Stuart Boersma

Quantitative Reasoning in the Contemporary World, 3: Assessing Student Learning

In this third paper in a series describing the Quantitative Reasoning in the Contemporary World course, the authors provide an adaptation of the Association of American Colleges and Universities quantitative literacy VALUE rubric. Describing achievement levels in six core competencies (interpretation, representation, calculation, analysis/synthesis, and communication), the resulting Quantitative Literacy Assessment Rubric (QLAR) is applicable to grading student work and has exhibited a high degree of reliability in two separate scoring tests (97% and 88% respectively). The distribution of the six core competencies across the 24 case studies in the authors’ quantitative reasoning casebook shows that interpretation, calculation, and analysis/ synthesis were present in most all of the case studies. In addition to acting as a reliable scoring tool, the QLAR can improve teaching, learning, and curricular materials.

Measuring Habits of Mind: Toward a Prompt-less Instrument for Assessing Quantitative Literacy

In this study, we offer a new “prompt-less” instrument for measuring students’ habits of mind in the field of quantitative literacy. The instrument consists of a series of questions about a newspaper article the students read. The questions do not explicitly solicit quantitative information; students’ habit of mind is assessed by their use of quantitative reasoning even when it is not asked for. Students’ answers were graded according to a modified version of the Quantitative Literacy Assessment Rubric (QLAR) published in this journal (vol. 4, issue 2). We applied the instrument and rubric to assess preand post-intervention habits of mind in opportunistic samples of two cohorts of students: the general (non-STEM) student body and (non-STEM) honors students at Central Washington University. The intervention was a QL course designed around a collection of newspaper articles to provide authentic context. The preand post-course assessment showed no statistically significant improvement in either group. We close with a discussion of practical aspects of using the rubric based on our experience of using it in this QL class.

Using a Media-Article Approach to Quantitative Reasoning as an Honors Course: An Exploratory Study

In this study, we investigate student performance on a basic skills assessment of percentages and ratios in two cohorts of students: the general (non-STEM) student body (cohort G) and (non-STEM) honors students (cohort H). Both cohorts used a media-article approach to the study of quantitative reasoning. A preand a post-intervention assessment were administered with a two-week intervention period consisting of critical analyses of the use of percentages and ratios in media articles. Using non-parametric techniques, no statistically significant improvement was measured in cohort G while cohort H students showed statistically significant improvement on several items.

False Positives and Referral Bias: Content for a Quantitative Literacy Course

An extended study of accuracy in medical screening is presented as a useful application to increase students’ quantitative reasoning skills. Two detailed examples are presented. The first explores the frequency of obtaining false positive results from a medical screening tool while the second examines the issue of referral bias and its effect on the apparent sensitivity and specificity of the screening tool. Results from student assessments indicate that the activity increases one’s ability to define terms such as “false positive” and “false negative” and increases one’s ability to read and compute with information obtained from a two-way table. Teacher assessment results indicate that the activity is challenging and could be used in existing high school or college classrooms. Additionally, links to a student activity, instructor notes, and Excel calculation tool are provided.

A Mathematician's Look at Foucault's Pendulum

That was when I saw the Pendulum. The sphere, hanging from a long wire set into the ceiling of the choir; swayed back and forth with isochronal majesty ... The time it took the sphere to swing from end to end was determined by an arcane conspirac.v between the most timeless of measures: the singularity of the point of suspension, the duality of the planes dimensions, the triadic beginning of Tt, the secret quadratic nature of the root, and the unnumbered perfection of the circle itself ... Were its tip to graze, as it had in the past, a layer of damp sand spread on the floor of the choir; each swing would make a light furrow, and the furrows, changing direction imperceptibly, would widen to fonn a breach, a groove with radial symmetry ...

See The Light! A Nice Application of Calculus to Chemistry

Abstract Some simple modeling with Riemann sums can be used to develop Beers Law, which describes the relationship between the absorbance of light and the concentration of the solution which the light is penetrating. A further application of the usefulness of Beers Law in creating calibration curves is also presented.

Angle of repose: an interdisciplinary lively application project

ABSTRACT A mathematician and a geologist team up to write an interesting interdisciplinary statistics application. While primarily focusing on whether piles of debris composed of different grain sizes have different angles of repose, the project quickly blossomed into a lively study of experimental design and sensitivity analysis. The project, as well as its merits, are briefly explained.