This article is based on the text of the Gulliford Lecture given by Professor Harry Daniels at the University of Birmingham in October 2005. Professor Daniels takes, as his starting point, Ron Gulliford's assertion that teachers need to learn from their experience of trying to teach children who are "hard to teach". He goes on to look at…

This paper proposes a model of learning dynamics and learning energy, one that analyzes learning systems scientifically. This model makes response to the learner action by means of some equations relating to learning dynamics, learning energy, learning speed, learning force, and learning acceleration, which is analogous to the notion of Newtonian…

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

Discovery learning in mathematics in the domain of probability based on hands-on experiments is normally limited because of the difficulty in providing sufficient materials and data volume in terms of repetitions of the experiments. Our cooperative, computational modelling and simulation environment engages students and teachers in composing and…

Progress assessment aims to assess students' performance and progress during a course of study. Its purpose is primarily developmental--to help students improve learning. Progress assessment is of special value in distance education in that it can motivate or pace distance learners throughout their course of study. It can help the tutor monitor…

A key factor in the transition to university is the enculturation of new students into both the discipline they are studying and effective study practices. Most significantly, students, whatever their chosen discipline, must learn to become autonomous learners. Too often this process is either left to chance or seen as a natural attribute of the…

Student learning is a complex incremental cognitive process; assessment needs to parallel this, reporting the results in similar terms. Application of fuzzy sets and logic to the criterion-referenced assessment of student learning is considered here. The constrained qualitative assessment (CQA) system was designed, and then applied in assessing a…

The focus of this article is the role of drawings in the journeys of young children towards literacy. The argument is that young children learn from home contexts a wide range of approaches towards literacy. At school their flexibility in using these approaches is reshaped into narrow versions of literacy based on learning to read, write and…

The publication and subsequent distribution and dissemination of "Birth to Three Matters, A Framework to Support Children in their Earliest Years" (DfES, 2002) marks a significant breakthrough in government recognition of the importance of the years from birth to three in shaping children's later learning. However, the Curriculum…

For the past ten years the management literature has increasingly discussed the concept of learning organizations. Yet, more that a decade later, few organizations have figured out how to create the structures and processes necessary to assure continuous learning. This article purports that this problem can be attributed to the mental models of…

People's mental models are viewed as being significant in achieving organizational outcomes, on the assumption that mental models influence people's acts. A fundamental issue in the area of organizational learning, then, is the relation between mental models, learning and performance. We contend that a fruitful line of work is to study persons as…

Building Blocks is a National Science Foundation-funded project designed to enable all young children to build a solid foundation for mathematics. To ensure this, we used a design and development model that drew from theory and research in each phase. Our design process is based on the assumption that curriculum and software design can and should…

Today, teaching and learning tend to be viewed from a constructivist perspective. Learning is regarded as a self-directed process of constructing meaning, which takes place in interaction. The teacher supports the learning process by selecting input and approaches that can scaffold the learning process and guide learners towards independent…

Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert-novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures…

Traditional assessment methods are not always suitable for diagnosing learners' knowledge structures at different levels of their expertise. This paper describes an alternative schema-based rapid assessment technique and its application in the area of arithmetic word problem solving. The technique is based on an assessment of the extent to which…