Mathematics learning and practice in and out of school: A framework for connecting these experiences

A variety of researchers in the last fifteen years have described how people learn and use mathematics in out-of-school situations. These researchers have found that mathematics learning and practice in and out of school differ in a number of ways. In this paper we examine and discuss these differences while maintaining the position that while some differences may be inherent, many differences can be narrowed so that mathematics learning and practice in school and out of school can build on each other and be connected. Before discussing a framework that we think sheds some light on connecting these experiences, we present some research from several of our studies that illustrates some of the differences between in-school and out-of-school mathematics practice and lays the groundwork for the discussion of the framework.We then discuss Saxe's (1991) research framework for gaining insight into the interplay between sociocultural and cognitive development processes through the analysis of practice participation (p. 13). Although Saxe's framework is a method for studying the interplay between sociocultural and cognitive development processes, we propose that it may be helpful in working towards connecting in-school and out-of-school mathematics learning and practice. Thus, we discuss the framework with illustrations from our own research, and then elaborate on ways to make this interplay between in-school and out-of-school contexts more deliberate.     

Cognitive,Motivational, and Volitional Dimensions of Learning: An Empirical Test of a Hypothetical Model

The principal aim of this research is to contrast empirically a hypothetical model developed on the basis of the fundamental assumptions of current self-regulated learning models. In line with evaluation criteria of model fit, a high rate of congruence between the hypothesized theoretical model and the empirical data was observed. Analysis of the effects between the variables of the model revealed the following relevant aspects: students' predisposition to feel responsible for the results of their academic behavior (internal attribution) is related to positive self-image (academic self-concept), both being important conditions for development of learning-oriented motivation (learning goals). All of this involves selection and use of learning strategies for deep information processing (deep learning strategies), which leads students to assume responsibility with high levels of persistence, perseverance, and tenacity so as to achieve goals defined by the motivational orientation. This persistence and effort to achieve the proposed goals has in turn a positive and significant effect on academic achievement.     

Scaffolding group explanation and feedback with handheld technology: impact on students’ mathematics learning

Based on strong research literatures, we conjectured that social processing of feedback by cooperating in a small group setting—with social incentives to ask questions, give explanations and discuss disagreements—would increase learning. We compared group and individual feedback, using two technologies: (1) Technology-mediated, Peer-Assisted Learning (TechPALS), which uses wireless handheld technology to structure feedback in small groups as they solve fractions problems and (2) a popular desktop product, which provides feedback to individual students as they solve fractions problems individually. Three elementary schools participated in a randomized controlled experiment conducted in the 2007–2008 school year. Students in the TechPALS condition learned more than did the control group students, with effect sizes ranging from d = 0.14 to d = 0.44. Analysis of observational data confirmed that students in the TechPALS condition participated socially in questioning, explaining, and discussing disagreements, whereas students in the individual condition did not. We conclude that an integration of technology, cooperative activity designs and broader educational practices can lead to impact on students’ mathematics learning.     

Do Spanish secondary school teachers really value different sorts of procedural skills?

The aim of teaching science at secondary school level is that of achieving the scientific literacy of all citizens. This must involve diverse objectives, among which may be found the development of procedural skills (thought, manipulative, communicative, etc.). The new curricula of many countries provide for these objectives. However, it is important to know to what extent the teaching staff consider them as true content to be taught. In this article, we analyse the opinions of secondary school teachers belonging to schools in north‐western Spain with regard to how they value different types of procedures. Our findings show that the surveyed teachers establish differences between various procedural skills as far as the recognition of their presence in the classroom and their evaluation are concerned, although it may be said that they generally value procedural skills highly. These findings are discussed. In addition, the persistence of traditional conceptions in the teaching of science, as well as the difficulty of assuming that the changes promoted by new curricular approaches are addressed, are highlighted.