This study investigates sixth-grade Turkish students' pattern-generalization approaches among arithmetical generalization, algebraic generalization, and naïve induction. A qualitative case study design was employed. The data was collected from four sixth-grade students through the Pattern Questionnaire (PQ) and individual interviews based on the…

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…

The prerequisite for teaching many skills and behaviors to children with intellectual disabilities is that the child has acquired the basic concepts. Teaching concepts plays a very active role in the independence of the child with intellectual disabilities and in the acquisition of higher level skills that they will learn in the future. The…

A key aspect of young children's development of algebraic reasoning is the process of visualising and identifying structures to both abstract and generalise. There has been a growing body of research focused on how students form generalisations, this article adds to the existing body of research by examining how young culturally diverse students…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

In the context of the sociocultural approach, the authors studied the problem of the development of the students' conceptual mental structures in the process of geometry teaching. An educational activity for the development of a generalized ability to solve geometry construction problems in electronic educational environment served as a…

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely,…

Cinquain is a poetic form, or stanza, of five lines that do not rhyme, which follows some strict rules. Cinquain is also considered to be a training means, a method, a technique, an instrument used for reflection, for synthesis of all knowledge on a particular topic (a being, an object, an ensemble of objects), towards developing one's creativity.…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

Exploratory learning environments (ELEs) promote a view of learning that encourages students to construct and/or explore models and observe the effects of modifying their parameters. The freedom given to learners in this exploration context leads to a variety of learner approaches for constructing models and makes modelling of learner behavior a…

The purpose of this study is to develop a history of science activity which can be used to improve middle school students' nature of science views. The activity was designed and implemented based on an explicit-reflective approach within the context of the circulatory system. The activity was designed for grade 6 students and implemented during…

History teachers, teacher-researchers, government agencies and history education academics in England often report that students are frequently incapable of producing complex, polythetic or developmental narratives over long time scales. This lack of an overview tends to result in deficiencies in their application of the key concepts of the…

This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is…

Paula Worth presents in this article a means of challenging students' tendency to generalise even when they know that they should not. How can teachers encourage their students to say something meaningful about the past while avoiding making unwarranted generalisations? Worth takes teachers through the process of planning her own enquiry designed…