Secondary-to-tertiary comparison through the lens of ways of doing mathematics in relation to functions: a study in collaboration with teachers

This article addresses the issue of transition from secondary to post-secondary education through collaborative research with teachers from both levels. It takes into account implicit elements in this transition. Research on the transition in mathematics education tends to focus more on the tertiary level, studying difficulties encountered by students or comparing curricula, tasks, and textbooks highlighting disruptions or cultural shifts. However, according to Hall (1959), and Artigue (2004) in a mathematical context, it is the implicit “ways of doing” that lead to the greatest cultural differences. In this article, attention is paid to the particular ways in which teachers’ ways of doing mathematics impact the transition. Ethnomethodology (Garfinkel, 1967) and its central concept of ethnomethods are used as the theoretical framework to conceptualize these ways of doing mathematics. A breaching situation presented to a group of secondary- and tertiary-level teachers engaged in collaborative research (Desgagné et al., 2001) brings to light familiar ways of doing mathematics. Our analysis focuses specifically on a comparison of the ways of doing mathematics related to functions at each level.     

History of mathematics in secondary school teachers’ training: towards a nonviolent mathematics education

In the context of mathematics teachers’ training, the concept of dépaysement épistémologique (epistemological disorientation) emphasizes that the contact with the history of mathematics, particularly with the use of original sources, pushes aside commonplace students’ perspectives about the discipline and offers them a critical look towards mathematics’s historical, social and cultural aspects. Conceptually supported by the theory of objectivation, an emergent sociocultural theory in mathematics education, this study describes the dépaysement épistémologique lived by future mathematics teachers engaged in the reading of historical texts. A phenomenological approach allowed us to clarify various meanings associated with students’ lived experiences and a dialogical perspective provides a way to get these meanings in tension through a polyphonic narration. Our reading of this polyphonic narration suggests that dépaysement épistémologique associated with the reading of historical texts encouraged empathy from students towards the authors and their future learners, opening up the possibility for a nonviolent mathematics education.     

Use of digital game based learning and gamification in secondary school science: The effect on student engagement,learning and gender difference

This study aimed to identify the impact of a game based learning (GBL) application using computer technologies on student engagement in secondary school science classrooms. The literature reveals that conventional Science teaching techniques (teacher-centered lecture and teaching), which foster rote learning among students, are one of the major concerns in Pakistan Education system. This leads to student disengagement in science lessons eventually resulting in student absenteeism and dropouts from the schools. This study consisted of five stages: (1) examining the impact of Digital Game-Based Learning (DGBL) and gamification on engagement, learning and gender difference, and literature related to using DGBL models for instructional design; (2) planning learning activities and developing a GBL application based on a specific content in Science; (3) conducting an intervention with a sample of 72 participants of 8th grade (aged 12–15) in a low cost private school of Pakistan following quasi-experimental research framework; (4) observing behaviour and emotions of the participants during science lessons; (5) conducting pre and post tests to assess the learning outcomes of participants followed by focus groups discussion. Analysis from Friedman test, Mann-Whitney U test, and Wilcoxon Signed Rank test show that the GBL application has a positive influence on student engagement. However, GBL application was not equally effective for all students since girls outperformed boys in terms of engagement and learning outcomes. This study gives insights into the development of better educational games to promote student learning.     

Teaching as Interaction: Challenges in Transitioning Teachers’ Instruction to Small Groups

Although small group instruction is often endorsed in teaching young children, teachers are rarely given explicit instruction on how to move instruction into small groups where effective adult-child interactions can take place. This study examines how 14 early childhood educators transitioned their instruction from whole to small group teaching after participating in a year-long program of professional development. The results indicate teachers’ previous definitions of “teaching as dissemination” interfered with their ability to take on new roles, design tasks, and manage time. Implications include the need for teacher educators to focus on how teaching through interaction shifts these aspects of the teaching process.     

