This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students' use of relations between mathematical elements when solving a…

The aim of this study is to measure the effects of teaching problem-solving strategies as an integrated part of the mathematical content prescribed by the curriculum. By implementing the designs principles developed in the previous study, we carry out a one-year-long teaching intervention in a Swedish upper secondary school. Pre- and post-tests…

This paper compares Revised Bloom's Taxonomy (RBT) and some of the major theories and frameworks that influence the teaching, learning, and assessment of mathematics. This comparison has been made to help students and researchers make decisions about which of the available theories and frameworks might best suit their study. The comparison…

This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

Though the No Child Left Behind Act of 2001 requires secondary students with Asperger's syndrome (AS) to take high-stakes mathematical tests, many students with AS exhibit weaknesses in mathematical and executive functioning skills. The purpose of this mixed-methods case study was to explore the use of differentiated mathematical strategies with…

More and more things that humans used to do can be automated on computer. In each case, complex tasks have been automated -- not to the extent that they can be done as well as humans, but better. I will draw and develop parallels to education -- showing how and why advances in the Structural Learning Theory (SLT) and the AuthorIT development and…

It is well known that math phobia is a common problem among young school children. It becomes a challenge to educational practitioners and academic researchers to figure out ways to overcome the problem. Collaborative team learning has been proposed as one of the alternatives. This study was part of a large and ongoing research project designed to…

The aim of this paper is to demonstrate that in spite of some superficial similarities the current mathematics reform in the US based on constructivist principles differs substantially from mathematical education based on Vygotskian cultural-historical theory (V.V. Davydov's mathematics program), and to illustrate the manner in which Davydov's…

This is the final report for a study whose original purpose was to develop a general theory of the situational constraints imposed by the routines of everyday life on arithmetic skills. Section 1 reviews the goals laid out in the proposal in relation to what was accomplished. Section 2 is the draft of "Everyday Cognition: Its Development in…

Research of expert-novice differences is reviewed seeking to show experts possess a large body of domain specific knowledge. It was postulated that experts possess schemas enabling them to classify problems, call up the appropriate automated rules, then apply these to obtain the solution. (DC)

Research was conducted investigating properties of skill in learning, in the domain of elementary algebra. Thinking-aloud protocols indicate that early knowledge of the subjects studied was fragmentary, rather than involving systematically flawed procedures. Computational models, developed to simulate observed errors, focused on the role of…

This paper discusses the central thesis that new research on estimation and mental computation will benefit from more focused attention on the situations in which they are used. In the first section of the paper, a brief discussion of cognitive theory, with special attention to the emerging notion of situated cognition is presented. Three sources…

This report on the Adult Math Skills Project includes sections on theory, empirical studies, and their implications. Section 1 presents an overview, noting that activity and setting are seen as mutually creating, sustaining, and changing the nature of problem solving. The empirical studies involved: (1) arithmetic practices among grocery shoppers;…