Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

Development in any domain is often characterized by increasingly abstract representations. Recent evidence in the domain of shape recognition provides one example; between 18 and 24 months children appear to build increasingly abstract representations of object shape [Smith, L. B. (2003). Learning to recognize objects. "Psychological…

Part of a collection of papers commissioned by Foundations, a career development project sponsored by the National Technical Institute for the Deaf (NTID), the paper reviews research on transfer of knowledge and skills from one situation to another. A transfer classification scheme is proposed based on the notion that an individual's knowledge can…

Students often fail to apply knowledge and skills learned in one context to other situations. Although the implicit assumption in educational practice has been that transfer takes care of itself, a knowledge of the mechanisms of transfer can enable educators to help their students integrate general and local knowledge. (TE)

When taught to link sorting to self-instruction ("I'm looking for blue triangles") children show perfect accuracy in sorting. This study investigated if this performance would generalize to new stimuli. One participant showed near-perfect generalization to all new stimulus sets (shapes, letters, pictures); two had difficulty with…

Transferability of skills in learning is discussed, focusing on the notions of cross-disciplinary, generic, core, and transferable skills and their role in the college curriculum. Cross-disciplinary or cross-curricular skills are examined in terms of their relationship to cognitive domains, and transferable skills in relation to social domains.…

Examines Krashen's Monitor hypothesis (claiming that no interface exists between acquisition and learning) and finds it inadequate due to the over-restrictive conditions necessary for its use. Alternative acquisition theories and ways in which to monitor under less restrictive conditions are also examined, and a communicative trigger is proposed…

Discusses issues and problems concerning concept development among students in elementary social studies programs. Suggests good teaching uses analogies and metaphors to facilitate learning. Recommends illustrating key concepts through myths, fables, and parables. Argues that using stories that show how things work allows students to apply the…

Semantic elaboration, a language-based mnemonic strategy, was taught to 15 students (aged five to nine years) with moderate learning difficulties over a six-month period, using pictures as stimuli. Among reported results was an improvement in overall performance on memorization of pairs of pictures. Generalization to items not used during teaching…

Although numerous research studies have shown that viewing educational television results in significant gains in preschool and school-age children's academic knowledge or skills, there is less consistent evidence regarding transfer of learning, the application of knowledge or skills learned in one context to a new problem or situation. This paper…

Presents a method for improving reading comprehension through direct instruction of inductive reasoning. Students gather clues to personality of characters as play progresses and from these arrive at an overall generalization concerning the complexities of the character. (SRT)

People use and extend their knowledge of the physical world constantly. Understanding how this fluency is achieved would be an important milestone in understanding human learning and intelligence, as well as a useful guide for constructing machines that learn. This paper presents a theoretical framework that is being developed in an attempt to…