Working for learning: teaching assistants developing mathematics for teaching

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken in parallel with advancement through the hierarchical undergraduate mathematics curriculum. Lave and Wenger’s work on communities of practice is used as a framework to explore the TAs’ learning of mathematics alongside their professional work in schools. This case illustrates how and where institution-based undergraduate teaching relates to work in school, and where it does not, thus signalling the importance of the TAs’ informal learning strategies in bringing together these experiences.     

Capitalizing on advances in mathematics and k-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations

This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the instructional design theory of Realistic Mathematics Education and the social negotiation of meaning. The main results of the comparison study found no significant difference between project students and comparison students on an assessment of routine skills and a significant difference in favor of project students on an assessment of conceptual understanding. Given these encouraging results, the theoretical underpinnings of the innovative approach may be useful more broadly for undergraduate mathematics education reform.     

Development,Evaluation and Use of a Student Experience Survey in Undergraduate Science Laboratories: The Advancing Science by Enhancing Learning in the Laboratory Student Laboratory Learning Experience Survey

Student experience surveys have become increasingly popular to probe various aspects of processes and outcomes in higher education, such as measuring student perceptions of the learning environment and identifying aspects that could be improved. This paper reports on a particular survey for evaluating individual experiments that has been developed over some 15 years as part of a large national Australian study pertaining to the area of undergraduate laboratories—Advancing Science by Enhancing Learning in the Laboratory. This paper reports on the development of the survey instrument and the evaluation of the survey using student responses to experiments from different institutions in Australia, New Zealand and the USA. A total of 3153 student responses have been analysed using factor analysis. Three factors, motivation, assessment and resources, have been identified as contributing to improved student attitudes to laboratory activities. A central focus of the survey is to provide feedback to practitioners to iteratively improve experiments. Implications for practitioners and researchers are also discussed.     

Understanding how a case-based assessment instrument influences student teachers’ learning approaches

In order to stimulate student teachers to thoroughly comprehend the main variables influencing their work, teaching and assessment strategies in teacher education have changed significantly. One of the changes in the assessment of student teachers in teacher education programs is the use of case-based assessment instruments. Such instruments evaluate the extent to which student teachers are able to handle authentic problems. It is expected that implementing this mode of assessment will stimulate student teachers to adopt a deep approach to learning. In this study we examine student teachers’ learning approaches in the context of case-based assessment. Hereto, we investigated the direct effects of the student teachers’ general beliefs on the cognitive demands of assessment on their learning approaches. Also the student teachers’ perceptions of the cognitive demands of the case-based assessment instrument were considered as a mediating variable. The present study is conducted in the Netherlands, in the third year of a 4-year initial teacher training program for primary education. A case-based assessment instrument, called the OverAll Test, was implemented as the major determinate of the third-year final examination grade of the student teachers.     

Teacher help for conceptual level raising in mathematics

A field study with 16-year-old students in senior general secondary education was undertaken with the following research question: “Do students working in pairs on investigation tasks with the computer attain more conceptual level raising in mathematics when they are supported by a teacher who stimulates their interaction (process help) than when they are supported by a teacher who gives mathematical help (product help)?” Students in both conditions improved, but the two types of help showed no significant difference in level raising. Also, students in both conditions had serious problems with the learning materials, and wanted the teacher to explain and correct more. For students at this level of education, learning with investigation tasks in small groups appears to be very difficult.     

Challenges for collaborative blended learning in undergraduate students

This study reports a quasi-experiment in collaborative blended learning (CBL) with undergraduate students who, despite being in a world-leading, enriched digital environment, were new to collaboration and CBL. The mixed-methods research found that only small improvements to students’ CBL took place over time, and explanations for this are proffered. The study found that the students needed specific and intensive instruction, practice, and development in how to collaborate, both with and without blended learning. Students discovered and appreciated the benefits, pitfalls, and challenges to collaboration and CBL largely by doing it: learning from experience. Collaboration and CBL do not release teachers from their instructional and pedagogical roles; rather, they place teachers and face-to-face instruction and practice in collaboration and CBL in classrooms, at the heart of effective practice and improvements here. Implications for teaching are suggested.     

