Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Delays between the onset of symptoms and first rheumatology consultation in patients with rheumatoid arthritis in the UK: an observational study

Objective To investigate delays from symptom onset to rheumatology assessment for patients with a new onset of rheumatoid arthritis (RA) or unclassified arthritis. Methods Newly presenting adults with either RA or unclassified arthritis were recruited from rheumatology clinics. Data on the length of time between symptom onset and first seeing a GP (patient delay), between first seeing a general practitioner (GP) and being referred to a rheumatologist (general practitioner delay) and being seen by a rheumatologist following referral (hospital delay) were captured. Results 822 patients participated (563 female, mean age 55 years). The median time between symptom onset and seeing a rheumatologist was 27.2 weeks (IQR 14.1–66 weeks); only 20% of patients were seen within the first 3 months following symptom onset. The median patient delay was 5.4 weeks (IQR 1.4–26.3 weeks). Patients who purchased over-the-counter medications or used ice/heat packs took longer to seek help than those who did not. In addition, those with a palindromic or an insidious symptom onset delayed for longer than those with a non-palindromic or acute onset. The median general practitioner delay was 6.9 weeks (IQR 2.3–20.3 weeks). Patients made a mean of 4 GP visits before being referred. The median hospital delay was 4.7 weeks (IQR 2.9–7.5 weeks). Conclusion This study identified delays at all levels in the pathway towards assessment by a rheumatologist. However, delays in primary care were particularly long. Patient delay was driven by the nature of symptom onset. Complex multi-faceted interventions to promote rapid help seeking and to facilitate prompt onward referral from primary care should be developed

A direct heuristic algorithm for linear programming

An O(n^{\mathrn{3}}) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure

Solving linear differential equations as a minimum norm least squares problem with error-bounds

Linear ordinary/partial differential equations (DEs) with linear boundary conditions (BCs) are posed as an error minimization problem. This problem has a linear objective function and a system of linear algebraic (constraint) equations and inequalities derived using both the forward and the backward Taylor series expansion. The DEs along with the BCs are approximated as linear equations/inequalities in terms of the dependent variables and their derivatives so that the total error due to discretization and truncation is minimized. The total error along with the rounding errors render the equations and inequalities inconsistent to an extent or, equivalently, near-consistent, in general. The degree of consistency will be reasonably high provided the errors are not dominant. When this happens and when the equations/inequalities are compatible with the DEs, the minimum value of the total discretization and truncation errors is taken as zero. This is because of the fact that these errors could be negative as well as positive with equal probability due to the use of both the backward and forward series. The inequalities are written as equations since the minimum value of the error (implying error-bound and written/expressed in terms of a nonnegative quantity) in each equation will be zero. The minimum norm least-squares solution (that always exists) of the resulting over-determined system will provide the required solution whenever the system has a reasonably high degree of consistency. A lower error-hound and an upper error-bound of the solution are also included to logically justify the quality/validity of the solution

Quantitative Reasoning and Its Role in Interdisciplinarity

The Real Science, Technology, Engineering Mathematics (STEM) Project was conducted in middle schools and high schools in Georgia, USA. The project supported the development of interdisciplinary STEM modules and courses in over 20 schools. A project focus was development of five 21st century STEM reasoning abilities. In this chapter, I provide classroom activities from the Real STEM project that exemplify each form of reasoning: complex systems; model-based; computational; engineering design-based; and quantitative reasoning. Quantitative reasoning plays a critical role in authentic real-world interdisciplinary STEM problems, providing the tools to construct data informed arguments specific to the problem context, which can be debated, verified or refuted, modeled mathematically and tested against reality. Yet quantitative reasoning is often misrepresented, underdeveloped, and ignored in STEM classrooms. The chapter finishes with a discussion of the impact of Real STEM