Computer Manipulatives in an Ordinary Differential Equations Course: Development, Implementation, and Assessment

The d’Arbeloff Interactive Mathematics Project or d’AIMP is an initiative that seeks to enhance and ultimately transform the teaching and learning of introductory mathematics at the Massachusetts Institute of Technology. A result of this project is a suite of “mathlets,” a carefully developed set of dynamic computer applets for use in the university’s ordinary differential equations course. In this paper, we present the rationale for such computer innovations, the philosophy behind their design, as well as a discussion of their careful development and implementation. Survey results are reported which yielded positive student feedback and suggestions for improvement.

Technology, Pedagogy, and Epistemology: Opportunities and Challenges of Using Computer Modeling and Simulation Tools in Elementary Science Methods

   This study infused computer modeling and simulation tools in a 1-semester undergraduate elementary science methods course to advance preservice teachers’ understandings of computer software use in science teaching and to help them learn important aspects of pedagogy and epistemology. Preservice teachers used computer modeling and simulation tools within their own science investigations; discussed general technology issues; and explored, evaluated, and taught their peers about a particular modeling tool. Preservice teachers expanded their vision of the software available and the role that software can play in science teaching, but desired fun, easy-to-use software with scientifically accurate information within a clear, familiar learning task. Such conflict provided a fruitful platform for discussion and for potentially advancing preservice teachers’ pedagogical and epistemological understandings.

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Language in Science Education as a Gatekeeper to Learning,Teaching, and Professional Development

In this study, I used a feminist poststructural perspective to explain how language is a gatekeeper in learning science, in achieving professional honors in teaching science, and in teaching science to English language learners. The various uses of language revealed interesting dynamics related to the culture of power of language and the culture of power of science along race–ethnicity, gender, and class dimensions for teachers. Teachers did not necessarily see language as having distinct purposes and uses. This further maintained the gatekeeping nature of language and discourse in science education. I discuss implications for looking at language in science education for teacher professional development and student learning.

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A categorization of the “whys” and “hows” of using history in mathematics education

This is a theoretical article proposing a way of organizing and structuring the discussion of why and how to use the history of mathematics in the teaching and learning of mathematics, as well as the interrelations between the arguments for using history and the approaches to doing so. The way of going about this is to propose two sets of categories in which to place the arguments for using history (the “whys”) and the different approaches to doing this (the “hows”). The arguments for using history are divided into two categories; history as a tool and history as a goal. The ways of using history are placed into three categories of approaches: the illumination, the modules, and the history-based approaches. This categorization, along with a discussion of the motivation for using history being one concerned with either the inner issues (in-issues) or the metaperspective issues (meta-issues) of mathematics, provides a means of ordering the discussion of “whys” and “hows.”

Designing Blended Inquiry Learning in a Laboratory Context: A Study of Incorporating Hands-On and Virtual Laboratories

This article reports on the development of a methodology that integrates virtual and hands-on inquiry in a freshman introductory biology course. Using a two time × two order-condition design, an effective combination (blend) of the two environments was evaluated with 39 freshman biology participants. The quantitative results documented no significant effect of presentation order but demonstrated a significant effect of the combined learning experience. The qualitative results showed a strong preference by students for the virtual work preceding the hands-on laboratory. The study provides practitioners an effective alternative to traditional instructional practices by combining virtual and hands-on inquiry learning.

The notion of historical “parallelism” revisited: historical evolution and students’ conception of the order relation on the number line

This paper associates the findings of a historical study with those of an empirical one with 16 years-old students (1st year of the Greek Lyceum). It aims at examining critically the much-discussed and controversial relation between the historical evolution of mathematical concepts and the process of their teaching and learning. The paper deals with the order relation on the number line and the algebra of inequalities, trying to elucidate the development and functioning of this knowledge both in the world of scholarly mathematical activity and the world of teaching and learning mathematics in secondary education. This twofold analysis reveals that the old idea of a “parallelism” between history and pedagogy of mathematics has a subtle nature with at least two different aspects (metaphorically named “positive” and “negative”), which are worth further exploration.

