Episodic Memory: A Neglected Phenomenon in the Psychology of Education

Contemporary educational psychology has employed models of procedural and semantic (or declarative) memory, but generally it has ignored a third form of memory (i.e., episodic memory) thought by some (e.g., Tulving, 1983,1985) to be especially important for explications of human functioning. Tulving's (1983,1985) ternary theory of memory is presented, with emphasis given to the acquisition, representation, and expression of knowledge in episodic memory. I argue that studies of pupils' episodic memories, their characteristics, and their functions may enhance the power and relevance of educational psychology with respect to understanding how pupils learn from instruction in classroom contexts. A conceptual framework and possible strategies for the conduct of instructional research are described that consider pupils' episodic memories as important mediating variables in learning from teaching.     

PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS

Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils’ problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil.     

Une introduction non classique aux algorithmes d'addition et de soustraction

The aim of our study was to analyze a didactical sequence for the teaching of addition and subtraction procedures and algorithms. In the conception of that sequence, we have taken into account diagnostic and repair models for procedural bugs in addition and subtraction algorithms, as well as learning and teaching methods for multi digit additions and subtractions. The didactical sequence included situations involving many of the characteristics associated with procedural bugs; however, when the children encountered those situations they had many conceptual tools to detect their mistakes and correct them, giving that way a meaning to the actions made in addition and subtraction procedures and algorithms. Our teaching activities were submitted to second grade school children (7–8 years old). The didactical interactions and the procedures used by children in problem solving activities were analyzed in order to get a better understanding of the interaction between numbers, numeration and operations knowledge which are involved in the construction of addition and subtraction procedures and algorithms and to relate children's knowledge acquisition to the didactical situations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Teachers’ Inclusive Strategies to Accommodate 5th Grade Pupils’ Crossing of Cultural Borders in Two Greek Multicultural Science Classrooms

The demographic changes in Greek schools underline the need for reconsidering the way in which migrant pupils move from their everyday culture into the culture of school science (a process known as “cultural border crossing”). Migrant pupils might face difficulties when they attempt to transcend cultural borders and this may influence their progress in science as well as the construction of suitable academic identities as a means of promoting scientific literacy. In the research we present in this paper, adopting the socioculturally driven thesis that learning can be viewed and studied as a meaning-making, collaborative inquiry process, we implemented an action research program (school year 2008–2009) in cooperation with two teachers, in a primary school of Athens with 85% migrant pupils. We examined whether the two teachers, who became gradually acquainted with cross-cultural pedagogy during the project, act towards accommodating the crossing of cultural borders by implementing a variety of inclusive strategies in science teaching. Our findings reveal that both teachers utilized suitable cross-border strategies (strategies concerning the establishment of a collaborative inquiry learning environment, and strategies that were in accordance with a cross-border pedagogy) to help students cross smoothly from their “world” to the “world of science”. A crucial key to the teachers’ expertise was their previous participation in collaborative action research (school years 2004–2006), in which they analyzed their own discourse practices during science lessons in order to establish more collaborative inquiry environments.     

The use of mathematical symbolism in problem solving: An empirical study carried out in grade one in the French community of Belgium

This article relates to an empirical study based on the use of mathematical symbolism in problem solving. Twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a “top-down” approach (an approach that is still applied within the French Community of Belgium): conventional symbols are presented to the pupils immediately with an explanation of what they represent and how they should be used. Teaching then focuses on calculation techniques (considered as a pre-requisite for solving problems). The results presented here show the abilities (and difficulties) demonstrated by the children in making connections between the conventional symbolism taught in class and the informal approaches they develop when faced with the problems that are put to them. The limits of the “top-down” approach are then discussed as opposed to the more innovative “bottom-up” type approaches, such as those developed by supporters of Realistic Mathematics Educations in particular.     

