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In 2010 a mathematics curriculum was introduced in Irish second level schools entitled 'Project Maths' (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. ]. This paper aims to examine the performance of 1st year undergraduate students' procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students' skills in each area and findings demonstrated that students perform statistically significantly better in the procedural skills in mathematics when compared to problem solving skills. These findings raise concerns around the lack of anticipated improved problem solving skills of a cohort of students exposed to this style of teaching and learning. The paper raises discussion surrounding the intended and actual teaching and learning taking place in second level classrooms along with consideration for the potential role of learned helplessness and the literacy issues. Recommendations are made for follow up qualitative research with stakeholders in mathematics education to better understand the 'why' of the results presented here. [ABSTRACT FROM AUTHOR]

In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being made and how this lack of progress is resolved. The purpose here is to give some idea of how a research mathematician might approach a research level problem. We also propose that the problem under discussion is one of many problems that tertiary students can valuably tackle using a discovery-based approach as a means of using their mathematical content knowledge as well as learning to be creative. [ABSTRACT FROM AUTHOR]

In order to learn the concept of statistical techniques one needs to run real experiments that generate reliable data. In practice, the data from some well-defined process or system is very costly and time consuming. It is difficult to run real experiments during the teaching period in the university. To overcome these difficulties, statisticians developed simple and very economical experiments, which can be performed in the class by the students. Stone studied the variation, bias, stability and statistical quality control through the Blind Paper Cutting (BPC) experiment. In this article, the Blind Paper Cutting experiment is demonstrated on the basis of basic principles of experiment design. A BPC experiment is performed considering different factors, and important factors to optimise the response are identified through complete factorial design. The appropriate response model using important factors has been constructed. [ABSTRACT FROM AUTHOR]

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for computer programming technology use in the context of pure or applied mathematical investigation. We illustrate it by examining the engagement (scheme development) of an undergraduate student engaged in 'authentic' programming-based mathematical inquiry work, i.e. complete inquiry work as mathematicians would do. Two schemes are elaborated, namely the scheme of validating the programmed mathematics and the scheme of articulating in the programming language a mathematical process. Our discussion evidences some specific features of the programming language as artefact associated with a general aim of mathematical inquiry, in particular in terms of articulation between mathematics and programming. [ABSTRACT FROM AUTHOR]

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration. [ABSTRACT FROM AUTHOR]

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a group of linear algebra students' mistakes on a set of linear algebra questions. The paper also details an in-time intervention (a pedagogical approach) to enhance students' understanding of linear algebra concepts through advancing their set theory knowledge. Mathematics teachers can consider similar approaches to address their students' mistakes. [ABSTRACT FROM AUTHOR]

This paper reports on a practitioner study of a first-year undergraduate service course that aligns a web-based, student-lecturer communication system with the mathematical curriculum. The report presents and analyses data from students and from the lecturer and outlines the nature of the technical interface. The paper indicates how communication of the students' affective learning needs had a positive influence on the professional development of the lecturer himself. Furthermore, it is claimed that the success of mathematics/statistics teaching that integrates emotional responses from learners is intimately related to the knowledge, skills, beliefs and values of the lecturer. [ABSTRACT FROM AUTHOR]

Papers presented at earlier Delta conferences reported on the use of collaborative tutorials and peer-tutors in undergraduate mathematics courses at The University of Auckland. This paper reports on significant developments within the Department's programmes, including the extension of the collaborative small-class tutorials to cover all first-year undergraduate courses in the department. It provides evidence of the effectiveness of the tutorial programme, as gauged from a survey of students' perceptions. Many of the students enrolled in the Tutoring in Mathematics course that initially trains and provides the peer-group tutors continue on as tutors in other mathematics courses within the Department. Some subsequently enrol in the University's Graduate Diploma in Teaching (Secondary). The effects of the tutoring course on tutors continuing to tutor at higher levels, and their performances as novice teachers in the Diploma course are examined. [ABSTRACT FROM AUTHOR]

This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors' concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured to go through material quickly to cover all the required topics and intended pacing. Furthermore, our results suggest that both intended pacing and feelings of pressure are poor indicators of instructional practices. [ABSTRACT FROM PUBLISHER]

The article discusses papers within the issue adapted from the Southern Hemisphere Conferences on the Teaching and Learning of Undergraduate Mathematics and Statistics with topics such as engineering, finance and group theory.

