Introduction to the Special Issue: Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses

Abstract

Mathematics for liberal arts courses are a staple of most mathematics departments and are often populated with students who have disengaged from mathematics. Inquiry-based learning is a student-centered pedagogical tool for re-engaging students in mathematics. In this paper, we introduce a Special Issue of PRIMUS on “Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses.”     

Learning Fractions by Splitting: Using Learning Analytics to Illuminate the Development of Mathematical Understanding

The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning, none of the research on these theories employs samples large enough to test theories at scale or nuanced enough to demonstrate how learning unfolds over time during instructional activities based on these theories. The work reported here uses learning analytics methods with fine-grained log data from an online fraction game to unpack how splitting (i.e. partitioning a whole into equal-sized parts) impacts learning. Study 1 demonstrated that playing the game significantly improved students’ fraction understanding. In addition, a cluster analysis suggested that exploring splitting was beneficial. Study 2 replicated the learning results, and a cluster analysis showed that compared to early game play, later game play showed more optimal splitting strategies. In addition, in looking at the types of transitions that were possible between a student’s early cluster categorization and later cluster categorization, we found that some types of transitions were more beneficial for learning than others.     

Recreating blood-brain barrier physiology and structure on chip: A novel neurovascular microfluidic bioreactor

The blood-brain barrier (BBB) is a critical structure that serves as the gatekeeper between the central nervous system and the rest of the body. It is the responsibility of the BBB to facilitate the entry of required nutrients into the brain and to exclude potentially harmful compounds; however, this complex structure has remained difficult to model faithfully in vitro. Accurate in vitro models are necessary for understanding how the BBB forms and functions, as well as for evaluating drug and toxin penetration across the barrier. Many previous models have failed to support all the cell types involved in the BBB formation and/or lacked the flow-created shear forces needed for mature tight junction formation. To address these issues and to help establish a more faithful in vitro model of the BBB, we have designed and fabricated a microfluidic device that is comprised of both a vascular chamber and a brain chamber separated by a porous membrane. This design allows for cell-to-cell communication between endothelial cells, astrocytes, and pericytes and independent perfusion of both compartments separated by the membrane. This NeuroVascular Unit (NVU) represents approximately one-millionth of the human brain, and hence, has sufficient cell mass to support a breadth of analytical measurements. The NVU has been validated with both fluorescein isothiocyanate (FITC)-dextran diffusion and transendothelial electrical resistance. The NVU has enabled in vitro modeling of the BBB using all human cell types and sampling effluent from both sides of the barrier.     

The Objective Borderline Method: a probabilistic method for standard setting

A new probability-based standard setting technique, the Objective Borderline Method (OBM), was introduced recently. This was based on a mathematical model of how test scores relate to student ability. The present study refined the model and tested it using 2500 simulated data-sets. The OBM was feasible to use. On average, the OBM performed well with specificity .88, sensitivity .51, false positive rate 3.4% and false negative rate 26%. These indices were insensitive to the borderline score range. This probability-based standard setting may be a useful addition to the range of standard setting methods available.     

Reference

INSIDE U.S. BUSINESS: A CONCISE ENCYCLOPEDIA OF LEADING INDUSTRIES by Philip Mattera (Homewood, IL: Dow Jones-Irwin, 1987—price not given)

DICTIONARY OF COMPUTERS, INFORMATION PROCESSING & TELECOMMUNICATIONS by Jerry Rosenberg (New York: John Wiley, 1987—$18.95, paper, with a hardback available as well)     

Applying Software Design Methodology to Instructional Design

The premise of this paper is that computer science has much to offer the endeavor of instructional improvement. Software design processes employed in computer science for developing software can be used for planning instruction and should improve instruction in much the same manner that design processes appear to have improved software. Techniques for examining the software development process can be applied to an examination of the instructional process. Furthermore, the computer science discipline is particularly well suited to these tasks. Thus, computer science can develop instructional design expertise for export to other disciplines to improve education in all disciplines and, eventually, at all levels.     

The use of motivation theory in engineering education research: a systematic review of literature

Motivation is frequently studied in the context of engineering education. However, the use of the term motivation can be inconsistent, both in how clearly it is defined and in how it is implemented in research designs and practice. This systematic literature review investigates the use of motivation across recent engineering education publications. Results show that the majority of engineering education publications referencing motivation as a concept do not provide a clear definition for the term, nor do they draw upon the existing body of literature surrounding motivation. Within the publications that do draw upon motivation literature, we found that a small number of frameworks were most prominent. We believe that both of these factors potentially inhibit the understanding of motivation in engineering education. Therefore, we provide a number of suggestions for how researchers and practitioners can work to rectify these trends.