This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…

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…

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…

Probability is generally considered one of the most challenging areas to teach in mathematics education due to its intricate nature. However, the simulation-based teaching method can increase students' accessibility significantly to the probability problems because it enables students to resolve the problems with minimal mathematical skills. By…

Functions form a central part of the U.S. mathematics curriculum. A large body of research shows that students at all levels, including preservice secondary mathematics teachers, have difficulties with defining function as a correspondence between two sets with a univalence condition. Those difficulties include privileging algebraic…

Mathematical calculations are an important part of chemistry. Those problems are difficult for students, especially if the task is set with a limiting reactant. The aim of this study was development of a Procedure for evaluation of cognitive complexity of the Stoichiometric Tasks with a Limiting Reactant. The procedure created included an…

Teaching geometry courses for preservice elementary teachers, we observed that difficulty with classifying shapes (and, in particular, composite 3-D shapes) persists even after work with simple shapes to support the writing of accurate and unambiguous definitions. We conducted a self-study of our teaching of 3-D concepts to uncover the concept…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

In formal education, the teaching of natural sciences begins when children are about 12 years old. Teachers justify this with the difficulty and abstraction of concepts in these sciences, and they refer to the theory of child development by Piaget. However, numerous examples from everyday life, from non-formal education, analysis of the…

This paper reviews the idea of threshold concepts in the context of conceptual change processes students experience at the cognitive and social dimensions of learning. Literature suggests that students' ontological views play a part in the development of their prior conceptions, which could be alternative to scientifically accepted ideas. It is…

Mathematics holds a relevant and unique place in the school curriculum as it is important for a better living of the individual. But, it is known that most of the students are considering mathematics as difficult. This study examines the difficulties perceived by high school students and teachers in learning and teaching mathematics. Two hundred…

A unit on animals was taught to 64 preschool children (44 in an experimental group and 20 in a control group). Children in the experimental group were taught nine major concepts over four levels of abstraction (designated as superordinate, intermediate, subordinate, or particular levels). Each concept was presented by means of an advance organizer…

The present research was designed primarily to investigate the type of instruction needed to help children learn difficult principles. A total of 159 fifth graders (each assigned to one of six experimental conditions) read lessons which dealt with principles from two content areas (mathematics and language arts). Lessons varied in the number of…

The difficulties that younger students experience in understanding concepts related to the use of variables in computer programming are examined through descriptions of two studies: (1) detailed case studies of six highly intelligent children--three fourth graders and three sixth graders--who learned to program in BASIC during 60 hours of…

This study compared the conceptual rule learning performance of normal and learning disabled children. Subjects for the study were 18 normal and 18 learning disabled children with mean ages of 9.4 and 9.3 years and mean IQ scores of 103.1 and 101.6 respectively. The children were matched for age, IQ, sex and race. Four types of rules (affirmation,…