Effects of a rubric for mathematical reasoning on teaching and learning in primary school

Rubrics are assessment tools that help students gain complex competencies. Our quasi-experimental study aimed to evaluate whether rubrics help teachers teach and assess mathematical reasoning in primary school and whether such an instrument might support student learning. In two Swiss cantons, 762 students in 44 5th- and 6th-grade primary classes worked on their reasoning competencies, and half of them additionally employed our standards-based rubric. All of the teachers received a 1-day training and participated in the final project evaluation. To standardise and support the teachers during the implementation phase, they received a detailed curriculum. An achievement test and questionnaires for students and teachers were administered before and at the end of the intervention. The results of our quantitative longitudinal analyses indicate that the rubric fosters the teachers’ perceived diagnostic skills but only indirectly impacts their use of formative feedback. Based on the students’ perceptions, however, we observed a direct effect of the rubric on formative feedback and student self-assessment. Effects on students’ outcomes could not be observed, but there are indications of effects mediated by self-regulation and self-efficacy.     

Social and Emotional Learning and Teacher–Student Relationships: Preschool Teachers’ and Students’ Perceptions

The study aimed to investigate how teachers’ perceptions of emotional intelligence, and social and emotional learning (SEL) relate to teacher–student relationships. Teachers’ perceptions of teacher–student relationships and the degree of agreement with students’ perceptions was also investigated. Preschool teachers from 92 public schools in central Greece completed the Self-Rated Emotional Intelligence Scale, the Teacher SEL Beliefs Scale, and the Student–Teacher Relationships Scale-Short Form for 238 students aged 5–6 years old. 170 students were interviewed using the Young Children’s Appraisal of Teacher Support. Regression analysis revealed that both teachers and students emphasized the role of teachers’ perceptions of SEL in positive teacher–student relationships. However, there was no agreement between teachers and students regarding teacher–student relationships. These findings and their implications for research and practice are discussed.     

Early Childhood Creativity: Challenging Educators in Their Role to Intentionally Develop Creative Thinking in Children

Creativity is a topic of wide global interest, often discussed in fields such as education, psychology and business (Runco, Divergent thinking and creative potential, Hampton Press, New York, 2013; Yoruk and Runco, Journal for Neurocognitive Research 56:1–16, 2014). However, the relationship of pedagogical practices in early childhood education and care (ECEC) as it applies to the development of creative thought processes of young children is a relatively new area for investigation. This paper presents recent research that examines the role of the educator as an intentional teacher within Australian early learning environments and investigates the relationship of this role to children’s developing creativity. Theoretically informed by Vygotsky’s sociocultural constructivist approach (Vygotsky, Mind in society: The development of higher psychological processes, Harvard University Press, Cambridge, MA, 1930, 1978) and neo-Vygotskian theories on creativity (John-Steiner and Moran, Educational Psychologist 31:191–206, 2012), this paper explores some of the beliefs and understandings of educators on creativity. Furthermore, this paper exposes some of the misconceptions of educators about children’s creative thinking as they engage in play-based learning activities. The evidence from this Australian study suggests that the role of the educator is pivotal in assisting children in the early development of creative thinking thus challenging their role as educators.     

A Critical Review of Line Graphs in Behavior Analytic Journals

Visual displays such as graphs have played an instrumental role in psychology. One discipline relies almost exclusively on graphs in both applied and basic settings, behavior analysis. The most common graphic used in behavior analysis falls under the category of time series. The line graph represents the most frequently used display for visual analysis and subsequent interpretation and communication of experimental findings. Behavior analysis, like the rest of psychology, has opted to use non-standard line graphs. Therefore, the degree to which graphical quality occurs remains unknown. The current article surveys the essential structure and quality features of line graphs in behavioral journals. Four thousand three hundred and thirteen graphs from 11 journals served as the sample. Results of the survey indicate a high degree of deviation from standards of graph construction and proper labeling. A discussion of the problems associated with graphing errors, future directions for graphing in the field of behavior analysis, and the need for standards adopted for line graphs follows.     

A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic process without a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teaching-learning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.