Challenges in deepening prospective teachers’ understanding of multiplication through justification

This article reports challenges faced by prospective elementary teachers as they revisited whole number multiplication through a sequence of tasks that required them to develop and justify reasoning strategies for multiplication. Classroom episodes and student work are used both to illustrate these challenges, as well as to demonstrate growth over time. Implications for the design of mathematics courses for prospective teachers’ are discussed. Although the study is situated in the context of multiplication, it has implications for teachers reasoning and justification in other areas of mathematics.

A research framework for creative and imitative reasoning

This conceptual research framework addresses the problem of rote learning by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of different reasoning types.

Deductive reasoning: in the eye of the beholder

This study examines ways of approaching deductive reasoning of people involved in mathematics education and/or logic. The data source includes 21 individual semi-structured interviews. The data analysis reveals two different approaches. One approach refers to deductive reasoning as a systematic step-by-step manner for solving problems, both in mathematics and in other domains. The other approach emphasizes formal logic as the essence of the deductive inference, distinguishing between mathematics and other domains in the usability of deductive reasoning. The findings are interpreted in light of theory and practice.

Jong-Hsiang Yang: a major promoter of Taiwanese science education

This article reviews the work of Jong-Hsiang Yang in science education and his efforts in creating a research culture in Taiwan. Following in Yang’s footprints, the rebuilding of science education, implementing a new science curriculum, and gaining the academic status of science education, we go through the important years of the development of science education in Taiwan. His leadership in introducing interpretive research methods and expanding international studies catalyzed profound changes to science education research in Taiwan.

Doctoral students’ use of examples in evaluating and proving conjectures

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and semantic reasoning strategies relative to a representation system of proof. We then use this conceptualisation as a basis for contrasting the behaviour of two successful mathematics research students whilst they evaluated and proved number theory conjectures. We observe that the students exhibited strikingly different degrees of example use, and argue that previously observed individual differences in reasoning strategies may exist at the expert level. We conclude by discussing implications for pedagogy and for future research.

Deep intuition as a level in the development of the concept image

To explicate certain phenomena, e.g., the possibility of deduction without definition, we hypothesize that an individual is able to understand and appreciate reasoning with a due feeling of its necessity when the concept image of each concept involved in the reasoning has reached a certain level of development; we then speak of deep intuition. This conception is presented (with a variety of examples) in the framework of D. Tall’s theory of three worlds of mathematics (‘conceptual-embodied’, ‘proceptual-symbolic’, and ‘formal-axiomatic’).

Sources of students’ frustration in pre-university level, prerequisite mathematics courses

This paper looks at sources of frustration in students of “prerequisite” mathematics courses (PMC), that is, courses required for admission into undergraduate programs in a large, urban, North American university. The research was based on responses to a questionnaire addressed to students and interviews with students and instructors. In the design of the questionnaire and the analysis of responses, an “institutional” theoretical perspective was taken, where frustration was conceived not only as a psychological process but also as a situation experienced by participants in a concrete educational institution. Several sources of frustration were identified as important in the group of respondents: the fast pace of the courses, inefficient learning strategies, the need to change previously acquired ways of thinking, difficult rapport with truth and reasoning in mathematics, being forced to take PMC, insufficient academic and moral support on the part of teachers, and poor achievement. These sources of frustration are discussed from the point of view of their impact on the quality of the mathematical knowledge that students develop in the PMC. Consideration is also given to the possibilities of improving the quality of this knowledge, given the institutional constraints implicated in the sources of students’ frustration.

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.

---

Measuring the impact of a university first-year experience program on student GPA and retention

In 1997 a medium-size Midwestern public university in the U.S. initiated a first year experience program. The program is designed to infuse added curricular and extracurricular components into core courses in an effort to integrate students into the university community. This article examined the FYE impact on grade point average (GPA) and retention after 1 year for the fall 2006 cohort of entering students. The findings suggest no positive FYE effect on retention, but on average FYE students earned higher GPAs than non-FYE students. Reducing the sample to include only courses identified as goal compatible FYE courses yielded a positive effect on retention and also accentuated the GPA differential. The estimated positive FYE impact on retention was larger for below average students (especially females) and smaller for above average students.

Providing Bottom-Up Support to Middle School Science Teachers’ Reform Efforts in Using Inquiry-Based Kits

Middle grades science teachers need professional support in practice as they implement new inquiry-based science. Professional development schools can provide this bottom-up support through connecting preservice and inservice teacher education programs in classroom practice. In this study, coteaching arrangements with secondary science education majors provided additional teachers in the classroom to support a materials-rich curriculum and the needed associated pedagogies. Science education majors provided needed assistance in troubleshooting difficulties with the new curriculum. They also provided needed content knowledge to support inquiry, along with creating moments and space for teachers to reflect on inquiry practice. Ongoing assistance by preservice teachers allowed inservice teachers to progress from logistical concerns in implementing kit curriculum to concerns regarding student learning and the supporting professional development.

