Open, Online, Calculus Help Forums: Learning About and From a Public Conversation

This study is an exploration of participation, community, and mathematical understanding in an open, online, calculus help forum. These forums, populated by members from around the world, are locations where students post queries from their coursework and receive assistance from volunteer tutors. The site under investigation has a spontaneous participation structure, meaning that any forum member can respond to a query and contribute to an ongoing discussion. From earlier work, we know that such forums foster mathematical dialogue, contain exchanges with sophisticated pedagogical moves, and exhibit a strong sense of community. In this study, we delve deeper into the functional aspects of activity (such as student positioning and pedagogical moves), the benefits that accrue from participation in tutoring as a communal activity, and the mathematical understanding that is evident in the way problems on limit and related rates are framed and solutions constructed. Based on an observational methodology, we find that the forum provides tutoring for students and support for tutors that is unique from our expectations of other learning environments, such as one-on-one tutoring and computer-based tutoring systems. Students position themselves with authority in the exchanges by making assertions and proposals of action, questioning or challenging others' proposals, and indicating when resolution has been achieved. Tutors, who generally have more experience and expertise than students, provide mathematical guidance, and, in exemplary exchanges, draw the student into making a mathematical discovery. The dedication of tutors to the forum community was evident in the presence of authentic, honest mathematical practices, in the generous provision of alternative perspectives on problems, and in the sincere correction of errors. Some student participants picked up on these aspects of community and expressed excitement and appreciation for this taste of mathematical discourse. The primary contribution of the tutors was their assistance in supporting students as they constructed productive framings for the exercises, and this was the help that students were most in need of. As a result of eavesdropping on this public conversation, we conclude that the forums are a public conversation that should be listened to by educational researchers, teachers, and designers of tutoring systems

Enhancing Free-text Interactions in a Communication Skills Learning Environment

Learning environments frequently use gamification to enhance user interactions.Virtual characters with whom players engage in simulated conversations often employ prescripted dialogues; however, free user inputs enable deeper immersion and higher-order cognition. In our learning environment, experts developed a scripted scenario as a sequence of potential actions, and we explore possibilities for enhancing interactions by enabling users to type free inputs that are matched to the pre-scripted statements using Natural Language Processing techniques. In this paper, we introduce a clustering mechanism that provides recommendations for fine-tuning the pre-scripted answers in order to better match user inputs

Using open ended, ill formed problems to develop and assess Engineering Mathematics competencies.

The purpose of this paper is to report upon how an engineering mathematics class was used to provide a vehicle for students to develop mathematical competencies and hence higher order thinking skills within the broader field of engineering education. Specifically it provided students with the opportunities to think mathematically, reason mathematically, pose and resolve mathematical problems, to use technology to model resolutions, interpret and handle mathematical symbolism and to communicate their resolutions to peers and staff. Using the report produced by the Mathematics Working Group of SEFI (European Society for Engineering Education), which details a framework for mathematics curricula in engineering education (SEFI, 2013), a methodology was identified. This methodology was also based on work previously undertaken by the author (Peters, 2017; Peters, 2015). In section 2.1 (p 13) the report lists and describes a set of eight mathematical competencies: (1) Thinking mathematically, (2) reasoning mathematically, (3) posing and solving mathematical problems, (4) modelling mathematically, (5) representing mathematical entities, (6) handling mathematical symbols and formalism, (7) communicating in, with, and about mathematics and, (8) making use of aids and tools. The report also points out the importance of developing assessment procedures pertinent to competency acquisition (p7). The evidence from this investigation concludes that the majority of students found the experience challenging but worthwhile. They considered they had learnt important skills including the ability to form assumptions, persistence, time management, project management and an enhancement of their mathematical skills in relation to engineering

Developing an Online Learning Community: A Strategy for Improving Lecturer and Student Learning Experiences

