Sixty (35 girls and 25 boys) 9th-grade students' conceptual understanding of the number line was qualitatively assessed through verbal explanations and visual representations. The assessment included an open-ended question focused on students' number line descriptions and the explanations coalesced around six features: sequential ordering (i.e.,…

Misconceptions occur as a result of learners' wrong beliefs and experiences, and because subsequent learning is built on these misconceptions, they cause new concepts to be learned incorrectly. Studies show that students have problems in making sense of many mathematical concepts in mathematics teaching processes and this situation can be…

This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students' Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices…

The purpose of this correlational study was to investigate the relationship of number sense comprehension and mathematics attitudes on mathematics achievement and intention to pursue a mathematics-related career for final-year high school students in Kenya. The sample for the study comprised of final-year high school students from three schools,…

During their school life, students learn mathematical topics that can be considered essential for the understanding of the property of density in the set of real numbers. Therefore, we detected a need to design and elaborate a Hypothetical Learning Path to include topics to help promote the learning of this property. This report shows results of a…

The study aims to investigate students' conceptualisation of the quantum numbers concept through their verbal descriptions and pictorial representations of the corresponding atomic structures. The study was conducted with the participation of 192 12th-grade students from six secondary schools in Northern Greece, via a paper-and-pencil test,…

Logarithms, pivotal in advanced mathematics and real-world applications, often present challenges to students who resort to rote memorization without grasping their essence. While the emotional dimensions of learning mathematics are increasingly recognized, research in this area remains limited. This dissertation addresses this gap by examining a…

An instructional approach is presented for teaching the mole concept to high school introductory-level chemistry classes. Extensions to the strategy are presented for more advanced classes. The strength of the approach is based upon discovery. Students discover the Avogadro number and the mole concept. The discovery is based upon calculations that…

Our goal in this article is to organise an epistemological matrix for the concept of rational number that contemplates its different meanings. Aiming at understanding the various ways to signify the rational numbers and based on the theoretical-methodological approach of conceptual profiles, we produce and analyse data from various sources,…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

Many Grade 9 mathematics learners face difficulties in solving number-pattern problems due to insufficient exposure to strategies in solving such problems. The aim of this exploratory qualitative study was to investigate Grade 9 mathematics learners' strategies in solving number-pattern problems. The problem-solving conceptual framework of Singer…

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their…

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…

In the study reported on here I evaluated the alignment between the Annual National Assessment (ANA) and Trends in International Mathematics and Science Study (TIMSS). Theoretical perspectives were drawn from the Survey Enacted Curriculum (SEC), while quantitative correlational methods were used to determine the alignment between ANA and TIMSS…

In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…