Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

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…

Although there has been extensive research on students' understanding of the particulate nature of matter (PNM), there is still a lack of research on contexts that can be used to teach this challenging topic. In a previous design-based research study, the authors developed a teaching-learning sequence (TLS) on the PNM in the context of crystal…

Circle and disc are fundamental concepts introduced in middle school, forming the basis for many other mathematical ideas. Students often face challenges in comprehending circles, discs, and their basic elements. This research examines the processes of sixth-grade students in constructing circles, discs, and their essential components within a…

This paper analyses the opportunities for presenting knowledge that are created when assessment allows senior high school biology students to draw on linguistic and visual resources when constructing meaning in response to short-answer examination-style questions requiring a sequential explanation. Students within one senior high school biology…

Instructional quality dimensions of cognitive demands and instructional support have been shown to have an impact on students' learning gains. Existing operationalizations of these dimensions have mostly used comprehensive ratings that combine various subdimensions of task quality and interaction quality. The current study disentangles interaction…

This study examined a cohort of middle school pre-service mathematics teachers' understanding of the rate of change as they engaged in a model development sequence. By adopting a design-based research perspective, a model development sequence on the concept of rate of change has been designed and implemented as part of a mathematical modeling…

A wide array of conceptual change strategies attempted to address students' persistent alternative conceptions, yet there remained ubiquitous struggles of teachers teaching abstract and highly contentious science concepts. This study investigated the effectiveness of the novel Conceptual Change Framework of Instruction (CCFI) in teaching eclipses…

This article reports on the development and piloting of a German version of a concept test to assess students' conceptual knowledge of density. The concept test was administered in paper-pencil format to 222 German secondary school students as a post-test after instruction in all relevant concepts of density. We provide a psychometric…

This study focused on addressing underperformance in chemistry in Anglophone West African countries. The main purpose of the study was to determine if factors such as gender, school location and ownership impact students' perception of the difficulty of chemistry concepts and to suggest how these difficult concepts can be made easy to learn from…

The study covers the development and testing of the alternative mechanics survey (AMS), a modified force concept inventory (FCI), which used automatically marked free-response questions. Data were collected over a period of three academic years from 611 participants who were taking physics classes at high school and university level. A total of…

The main goal of this study was to validate the strategy for the assessment of the cognitive complexity of chemical kinetics exam items. The strategy included three steps: 1) assessment of the difficulty of concepts, 2) assessment of distractor value, and 3) assessment of concepts' interactivity. One of the tasks was to determine whether there…

Mole, molar mass and the Avogadro number are used constantly to measure the amount of substance in chemical changes. However, students have difficulty in understanding these concepts because they are not familiar with measuring very small amounts of matter that cannot be seen and weighed in daily life, like atoms. The mole concept was developed to…

Literature suggests that students need to be exposed to cognitively demanding tasks (CDT). In this qualitative study, we examined in-service secondary school teachers' challenges in understanding (e.g. recognizing, solving, and designing) and implementing cognitively demanding tasks in mathematics classrooms. Purposive sampling consisted of eleven…

Organic qualitative analysis is one of the challenging chemical concepts in students learning of chemistry. The West African Examinations Council chemistry chief examiners for years, have lamented on students' poor performance in organic qualitative analysis at the senior high school level. This study, therefore, investigated chemistry students'…