In this study, the teaching experiment methodology is used to observe firsthand a gifted student's mathematical learning and reasoning. A series of teaching experiments was conducted with 1 gifted and 1 average 7th-grade student to investigate how the gifted student's mathematical concepts and operation constructions differed from those of the…

Science has been an important partner of the field of learning disabilities since its inception. Special educators have used science to confirm or reject approaches to identifying and teaching students with disabilities. Current research and practice is using science to find better approaches to preventing learning difficulties and reducing the…

Gifted students with spatial strengths are often overlooked and underserved in American schools. These students have remarkable areas of talent but often have verbal learning difficulties that prevent them from being identified for gifted services. This article focuses on definitions of spatial ability, characteristics of these learners, possible…

In this paper, the contradiction of practising zero tolerance in inclusive schools is discussed using the critical method of Skrtic's immanent critique. The authors contend that the policy of inclusive schools for all is contradicted and undermined by the practice of zero tolerance policies, especially suspensions, expulsions and segregation.…

This paper explores the wide range of pure mathematics that becomes accessible through the use of problems involving powers. In particular we stress the need to balance an applied and context based pedagogical and curricular approach to mathematics with the powerful pure mathematics beneath the simplicity of easily stated and understandable…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…

Many aspects of the problem-based learning cycle aim at stimulating students to elaborate on their knowledge. This elaborative process is considered to be one of the most effective study aids for learning and applying information. One of the opportunities to stimulate this elaboration process is by offering students more, and more diverse,…

Background: Student feedback is a valuable method to evaluate the quality of education. Using a WEB-based questionnaire, the objective of this study was to evaluate the factors that may affect the ratings given by the students and the impact of those ratings on the instructor's teaching performance. Methods: The questionnaire was organized into…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

Critical thinking has long been a goal of social studies education, and its importance has been reiterated in documents delineating standards for the social studies. Yet, teaching critical thinking is problematic because there are competing definitions and practices and many barriers to its implementation (Wright 1995; Onosko 1989). In this…

This article relates to an empirical study based on the use of mathematical symbolism in problem solving, twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a…

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

The importance of feedback as an aid to self-assessment is widely acknowledged. A common form of feedback that is used widely in e-learning is the use of model answers. However, model answers are deficient in many respects. In particular, the notion of a "model" answer implies the existence of a single correct answer applicable across multiple…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…