Quantitative Literacy

The Passport Learning Outcomes, based on the LEAP Essential Learning Outcomes, describe the learning required to satisfy lower division general education requirements in quantitative literacy. Additional academic work in this or other content areas may be needed to fulfill upper division general education, academic minor and/or academic major requirements. No single student is expected to demonstrate ALL of these Proficiency Criteria nor is this intended to be a list of all possible Proficiency Criteria.

QUANTITATIVE LITERACY
Passport Learning Outcome Feature: Computational Skills
Passport Learning Outcome (what the student has learned): Demonstrates proficiency with arithmetic and algebraic computational skills, and extends them, for example, to geometric and statistical computations.

Transfer Level Proficiency Criteria (evidence of proficiency of the learning outcome appropriate at the transfer level)

Solves problems or equations of the appropriate level for the desired quantity. 

• Uses logarithms to correctly solve a compound interest problem for the desired time.
• Solves linear and quadratic algebraic equations accurately and reliably without the aid of a calculator.
• Correctly computes the mean, median, mode, and standard deviation for a given numerical data set.
• Rearranges the margin of error formula to find the desired sample size for a given confidence level and margin of error.
• Finds the area or volume of general geometric objects by decomposing them into more basic components (circles, triangles, rectangles, cubes, etc.) and accurately converts measurements in different units to a common unit.
• Uses the ideal gas law to compute how one variable is affected as another is changed.
• In problems where units are provided, gives answer in correct units. Also, uses units as a check when solving algebraic problems where units are given.
• Uses a spreadsheet or simple computer programs to automate multiple instances of arithmetic calculation.
• Calculates present and future values of money by evaluating appropriate formulas.
• Determines proportional relationships between the areas/volumes of figures given side (or other) measurements.

PLO Feature: Communication of Quantitative Arguments
Passport Learning Outcome (what the student has learned): Expresses quantitative information symbolically, graphically, and in written or oral language.

Transfer Level Proficiency Criteria (evidence of proficiency):

Correctly uses mathematical notation in all aspects of the solution of a typical problem at the appropriate level.

• Accurately converts between proper mathematical notation/expressions and written / oral narrative.
• Expresses answer and intermediate steps with correct units.
• Uses appropriate language to link between different steps of stating or solving problems. Avoids using “=” to mean anything other than equality.
• Uses function notation and parentheses correctly in solving problems.
• States the conclusion to a significance test and writes an explanation of the rationale for the conclusion.

Makes appropriate use of graphical objects (such as geometrical figures, graphs of equations in two or three variables, histograms, scatterplots of bivariate data, etc.) to supplement a solution to a typical problem at the appropriate level.

• Includes an appropriate graph to support or emphasize trends or findings.
• Draws two consecutive iterations of the Koch Snowflake to demonstrate that perimeter increases at each step.
• Uses graphs or plots (box-and-whisker, bar graph, etc.) to illustrate a comparison between two related data sets.
• Illustrates important values (such as median, mean, or extrema) on a graph or histogram of the data under analysis.
• Uses a graph to correctly present the data collected in a scientific experiment.

PLO Feature: Analysis of Quantitative Arguments
Passport Learning Outcome (what the student has learned): Selects and uses appropriate numeric, symbolic, graphical and statistical reasoning to interpret, analyze and critique information or line of reasoning presented by others.

Transfer Level Proficiency Criteria (evidence of proficiency):

• Determines whether a given sequence of steps constitutes a valid line of reasoning (such as a proposed proof of a mathematical theorem or solution to a quantitative problem).  If not a valid method, is able to explain why not.
• Reads passages that use basic statistics (such as from a newspaper story) and correctly articulates how those statistics could have been calculated and gives a correct analysis of their potential meaning. For example, distinguishes between results that show statistical correlation and causation.
• When presented with an estimate based on sample data, asks if that sample was randomly chosen, and if not, considers whether that is relevant.
• Uses present-value and future-value formulas to evaluate claims made about investment opportunities.
• Critiques the quantitative results obtained from a scientific experiment.

PLO Feature: Formulation of Quantitative Arguments
Passport Learning Outcome (what the student has learned): Recognize, evaluate, and use quantitative information, quantitative reasoning and technology to support a position or line of reasoning.