613名小学生自我效能感状况及其与自主学习策略的关系研究

本研究通过问卷调查,考察613名小学生自我效能感状况及其与自主学习策略的关系。结果如下:(1)613名小学生的总体自我效能感较高;(2)两所学校之间小学生能力自我效能感差异显著;(3)在能力自我效能感方面,6年级与4、5年级存在显著差异;(4)小学生在总体自我效能感、能力自我效能感和行为自我效能感上都存在极其显著的性别差异;(5)小学生自我效能感与自主学习策略相关显著,小学生的自我效能感能够预测自主学习策略的运用。     

STUDENTS�� EVALUATION OF THE CREDIBILITY OF SCIENTIFIC MODELS THAT REPRESENT NATURAL ENTITIES AND PHENOMENA

The purpose of the current study was to explore learners’ evaluation of the credibility of scientific models that represent natural entities and phenomena. Participants were 845 students in grades 9 – 11 (aged 15 – 17 years) and 108 prospective science teachers in Oman, totaling 953 students. A survey called Epistemologies about the Credibility of Scientific Models was designed to explore participants’ epistemological positions regarding the credibility of scientific models. This instrument was based on a credibility taxonomy proposed by the author. This taxonomy was composed of four epistemological levels: certainty, imaginary, suspicious, and denial; thus, it was called the CISD taxonomy. Findings revealed that natural entities and phenomena were assigned to CISD levels according to their level of abstractness. This level of abstractness is usually constructed by the most frequently used models to represent each natural entity or phenomenon. For instance, entities, which were usually represented by photographs or micrographs, such as meteors and meteorites, blood cells and bacteria, fell at the certainty level. On the other hand, theoretical entities such as electron cloud and photons had a high suspicious–denial combinational level. Some entities, with possible competing concrete–abstract parallel nature of the scientific models that represent them, had both high certainty and suspicious–denial levels. The overall students’ epistemological perceptions across grade levels showed a decrease in the certainty level and an increase in the imaginary level. It might also be plausible to conclude that new, detailed microscopic and more abstract knowledge raised the suspicious and denial levels of some entities. Further research based on qualitative research methodologies is needed to explore these findings.     

An Experimental Research on Error Patterns in Written Subtraction

Pupils' mistakes, if suitably analysed, may give useful suggestions for improving the teaching/learning process of mathematics. We present here the main issues of an investigation on a population of 732 Italian pupils (9–12 years old), addressed to determine the typology of errors in performing written subtraction. We compared our results with those emerging from a study carried out in Brazil on pupils of the same age, concerning the errors in performing the usual algorithm of written subtraction. In our study, one group of Italian pupil utilized the usual algorithm and another group utilized an algorithm also called ‘Austrian subtraction', which was commonly taught in the primary schools of Trieste (Italy) up to the sixties and is still taught in Austria. We attempted to assess whether certain error patterns depend on different ethnic–cultural situations, teaching methods and algorithm used, and to what extent. We briefly present results from the experimental research and subsequent developments.     

The nature of prospective mathematics teachers’ pedagogical content knowledge: the case of multiplication of fractions

The purpose of this study was to investigate prospective mathematics teachers’ knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers’ knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions was examined. Data were collected from 17 Turkish prospective teachers at the end of the spring semester of the 2004–2005 academic year. A case study design was used in which data were collected through the Multiplication of Fractions Questionnaire and semi-structured interviews. The prospective teachers suggested many difficulties that elementary grade level students may have and stated that these difficulties stemmed from students’ lack of formal knowledge and rote memorization of the algorithms. In addition, the prospective teachers suggested many strategies that could be used to overcome these misconceptions or difficulties. These strategies could be grouped under three headings: strategies based on teaching methods, strategies based on formal knowledge of fractions, and strategies based on psychological constructs.     

Les élèves et l'histoire dans l'examen français du certificat d'études primaires entre 1918 et 1926

This article presents the method used to study examination papers written by young pupils. This sort of pupils’ work can give information on who are involved in examinations.

‐ The pupils: what they learn in history and how they produce answers;

‐ The teachers: what they teach in their class and how;

‐ The juries: how they assess by means of a grade the minimum knowledge of most of the pupils who are to leave school.

