Helena P. Osana

Reciprocal Teaching procedures and principles: two teachers' developing understanding

The effectiveness of Reciprocal Teaching, a reading comprehension instructional technique, has been repeatedly demonstrated. According to Brown and Campione (Innovations in Learning, Erlbaum, Mahwah, NJ, pp. 289–325, 1996) ‘‘lethal mutations’’ are abundant because of teachers’ focus on how to do the procedures of Reciprocal Teaching and lack of understanding of the learning principles upon which the method is based. This investigation reports conceptual growth and the misinterpretations of the procedures and learning principles that two Schools for Thought teachers held as they developed their understanding across training sessions. We claim that studying the development of teacher thinking can be particularly useful to those revamping teacher education programs. r 2003 Elsevier Science Ltd. All rights reserved.

Mathematics Anxiety in Preservice Teachers: Its Relationship to their Conceptual and Procedural Knowledge of Fractions

The objective of the present study was to examine the relationship between mathematics anxiety and the procedural and conceptual knowledge of fractions in prospective teachers. Thirty-two preservice teachers enrolled in an elementary mathematics methods course were administered the Revised Mathematics Anxiety Rating Scale (RMARS, Baloğlu, 2002). Procedural and conceptual knowledge of fractions was assessed with a validated paper and pencil test (Saxe, Gearhart, & Nasir, 2001) and with four additional problems created by the researchers. Results indicated that as mathematics anxiety scores increased, scores on the validated measure of procedural knowledge of fractions decreased. The same relationship was found between the RMARS and the validated measure of conceptual knowledge. The findings provide some insight on the cognitive and pedagogical factors associated with mathematics anxiety in the preservice teacher population, underscoring the importance of facilitating their proficiency in both mathematical procedures and concepts.

Exploring adolescent decision making about equity: Ill-structured problem solving in social studies

Abstract The nature of adolescent decision making was investigated using a task that hinged on gender equity, a central concept in citizen education classrooms. Eighteen 10th-grade students were individually interviewed and asked to make a decision about allocating scholarship money to four pairs of fictional candidates seeking either nursing or engineering degrees. The candidates in each pair differed on various dimensions, including major, GPA, and financial need. Interviews were audiorecorded and transcribed for qualitative analyses. The model that emerged from the data revealed that adolescent decision making is a constructive and recursive process, and the students’ simplistic notions of equity inhibited the search for alternatives and their evaluation. The findings point to the important relationship between concept representation and social reasoning.

The impact of print exposure quality and inference construction on syllogistic reasoning

This study extended the work of S. Siddiqui, R. F. West, and K. E. Stanovich (1998), who studied the link between general print exposure and syllogistic reasoning. It was hypothesized that exposure to certain text structures that contain well-delineated logical forms, such as popularized scientific texts, would be a better predictor of deductive reasoning skill than general print exposure, which is not sensitive to the quality of an individuals reading activity. Furthermore, it was predicted that the ability to generate explanatory bridging inferences while reading would also be predictive of syllogistic reasoning. Undergraduate students (N = 112) were tested for vocabulary, nonverbal cognitive ability, exposure to general print, exposure to popularized scientific literature, and the ability to comprehend texts distinguished by the number of inferences that must be generated to support comprehension. Hierarchical multiple regression analyses showed that a combined measure of exposure to general and scientific literature was a significant predictor of syllogistic reasoning ability. Additionally, the ability to comprehend high-inference-load texts was related to solving syllogisms that were inconsistent with world knowledge, indicating an overlap in deductive reasoning skill and text comprehension processes.