Many researchers and practitioners are appealing for more innovative approaches where online lecturer use of technology is guided by a clear philosophy of learning to engage students in more meaningful learning. This research aimed to better understand teaching and learning in an online learning environment through the development and application of an appropriate pedagogical framework to facilitate successful learning experiences. To achieve this aim, a qualitative interpretive methodology was adopted to case study an online lecturer and his 14 students' experiences in a semester long fully online asynchronous graduate Research Methods course in a New Zealand tertiary institution. The study had three phases. Phase 1, the Review Phase, was a baseline survey to elicit the views of various online lecturers and their students on the nature of online learning and how learning can be successfully facilitated in such environments. The findings and recommendations from the literature led to identifying five guiding principles to frame the development of a pedagogical intervention. The principles, which map onto five key sociocultural ideas, depict learning as a mediated, situated, distributed, goal-directed and participatory activity within a socially and culturally determined learning community. Phase 2, the Designing the Intervention and Implementation Phase, concerned designing an intervention to facilitate student learning experiences. An emergent and iterative strategy, the negotiated intervention strategy, framed the collaborative design process used by the researcher to work with the case study lecturer. Teaching strategies supporting each of the guiding principles were shared with the lecturer, planned for and implemented in the case study course. Phase 3, the Evaluation Phase, examined how successful the intervention was in terms of three planes of participant development: personal, interpersonal and community. The key findings from this research highlight successful online teaching and learning experiences as involving active and changing participation in a learning community. This participation is framed and shaped by the use of authentic and relevant tasks that situate activity; interaction and teamwork to tap into cognition as distributed; goal-directed activities; and Web-based technological tools and activities to mediate action. Participation is realised through the kinds of roles members of the community adopt in support of intellectual, social and emotional development over time. Overall, the findings confirm the value of a sociocultural approach in the design and facilitation of online learning experiences. The notion of participation in a learning community through the adoption of different roles provides a useful orientation for understanding lecturer and student responsibilities and strategies to serve different purposes of teaching and learning. These ideas inform our understanding of appropriate conditions for successful teaching and learning and have important implications for guiding teaching-learning practices in online learning environments

Online collaborative learning in tertiary ICT education to enhance students' learning in Malaysia

This study investigated the nature of students’, and student group, interactions through the incorporation of an online collaborative learning (OCL) initiative, with its aim to enhance students’ learning in a Malaysian tertiary classroom. In order to contribute to knowledge and understanding about the nature and quality of OCL, the learning processes and outcomes were drawn predominantly from Harasim’s model, with inclusion of a socio-cultural framework aimed at enhancing learning outcomes for undergraduate science and ICT education students. Harasim’s model of OCL that was used in the intervention includes steps to setting up the stage and a system for Idea Generating (IG), modeling and guiding the OCL discussions for Idea Organizing (IO), and evaluating and reflecting the OCL discussions for Intellectual Convergence (IC). The interactions in OCL were analysed through four dimensions: participative, interactive, social, and cognitive in support of the students’ cognitive, social and emotional development. The OCL intervention in this study was conducted through an ICT education course in a Malaysian university that required OCL discussions for 13 weeks: the first four weeks were intra-group work discussions (Task 1), followed by four/five weeks of inter-group work discussions (Task 2), and the remaining four weeks were for the final intra-group work discussions (Task 3). The OCL intervention was aimed at facilitating interdisciplinary collaboration and interaction between students from Chemistry, Physics and Mathematics majors through the university’s Learning Management System (Moodle), which provided the shared space for the OCL discourse and tools for collaboration. A total of nine groups of four to six students (N=46) were involved in this study. In order to evaluate the OCL intervention using a holistic view, an interpretive approach that included the collection of quantitative and qualitative data was adopted to frame the collection and analysis of the data. Quantitative data were obtained from online questionnaires, together with online data based on the frequency of students’ posts in participative, interactive, social, and cognitive dimensions. Qualitative data were gathered via interviews with students (group and post-course interviews) and lecturers, and online transcripts that included online postings and students’ online journal entries. These data were collected and analysed in order to triangulate the findings and to help the researcher assess the extent to which the intervention was successful in enhancing students’ learning. The findings from the study revealed the nature of students’ interactions in OCL correspond with particular socio-cultural views that students’ interactions are characterised based on the participative, interactive, social and cognitive dimensions in support of the students’ cognitive, social and emotional development. From a socio-cultural perspective, the outcomes that arose from the study included: • The socio-cultural learning constructs have been useful as a framework for the analysis of the OCL intervention based on the participative, interactive, social and cognitive dimensions. • The affordances of the OCL group work helped the students’ in their group work. • The constraints of OCL influence the communication methods, and interaction styles used by students in achieving task goals through group work in the OCL intervention. The findings also show students’ interactions and student group interactions were an important part of the learning process. The implementation of OCL intervention into the course can lead to the facilitation of the student group learning process as well as supporting their cognitive, social and emotional development, and potential constraints from the technology (e.g. Internet connection) or the lack of social and verbal cues (e.g. facial expression) can lead to different working methods of communication for achieving task goals and different styles of interactions. Overall, the findings of the study indicate the value of OCL in a tertiary classroom to enhance learning