Engaging Mathematics Students Through Undergraduate Research

Science education has a long history of engaging undergraduate students in inquiry-based learning. Every undergraduate student studying a scientific discipline has first hand experience with the application of scientific method and the technology and practice of their discipline (in the first instance, through their laboratory classes). Such classes are primarily educator-led and subject content-focused. Recent years have seen greater inclusion of student-led and research-focused activities across programs, as seen in Zoology in Edwards et al (2007) and in Chemistry and Physics in McDonagh et al (2011), for example. Mathematics is perhaps the only scientific discipline where this inclusion has yet to broadly manifest itself. This paper will describe how undergraduate research is being incorporated into experiences of third-year mathematics students. As suggested by Beckman and Hansel (2009), we will provide our own definition of undergraduate research as ‘an inquiry or investigation that is original in scope, of an experimental, a theoretical or a creative nature, undertaken in a rigorous manner by undergraduate students, that is open to public scrutiny, and that makes a contribution to a discipline(s)’. Here then, we seek to engage students with the full range of research activities, from the formulation of the research questions, to the dissemination of results. Further, students are empowered to lead the research in collaboration with each other and with the academic staff, with the product a publication in a peer-reviewed, international journal

Enhancing learning and measuring learning outcomes in mathematics using online assessment

In its narrowest form, ‘assessment’ seeks to measure the degree to which learning objectives have been met. In a broader context, it seeks to measure the achievement of graduate attributes. As such, assessment tasks should include life-like, authentic or situated activities (Cumming and Maxwell 1999). For many disciplines, including mathematics, computer technology can be seen as part of such a context. However, Englebrecht and Harding (2004) find that ‘many teachers of mathematics still shy away from granting technology the same significant role in the assessment process.’(p.218). This paper proposes that online assessment offers an authentic environment under which to assess computer laboratory skills in mathematics, and further, that careful attention to the design of online assessment tasks can enhance student learning

Steps toward mastery learning in a first year mathematics service subject

Student retention and progression have been identified as two of the most pressing concerns for higher education (Krause, Hartley, James and McInnis, 2005), and for of students of Science, Technology, Engineering and Mathematics (STEM) in particular (Universities Australia, 2012; Office of the Chief Scientist, 2012). These concerns are unlikely to lessen as “The emphasis of the higher education sector on the first year must intensify as the student population grows and diversifies” in response to government policy (James, Krause and Jennings, 2010, p72). Coincidentally, the research literature points to the fact that for a significant proportion of first-year students experiences are neither personally satisfying nor academically successful (McInnis, 2001; Tinto, 1993), and that “Missing from the literature are clear mechanisms for assisting or enabling the [first-year] transition” (Bowles et al, 2011, p64). It is proposed that the introduction of elements of mastery learning (if not mastery learning itself) into first-year mathematics subjects will go a long way to address these concerns. This paper describes and analyses the implementation of elements of mastery learning in a first year Mathematics service subject

Meeting expectations – a focus on professional practice in a final year undergraduate mathematics course

This paper argues that achievement of many of the attributes required of graduates in professional practice in operations research, or quantitative management science, can be developed best through a learning design that reflects current professional knowledge, skills and values. This necessarily places the focus of the learning design squarely on the student, with technology and communication at the nexus of the subject learning activities, and assessment tasks tailored to reflect this. The first steps in the examination of the effectiveness of this form of learning design are undertaken for a final year capstone subject in the Quantitative Management Science major in a Bachelor of Science program. This examination is undertaken from the perspective of students and teaching staff, through the analysis of discussions with students conducted at milestones throughout the semester. Positive student outcomes can be identified

Blended learning in a first year mathematics subject

This paper argues that the achievement of learning objectives for a first year mathematics subject, Operations Research Modelling, can be best fostered through a blended learning design. ‘Blended learning’ can be used in a variety of contexts. In this paper, the definition used is that of the integration of ‘traditional’ learning activities ─ lectures, tutorials, Mathematica and optimisation laboratories, and paper-based assessment tasks ─ with learning activities and environments more usually associated with other disciplines ─ collaborative learning, online assessment, peer review, cases studies, spreadsheet technology, and the information and communication technology, Blackboard. It is argued that a blended learning design includes learning activities that more closely mirror professional practice, and is more likely to encourage a deep approach to learning. Effectiveness of the blended learning design is examined from the perspective of students and teaching staff, through the analysis of responses to questionnaires and comments collected

Interacting Psycho-economic Expectations Ratios with Equity/debt Realities Suggests a Crisis Warning Method

The recent April 2011 meeting of the G20 countries considered possible development of a global early warning system to avoid any future financial crisis. Psycho-economic factors are strong drivers of greed, fear and non-rational behavior and experience shows that they should not be excluded from such a project. Rational, logical behavior for attitude and actions has been an assumption in most financial models prior to the advent of the 2008 crisis. In recent years there has been an increasing interest in relating financial activity to phenomena in physics, turbulence, neurology and recent fMRI experiments show that cortical interactions for decisions are affected by previous experience. We use an extension of two Lotka-Volterra (LV) interactive equations used in a model for the 2008 crisis but now with fluctuation theory from chemical physics to interact the two previously used heterogenous interacting agents, the psycho-economic ratio CE of investor expectations (favourable/unfavourable) and the reality ratio of equity/debt. The model provides a variable, M, for uncertainties in CE arising from the ability of the economy to affect the financial sector. A condition obtained for keeping rates of change in M small to avoid divergence of spontaneous fluctuations, provides a quantifiable time dependent entity which can act as a warning of impending crisis. The conditional expression appears to be related to an extension of Ohm's law as in a recently discovered "chip" and memory; the memristor. The possible role of subthreshold legacies in CE from the previous crisis appears to be possible and related to recent neurological findings

Rationale

Abstract: This paper argues that the achievement of learning objectives for a first year mathematics subject, Operations Research Modelling, can be best fostered through a blended learning design. ‘Blended learning ’ can be used in a variety of contexts. In this paper, the definition used is that of the integration of ‘traditional ’ learning activities ─ lectures, tutorials, Mathematica and optimisation laboratories, and paper-based assessment tasks ─ with learning activities and environments more usually associated with other disciplines ─ collaborative learning, online assessment, peer review, cases studies, spreadsheet technology, and the information and communication technology, Blackboard. It is argued that a blended learning design includes learning activities that more closely mirror professional practice, and is more likely to encourage a deep approach to learning. Effectiveness of the blended learning design is examined from the perspective of students and teaching staff, through the analysis of responses to questionnaires and comments collected