Extension Procedures for Confirmatory Factor Analysis

We present factor extension procedures for confirmatory factor analysis that provide estimates of the relations of common and unique factors with external variables that do not undergo factor analysis. We present identification strategies that build upon restrictions of the pattern of correlations between unique factors and external variables. The first restriction minimizes the sum of squared correlations between unique factors and external variables. This approach is similar to the traditional factor extension procedure. The second restriction minimizes the complexity of the pattern of external correlations of unique factors. This approach has similarities with the simple structure ideal imposed on most factor rotation strategies. The procedures are illustrated with a real data example that demonstrates their applicability to real-world research questions.     

Studying the classroom implementation of tasks: High-level mathematical tasks embedded in ‘real-life’ contexts

Mathematical tasks embedded in real-life contexts have received increased attention by educators, in part due to the considerable levels of student engagement often triggered by their motivational features. Nevertheless, it is often challenging for teachers to implement high-level (i.e., cognitively demanding), real-life tasks in ways that exploit their motivational features without overshadowing the mathematics involved. This paper proposes an analytic framework for describing and explaining the classroom implementation of different kinds of tasks, and uses this framework to analyse a classroom episode where a secondary teacher implemented with low fidelity a high-level, real-life mathematical task. Implications for research are discussed.     

Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts

Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively unexplored in the domain of teaching and learning of mathematics, and has not been examined with respect to students' major field of study. In this study, we examined the performance of 95 senior undergraduate mathematics and education majors in symbolic and verbal tasks about the contraposition equivalence rule. The selection of two different groups of participants allowed for the examination of the hypothesis that students' major may influence the relation between their performance in tasks about contraposition and the context(symbolic/verbal) wherein this is placed. The selection of contraposition equivalence rule also addressed a gap in the body of research on undergraduate students' understanding of proof by contraposition. The analysis was based on written responses of all participants to specially developed tasks and on semi-structured interviews with 11 subjects. The findings showed different variations in the performance of each of the two groups in the two contexts. while education majors performed significantly better in the verbal than in the symbolic tasks, mathematics majors' performance showed only modest variations. The results call for both major- and context- specific considerations of students' understanding of logical principles, and reveal the complexity of the system of factors that influence students' logical thinking.     

Developing and Enacting Culturally Relevant Pedagogy: Voices of New Teachers of Color

ABSTRACT

A group of preservice and first year teachers share their experiences as new teachers of Color entering the profession in urban public schools. Specifically, these novice teachers discuss the transition from an urban education teacher preparation program into the classroom and their successes and challenges enacting culturally relevant pedagogy. Findings showcase understanding self, community, and collaboration among critical pedagogues and navigating theory and practice as emergent themes. These new teachers speak to the journey of becoming the teachers they want to become and the challenges they encounter in public K-12 schools. Implications are presented to highlight the power and passion of these new teachers and how we, as critical scholars, must learn from them and work with them as we seek to disrupt the dominant, middle class, white discourse in teacher education programs and educational research.     

Judging students' achievement goal orientations: Are teacher ratings accurate?

Using the theoretical framework of achievement goal theory, this study investigated the accuracy of teachers' judgments of their students' motivation. Self-report data were gathered on the mastery, performance-approach, and performance-avoidance goals of 1140 German secondary school students (mean age = 14.24) in five academic subjects (English, Mathematics, German, second foreign language, and Biology). Their teachers in each of the five subjects (N = 176) were asked to judge students' achievement goals. Multilevel regression analyses revealed that teacher ratings of students' motivation statistically significantly predicted student ratings in all five subjects for mastery and performance-approach motivation, but not for performance-avoidance motivation. Assessment of differences in teachers' judgment accuracy across classrooms revealed some variability in teachers' ability to judge their students' mastery and performance-approach goals. Exploratory analyses showed that teaching experience, teacher gender, student age, and student gender did not systematically explain variation in judgment accuracy. Future research should examine other characteristics potentially influencing teachers' judgment accuracy and investigate the effect of teachers' judgment accuracy on students' motivation.     

Schoolteachers,social control and professional conflict: government procedures brought against schoolteachers in Galicia (1859–1910)

This article aims to analyse the disciplinary procedures brought against public schoolteachers in Galicia from 1859 until 1910. The article starts with the presentation of the legal basis for the government inquiries and the administrative framework in which they were implemented. Following is an examination of the evolution of the inquiries, the origin of the complaints, the charges filed against the teachers and the sanctions proposed. Lastly some examples are provided of the most widespread offences, consisting of abandonment of teaching as well as other charges of moral misconduct such as cohabitation and sexual abuse of the children.