The problem here is to follow the route from laws and decrees to real teachers and real pupils. Therefore, this research relies on source material such as annual primary inspector reports, annual local teachers’ meetings with model lessons, and, above all, examination papers. For this last source, a popular examination in France at that time was used: the Certificat d'Etudes, which was given at the end of the primary curriculum for 13‐year‐old pupils. By chance, the Departmental Archives of the Somme region still has 4058 history test examination papers from 1918 to 1926.     

Hypothesis testing in science: group consensus and the acquisition of conceptual and procedural knowledge

Hypothesis testing has been seen by science educators as a context which supports the integrated acquisition of conceptual and procedural knowledge. However, research suggests potential conflicts between the conditions conducive to conceptual growth and those conducive to procedural. The study reported here with 9- to 12-year old pupils endorses this, but suggests that the problems can be overcome given tasks where pupils: (a) debate their conceptual knowledge and reach consensus; (b) subject their consensual positions to guided experimental appraisal and draw conclusions from what transpires. It is argued that the demonstrated role of consensus has consequences not just for educational practice but also for psychological theories of development and learning.     

The Adidactic Interaction with the Procedures of Peers in the Transition from Arithmetic to Algebra: A Milieu for the Emergence of New Questions

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of each student with the procedures generated by other students during stage 1. The two kinds of processes – adaptation to a milieu and social interactions – play a critical role in the change of “rationality” required for the move from arithmetic to algebra. Both the design of the initial mathematical problem given to the students and the organization of the interactions leading to the debate under study in this article are based on this hypothesis. The research presented in this article is set in a broader work of didactic engineering that aims at studying didactic conditions for making a connection between arithmetic practices and algebraic practices.     

Investigating pupils' images of mathematicians

This paper describes a research project that had two goals: (1) to design and develop a tool with which to investigate pupils' images of mathematicians; and (2) to use the device to compare those images held by lower secondary pupils (ages 12–13) in five countries. We report that with small cultural differences certain stereotypical images of mathematicians are common to pupils in all of these countries and these images indicate that for pupils of this age mathematicians and the work that they do are, for all practical purposes, invisible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Collaboration, scaffolding and the promotion of problem solving strategies in Mexican pre-schoolers

Research in Mexican schools, drawing upon earlier research in the UK, has led to the development and use of a method for describing, comparing and evaluating the particular approaches and interactional strategies used by teachers and learners. Using this method, qualitative and quantitative comparisons are made to distinguish between teachers who use a conventional, formal, directive approach when teaching 5-year-old children mathematical skills (called the “Official” method) and those who use a more interactive, collaborative, supportive, “scaffolded” approach to teach similar classes of children (called the “High Scope” method). In an earlier study, we found more competent and independent problem-solving among High/Scope pupils than among their peers taught by the Official method. In the present study, discourse analysis and statistical analysis of the relative frequencies of types of teacher-pupil interaction in the classrooms of two “Official” teachers and two “High’ Scope” teachers are used to explain the improved problem-solving of the “High Scope” pupils. The findings support the view that by creating a more collaborative, scaffolded version of classroom education, teachers can more successfully enable children to develop their own problem-solving skills, learning strategies and curriculum-related understanding. The research also contributes to the development and implementation of methods for promoting a more effective style of teacher-learner interaction in the classroom.     

Connaissances utilisées par des elèves de 8 à 12 ans dans la formulation de problèmes arithmétiques concrets

This study analyses children development of semantic, linguistic, procedural and schematic knowledge in the context of writing arithmetic word problems. 139 children aged between 8 and 12 years old were presented with a task which consisted in writing arithmetic word problems, according to some contraints: words, questions or measures to include in their problems; type of problems to write. Results show the relevance of actual theoritical models of problem solving (Mayer, 1983; Kintsch & Greeno, 1985). Schematic knowledge seem indeed more important than other knowledge in the process of writing arithmetic word problems; semantic knowledge are also used to choose relevant numbers or measures; the roles of linguistic and procedural knowledge seem less evident. Finally, some hypotheses related with the development of mental models of arithmetic word problems are formulated.     