Addressing the Effects of Reciprocal Teaching on the Receptive and Expressive Vocabulary of 1st-Grade Students

This study evaluated the effects of Adapted Reciprocal Teaching (ART) on the receptive and expressive flight-word vocabulary of 1st-grade students. During ART, classroom interactions produced narrative contexts within which students assumed responsibility for applying new flight words in personally meaningful ways. Students in the control group also received interactive storybook instruction, but classroom interactions were led primarily by the teacher and focused only on the meanings of unfamiliar flight words. Students were assessed using the Receptive Flight Word Vocabulary Test (RFVT) and the Expressive Flight Word Vocabulary Test (EFVT). The data demonstrated that after the instructional intervention, the students in the ART group acquired significantly more target words (as measured by performance on the RFVT and the EFVT) than students in the control group. Results are interpreted in light of generative learning theory, and practical implications for introducing vocabulary in the early school years are addressed.

Analysis of tasks in pre-service elementary teacher education courses

This paper presents some results of research aimed at contributing to the development of a professional knowledge base for teachers of elementary mathematics methods courses, called here ‘teacher educators’. We propose that a useful unit of analysis for this knowledge could be the tasks in which teacher-educators engage pre-service teachers, and that the tasks could be indexed by a system of nested categories of actions required in the tasks and the analytic tools for carrying them out. The paper develops the seed of such an indexing framework, based on analyses of tasks in two methods courses. We argue that this seed is robust enough to be expandable, in the sense that categories could be added to it without destroying the existing ones. An expanded index, accompanied by a bank of tasks, would facilitate the development of a unified discourse to bring together, represent, and communicate, the vast experience of teacher educators.

A Review on Problem Posing in Teacher Education

Over the last two decades, researchers have shown increased interest in problem posing in mathematics professional development. In the context of teaching mathematics, problem posing can entail asking questions during classroom interactions to assess student understanding, modifying existing problems to adjust the difficulty level of a task, and creating problems to meet instructional objectives. In this chapter, we review the research conducted between 1990 and 2012 on problem posing in mathematics methods courses in elementary teacher education. Despite the range of foci, goals, and theoretical perspectives in the literature, we describe ways in which problem posing has been investigated in the preservice teacher population. Despite the paucity of empirical studies, we were able to group these studies into three distinct categories: (a) problem posing as a skill integral to the practice of teaching mathematics; (b) problem posing as an activity separate from teaching; and (c) problem posing as a tool to assess an outcome variable (for researchers) or as a tool for teaching or assessing the development of preservice teachers’ knowledge or beliefs. Implications for mathematics teacher educators that stem from the review of the literature are discussed.

A Tale of Two Researchers: Commonalities, Complementarities, and Contrasts in an Examination of Mental Computation and Relational Thinking

This paper describes a research collaboration between an educational psychologist and a mathematics education researcher, namely a didacticien des mathematiques. Our joint project aimed to explore the mental computation strategies of preservice teachers in an elementary mathematics methods course and to investigate the relationship between mental computation and relational thinking. The primary objective of the paper, however, is to go beyond the data and their interpretation. We describe the commonalities, complementarities, and points of contrast that emerged between us as researchers who hail from different disciplines, but who have the same overarching interests in mathematical thinking. In particular, we untangle issues we encountered during our collaboration related to our research questions, methodologies, and epistemological stances. We detail the ways in which we navigated these issues in the context of the research and describe what we learned about our own disciplinary perspectives and each other’s. We conclude by discussing what our story offers as a means of reflecting on our individual fields and potential interactions between them.

Manipulatives, Diagrams, and Mathematics: A Framework for Future Research on Virtual Manipulatives

Our objective in this chapter is to present a framework that can be used as a guide for designers of virtual manipulatives and for researchers who study their effects on student learning in mathematics. Because a significant amount of research has been devoted to the effects of concrete manipulatives on student learning, the crux of the framework is based on the existing literature in this area. Specifically, the framework consists of three interrelated components that align with the research on students’ learning with external representations: the surface features of the representations themselves, the pedagogical contexts that support students’ meaning making, and the students’ perceptions and interpretations of the representations. Where applicable, we integrate the research on virtual manipulatives to support the validity of the framework itself and its applicability for researchers of virtual mathematics tools.