Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.

Mathematics knowledge for teaching and the classroom environment

This study investigated the classroom environment in an underperforming mathematics classroom. The objectives were: (1) to investigate the classroom environment and identify influences upon it, and (2) to further explore those influences (i.e., teacher knowledge). This was completed using a diachronic case study approach in which data were gathered during lesson observations and coaching sessions. These data were analysed to describe and exemplify the classroom environment, then further described against forms of teacher knowledge. Conjectures regarding the importance of teacher knowledge of content were made which formed a base for developing a model of teacher planning and pedagogy.

STEM: Challenges and opportunities for mathematics education

Climbing Mountains, Building Bridges is a rich theme for exploring some of the “challenges, obstacles, links, and connections” facing mathematics education within the current STEM climate (Science, Technology, Engineering and Mathematics). This paper first considers some of the issues and debates surrounding the nature of STEM education, including perspectives on its interdisciplinary nature. It is next argued that mathematics is in danger of being overshadowed, in particular by science, in the global urgency to advance STEM competencies in schools and the workforce. Some suggestions are offered for lifting the profile of mathematics education within an integrated STEM context, with examples drawn from modelling with data in the sixth grade.

Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Investigating the effectiveness of an ecological approach to learning design in a first year mathematics for engineering unit

This is presentation of the refereed paper accepted for the Conferences' proceedings. The presentation was given on Tuesday, 1 December 2015.

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Tutoring with higher mathematics and the use of technology

We discuss three approaches to the use of technology as a teaching and learning tool that we are currently implementing for a target group of about one hundred second level engineering mathematics students. Central to these approaches is the underlying theme of motivating relatively poorly motivated students to learn, with the aim of improving learning outcomes. The approaches to be discussed have been used to replace, in part, more traditional mathematics tutorial sessions and lecture presentations. In brief, the first approach involves the application of constructivist thinking in the tertiary education arena, using technology as a computational and visual tool to create motivational knowledge conflicts or crises. The central idea is to model a realistic process of how scientific theory is actually developed, as proposed by Kuhn (1962), in contrast to more standard lecture and tutorial presentations. The second approach involves replacing procedural or algorithmic pencil-and-paper skills-consolidation exercises by software based tasks. Finally, the third approach aims at creating opportunities for higher order thinking via "on-line" exploratory or discovery mode tasks. The latter incorporates the incubation period method, as originally discussed by Rubinstein (1975) and others.