IMPACT OF EXPLICIT PRESENTATION OF SLOPES IN THREE DIMENSIONS ON STUDENTS’ UNDERSTANDING OF DERIVATIVES IN MULTIVARIABLE CALCULUS

In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of slopes in three dimensions (3D) is seen with the introduction of partial derivatives. The nature of the discussions indicates that authors seem to assume that students are able to naturally extend the concept of a 2D slope to 3D and correspondingly it is not necessary to explicitly present slopes in 3D. This article presents results comparing students that do not explicitly discuss slopes in 3D with students that explicitly discuss slopes in 3D as a precursor to discussing derivatives in 3D. The results indicate that students may, in fact, have significant difficulty extending the concept of a 2D slope to a 3D slope. And that the explicit presentation of slopes in 3D as a precursor to the presentation of derivatives in 3D may significantly improve student comprehension of topics of differentiation in multivariable calculus.

     

The effects of service convenience and perceived quality on perceived value,satisfaction and loyalty in low-cost fitness centers

Due to its importance in fitness centers, a number of authors have explored and analyzed loyalty. However, two characteristics not yet examined are service convenience in fitness center chains and low-cost fitness centers (an emerging business model). In the present study, the authors sought to understand the relationship among perceived quality and service convenience on perceived value, satisfaction, and client loyalty in low-cost fitness centers. Clients (N = 763; 381 women and 382 men) from three low-cost Spanish fitness centers were surveyed, revealing a positive relationship among the variables studied. Findings demonstrate the importance of proper management of non-monetary sacrifices and perceived quality by the managers of these sport organizations, since client loyalty could depend on factors of these emerging sport models.     

Letter names, letter sounds and phonological awareness: an examination of kindergarten children across letters and of letters across children

In this study 149 kindergarten children were assessed for knowledge of letter names and letter sounds, phonological awareness, and cognitive abilities. Through this it examined child and letter characteristics influencing the acquisition of alphabetic knowledge in a naturalistic context, the relationship between letter-sound knowledge and letter-name knowledge, and the prediction of Grade 1 phonological awareness and word identification from these variables. Knowledge of letter sounds was better for vowels and for letters with consonant–vowel names than for those with vowel–consonant names or names bearing little relationship to their sounds. However, there were anomalies within each category reflecting characteristics of the individual letters. Structural equation modelling showed that cognitive ability, comprising receptive vocabulary, non-verbal reasoning, rapid automatized naming of colours, and phonological memory significantly contributed to alphabetic knowledge and phonological awareness. In turn, letter-name knowledge but not phonological awareness predicted letter-sound knowledge and subsequent reading skill.This research was supported by a grant from the Social Sciences and Humanities Research Council of Canada to the first author. Thank you is extended to the participating schools and children and to Ian Newby-Clark for his orientation to AMOS. Michelle Bell, Shelly Moretti and Jodi Page have since graduated from the University of Guelph     

The relative effects of university success courses and individualized interventions for students with learning disabilities

Little is known about the relative effects of post‐secondary learning services for students with learning disabilities. We compared outcomes for students with learning disabilities who selected to: (1) take an academic learning success course (course‐intervention), (2) have regular individual interventions (high‐intervention) or (3) use services only as needed (low‐intervention). Pre‐ and post‐test comparisons revealed improvements in academic self‐efficacy and academic resourcefulness for students in the course‐ and high‐intervention groups. The course‐intervention group also showed decreases in their failure attributions to bad luck and increases in their general repertoire of learned resourcefulness skills in comparison to the high‐intervention group and had significantly higher year‐end GPAs in comparison to the low‐intervention group. Here we find positive outcomes for students with learning disabilities taking a course that teaches post‐secondary learning and academic skills.     

The Reading–Spelling Connection: Developing and Evaluating a Beginning Spelling Intervention for Children at Risk of Reading Disability

Abstract In this article, we describe the development and evaluation of a beginning spelling intervention for young children at risk of reading disability. We first summarize the literature that supports beginning spelling as an ideal method for strategically integrating the beginning reading big ideas of phonemic awareness and alphabetic understanding. We then summarize the literature on effective instructional principles for students at risk of reading disability. Next, we describe how instructional design was applied to the development of an intervention for young children at risk of reading disability, then summarize the findings of an experimental study supporting the effectiveness of this intervention. Finally, we provide selected examples from the spelling intervention to illustrate the findings' translation into instructional practice.     

The power of learning in action learning: a conceptual analysis of how the five schools of adult learning theories are incorporated within the practice of action learning

Action learning has the ability to solve complex problems and to significantly increase the speed and quality of individual, team and organizational learning. Its theoretical base and relationship to adult learning orientations and the source of this power remain relatively unexplored. The authors conducted an extensive review of the literature in order to examine how each of the six critical components of an action learning program (namely; a problem or task, a group, the reflective inquiry process, action, learning, and an action learning coach) incorporates and applies five major adult learning schools (behaviorist, cognitivist, humanist, social and constructivist). An empirical example from the authors’ experience is presented to illustrate the extent and range in which action learning incorporates each of the five schools of adult learning.     

Writing in Mathematics: An Alternative Form of Communication for Academically Low‐Achieving Students

Abstract. Classroom communication figures prominently in current math reform efforts. In this study, we analyze how one teacher used writing to support communication in a seventh‐grade, low‐track mathematics class. For one school year, we studied four low‐achieving students in the class. Students wrote in journals on a weekly basis. Using classroom observations and interviews with the teacher, we developed profiles of the four students, capturing their participation in class discussions. The profiles highlighted an important similarity among the four students: marginal participation in both small‐group and whole‐class discussions. However, our analysis of the students' journals identified multiple instances where the students were able to explain their mathematical reasoning, revealing their conceptual understanding, ability to explain, and skill at representing a problem. In this respect, journals potentially facilitate another important form of classroom communication. The promise of writing is that it offers an alternative to the visions of classroom communication that are strictly oral in nature.