Learning About Bird Species on the Primary Level

Animal species identification is often emphasized as a basic prerequisite for an understanding of ecology because ecological interactions are based on interactions between species at least as it is taught on the school level. Therefore, training identification skills or using identification books seems a worthwhile task in biology education, and should already start on the primary level. On the primary level, however, complex interactions could not be taught but pupils are often interested in basic knowledge about species. We developed a hands-on, group-based and self-determined learning phase organized in workstations. About 138 pupils (2nd–4th graders) participated in this study. The two groups received an identification treatment with six different bird species. These were presented either as soft toys or as taxidermy specimen. Both groups scored similar prior and after the treatment (posttest 1) and with a delay of 6–8 weeks (posttest 2). More complex general linear modeling revealed a significant influence of prior knowledge, treatment and of grade (2nd, 3rd or 4th grade) on the first posttest while in the retention test gender differences emerged. We suggest that soft toys may be of equal value for teaching species identification on the primary level compared to natural taxidermic specimen, especially when considering pricing, insensitivity to handling, and contamination with agents used for preservation.

Mathematics in Physics Education: Scanning Historical Evolution of the Differential to Find a More Appropriate Model for Teaching Differential Calculus in Physics

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of physics. As a first step to identify the origin of this situation and to revert it, we have done a historic and epistemological study aimed at clarifying the role and the meaning of the differential in physics and at improving curricular and teaching models in the sense of Gilbert et al. (Gilbert J.K., Boulter C., & Rutherford, M.: 1998a, International Journal of Science Education 20(1), 83–97, Gilbert J.K., Boulter C., & Rutherford, M.: 1998b, International Journal of Science Education 20(2), 187–203). We describe the contributions of Leibniz and Cauchy and stress their shortcomings, which are overcome by the alternative definition proposed by the French mathematician Fréchet, dating from early 20th century. As a result of this study, we answer to some fundamental questions related to a proper understanding of the differential in physics education (for 17–19 years old students).     

Triadic interaction in clinical task-based interviews with mathematics teachers

A clinical task-based interview can be seen as a situation where the interviewer–interviewee interaction on a task is regulated by a system of explicit and implicit norms, values, and rules. This paper describes how documenting and mapping triadic interaction among the interviewer, the interviewee, and the knowledge negotiated can be used to increase procedural replicability of the interview and accuracy of drawn conclusions about the interviewee’s thinking process. Excerpts from interviews with 25 inservice mathematics teachers working on a task to make up a problem whose solution requires division of two fractions are discussed. The excerpts illustrate the relationship between methodological decisions taken by the interviewer during the interview and the applicability of the interview output to the research questions. A divergent analysis of the interviews with these teachers, which spanned over two years and were conducted by four interviewers, is used to offer a framework for analyzing data collected in clinical task-based interviews.     

Attitudes Towards the Elderly Among German Adolescents

Many societies are encountering significant changes in their population structure as the number of older people is increasing while children and adolescents become fewer. This study examines pupils' attitudes towards elderly people in Germany. A total of 935 pupils (458 boys, 477 girls) participated in this study. Grade distribution was as follows: 192 (5th grade), 148 (6th grade), 208 (7th grade), 219 (8th grade), and 168 (9th grade). We provide evidence for two underlying latent factors, “prejudice” and “appreciation.” The “prejudice” factor contained prejudices and negative attitudes towards old people, and the “appreciation” factor contained items that were positively related to old people. On average, pupils valued old people. Based on a multivariate general linear model, we found a significant influence of gender, grade, and distance to grandparents. Girls valued old people higher, thus rating them higher on the appreciation scale. However, effect size was comparably low. No differences existed concerning the prejudice scale. Grade effects showed that prejudice increases and appreciation declines with increasing age. Distance to their grandparents significantly influenced the attitudes. Pupils with grandparents in the near vicinity valued old people more than pupils with their grandparents farther away. We suggest implementing intergenerational educational programs in primary school and in 5th and 6th grade in Germany.