The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

Creative thinking in mathematics is an essential 21st Century skill that can be developed and encouraged through an exploration of mathematical concepts. In the context of the new "Australian Curriculum: Mathematics," this article explores the possibilities that are unlocked when students engage with tasks creatively in mathematics. By…

The understanding of analytical chemistry and its application in different areas of life science is something that should be encouraged for students studying chemistry, and also something that appeals to many students. Life science includes a vast variety of areas, out of which some are more easily approached in student projects. The chemical…

This study investigated in-service teachers' conceptualization of the pure imaginary number, within the Cartesian form, "a" + "ib" where "a" and "b" are real numbers and "i" is the imaginary unit. As part of a larger design-based research study, in which a professional development (PD) program was…

This paper aims to clarify how the use of the GeoGebra dynamic geometry program helps students understand the relationships between different representations of a linear function and develop the ability to plot a linear function. The study was based on a quasi-experimental design. In control classes, the topic of functions was presented without…

Textbooks play an important role in teachers' instructional decisions (Jones & Tarr, 2007), which consequently affects students' learning. This paper reports on a comparison of the elementary mathematics textbooks used in Iran and the United States, the Go-Math textbook. I analyzed topic sequences, frequency of the tasks, and cognitive demands…

This paper reports the results of research in which the objective was to explore the preconceptions of slope in seventh-grade students. Preconceptions are understood as students' knowledge prior to the formal teaching of a certain concept. For data collection, task-based interviews composed of ten tasks applied to 21 Mexican students were used.…

This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and…

In this study, we look at student perceptions of a first course in linear algebra, focusing on two specific aspects. The first is the statement by Carlson that a fog rolls in once abstract notions such as subspaces, span and linear independence are introduced, while the second investigates statements made by several authors regarding the negative…

Music can be defined as the art (or science) of blending vocal and/or instrumental sounds to produce form and harmony. This paper is about the mathematics which underlies both music theory and how different instruments create sounds/notes. Consideration will be given to scales, intervals, and harmonics but not rhythm although it is a fundamental…

This study aimed to examine the effect of using the flipped classroom model on students' proportional reasoning. In this context, the study focused on students' achievement and solution strategies for proportional reasoning problems. The participants of the study were 56 seventh-grade students, who were determined by convenience sampling method.…

The purpose of this study is to comprehensively describe the results of the analysis of the ability to understand concepts and misconceptions in terms of differences in learning styles, as well as gender differences. The data to be collected in this study is in the form of primary data and secondary data. The primary data is obtained from primary…

Research has shown that many primary students experience transition barriers between additive and multiplicative thinking. This paper analysed responses from 253 Years 3 to 6 students to a diagnostic assessment which consists of whole number multiplication and division problems involving equal groups, arrays, multiplicative comparison and…

Research shows the salient place of mathematical teaching talk, including the mathematical-linguistic practices of naming and explaining, in the enactment of students' mathematical talk and learning with understanding in the classroom. Our study was developed to examine the noticing of two groups of secondary-school mathematics teachers in one-day…

In Ireland, Initial Teacher Education [ITE] standards require all teachers to possess an adequate level of numeracy themselves in order to teach for numeracy learning across the school curriculum. This paper reports on a study that investigated 204 pre-service post-primary teachers' numeracy capabilities. Analysis of questionnaire data from…