Over the last two decades, many Australian universities have relaxed their selection requirements for mathematics-dependent degrees, shifting from hard prerequisites to assumed knowledge standards which provide students with an indication of the prior learning that is expected. This has been regarded by some as a positive move, since students who may be returning to study, or who are changing career paths but do not have particular prerequisite study, now have more flexible pathways. However, there is mounting evidence to indicate that there are also significant negative impacts associated with assumed knowledge approaches, with large numbers of students enrolling in degrees without the stated assumed knowledge. For students, there are negative impacts on pass rates and retention rates and limitations to pathways within particular degrees. For institutions, the necessity to offer additional mathematics subjects at a lower level than normal and more support services for under-prepared students impacts on workloads and resources. In this paper, we discuss early research from the First Year in Maths project, which begins to shed light on the realities of a system that may in fact be too flexible. [ABSTRACT FROM PUBLISHER]

Finance threshold concepts are the essential conceptual knowledge that underpin well-developed financial capabilities and are central to the mastery of finance. In this paper we investigate threshold concepts in finance from the point of view of students, by establishing the extent to which students are aware of threshold concepts identified by finance academics. In addition, we investigate the potential of a framework of different types of knowledge to differentiate the delivery of the finance curriculum and the role of modelling in finance. Our purpose is to identify ways to improve curriculum design and delivery, leading to better student outcomes. Whilst we find that there is significant overlap between what students identify as important in finance and the threshold concepts identified by academics, much of this overlap is expressed by indirect reference to the concepts. Further, whilst different types of knowledge are apparent in the student data, there is evidence that students do not necessarily distinguish conceptual from other types of knowledge. As well as investigating the finance curriculum, the research demonstrates the use of threshold concepts to compare and contrast student and academic perceptions of a discipline and, as such, is of interest to researchers in education and other disciplines. [ABSTRACT FROM PUBLISHER]

Graduates with well-developed capabilities in finance are invaluable to our society and in increasing demand. Universities face the challenge of designing finance programmes to develop these capabilities and the essential knowledge that underpins them. Our research responds to this challenge by identifying threshold concepts that are central to the mastery of finance and by exploring their potential for informing curriculum design and pedagogical practices to improve student outcomes. In this paper, we report the results of an online survey of finance academics at multiple institutions in Australia, Canada, New Zealand, South Africa and the United Kingdom. The outcomes of our research are recommendations for threshold concepts in finance endorsed by quantitative evidence, as well as a model of the finance curriculum incorporating finance, modelling and statistics threshold concepts. In addition, we draw conclusions about the application of threshold concept theory supported by both quantitative and qualitative evidence. Our methodology and findings have general relevance to the application of threshold concept theory as a means to investigate and inform curriculum design and delivery in higher education. [ABSTRACT FROM PUBLISHER]

At the University of Helsinki, special effort has been put to help beginning maths students to get started with their studies. This involves new ways of teaching a lecture course and new ways of giving peer support to the students. The results have been promising: the number of students passing certain important courses has been at least doubled compared to the earlier prevailing level. The present article describes the work done in connection to a lecture course and the thinking that lies behind it. A paper on peer support is planned. [ABSTRACT FROM AUTHOR]

This paper reports studies of the interaction between the intuitive, the formal and the procedural aspects in the processes of mathematical understanding of Peter, a first-year undergraduate of Mathematics. Using an activity and an interview, an attempt is made to analyse his mental operations. The way in which he handles visual-graphic representations in a problem of uniformly accelerating motion in order to reach mathematical conclusions and justify them with strict formal reasoning, making the transition from the intuitive assumptions to the mathematical argumentation, is studied. The 'focal analysis' of the interview's content allows for an in depth investigation of qualitative elements of the student's mathematical thought. The study of the cognitive operations through the interconnection of various theoretical perspectives may lead to teaching interventions in order to develop students' intuitive forces in a controlled manner, so that the formal mathematical thinking process can be promoted. This case study is part of a wider action research aiming to introduce first-year undergraduates to basic Calculus concepts. [ABSTRACT FROM AUTHOR]

It seems self-evident that there is a significant gap between secondary school and university mathematics, even though the gap may take different forms, which vary with different education systems in different places and at different times. This paper attempts to capture some common forms of this gap, and in particular, it discusses some core factors that are directly related to the nature of mathematics. Further, it also attempts to find ways to bridge the gap more easily and surely for students. [ABSTRACT FROM AUTHOR]

