it is dedicated to analyzing the training of teachers who teach mathematics from a historical perspective. To this end, it uses the concepts of mathematics to teach and mathematics for teaching, indicating research results, characterizing the professional…

A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

What is the connection between advanced mathematics and teaching secondary mathematics? I address this question, drawing on insights from the Special Issue on "Personal Mathematical Knowledge in the Work of Teaching" ("CJSMTE" 13(2), 2013) and reflecting on my personal teaching experience.

Background: Dot enumeration is the basic mathematics competency in young children and a significant indicator of later mathematics achievement. Aim: The present study focused on (1) how children's dot enumeration ability changed as they progressed from late kindergarten years (K3) to the second year of primary school in Hong Kong (P2), and (2) the…

Creativity plays an important role in mathematics, but it can be overlooked in undergraduate courses. This article describes three ways an existing first-year math seminar was modified to increase its focus on creativity: introducing readings and discussions related to creativity, drawing connections to creativity in other disciplines, and adding…

Currently, studies focusing on mathematics education pay more attention to the study of the lecturer's knowledge, aiming to understand this knowledge, its development, and how it is reflected in the practice of teaching. Following this line of research, the present study is based in the "Mathematics Teacher's Specialized Knowledge…

The article identifies three narratives about mathematics education. The first claims that mathematics is a wonderful subject, which provides a true foundation for human knowledge and progress. The second presents mathematics as a suspicious subject, which serves functions of oppression. The third highlights that mathematics has critical…

Researchers, who have studied the understanding of the density property in the set of decimal numbers, have shown that the student uses the property of the discrete of natural numbers to solve tasks related to density. So, a restructuring of concepts is necessary, that is, a conceptual change from "the discrete" to "the dense".…

Previous research has demonstrated a link between spatial and math skills. However, little research has examined this relation longitudinally. The present study examines the development of and reciprocal relations between spatial and math skills in elementary school students. We administered two spatial tasks and a math task to 312 first- through…

For Freudenthal, the practice of mathematics in the curriculum is not a set of predetermined theories, goals and means. On the contrary, it is always associated with positively understood phenomenological processes in mathematics, as the curriculum is often used in conjunction with the transformation or development of practice. For Freudenthal…

Although schools with a high concentration of ethnic minorities often underperform, not much is known about the factors that predict high and even excellent achievement of pupils within these schools. Therefore, we examined which concrete diversity practices and key psychological processes increase or decrease the likelihood/odds for high and…

This study employed student choice and tiered worksheets as strategies of differentiated instruction on Quadratic Equations in addressing students' non-compliance with assignments in a flipped classroom. In each lesson, students choose among the instructional materials with guide questions to assist them in focusing on key areas during the…

Large scale international assessments depend on invariance of measurement across countries. An important consideration when observing cross-national differential item functioning (DIF) is whether the DIF actually reflects a source of bias, or might instead be a methodological artifact reflecting item response theory (IRT) model misspecification.…

Background/Significance: College algebra traditionally serves as the default math requirement for community college students. Lattimore and Depenbrock (2017) reported that approximately two-thirds of community college enrollees are required to take this course, yet nearly 80% fail to complete it, making it "the single most failed course in…

To provide quality mathematics education for disadvantaged groups of middle school students and continue to offer quality practicum experience to future teachers during the COVID 19 outbreak, we founded the Online Laboratory School. This school was free and open to public school students: 130 middle school students throughout Turkey attended for a…