Literature on student ideas about circuits largely focuses on misunderstandings and difficulties, with seminal papers framing student thinking as stable, difficult to change, and connected to incorrect ontological categorizations of current as a thing rather than a process. In this paper, we analyzed 417 student responses to a conceptual question…

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.…

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…

This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

This article presents a systematic review of research related to the use of robotics construction kits (RCKs) in P-12 learning in the STEM disciplines for typically developing children. The purpose of this review is to configure primarily qualitative and mixed methods findings from studies meeting our selection and quality criterion to answer the…

The authors discuss the results of their study into the behavior, values, and attitudes of students and teachers. They found that each person has a particular approach to learning or teaching that is most comfortable for them. Four learning/teaching channels are detailed: concrete sequential, abstract sequential, abstract random, and concrete…

Presents a developmental approach to teaching programing at all educational levels which stresses concepts rather than syntax; provides motivation, relevant examples, and activities; proceeds from concrete to pictorial to abstract according to age and experience of learners; and utilizes increasingly complex activities building upon and extending…

Previous research has shown that sequences in which instances from the same category appear successively facilitate performance in concept attainment. This could be due to subjects adopting strategies which involve comparisons of instances from within the same category. However, if subjects were to adopt a strategy involving comparisons of…

The first section of this paper deals with the question of whether Piaget is a developmental or a learning theorist; the second section relates Piaget's research findings and developmental theory to a sequence of curriculum units in mathematics. It is suggested that Piaget makes no distinction between learning and development of cognitive…

Nine students (ages 7 to 11) with math disabilities were effectively taught using an instructional sequence that moved from the concrete to the semiconcrete to the abstract. Subjects needed between three and seven lessons using manipulative devices and pictures before being able to do abstract-level problems. (Author/DB)

The criterion problem in the neoPiagetian cognitive-developmental literature is reviewed. This problem has provoked debate in the context of three empirical questions: concept age norms, concept training effects, and concept invariant sequences. It is argued that only the question of invaniant sequences in same-stage concepts is theoretically…

Reports that complex abstractions may be easily acquired by persons of less than 75 IQ if the method of presentation of the abstractions ensures maximum visibility of relevant details. (FL)