Developing a mathematics curriculum to improve learning behaviors and mathematics competency of children

The authors investigated the effect of a mathematical curriculum (CU) developed based on verbal and practical activities on the mathematical competency (MC) and learning behaviors (LB) of preschool children. In a quasi-experimental design, 60 children (5- to 6-year-old girls) were selected using the accessible sampling method. The children were randomly divided into an experimental group and a control group, and the relevant concepts were taught to the children in both groups. While the control group received the typical kindergarten education based on the usual textbooks and worksheets, the CU was taught to the experimental group. Structural equation modeling was used to model the data and statistical evaluation. The results demonstrated a significant difference between the two groups in MC and LB. The CU significantly improved MC directly, and indirectly through the improvement of LB (i.e., engagement and learning focus, verbal behaviors, and type of activity).     

Student activity and learning outcomes in a virtual learning environment

The aim of the study was to explore the relationship between degree of participation and learning outcomes in an e-learning course on medical informatics. Overall activity in using course materials and degree of participation in the discussion forums of an online course were studied among 39 medical students. Students were able to utilise the course material in discussion groups focusing on the lectures, quizzes and students’ own notes. Each student’s data recording of activities and individual participation in discussion in the online course was analysed in order to assess which activities predicted learning outcome. Higher course grades were associated with studying the course material frequently and also with regular participation in reading postings and replying to them. There were no connections between learning outcome and the students’ original contributions to the discussion forums. There were no statistically significant differences between male and female students in how they utilised the various components of the learning material.     

Formative assessment in mathematics for engineering students

In this paper, we present a range of formative assessment types for engineering mathematics, including in-class exercises, homework, mock examination questions, table quizzes, presentations, critical analyses of statistical papers, peer-to-peer teaching, online assessments and electronic voting systems. We provide practical tips for the implementation of such assessments, with a particular focus on time or resource constraints and large class sizes, as well as effective methods of feedback. In addition, we consider the benefits of such formative assessments for students and staff.     

Assessment for learning: using programmatic assessment requirements as an opportunity to develop information literacy and data skills in undergraduate students

Departments and programmes in higher education are required to participate in an increasing number of programme, course and student assessments. These assessment requirements are also opportunities to develop student skills related to scientific literacy and research, if students are included in the process of developing, administering and interpreting these assessments. This paper describes a course designed to build student research skills through incorporating undergraduate students into the process of programme review for a psychology department, a comprehensive assessment required of this department every five years. This course proved to be an effective way to engage students, as students developed and administered assessment surveys, analysed and interpreted results, and prepared both a professional report for the department as well as a research presentation. The paper discusses recommended course activities, and shows how this opportunity can benefit students and faculty in a myriad of ways.     

Learning a practice through practise: presenting knowledge in doctoral spoken presentations

Learning to ‘become doctor’ requires PhD candidates to undertake progressive public displays – material and social – of knowledge. Knowledge in doctoral pedagogy is primarily realised textually, with speaking and writing remaining as the primary assessment rubrics of progress and of the qualification. Participating textually begins, in a public sense, with the Confirmation of Candidature presentation/paper and culminates in a Viva Voce/dissertation. Drawing on linguistic ethnographic observations and analyses, this paper uses practice-based perspectives to examine a doctoral candidate practising to present knowledge publicly in a university research centre. The paper focuses on sociomaterial shifts in the trial run and final delivery of the two presentations examining how the candidate is initiated into new actions in response to these changes. Findings reveal how the candidate engages with collective understandings of the practice of presenting knowledge provided by feedback from her doctoral ‘friends’. Learning a practice through practise highlights the importance of participating as learning and learning as participating. This is particularly so in a time of change for doctoral pedagogy, when honing a practice collectively is argued to be advantageous in a localised setting that recognises and fosters the benefits of participation.     