A cultural-historical reading of “Culturally Sensitive Schooling”: thinking beyond a constructivist view of science learning

“Culturally-Sensitive Schooling” as proposed by Brayboy and Castagno offers an important way of thinking about the relations between formal and informal science learning and between Western and Indigenous science. The constructivist framework adopted by Brayboy and Castagno in their discussions is consistent with the theoretical approach traditionally used by many researchers and scholars interested in science learning. In this article I explore the basic concepts introduced in their paper, but use a different theoretical lens for explicating concept formation. Through a cultural-historical reading of “Culturally Sensitive Schooling,” different insights can be gained about the relations between everyday informal learning and schooled learning in science. I argue that dialectical logic is more productive for re-theorising science teaching and learning in culturally diverse communities.

More than a conversation: using cogenerative dialogues in the professional development of high school chemistry teachers

This paper focuses on content-based and pedagogical instructors’ use of cogenerative dialogues to improve instructional practice and to evaluate program effectiveness in a professional development program for high school chemistry teachers. We share our research findings from using cogenerative dialogues as an evaluative tool for general assessment of various program-related issues. We discuss how engaging students in cogenerative dialogues improved teaching and learning in chemistry and chemistry education courses. This research provides insights and direction for improving content-based professional development programs for science teachers and the learning experiences of high school science students. Cogenerative dialogue has the potential to expand evaluation methodologies that will position participants more centrally in not only the collection of data, but also the analysis of these data to catalyze transformative practices in educational programs.

Lecturers on teaching within the ‘supercomplexity’ of Higher Education

While a vast literature exists on students and their learning, work on lecturers and their teaching continues to lag some way behind. This paper explores the notion that the complexity of Higher Education (HE) today significantly impacts upon what goes on in the classroom through a two-tiered study. Semi-structured interviews were conducted to explore lecturers’ perceptions and experiences of teaching a specific module. Interviewees raised issues pertaining to the wider departmental, institutional and socio-political context. Consequently, focus groups were run with key people in the University to explore their perceptions of teaching and learning within the current HE climate. The findings suggest that lecturers perceive numerous external factors to impinge upon their teaching and attempt to militate against these in various ways in order to achieve ongoing enhancement of learning for students.

Mary Budd Rowe: a storyteller of science

This article examines Mary Budd Rowe’s groundbreaking and far-reaching contributions to science education. Rowe is best known for her research on wait-time: the idea that teachers can improve the quality and length of classroom discussions by waiting at least 3 s before and after student responses. Her wait-time research grew from and helped inform her staunch advocacy of science education as inquiry; Rowe saw wonder and excitement as central to the teaching and learning of science. She spent much of her professional life designing professional development experiences and innovative curriculum materials to help teachers, particularly elementary school teachers, enact inquiry in their classrooms.

Critical physics agency: further unraveling the intersections of subject matter knowledge, learning, and taking action

In this rejoinder to Bryan Brown and John Reveles, we highlight the facts that (a) sociocultural theories of learning do not go far enough because they fail to address a number of issues and (b) we require concepts such as power and positionality to understand science learning.

Clergy’s Views of the Relationship between Science and Religious Faith and the Implications for Science Education

Since many teachers and students recognize other kinds of knowledge (faith) based on other ways of knowing, consideration of these realities is appropriate for the science education community. Understanding the multitude of ways that clergy view relationships between science and faith (i.e. alternative ways of knowing) would assist in understanding various ways that people address complex issues arising from ideas about science and faith. We administered a questionnaire composed of multiple-choice and short answer items to 63 United Methodist ministers. Findings included (1) that formal, organized faith contexts (e.g. church services) serve as informal science education opportunities, (2) participants demonstrated considerable diversity regarding the types of relationships developed between science and faith, and (3) participants recognized a need exists for better understandings of science and its relationship to faith for them, their colleagues, and their congregations.

