SECONDARY SCHOOL STUDENTS’ UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION

In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students’ responses in 3 written tasks and the interviews with 18 of them are analyzed. Though MI is treated operationally in school, the students, when challenged, started to recognize the structural characteristics of MI. In the case of proof construction, we identified 2 types of transition from argumentation to proof, interwoven in the structure of the geometrical pattern. In the first type, MI was applied to the algebraic statement that derived from the direct translation of the geometrical situation. In the second type, MI was embedded functionally in the geometrical structure of the pattern.     

Teaching Explicitly and Reflecting on Elements of Nature of Science: a Discourse-Focused Professional Development Program with Four Fifth-Grade Teachers

The nature of science (NOS) has become a central goal of science education in many countries. This study refers to a developmental work research program, in which four fifth-grade elementary in-service teachers participated. It aimed to improve their understandings of NOS and their abilities to teach it effectively to their students. The 1-year-long, 2012–2013, program consisted of a series of activities to support teachers to develop their pedagogical content knowledge of NOS. In order to accomplish our goal, we enabled teacher-researchers to analyze their own discourse practices and to trace evidence of effective NOS teaching. Many studies indicate the importance of examining teachers’ discussions about science in the classroom, since it is teachers’ understanding of NOS reflected in these discussions that will have a vital impact on students’ learning. Our proposal is based on the assumption that reflecting on the ways people form meanings enables us to examine and seek alternative ways to communicate aspects of NOS during science lessons. The analysis of discourse data, which has been carried out with the teacher-researchers’ active participation, indicated that initially only a few aspects of NOS were implicitly incorporated in teacher-researchers’ instruction. As the program evolved, all teacher-researchers presented more informed views on targeted NOS aspects. On the whole, our discourse-focused professional development program with its participatory, explicit, and reflective character indicated the importance of involving teacher-researchers in analyzing their own talk. It is this involvement that results in obtaining a valuable awareness of aspects concerning pedagogical content knowledge of NOS teaching.     

Assessing the difference in learning gain between a mixed reality application and drawing screencasts in neuroanatomy

Augmented, mixed, and virtual reality applications and content have surged into the higher education arena, thereby allowing institutions to engage in research and development projects to better understand their efficacy within curricula. However, despite the increasing interest, there remains a lack of robust empirical evidence to justify the mainstream acceptance of this approach as an effective and efficient learning tool. In this study, the impact of a mixed reality application focused on long spinal cord sensory and motor pathways is explored in comparison to an existing resource already embedded within an active curriculum (e.g., anatomy drawing screencasts). To assess the changes in learner gain, a quasi-randomized control trial with a pre- and post-test methodology was used on a cohort of Year 2 medical students, with both the absolute and normalized gain calculated. Similar patterns of learner gain were observed between the two groups; only the multiple-choice questionnaires were shown to be answered significantly higher with the screencast group. This study adds important empirical data to the emerging field of immersive technologies and the specific impact on short-term knowledge gain for neuroanatomy teaching, specifically that of long sensory and motor pathways. Despite the limitations of the study, it provides important additional data to the field and intends to support colleagues across the education landscape in making evidence-informed decisions about the value of including such resources into their curricula.