Transfer Level Proficiency Criteria (evidence of proficiency):

• Correctly formulates, organizes, and articulates solutions to theoretical and application problems at the appropriate level.
• Gives a correct argument why the Koch snowflake has finite area but infinite perimeter.
• Analyzes quantitative data collected in an experiment.
• Uses optimization techniques to maximize profit for a business.
• Correctly proves that an irrational number is irrational (for example, 2 or 1.010010001… ).
• Uses graphs, diagrams, and charts to compare data sets and draw conclusions.
• Given the results for a hypothesis test or confidence interval, draws an accurate conclusion.
• Describes a scenario in which poll voting (plurality method) gives a different result from ranked preference voting.
• Uses a graph and/or appropriate formulas to find the maximum or minimum value of a quadratic polynomial, and distinguishes between the value at which the maximum occurs and the maximum value itself.
• When using linear programming, shows an appropriate graph and the details of how the optimum value is obtained.
• Employs proportional reasoning to explain why a subpopulation is over or under represented in a sample.
• Creates a graph to determine the real zeros of a quadratic or cubic equation.

PLO Feature: Mathematical Process
Passport Learning Outcome (what the student has learned): Design and follow a multi-step mathematical process through to a logical conclusion and critically evaluate the reasonableness of the result.

Transfer Level Proficiency Criteria (evidence of proficiency):

Correctly solves a variety of different problem types (at the appropriate level) that involve a multi-step solution.

• Selects an algorithm (such as Cheapest Link Algorithm) for working with a graph theory problem (Travelling Salesman) and correctly applies it to the exercise.
• Based on given data, correctly computes a confidence interval or hypothesis test.
• Uses synthetic division, factoring, graphing, and other related techniques to find all the (real) zeros of a suitable cubic/quartic polynomial.
• Writes a computer program to do a multi-step calculation that involves multiple cases.  For example, identify whether the input is a prime number, factor the input, or sort a list of numbers. Does appropriate error checking on the resulting computer program.
• Calculates multiple monthly loan payments for a given principal and different interest rates/times.  Then uses the figures to compare the total cost of the loans.
• Given three linear relationships for three unknowns, correctly solves for the desired quantities.
• For a given velocity and rate of deceleration, calculates the distance required to stop.
• Correctly solves an optimization problem, justifying why their solution is in fact an optimal one (for example, using linear programming or differential calculus).

Considers the validity of a result from a multi-step problem.

• Rarely submits solutions that involve an answer of the wrong order of magnitude or involving the wrong type of information (such as a graphical solution when a numeric one is called for).
• Where possible, checks solutions with the original problem.
• Looks for signs of model breakdown when using an exponential growth function in a real-world setting.
• Evaluates the validity of experimental data.
• Recognizes, quantifies (where possible), and articulates the possibility of error (type I or II, as appropriate) in a significance test.
• Recognizes nonrandom sample data as nonrandom and considers the possible impact to conclusions.

PLO Feature: Quantitative Models
Passport Learning Outcome (what the student has learned): Create, analyze and apply appropriate quantitative models to solve quantitative theoretical and real-world problems.

Transfer Level Proficiency Criteria (evidence of proficiency):

Correctly solves problems at the appropriate level in which the student is required to choose an appropriate technique or formula.

• Given a floor plan, the cost of the carpet per yard from a roll of given width, and the cost of making a cut, devises a scheme to carpet a floor plan (including converting between units such as square feet and square yards) and calculates the cost.
• Selects the correct model (linear, exponential, logistic, etc.) for a population growth problem and then uses it to solve for the population size at a given time.
• Given sample data, calculates confidence intervals for population means and correctly interprets results.
• Constructs applicable linear demand and quadratic revenue functions from given data, then uses the model to determine the price and quantity that maximizes revenue.
• Given an estimated growth rate per year and a desired investment value after a certain number of years, calculates the initial investment required to reach that value.
• Solves problems that involve adding rates. (For example if person A requires 4 hours to do a job, and person B requires 3 hours, how long is required for A and B to do this job together?)
• Selects the correct function type to model a set of real-world bivariate data, determines appropriate values for the constants in the model, and uses the model to answer questions.
• Utilizes vectors to solve problems involving direction and magnitude.

Quantitative Literacy Course List, Pilot States