The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a…

Meta-reasoning refers to processes by which people monitor problem-solving activities and regulate effort investment. Solving is hypothesized to begin with an initial Judgment of Solvability (iJOS)--the solver's first impression as to whether the problem is solvable--which guides solving attempts. Meta-reasoning research has largely neglected…

The article aims to study the verbal collaborative interaction in both symmetrical and asymmetrical dyads according to specific individual cognitive competence. The interaction was analyzed in terms of cognitive and non-cognitive aspects. 19 dyads (38 fifth and sixth graders) participated. First, they individually solved a set of logical problems…

The formalism of quantum mechanics includes a rich collection of representations for describing quantum systems, including functions, graphs, matrices, histograms of probabilities, and Dirac notation. The varied features of these representations affect how computations are performed. For example, identifying probabilities of measurement outcomes…

Background: Analogical reasoning (AR) is renowned for being a complex activity. Young children tend to reason by association, rather by analogy, and people with intellectual disability present problems of memorization. Both these populations usually show low performances in AR. The present author investigated whether familiar material and external…

There is a heated debate on whether observed gender differences in some figural matrices in adults can be attributed to gender differences in inductive reasoning/G[subscript f] or differential item functioning and/or test bias. Based on previous studies we hypothesized that three specific item design features moderate the effect size of the gender…

In this paper, we present a study of a large corpus of student logic exercises in which we explore the relationship between two distinct measures of difficulty: the proportion of students whose initial attempt at a given natural language to first-order logic translation is incorrect, and the average number of attempts that are required in order to…

The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical induction or the well-ordering principle. The method of iteration depends only on the fact that any strictly decreasing sequence of…

Many people believe that environmental factors promote giftedness and invest in many programs to adopt gifted students providing them with challenging activities. Intellectual giftedness is founded on fluid intelligence and extends to more specific abilities through the growth and inputs from the environment. Acknowledging the roles played by the…

Piaget has hypothesized that concrete and formal operations can be described by specific logical models. The present study focused on assessing various aspects of four concrete operational groupings and two variations of two formal operational characteristics. Six hundred twenty-two 9-14 year old students participating in the Human Sciences…

A heuristic procedure can be used to teach organizational skills to students of technical writing. Designed to allow students on their own to explore ways that numbers can be used to give a definite shape to technical information, its central feature is a matrix composed of a series of control numbers (horizontal axis) and organizing concerns…

Two experiments which investigated the young child's ability to deal with multiplicative classes and relations (considered behavioral indices of concrete operations thought) in double series and cross class matrices are described and discussed. In the initial study, 160 children from preschool through grade 2 received six matrix subtasks…

A series of Piagetian concrete operations period tasks dealing with classificatory concepts was administered to 280 children (40 subjects from each of seven levels--preschool, kindergarten, and first, second, third, fourth, and sixth grades). Significant main effects for age were found for all the tasks. Few significant sex differences were…

Matrix tasks designed to assess the logical properties of multiple classification and multiple seriation were administered to 105 first, third, and fifth grade children. The tasks included cross-class and double series matrices, each of which had a reproduction and a transposition instructional set, and a revised set of cross-class and double…