This essay considers the non-instrumental vision of the learning society through the analysis of its conceptual logic and meaning based on A. J. Cropley's approach. It outlines a view of the learning society whereby learning is an end in itself rather than a means of achieving other economic or civic purposes, as currently described in relevant…

When enumerating small sets of elements nonverbally, human infants often show a set-size limitation whereby they are unable to represent sets larger than three elements. This finding has been interpreted as evidence that infants spontaneously represent small numbers with an object-file system instead of an analog magnitude system (Feigenson,…

Piaget (1971) made a distinction between intuitive (preoperational) time and operational (logico-mathematical) time. According to Piaget, operational time develops around 7-8 years of age and is characterized by children's ability to deduce, for example, that if A was born before B, A will always be older than B. When time is still intuitive,…

This study examines the views of people involved in mathematics education regarding the commonly stated goal of using mathematics learning to develop deductive reasoning that is usable outside of mathematical contexts. The data source includes 21 individual semi-structured interviews. The findings of the study show that the interviewees ascribed…

The purpose of this article is to provide an image of what proof could look like in beginning algebra, a course that nearly every secondary school student encounters. The authors present an actual classroom vignette in which a rich opportunity for student reasoning arose. After analyzing the proof schemes at play, the authors provide a…

This case study examined the development and evaluation of an interdisciplinary first-year learning community designed to stimulate scientific reasoning and critical thinking. Designed to serve the needs of scholarship students majoring in mathematics and natural sciences, the six-credit learning community course was writing-intensive and…

In classrooms, science is usually taught within the cognitive domain while the psychomotor learning domain is achieved through performing science experiments in the laboratory. Although students attend civic and moral education and pastoral care classes where values and life skills are often taught directly, learning experiences in most school…

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…

Logical reasoning skills are important for a successful mathematical learning and in students' future career. These skills are essential for a primary school teacher, because they need to explain solving methods and solutions to their pupils. In this research we studied pre-service primary school teachers' logical reasoning skills. The results…

The purpose of this article is to examine the literature on teaching statistics for useful ideas that teachers of language testing courses can draw on and incorporate into their teaching toolkits as they see fit. To those ends, the article addresses eight questions: What is known generally about teaching statistics? Why are students so anxious…

Mike Shaughnessy is Professor Emeritus of Mathematics and Statistics at Portland State University in Oregon. He served as co-chair for the Board for the Special Interest Group for Research in Mathematics Education of the American Educational Research Association from 2005-2007. A member of the Board of Directors of the National Council of Teachers…

This paper reports on a study of how students' reasoning about socioscientific issues is framed by three dynamics: societal structures, agency and how trust and security issues are handled. Examples from gene technology were used as the forum for interviews with 13 Swedish high-school students (year 11, age 17-18). A grid based on modalities from…

The international adoption entrance story is an unexplored topic in the adoption literature. The stories that families tell of beginning life with their new children has important implications for the development of an autobiographical narrative of an adopted child. A coherent autobiographical narrative is vital for healthy childhood development.…

The Latin Square Task (LST) was developed by Birney, Halford, and Andrews [Birney, D. P., Halford, G. S., & Andrews, G. (2006). Measuring the influence of cognitive complexity on relational reasoning: The development of the Latin Square Task. Educational and Psychological Measurement, 66, 146-171.] and represents a non-domain specific,…

Many beginning university students struggle with the new approaches to mathematics that they find in their courses due to a shift in presentation of mathematical ideas, from a procedural approach to concept definitions and deductive derivations, and ideas building upon each other in quick succession. This paper highlights this struggle by…