The transition (`gap') between secondary and tertiary education in mathematics is a complex phenomenon covering a vast array of problems and issues. The aim of this paper is to present the ways in which the issues of mathematics transition have been dealt with at McMaster University. Roughly, the process of transition has been broken into three stages: students' voluntary preparation for university mathematics courses facilitated by the Mathematics Review Manual; administration of Mathematics Background Survey; and redesign of the first-year Calculus (and subsequently, other mathematics courses). [ABSTRACT FROM AUTHOR]

This paper reports on a collaboration between three authors; two mathematicians in a Swedish university and a UK-based mathematics educator. The focus of the enquiry was the evaluation of the experience of Swedish first-year undergraduate engineers required, in their mathematics class, to learn to use the programming language Matlab . Students were interviewed and their responses compared with the intentions and expectations of lecturers. Students discerned a lack of clarity in course planning but also had many very sensible suggestions to make, the implementation of which would, they claimed, facilitate their learning. [ABSTRACT FROM AUTHOR]

Students' difficulty with reasoning and justification in the context of proofs in geometry has been well documented. Studies reveal that many of the ideas that students are asked to prove are known to be true, and therefore, the process of such proof is likely to remain meaningless and purposeless. The implication of this claim is that students need to be asked to prove mathematical assertions that are not known to them to be true. This puts an enormous responsibility on teachers. The purpose of this paper is to provide examples of 'non-traditional conjectures' that can be explored in the dynamic geometry environment of computer construction programs. [ABSTRACT FROM AUTHOR]

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of given improper integrals, but also intuitive questions and some paradoxical results too (for example, a figure with an infinite longitude which closes the same area as the unit circumference, or an infinite figure with a finite volume). In particular, the students were asked to interpret most of the results they had obtained. Answers given by the students to each of the questions were categorized, which allowed some initial conclusions to be reached regarding this research. From analyses carried out, one can conclude that there are students who have difficulties in articulating the different systems of representation, and have problems in connecting and relating this knowledge as a generalization of previous concepts, such as definite integrals, series and sequences. [ABSTRACT FROM AUTHOR]

The paper reports a compilation of results from three studies conducted over three years to determine students' conceptions of mathematics, and orientations they follow in learning the subject. Respondents were 459 first year mathematics students from four universities and one teacher college. Results indicated that more than half the sample reported mathematics to be a subject made of numbers and formulae that could be memorized. This suggests a shallow emphasis when learning the subject, with no intention to understand. However, most students passed their examinations. It was concluded that there was no statistically significant relationship between examinations results and students' learning orientations. It is recommended that lecturers should foster students' meta-learning capabilities and an awareness of different learning strategies. [ABSTRACT FROM AUTHOR]

The advancement of computer graphics in the past decade has contributed to an enormous change in the way mathematics is taught at the college level. Although Calculus has been the main benefactor of this advancement, the topic of ordinary differential equations has undergone fundamental changes in its curriculum in favour of the visual and numerical aspects of the course. This paper investigates students' acceptance of solving a differential equation geometrically. The setting is an introductory course on ordinary differential equations offered to engineering students, in which a reformed approach was adopted. Data were gathered from exams, and interviews were conducted with six students who volunteered to take part in the study. Results show that students initially showed reluctance to accept this geometric approach, but many of them eventually accepted it, appreciated its usefulness, and wished that other math courses be offered in a similar way. [ABSTRACT FROM AUTHOR]

In a recent survey Sutherland and Dewhurst itemized the extent to which various types of departments expected selected mathematical topics in the background of incoming undergraduates. Using the results of diagnostic tests it is possible to estimate the actual capability of students with given prior qualifications to provide a 'probable preparedness' in specific topics. This paper compares expectations with probable preparedness in a range of topics. It is found that while some departments have realistic expectations about the background of their incoming students, others seem over-optimistic about the mathematical knowledge of today's students. Sometimes, topics that the department actually requires must in fact be covered ab initio with the students that they recruit. [ABSTRACT FROM AUTHOR]

A research method consisting of written tests and individual interviews was introduced to examine first-year university students' understanding of fundamental calculus concepts. Six hundred and thirty students from three South African universities were subjected to the tests pertaining to this study. Several misconceptions underlying students' understanding of calculus concepts were identified. This paper deals mainly with some of the common errors and misconceptions relating to students' understanding of 'limit of a function' and 'continuity of a function at a point'. [ABSTRACT FROM AUTHOR]