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Socio-emotional orientations and teacher change

In this article we consider how elementary education students’ views of mathematics changed during their mathematics methods course. We focus on four female students: two started the course with mainly positive views of mathematics and a task orientation, two with negative views of the subject and an ego-defensive orientation. The biggest change observed was that the trainees’ views of teaching and learning mathematics became more positive. Moreover, what had been an ego-defensive orientation changed towards a social-dependence orientation. The crucial facilitators of change seemed to be (1) handling of and reflection on one’s experiences of learning and teaching mathematics, (2) exploring content with concrete materials, and (3) collaboration with a partner or working as a tutor of mathematics.

Compatibility between cultural studies and conceptual change in science education: there is more to acknowledge than to fight straw men!

In this response, we attempt to clarify our position on conceptual change, state our position on mental models being a viable construct to represent learning, indicate important issues from the social cultural perspective that can inform our work on conceptual change and lastly comment on issues that we consider to be straw men. Above all we argue that there is no best theory of teaching and learning and argue for a multiple perspective approach to understanding science teaching and learning.

Is student-centered pedagogy impossible in Hong Kong? The case of inquiry in classrooms

Hong Kong has been actively promoting a student-centered approach to teaching since the 1980s. Despite this effort, students in Hong Kong still tend to be traditional learners who rarely experience and gain from real student-centered learning. While teachers hold a “quantitative” concept of learning and focus on transmitting declarative knowledge to students (Biggs and Watkins, Classroom learning: Educational psychology for the Asian teacher, 1995), students generally practise “rote learning.” Constructive learning models such as inquiry remain little used by students in most Hong Kong classrooms. This article reports a study that examines the feasibility of implementing inquiry method in Kong Kong’s primary classrooms. It analyses the implementation and some outcomes of an inquiry-based project conducted in two local primary schools—a traditional elite Catholic school and a progressive, less-privileged school. Finally, it discusses the contextual factors as well as cultural issues on teachers’ perception and implementation of inquiry in teaching. These factors include the following: impacts of prevailing ideology in the community of Hong Kong, and the top-down policy-making and management by the government.

Postcolonial foldings of space and identity in science education: limits, transformations, prospects

The four essays reviewed here constitute a worthwhile attempt to discuss various aspects of postcolonial theory, and offer constructive ideas to ongoing academic as well as public conversations with respect to whether science education can meet the challenges of educating an increasingly diverse population in the 21st century. These essays are grounded in the assumption that it is difficult to make meaningful and transformative changes in science education so that educators’ efforts take into consideration the dramatic changes (i.e., diverse culture and racial origins, language, economic status etc.) of ‘an era of globalization’ in order to meet the demands of today’s schools. Each of these four essays problematizes various aspects of the social and cultural conditions of science education nowadays using different ‘postcolonial’ ideas to interpret the implications for science learning and teaching. Although the term ‘postcolonial’ has certainly multiple meanings in the literature, we use this term here to describe the philosophical position of these essays to challenge long-standing and hegemonic practices and taken-for-granted assumptions in science education. Through critical analysis of these essays, we engage in a dialogue with the authors, focusing on two of what seem crucial issues in understanding the potential contributions as well as the risks of postcolonial concepts in science education; these issues are space and identity. We choose these issues because they permeate all four essays in interesting and often provocative ways.

The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

Teachers’ Perspectives on a Professional Development Intervention to Improve Science Instruction Among English Language Learners

Our 5-year professional development intervention is designed to promote elementary teachers’ knowledge, beliefs, and practices in teaching science, along with English language and mathematics for English Language Learning (ELL) students in urban schools. In this study, we used an end-of-year questionnaire as a primary data source to seek teachers’ perspectives on our intervention during the first year of implementation. Teachers believed that the intervention, including curriculum materials and teacher workshops, effectively promoted students’ science learning, along with English language development and mathematics learning. Teachers highlighted strengths and areas needing improvement in the intervention. Teachers’ perspectives have been incorporated into our on-going intervention efforts and offer insights into features of effective professional development initiatives in improving science achievement for all students.