Tracy S. Craig

Learning as acquiring a discursive identity through participation in a community: improving student learning in engineering education

In this paper, we propose that learning in engineering involves taking on the discourse of an engineering community, which is intimately bound up with the identity of being a member of that community. This leads to the notion of discursive identity, which emphasises that students’ identities are constituted through engaging in discourse. This view of learning implies that success in engineering studies needs to be defined with particular reference to the sorts of identities that students develop and how these relate to identities in the world of work. In order to achieve successful learning in engineering, we need to recognise the multiple identities held by our students, provide an authentic range of engineering-related activities through which students can develop engineering identities and make more explicit key aspects of the discourse of engineering of which lecturers are tacitly aware. We include three vignettes to illustrate how some of the authors of this paper (from across three different institutions) have applied this perspective of learning in their teaching practice.

Categorization and analysis of explanatory writing in mathematics

The aim of this article is to present a scheme for coding and categorizing students’ written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students’ written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students’ level of engagement with the mathematical material and with their stance towards knowledge.

Conceptions of mathematics and student identity: implications for engineering education

Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students’ conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically important as they can impact on student learning and have the potential to influence how and what we teach. As part of ongoing longitudinal research into the experience of a cohort of students registered at the authors institution, students’ conceptions of mathematics were determined using a coding scheme developed elsewhere. In this article, I discuss how the cohort of students choosing to study engineering exhibits a view of mathematics as conceptual skill and as problem-solving, coherent with an accurate understanding of the role of mathematics in engineering. Parallel investigation shows, however, that the students do not embody designated identities as engineers.

Proficiency in the multiplicative conceptual field : using Rasch measurement to identify levels of competence

Abstract In the transition years, Grades 7 to 9, the shift from natural numbers to rational numbers and the associated multiplicative concepts prove challenging for many learners. The new concepts, operations and notation must be mastered if the student is to thereafter rise to meet the challenges of algebra and more advanced and powerful mathematics. The multiplicative conceptual field (MCF) groups together such concepts as fraction, ratio, rate, percentage and proportion, all of which are related yet subtly distinct from one another, each with its own challenges. Rasch analysis allows us to compare the difficulty of mathematical problems located within the MCF while, on the same scale, locating the degree to which individual learners have mastered the necessary skill set. Such location of problems and learners on the same unidimensional scale allows for fine-grained analysis of which aspects of the problems being analysed make one problrm more difficult than another. Simultaneously the scale gives the teacher clear evidence of which students have mastered which concepts and skills and which have not, thereby allowing more targeted assistance to the class and individual learners. This paper illustrates the process involved in such analysis by reporting on results located within a larger study. It is suggested that implementing Rasch analysis within the school classroom on appropriately designed assessment instruments would provide clarity for the teacher on the locations of difficulty within the problems used in the assessment and the relative degree to which individual learners are achieving success at mastering the targeted concepts.

The role of expository writing in mathematical problem solving

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the effectiveness of using writing as a tool for deeper engagement with mathematical problems. Students’ claims about, and tutor observations of, problem-solving behaviour were analysed through the lens of Piagets theory of cognitive development. Examples of enhanced problem-solving behaviour are presented as well as reports from student interviews that writing ‘forces’ deeper engagement. The analysis of students’ work and their reflections indicated that writing about problem-solving processes potentially resulted in a cognitive perturbation when students were forced to confront their incomplete understanding (and hence their unstable knowledge structures) and therefore had to achieve a deeper level of understanding in order to adequately describe the solution process.

Challenging assumptions of notational transparency: the case of vectors in engineering mathematics

ABSTRACT The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing the components of a vector are discussed in historical and current context. Popular mathematical texts use the two notations as if they are transparent and interchangeable. In this research project, engineering students’ proficiency at vector analysis was assessed and the data were analyzed using the Rasch measurement method. Results indicate that the students found items expressed in unit vector notation more difficult than those expressed in parenthesis notation. The expert experience of notation as transparent and unproblematically symbolic of underlying processes independent of notation is shown to contrast with the student experience where the less familiar notation is experienced as harder to work with.

Language and Communication in Mathematics Education

The topic of “Language and Communication in Mathematics Education” covers a wide range of areas of interest, ranging from the question of what constitutes “language” in mathematics, through investigations of communicative interactions in mathematics classrooms and study of issues involved in teaching and learning mathematics in multilingual settings. This breadth was well represented in the papers accepted for presentation in the Topic Study Group at ICME12. In order to facilitate discussion, the paper presentations in each session were divided into two sets, with participants choosing which set to attend. This allowed the discussion to focus in greater depth on common themes. In addition, one session of the TSG was devoted to a panel discussion on the topic of “Theoretical and methodological issues in studying language in mathematics education” and a final plenary meeting enabled participants to reflect on the TSG as a whole, the common issues addressed, the lessons learnt and aspirations for future work on the topic. In this report, we present an overview of the major themes arising in the papers presented and in the discussions during the congress.

Elephant Delta 2015: Think Big!

The Southern Hemisphere Conferences on the Teaching and Learning of Undergraduate Mathematics and Statistics have been taking place (with slightly shifting names) since 1997, located in South Africa, New Zealand, Australia and Argentina. Otherwise known as ‘Delta’ conferences, the 2015 conference, the tenth of its name, is Elephant Delta, with the theme ‘Think Big!’ The papers included in this special issue resonate with that theme in their global scope, their grain size of engagement with knowledge generation and in their disciplinary scope across mathematics, statistics and finance. These few, select, papers together with the conference Proceedings as well as the presentations themselves in Port Elizabeth, South Africa, November 2015, will form a body of work representing the researchers within this Delta community, a community which indeed Thinks Big. In their paper, ‘Issues and trends: a review of Delta conference papers from 1997 to 2011’, Henderson and Britton [1] categorized Delta papers published in the International Journal of Mathematical Education Science and Technology (iJMEST) and the Proceedings. When making a call for reviewers for this issue, in expectation of submissions, we adapted and modified this classification as two different categories: Category I: Calculus; Linear Algebra; Differential Equations; Advanced Analysis; Abstract Algebra; Numerical Analysis; Discrete Mathematics; Modelling and Applications; Proof; Statistics; Geometry. Category II: Technology and Visual Learning; Teaching and Learning; General Pedagogy; Student Resources; Transition from High School to Tertiary; High School Topics; Learning Difficulties; Pre-service and In-service Teachers; Professional Development; Assessment. The papers submitted for this special issue and accepted after a process of peer review clearly could be tagged with these categories; however, we close our editorial with a suggestion of two additional categories. This special issue of the iJMEST comprises papers of a high standard from different scholars globally, reporting on their research. The nine papers published in this issue fall under different topics from both categories in the fields of engineering, finance, pure mathematics and statistics. With this issue, we have the opportunity to gain insight into what theoretical resources and new developments are currently of interest to the Delta community globally and the consequent opportunities for debate and further research. Each paper offers quite different insights from the others and we discuss them individually. The literature of mathematics and statistics education within the tertiary environment is frequently concerned with the first one or two years of mathematical studies, an emphasis which is understandable due to the larger classes at the earlier levels and challenges related to the school–university transition. It is always interesting, therefore, to read the literature on mathematics education at the more advanced level, as reported in Cornock’s paper on using Rubik’s cube to teach group theoretic concepts. The group theory module was a pure mathematics module presented to students studying applied sciences at Sheffield Hallam University. The abstract concepts of group theory were explored through use of the cubes,