The effects of cooperative learning on Turkish elementary students’ mathematics achievement and attitude towards mathematics using TAI and STAD methods

This study was designed to compare the effects of Team Assisted Individualization (TAI) and Student Teams-Achievement Divisions (STAD) on fourth grade students’ academic achievement in and attitudes towards mathematics. Seven classes of a school were randomly selected for this experimental study. Two of these were given instruction through TAI; two through STAD, and the remaining three were treated as a control group. For the purpose of the data analysis regarding academic achievement, the 3 X 1 covariance analysis was used to compare the groups. As a result of this comparison, both the TAI and STAD methods were found to have positive effects (d = 1.003 for TAI and d = 0.40 for STAD) on students’ academic achievement in mathematics. The pairwise comparisons showed that the TAI method had a more significant effect than the STAD method. The scores for the attitude towards mathematics were analyzed by using non-parametric statistics. As a result of this analysis, no significant difference was observed regarding students’ attitudes towards mathematics.     

Collaborative research for assessment for learning

This paper reports on a collaborative research study between three secondary teachers and two university researchers, initiated by the teachers, into the practice and impacts of assessment for learning in science, geography and history classes. The research provides insights into how teachers and researchers can collaborate to develop a research and practice agenda. The study illustrates the need for a dynamic interconnection between the personal, micro or school-related level and the macro or policy level factors. The findings highlight the importance of external support, shared teacher knowledge and beliefs, professional experimentation, and shared reflection on student responses to classroom innovations.     

Mathematics achievement and mathematics learning strategies: Cognitive competencies and construct differentiation

Responding to a survey requires cognitive abilities similar to those for any other linguistic task. We argue that, when faced with a cognitively challenging task, individuals respond by simplifying the task, declining it, or performing it poorly. Using the 2003 Program for International Student Assessment (PISA 2003) data sets, we document that the extent of construct differentiation in students’ mathematics learning strategies is strongly associated with their level of mathematics achievement. Likewise, the higher the level of mathematics achievement, the lower is the probability of a non-response to the mathematics learning strategy questions. Finally, the higher the students’ level of mathematics achievement, the more varied were their responses to the learning strategies items. These associations were examined across 40 participating countries.     

Blogging as a social medium in undergraduate courses: Sense of community best predictor of perceived learning

The purpose of the study was to examine pre-service teachers' sense of community, perception of collaborative learning, and perceived learning. Fifty pre-service teachers from two undergraduate ICT courses which incorporated blogs participated in this study. The data were obtained via three online questionnaires (Collaborative Learning scale, Sense of Community scale, and Perceived Learning scale) administered throughout Fall 2009-2010. The research questions were answered by using Pearson Product-Moment Correlation and multiple linear regressions. Results indicated that the pre-service teachers had positive feelings about the collaborative learning and perceived learning; also, they had moderate feelings related to sense of community in the classes which incorporated blogs. Additionally, to a great extent sense of community and to a much lesser extent of computer knowledge level were the predictors of explaining their learning perceptions.     

Learning mathematics for teaching in the student teaching experience: two contrasting cases

Student teaching (guided teaching by a prospective teacher under the supervision of an experienced “cooperating” teacher) provides an important opportunity for prospective teachers to increase their understanding of mathematics in and for teaching. The interactions between a student teacher and cooperating teacher provide an obvious mechanism for such learning to occur. We report here on data that is part of a larger study of eight student teacher/cooperating teacher pairs, and the core themes that emerged from their conversations. We focus on two pairs for whom the core conversational themes represent disparate approaches to mathematics in and for teaching. One pair, Blake and Mr. B., focused on controlling student behavior and rarely talked about mathematics for teaching. The other pair, Tara and Mr. T., focused on having students actively participating in the lesson and on mathematics from the students’ point of view. These contrasting experiences suggest that student teaching can have a profound effect on prospective teachers’ understanding of mathematics in and for teaching.

A case study: Problem-based learning for civil engineering students in transportation courses

This paper describes two case studies where problem-based learning (PBL) has been introduced to undergraduate civil engineering students in University College Dublin. PBL has recently been put in place in the penultimate and final year transport engineering classes in the civil engineering degree in University College Dublin. In this case study, the paper describes how PBL was introduced, the impacts of its introduction and the feedback received by students regarding PBL. PBL was introduced in these years to help students to become deep and active learners and to help them in the transition from passive note taker to researcher and lifelong learner.