Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an algebraic structure to get a sense of those properties which form the basis of the fundamental definitions. We will explain the transition from examples to abstract algebra as a series of shifts of attention and in this paper we will use a case study to examine the initial shift, which we will call apprehending a structure, and examine how one student came to apprehend the structure of the commutative ring Z₉₉.     

Flexible use of lexical and sublexical information in word recognition

Within the dual‐route framework it is hypothesised that readers exhibit flexibility in their use of lexical and non‐lexical information in word naming. In the present study, participants named high‐ and low‐frequency regular one‐syllable English words embedded within lists of regular or irregular one‐ or two‐syllable English words. A large number of irregular words should bias the reader toward the lexical route, whereas a list consisting exclusively of regular words should allow more efficient use of sublexical information present in the word. Word frequency effects were obtained when the list was dominated by either regular or irregular two‐syllable filler words. Furthermore, there was an interaction between frequency and regularity for the one‐syllable words, indicating that the frequency effect was significantly larger when the fillers were one‐syllable irregular words relative to one‐syllable regular words. These results extend those reported for a shallow orthography, and indicate strategic control over the use of phonological and lexical information in English word recognition.     

Reframing Resources in Engineering Teaching and Learning

Abstract

The notion of “resources” is often framed in an economic sense: money, time, equipment and the like. The authors reconceptualise this notion, situating resources as embedded in curricular frameworks, teacher practice and student experience. This leads them to define resources as “the potential to participate in socio-cultural action” which is illustrated in this article through a series of reflections on the part of the authors, all within the context of engineering education. First, they demonstrate that curriculum can be productively thought of as a route marker for the development of resources that students need in order to enact their role as professional engineers. Thereafter, they show that lecturers bring tacit resources of trust, care, creativity and credibility to the teaching and learning space, and that these are necessary to overcome the inertia that often resists the transformation of teaching and learning practice. Finally, they reflect on how students’ prior learning experiences can be harnessed as a resource for teaching and learning. In so doing, they present resources as tied to sociocultural practices and personal and institutional histories, and encourage others to take up these ideas so as to consider how resources, viewed in the authors’ sense, are valued within (engineering) education.     

Facing and managing dilemmas as a clinical educator

Although clinical educators make an important and irreplaceable contribution to the education of students undertaking qualifications that will enable them to practise as health professionals, little is known about the day‐to‐day experiences of clinical educators and the complexities of clinical education that may contribute to the problems or to the successes of clinical educators. This paper reports on one aspect of a study that sought to increase the understanding and appreciation of the roles and responsibilities of being a clinical educator. The lived experiences of clinical educators in speech pathology ¹ 1. Also known as speech‐language pathology in North America and speech‐language therapy in the UK. View all notes were explored in depth, over a sustained period of time, in an attempt to understand what it is like to be a clinical educator. This paper uses narrative data to illustrate dilemmas faced by clinical educators in our study, and discusses implications pertinent to clinical educators in a range of health disciplines in higher education.     

Five Critical Stances Towards Liberal Philosophy of Education in Britain

In this paper John White argues that there has been a decline in interest in and support for liberalism in British philosophy of education. He provides examples of work by leading figures in the field that demonstrates scepticism about the key liberal value of autonomy and offers an analysis of new influences in the field that have contributed to this decline. In particular he notes the increase of work from a religious perspective. Doubts are expressed about the practical relevance to education of some of these avenues of thought, and the suggestion is made that they cause those within the field to be more out of touch with society at large, in which liberal values have continued to be the major source of animation. The paper is followed by short responses from four philosophers of education whose work he criticises.     

Changing Minds With the Story of Adaptation: Strategies for Teaching Young Children About Natural Selection

Research Findings: Educational guidelines recommend a delayed, piecemeal approach to instruction on adaptation by natural selection. This approach is questionable given suggestions that older students’ pervasive misunderstandings about adaptation are rooted in cognitive biases that develop early. In response to this, Kelemen et al. (2014) recently showed that young children can learn a basic yet comprehensive explanation of adaptation by natural selection from a picture storybook intervention. However, this research was conducted in a laboratory-based setting with children from middle and higher socioeconomic backgrounds. To further explore the intervention’s efficacy, this investigation examined whether Kelemen et al.’s (2014, Experiment 2) findings extend to a more diverse sample of children tested in a more naturalistic setting, namely, after-school programs. After a 10-min picture storybook reading that described adaptation within a fictitious but realistic mammal species, 5- to 6- and 7- to 8-year-old children’s learning of adaptation was examined. Results revealed that younger and older children benefitted from the intervention; however, older children displayed pronounced learning and generalization. Practice or Policy: Findings confirm that children are capable of learning complex biological ideas and that comprehensive storybook interventions are simple but powerful teaching tools. Implications for instruction on natural selection are discussed.     

Differences in transitional needs of high school students with and without learning disabilities

Studies investigating the post-high-school vocational status of individuals with disabilities have frequently found that these individuals are more likely to be unemployed, underemployed, or employed part-time, when compared to nondisabled peers. Transition programs are needed for adolescents with disabilities to facilitate their vocational success. The current study surveyed 80 high school students with learning disabilities (LD) and 80 nondisabled (NLD) peers to determine their transitional needs. Results indicated that (a) more students with LD than NLD students are involved in transition programs; (b) career goals were established by the majority of both groups; (c) parents provided most of the assistance in making career decisions; and (d) twice as many NLD students as students with LD wanted to go to college, while twice as many students with LD as NLD students wanted to enter the job market. More students with LD than NLD students were aware of vocational rehabilitation (VR) services, but the number was still below 50%. The majority of the information about VR services came from the school.     

A study of an adapted social–emotional learning: Small group curriculum in a school setting

Clinicians and training programs strive to implement evidence‐based practices and manualized treatments with fidelity. However, the constraints of a local setting may limit the extent to which this is possible. In the current study, an adapted model of an evidence‐based social–emotional learning small group curriculum, the Incredible Years Children’s Small Group Training Series (Webster‐Stratton, 2004), was implemented and evaluated in an elementary school setting. Results of the study demonstrated statistically significant decreases in problem behaviors and intensity of problem behaviors, as rated by teachers. Teachers also reported improvement in classroom behavior, emotion regulation, problem‐solving, and friendship skills, as well as a high overall level of satisfaction with the intervention itself. Discussion of the results includes a review of the strengths and limitations associated with outcome research in a naturalistic setting, suggestions to consider when adapting evidence‐based programs, and recommendations for future research.