The Impact of an Engineering Design Curriculum on Science Reasoning in an Urban Setting

This study examines the use of engineering design to facilitate science reasoning in high-needs, urban classrooms. The Design for Science unit utilizes scaffolds consistent with reform science instruction to assist students in constructing a design solution to satisfy a need from their everyday lives. This provides a meaningful context in which students could reason scientifically. Eighth grade students from two urban schools participated in the unit. Both schools contained large percentages of racial/ethnic minority and economically disadvantaged students. Students demonstrated statistically significant improvement on a paper-and-pencil, multiple-choice pre and post assessment. The results compare favorably with both a high-quality inquiry science unit and a traditional textbook curriculum. Implications for the use of design-based curricula as a viable alternative for teaching science reasoning in high-needs, urban settings are discussed.

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.

Exam Scams and Classroom Flimflams: Urban Legends as an Alternative Lens for Viewing the College Classroom Experience

Campus-based urban legends have the potential to convey and construct student culture in higher education. Basic qualitative and humanistic research methods were used to collect, analyze, and interpret legends related to the academic experience of collegiate life.

Design and development research: a model validation case

This is a report of one case of a design and development research study that aimed to validate an overlay instructional design model incorporating the theory of multiple intelligences into instructional systems design. After design and expert review model validation, The Multiple Intelligence (MI) Design Model, used with an Instructional Systems Design (ISD) Model, was tested for use by four practicing instructional designers. Instruction developed for learners using this model was then evaluated measuring post-test and attitudinal scores with 102 participants. This report also provides a reflection on the lessons learned in conducting design and development research on model validation. The procedures and findings have implications for the processes involved in instructional design model validation through designer use and program implementation.

Listening and reflecting: an introduction to the special issue

The topic of listening has been broadly neglected in educational studies. This special issue presents studies on the connections between listening and reflecting in educational contexts.

Supporting Faculty Grassroots Leadership

Various factors are making faculty leadership challenging including the rise in part-time and non-tenure-track faculty, the increasing pressure to publish and teach more courses and adopt new technologies and pedagogies, increasing standards for tenure and promotion, ascension of academic capitalism, and heavy service roles for women and people of color. This article focuses on describing actions taken by institutional agents and aspects of campus environments which are supportive of grassroots faculty leadership. While there are many conditions which inhibit faculty leadership (i.e., part-time and contingent faculty trends, rising publication standards, etc.), our study demonstrated certain campus conditions or characteristics can overcome the forces of change including counting leadership as service, creating campus networks, addressing dysfunctional department dynamics, fostering role models, supporting faculty who question or challenge decisions, ensuring flexibility and autonomy, and altering contingent faculty contracts to include service and leadership.

Homicides in Higher Education: Some Reflections on the Moral Mission of the University

This essay on the ethical mission of the university explores extremes of anti-social behavior, visiting numerous crime scenes before concluding that contemporary higher education has lost the capacity—and even the language—for taking character development seriously. In his attempt to determine whether coincidently traditional-liberationist-diversiphilic-apathetic colleges can morally improve their charges, Peter Wood collects a wrenching compendium of violent academic mayhem.

Analytic Frameworks for Assessing Dialogic Argumentation in Online Learning Environments

Over the last decade, researchers have developed sophisticated online learning environments to support students engaging in dialogic argumentation. This review examines five categories of analytic frameworks for measuring participant interactions within these environments focusing on (1) formal argumentation structure, (2) conceptual quality, (3) nature and function of contributions within the dialogue, (4) epistemic nature of reasoning, and (5) argumentation sequences and interaction patterns. Ultimately, the review underscores the diversity of theoretical perspectives represented within this research, the nature of dialogic interaction within these environments, the importance of clearly specifying theoretical and environmental commitments throughout the process of developing or adopting an analytic framework, and the role of analytic frameworks in the future development of online learning environments for argumentation.

A science need: Designing tasks to engage students in modeling complex data

In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaput’s belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in reasoning about data. A Science of Need embodies the utility value of mathematics, and engages students in seeing the importance of mathematics in both their current and their future lives. An extended example of the design of tasks that require students to generate, test, and revise models of complex data is used to illustrate the ways in which attention to the contributions of students can aid in the development of both useful and theoretically coherent models of mathematical understanding by researchers. Tools such as Fathom are shown as democratizing agents in making data modeling more expressive and intimate, aiding in the development of deeper and more applicable mathematical understanding.

Intellectual innovation or intellectual retrofitting: on agency, culture and access to science education

A great challenge in education research involves the difficulty of differentiating between studies that apply commonly understood theoretical perspectives and recognizing studies that merely rename old theoretical frameworks. This conflict between intellectual innovation and intellectual retrofitting emerges as central to Basu, Calabrese-Barton, Clairmont, and Lock’s exploration of the relationship between critical agency and student identity development in science.