Formative assessment has become a focus of classroom teachers as a quick method to assess students' progress in their classrooms. For students to be prepared for summative assessments, it is important to separate the traditional forms of summative assessment from the everyday practice and feedback that is formative assessment. Mathematics teachers…

Research suggests that troubleshooting activities that require students to reflect on teacher-crafted erroneous examples; i.e., erroneous solutions to problems that correspond to widespread naïve ideas, are beneficial to learning. One possible explanation to these beneficial effects is that troubleshooting activities encourage students to test the…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…

Developing students' competence in algorithmic thinking is emerging as an objective of mathematics education, but despite its inclusion in mathematics curricula around the world, research into students' algorithmic thinking seems to be falling behind in this curriculum reform. The aim of this study was to investigate how the mathematical modelling…

Backward transfer is defined as the influence that new learning has on individuals' prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students' prior ways of reasoning about linear functions. Two algebra classes and their teachers…

This study addresses a significant gap in educational research by employing statistical methods to measure the sequencing of different components and content topics in textbooks. It is well-documented that the structure and sequencing features of textbooks play a crucial role in enhancing students' learning. However, existing literature has…

Students' competence in solving trigonometry has been in doubt but little attention has been given in the area of research. An assessment of students' answers to trigonometry problems is crucial to dealing with their conceptual challenges. This study employed a descriptive qualitative research design, with the goal of evaluating errors made by…

Mathematics textbooks are commonly considered to be tools for efficient teaching and implementing change in mathematics classrooms worldwide, helping teachers to teach and learners to learn. When the content as described in the curriculum is not faithfully and relevantly represented in textbooks, learners' opportunity is limited. Against this…

Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised…

Background/purpose: This study aimed to investigate the differences among the equations used in estimating the reliability coefficient using the half-split method. These equations demonstrate Spearman-Brown's, Rulon's, Guttman's, Mosier's, Flanagan's, and Horst's. Materials/methods: The study instrument was a 43-item scale for evaluating the…

Technological mediation has gained relevance in teaching mathematics. Its usefulness and impact depend, to a great extent, on how students approach the learning of the discipline. Two independent instrumental studies were conducted to analyze the psychometric properties of the Spanish version of the Mathematics and Technology Attitudes Scale…

This paper reports on the development of complex unfamiliar mathematics questions using conventional mathematics questions. The autoethnographic research data included retrospective reflections of two educators and review of literature. Data analysis resulted in a three-phase development process: identifying conventional questions and subject…

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.,…

It has been over thirty years since the nuclear reactor meltdown at the Chernobyl nuclear power plant, but why there is still an officially designated exclusion zone? The Chernobyl Disaster Task combines the learning of exponential functions with properties of radioactive substances to help students understand the ongoing effects of the meltdown.…