In this study, I analyzed and compared definitions of special quadrilaterals presented in the US and Turkish secondary school mathematics textbooks. To this end, seven textbooks from each country were examined based on the following features of mathematical definitions: form of presentation and mathematical correctness, minimality, the nature of…

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

Algebra is considered an important high school course because it is recognized as the gateway to higher mathematics, college opportunities, and well-paying jobs. In the United States, most secondary schools require students to be proficient in algebra to be able to graduate from high school. One major component of algebra is word problem solving,…

Take a deeper dive into understanding the five practices-anticipating, monitoring, selecting, sequencing, and connecting-for facilitating productive mathematical conversations in your middle school classrooms and learn to apply them with confidence. This follow-up to the modern classic, "The 5 Practices in Practice: Successfully Orchestrating…

This is a common experience among education researchers: we notice a surprising instructional move enacted by a teacher. After deeper reflection, we ask, "How many other teachers in Singapore do this?" In this paper, we describe an instrument we designed that is part of the resource needed to answer such questions. [This paper is the…

Roots is one of these mathematical topics that students encounter multiple times in their studies of mathematics. Growing from the commognitive framework, this study is concerned with intra-commognitive conflicts where the same discursant develops incommensurable discourses on 'the same' mathematical object (square roots, in this case) and…

The literacy proficiency development is one of concerns in education generally, so is in mathematics education as well. The growth of literacy proficiency is one of the issues in education, because it is very important to problem solving skills in students' real life. This research aimed to describe the growth of lower secondary school and upper…

The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher's knowledge effects the students' knowledge. A teacher should use appropriate mathematical explanation to be understood well by…

This paper reports on a study conducted with Grade 11 learners as participants, in four public high schools in a rural district of the Eastern Cape Province of South Africa. The central objective was to investigate the mathematical discourses of Grade 11 learners related to the word, algebraic and graphic representations of asymptotes of the…

The purpose of this text is to map knowledge conveyed at the discipline of Methodology of Mathematical Sciences at Escola Normal Superior of Coimbra that began functioning in 1912 until 1930. Firstly, requirements for admission to the school are addressed; secondly, a description of the first year disciplines, the pedagogical practice of the…

The study aimed to develop and validate learning module on exponential and logarithmic functions based on the Understanding by Design lesson plan. The study was descriptive in nature, describing the instructional materials and its properties. The research flow was based on the works of Emily K. Dunsker in 2005 and the suggested procedure on…

The purpose of this mixed methods study was to investigate the effect of a graphing calculator (GC) intervention on Grade 11 learners' achievement in quadratic inequality problem solving. The quantitative aspects of the study involved an experimental and control group design in which the experimental group received instruction using the GC…

Activities that play a significant role in mathematical thinking and problem-solving are mathematical problem posing. Scientific Approach with What-If-Not strategy (SA-WIN) is innovative learning that can improve the Mathematical Problem Posing Ability (MPPA) of students rather than Conventional Teaching (CT). This study aims to analyze the…

In this article, we describe the experiences of two preservice teachers (PSTs) who served as teaching assistants (TAs) in a secondary mathematics teaching methods course. As TAs, the PSTs approximated practice by being independently responsible for a learning environment and leading discussions with groups of students. Although the PSTs felt…

Mathematics evidenced un/manifested in/active, un/changeable, im/pure and primordial nature; therefore, it is illimitable to define as finite. It exists in the engineering of this universe. Philosophy of Mathematics studies abstract entities such as assumption and implication. Mathematics educators regard it as deductive tool and relate to solving…