The process of generating and evaluating diagnoses and selecting appropriate investigative or management procedures is based on a constant acquisition, interpretation, and evaluation of critical findings. Common assessments of these processes are often limited to scoring the accuracy of the diagnoses, investigative procedures, or management…

This paper examines the role of scaffolding in the process of abstraction. An activity-theoretic approach to abstraction in context is taken. This examination is carried out with reference to verbal protocols of two 17 year-old students working together on a task connected to sketching the graph of |f|x|)|. Examination of the data suggests that…

In this paper, we present a didactic analysis of the mathematical concept of implication under three points of view: sets, formal logic, deductive reasoning. For this study, our hypothesis is that most of the difficulties and mistakes, as well in the use of implication as in its understanding, are due to the lack of links in education between…

The concept model addressed in this paper is the set of assumptions, data, and inferences used in the instructional design of concept learning. A new way of looking at concepts is presented that takes into account the declarative and metacognitive components of concept learning and use. Implications for instruction are outlined. The paper is…

In the pursuit of the question as to whether there are significant relationships between certain measures of personality and abstract or critical thinking, it was believed that should significant relationships exist, they may prove useful as one of the factors among several used in the selection of teachers. A paucity of literature citations…

This study examined children's development of the concept of the reciprocal relationship of question and answer by asking subjects to form questions to fit given answers and to form answers for given questions. A total of 72 children (18 per grades 1, 4, 7, and 10) participated in the study. Each child was tested individually on two tasks (the…

This speech discusses concrete entities and abstract phenomena--focusing especially on the ideas of Plato and Aristotle. The author first explains that, according to Plato and Aristotle, there is a qualitative difference between things classified as concrete and those labeled abstract. She then questions whether there really is a difference…

Piaget's studies clearly highlight two qualitative advances made during the preoperational period. The first is the breakthrough of representational intelligence, beginning around 2 years of age. The second is the emergence of coordinated representational thought, beginning around 4 years of age. This paper focuses on the second advance, which…

A study investigating developmental differences in the ability to reason with conditional propositions used five variations of Wason's selection task to assess conditional reasoning in 132 eighth, tenth, and twelfth grade adolescents. In addition to examining developmental differences, the study had as an objective to examine the role of semantic…

Advocates and teachers of critical thinking tend to deny that intuition and justification are logical, even though they assume that both processes are rational. However, it can be demonstrated that the relation between intuition and inference, between justification and explanation, is dialectical and complementary, so that there is no mystery as…

Arguing that understanding what lies behind the apparent usability of direct manipulation style interfaces might not only help in building better interfaces, but can also draw attention to possible side effects, this paper uses examples from a prototype data manipulation system to pursue a characterization of direct manipulation interfaces as…

The effect of using either abstract or concrete words on verbal problem solving was examined in this study. Twelve undergraduate students in each of two conditions mentally solved identically structured problems by reordering and chaining together previously memorized pairs of words. Subjects who received concrete words both memorized the word…

This paper discusses what the theory of abstraction is about, the need for a theory of abstraction in mathematics education, and the requirements that such a theory should meet. All three are reconsidered from a personal point of view. (KHR)

In this paper we report on a research aimed to identify and characterize secondary school students' reasoning and proof abilities when working with 3-dimensional geometric solids. We analyze students' answers to two problems asking them to prove certain properties of prisms. As results of this analysis, we get, on the one side, a characterization…

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…