Instruction facilitating the abstraction and transfer processes necessary for deep conceptual understanding is notoriously difficult. Individual differences in learning strategies are one possible explanation for variation in transfer outcomes. Prior work has shown that rule-abstraction learning strategies facilitate knowledge transfer better than…

The ability to properly evaluate one's own academic progress has long been considered a predictor of academic success. However, its distinctive role in the context of computational mathematics remains underexplored. Grounded in social cognitive theory, this study investigates the critical role of self-regulated learning (SRL) strategies in…

Literature suggests that "current characterizations of the terms procedural knowledge and conceptual knowledge are limiting and are, in fact, impediments to careful investigation of these constructs" (Star, 2005, p. 405). We examined secondary mathematics teachers' understanding of procedural and conceptual knowledge at superficial and…

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…

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…

The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

There are many reasons to be curious about the way people learn, and the past several decades have seen an explosion of research that has important implications for individual learning, schooling, workforce training, and policy. In 2000, "How People Learn: Brain, Mind, Experience, and School: Expanded Edition" was published and its…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

The question of whether skills in achieving understanding and retention of information at high levels of abstraction can be taught is addressed by analyzing some of the mental processes involved, and briefly reviewing a number of attempts that have been made to induce these processes. (Author)

A research project explored the idea that reasoning develops in distinct phases of thinking as individuals journey from simplistic learning of facts to highly proficient consequence predicting of integrated relationships. These results were derived from a study that examined the thinking processes and problem-solving actions of 13 students and…

Four experiments investigated children's ability to notice and remember events in which the acquisition of factual information occurs. Results indicated that children tend to report they have known newly learned information for a long time, suggesting that children have some understanding of knowledge acquisition, but not at the level of adults.…

Examined the nature of perceptual classification in children and young adults. Found that most children attend selectively to one stimulus dimension when making perceptual classification judgments. Suggests that this developmental trend does not appear to be a holistic-to-analytic shift but rather a trend toward greater consistency in following a…

Investigated is the extent to which students' nonscientific beliefs change by comparing before and after instruction as a function of students' reasoning skill. Nonscientific beliefs discussed include special creation, orthogenesis, the soul, nonreductionism, vitalism, teleology, and nonemergentism. (KR)

In this interview, author Art Costa asserts that the teaching of either content or thinking skills in isolation is unproductive. To combine these approaches, he recommends selecting content for its relationship to thought processes. He also observes that administrators who model intelligent behavior thereby create a climate for thinking. (TE)