Online Education: What Works in Mathematics

Florida State University and University of Helsinki Information technology has the potential to deliver education to everybody by high quality online courses and associated services, and to enhance traditional face-to-face instruction by, e.g., web services offering virtually unlimited practice and step-bystep solutions to practice problems. Regardless of this, tools of information technology have not yet penetrated mathematics education in any meaningful way. This is mostly due to the inertia of academia: instructors are slow to change their working habits. This paper reports on an experiment where all the instructors (seven instructors and six teaching assistants) of a large calculus course were required to base their instruction on online content. The paper will analyze the effectiveness of various solutions used, and finishes with recommendations regarding best practices.

How education should link with career paths

How good is your pharmacy practice? And what does “good” look like? Take a look back at the education and training you have received in your career to date. Has it stood you in good stead? Certainly there is a need to establish a model of professional education and development that produces good pharmacists — you should be able to demonstrate your competence regardless of your sector of work. It may help if we move away from the view that excellence in pharmacy practice is primarily defined by where you practise and the kind of job that you do. The Modernising Pharmacy Careers programme’s aspirations to integrate the undergraduate degree with the preregistration training year are bold and to be applauded — provided the outcome delivers changes that are more than superficial. The new model needs to deliver greater integration of education with practice, while retaining an adequate science base. Theory should be put into the context of practice-based, cross-sector learning needs and opportunities. For example, is the classroom really the best environment in which to learn dispensing? Pharmacokinetic theory could be put into context through creatively designed work placements. And it might make more sense to learn patient counselling in a community pharmacy, and so on. Is it resources we lack to make this happen? Or do we lack the collective will to be imaginative, to be radical and to conceive new approaches to professional education? Implicit in this new approach to education is the expectation that pharmacists should teach and mentor and, conversely, that those who teach should also engage in relevant practice. University education must produce graduates whose knowledge and competence are useful to employers. Moreover, graduates must be adequately prepared to enter any area of the profession endowed with professional self-confidence (something, arguably, that needs further development within the pharmacy psyche). Of course, becoming qualified is just the beginning. Post-qualification, pharmacists need structured career paths that foster this professional confidence, support learning and ensure recognition. To this end, the Royal Pharmaceutical Society-led professional curriculum group is working to define knowledge, skills and experience for all areas of advanced practice. More than ever, the profession needs to adopt a culture of learning, teaching and practice research that is unified. The question is: how do we move away from merely collecting qualifications (trophies) to developing meaningful careers? Pharmacists in all areas and at all levels of the profession need to consider their own willingness to make this shift. The RPS and MPC are leading the way, but are we following?

The development, application, and implications of a strategy for reflective learning from experience

The problem on which this study focused was individuals' reduced capacity to respond to change and to engage in innovative learning when their reflective learning skills are limited. In this study, the preceding problem was addressed by two primary questions: To what degree can mastery of a strategy for reflective learning be facilitated as a part of an academic curriculum for professional practitioners? What impact will mastery of this strategy have on the learning style and adaptive flexibility of adult learners? The focus of the study was a direct application of human resource development technology in the professional preparation of teachers. The background of the problem in light of changing global paradigms and educational action orientations was outlined and a review of the literature was provided. Roots of thought for two key concepts (i.e., learning to learn from experience and meaningful reflection in learning) were traced. Reflective perspectives from the work of eight researchers were compared. A meta-model of learning from experience drawn from the literature served as a conceptual framework for the study. A strategy for reflective learning developed from this meta-model was taught to 109 teachers-in-training at Florida International University in Miami, Florida. Kolb's Adaptive Style Inventory and Learning Style Inventory were administered to the treatment group and to two control groups taught by the same professor. Three research questions and fourteen hypotheses guided data analysis. Qualitative review of 1565 personal documents generated by the treatment group indicated that 77 students demonstrated "double-loop" learning, going beyond previously established limits to perception, understanding, or action. The mean score for depth of reflection indicated "single-loop" learning with "reflection-in-action" present. The change in the mean score for depth of reflection from the beginning to end of the study was statistically significant (p $<$.05). On quantitative measures of adaptive flexibility and learning style, with two exceptions, there were no significant differences noted between treatment and control groups on pre-test to post-test differences and on post-test mean scores adjusted for pre-test responses and demographic variables. Conclusions were drawn regarding treatment, instrumentation, and application of the strategy and the meta-model. Implications of the strategy and the meta-model for research, for education, for human resource development, for professional practice, and for personal growth were suggested. Qualitative training materials and Kolb's instruments were provided in the appendices.

