Outcomes for a Quantitative Reasoning Course

When we look at reports summarizing enrollment trends in college mathematics (like CBMS; see http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf) the entry “Quantitative Reasoning” (QR) does not appear — which will likely change, given the increase in the number of colleges offering QR. As a profession, we have not settled on the general nature of the learning outcomes for a college level QR course. As a supplement to the entry of Principles for a QR course, I will list our QR outcomes; these are from our Math119 Math – Applications for Living course.

So, here is the list of outcomes:

Use mathematical principles, concepts, processes, and rules to investigate, formulate, and solve problems in disciplinary and career contexts.
Work with others in teamed situations using mathematical principles, concepts, processes, and rules to investigate, formulate, and solve problems in disciplinary and career contexts.
Use appropriate tools and equipment, including graphing calculators, in investigating, and solving problems in disciplinary and career contexts.
Use standard references and resources, both print and electronic, from disciplinary and career areas as resources in investigation, formulating, and solving problems in disciplinary and career contexts.
Use measurable attributes of objects and the units, systems, and processes of measurement in disciplinary and career contexts.
Apply appropriate techniques, tools, and formulas to determine measurements in disciplinary and career contexts.
Use and develop formulas for applied situations in disciplinary and career contexts.
Use proportions, ratios, and percents in disciplinary and career contexts.
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships as they apply in disciplinary and career contexts.
Specify locations and describe spatial relationships using coordinate geometry and other representational systems in disciplinary and career contexts.
Apply transformations and use symmetry to analyze situations in disciplinary and career contexts.
Formulate questions in disciplinary and career contexts that can be addressed with data and collect, organize, and display relevant data to answer them.
Select and use appropriate statistical methods to analyze data in disciplinary and career contexts.
Develop and evaluate inferences and predictions that are based on data in disciplinary and career contexts.
Understand and apply basic concepts of probability in disciplinary and career contexts.

We blend occupational and academic contexts in this class, as you can see from these outcomes. As you would expect, some outcomes are emphasized more than others. Proportionality and percents are very important in the class; functions are emphasized using a variety of representations.

When I teach this course, I organize the content in these units:

Quantities and Geometry
Converting units (linear, area and volume) and dimensional analysis; significant digits; scientific notation; geometry (2D and 3D) applied to objects, including compound objects (2D).
Percents and Finance
Growth and decay to algebraic statements; relative change; interest; savings plan balance; savings plan payment; loan payment.
Statistics
Concepts (population, sample, bias, hypotheses, significance); confidence interval; measures of center; distributions (concepts — symmetry, variation); communicating statistical information (frequency tables, bar graphs, histograms, line charts, 5-number summary).
Probability
Calculating outcomes; basic probability; sequences of events (independent and dependent); at least once probability; counting formulas (sequences, permutations, combinations)
Functions and Models
Linear and exponential models; writing models from verbal statements; solving for parameters (finding slope and y-intercept in context, finding multiplier and starting value in context); doubling time and half life; logistic growth; solving exponential equations numerically; graphing linear and exponential functions (including creating scales for axes).

This is not an easy class. Regardless of background, many students have difficulty with the transitions from verbal information to mathematical symbolism. We blend presentations and workshop activities in class, and — due to student effort — usually get a pass rate about 70%.

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