The effects of Chinese painting appreciation education on the artistic achievement of junior high school students in Taiwan

For the Chinese, fine art is one of the most important items in human life. The goals of fine arts education enhance the student so that s/he can make reasonable judgments about work, gain knowledge of color and understand the process of designing environmental layouts. Related technique and creativity training are offered students in accordance with individual differences and social expectations.^ Traditionally, Taiwan's junior high school fine art program teaches mainly painting technique. The Ministry of Education in Taiwan determines the curriculum of junior high school fine art education. The purpose of this study was to determine the effects of teaching Chinese painting appreciation on the artistic achievements of junior high school students in Taiwan. The subjects were seventh grade students who had never learned Chinese painting before. Two classes were randomly chosen from each target school and were designated as the experimental or control group. Instruction in all groups was delivered by the researcher himself. At the end of the study, data about subjects' related knowledge, creative technique, and feeling toward Chinese painting were systematically collected and analyzed.^ The result of the study was that students in the experimental group were more motivated to learn Chinese painting than were the students in the control group. Students in the experimental group made better progress in the development of creative skill, had better critical ability, and demonstrated better performance in Chinese painting form, set up, stroke and color of related knowledge than did students in the control group. It was therefore concluded that Chinese painting appreciation education can promote better artistic achievement and that this approach should be used in other areas of art education. ^

A distance education case study: A comparison of instructional delivery methods practiced by higher education faculty and emerging standards

The purpose of this research was to compare the delivery methods as practiced by higher education faculty teaching distance courses with recommended or emerging standard instructional delivery methods for distance education. Previous research shows that traditional-type instructional strategies have been used in distance education and that there has been no training to distance teach. Secondary data, however, appear to suggest emerging practices which could be pooled toward the development of standards. This is a qualitative study based on the constant comparative analysis approach of grounded theory.^ Participants (N = 5) of this study were full-time faculty teaching distance education courses. The observation method used was unobtrusive content analysis of videotaped instruction. Triangulation of data was accomplished through one-on-one in-depth interviews and from literature review. Due to the addition of non-media content being analyzed, a special time-sampling technique was designed by the researcher--influenced by content analyst theories of media-related data--to sample portions of the videotape instruction that were observed and counted. A standardized interview guide was used to collect data from in-depth interviews. Coding was done based on categories drawn from review of literature, and from Cranton and Weston's (1989) typology of instructional strategies. The data were observed, counted, tabulated, analyzed, and interpreted solely by the researcher. It should be noted however, that systematic and rigorous data collection and analysis led to credible data.^ The findings of this study supported the proposition that there are no standard instructional practices for distance teaching. Further, the findings revealed that of the emerging practices suggested by proponents and by faculty who teach distance education courses, few were practiced even minimally. A noted example was the use of lecture and questioning. Questioning, as a teaching tool was used a great deal, with students at the originating site but not with distance students. Lectures were given, but were mostly conducted in traditional fashion--long in duration and with no interactive component.^ It can be concluded from the findings that while there are no standard practices for instructional delivery for distance education, there appears to be sufficient information from secondary and empirical data to initiate some standard instructional practices. Therefore, grounded in this research data is the theory that the way to arrive at some instructional delivery standards for televised distance education is a pooling of the tacitly agreed-upon emerging practices by proponents and practicing instructors. Implicit in this theory is a need for experimental research so that these emerging practices can be tested, tried, and proven, ultimately resulting in formal standards for instructional delivery in television education. ^

Intuition as it relates to curriculum, instruction, and resulting academic success in elementary school

Regardless of the fact that children learn in significantly different ways, most curriculum and instruction are guided by the idea that sequential organization of the material to be learned is the best and most efficient way of presenting information to children. Children who learn and think intuitively are denied their preference, forced to conform to the sequential nature of the curriculum and instruction. Based on the theory of psychological type, this study sought to identify any relationship between a student's cognitive style of learning, either Sensing or Intuitive, and his/her academic success in elementary school. The Murphy-Meisgeier Type Indicator for Children was used to identify the cognitive style of students in grades two through eight in a small, private, parochial school. Scores on a standardized achievement test and grades were then analyzed to see if there was a relationship of cognitive style to grades and achievement test scores. Also, the researcher investigated whether or not the teacher's cognitive style had any relationship to students' cognitive style and academic achievement. Although none of the results was statistically significant, the achievement test scores indicated that Sensing students score higher in reading, mathematics concepts, and mathematics computation. However, Intuitive students had higher mean grades in reading and language arts, and virtually equal means mathematics concepts and computation. It was also found that all students, both Sensing and Intuitive, had higher mean grades in the classes of Intuitive teachers. ^