"In a completely rational society, the best of us would aspire to be teachers and the rest of us would have to settle for something less, because passing civilization along from one generation to the next ought to be the highest honor and the highest responsibility anyone could have."
Lee Iacocca
Mathematical Tools for the Real World (FDMAT 108)
Within the framework of the BYU-Idaho Learning Model, FDMAT 108 will enable students to develop quantitative reasoning skills that will benefit them in their subsequent course work, careers, and daily lives. The following five objectives are outlined along with their corresponding measurable outcomes of the course:
Outline of Objectives and Outcomes
1. Develop the necessary arithmetic and basic algebraic skills to succeed in daily life.
Students will be able to:
• Properly apply unit conversions in their problem solving techniques.
• Calculate appropriate absolute and relative changes in finding percentages.
• View percentages in terms of fractions, changes, and comparisons.
• Apply the of versus more than rule with percentages.
• Demonstrate the difference between percentage and percentage point.
• Solve simple one and two-step equations.
• Algebraically solve for the different variables structured within an applied formula.
2. Analyze and critique real-world issues and arguments involving probability and statistics.
Students will be able to:
• Discuss coherently the potential for abuse and misuse of statistics and be able to critique, at their level of ability, the validity of statistical studies found in professional journals.
• Describe the abuse of statistical graphs often found in the media.
• Describe the role of randomness, placebos, single and double-blinded studies, control vs. experimental groups and other key concepts found in inferential statistics.
• Point out the difference between correlation and causation.
• Describe the difference between weak and strong correlation and between positive and negative correlation.
• Calculate and interpret the mean, median, mode, range, and standard deviation of a data set.
• Calculate and interpret the five-number summary, z-scores, percentiles, and outliers of data.
• Construct histograms, box plots, pie charts, scatter plots and demonstrate pros and cons.
• Form a basic assessment of the role of hypotheses, margin of error, and statistical inference.
• Calculate the margin of error for proportional data and construct a 95% confidence interval.
• Show rudimentary understanding of the roles hypotheses, margin of error, and statistical significance play in research.
• Identify normal, uniform, positively, and negatively-skewed distributions.
• Appropriately apply the 68-95-99.7 Rule to both data and population contexts.
• Gain facility with the Complement, And, Or, and At Least Once Rules from basic probability.
• Describe and interpret the notion of the Law of Large Numbers and expected value with real applications.
• Discuss, in a cogent manner, the mathematical, social, and moral issues that arise in lottery and other gambling activities including the gambler’s fallacy.
• Discuss risk and the role it plays in our society and the decisions we make.
• Show how to count arrangements using repetition, factorials, permutations, and combinations.
3. Explore the use of mathematical models in describing and making predictions about real-world phenomena.
Students will be able to:
• Discuss the role of mathematical formulae, graphs, and numeric tables in modeling real-world issues such as finance, populations, probabilities, etc.
• Describe the specific differences between linear and exponential growth.
• Construct exponential models to accommodate forecasting future values of a variety of phenomena.
• Apply the Rule of 70 to calculate doubling time and half-life periods for modeling.
4. Understand the dangers of debt, the power of compound interest, and the advantages and disadvantages of various financial choices.
Students will be able to:
• Construct a reasonable budget based on income, savings, and expenses and demonstrate the importance of taking control of one’s personal finances.
• Demonstrate the astonishing power of compound interest and the role it plays in investments.
• Describe the difference between annual percentage rate and annual percentage yield.
• Calculate both the annual return and total return as a percentage on an investment.
• Calculate the future value of both lump sum and annuity investments as well as solving for present value and time.
• Demonstrate competence with the mathematics of installment loans by constructing amortization schedules using a spreadsheet.
• Discuss the pros and cons of paying extra principal on a long-term loan.
• Gain facility in describing the relationship between principal and interest in the context of both debt and investment.
• Discuss the key elements of liquidity, risk, and return and their relationship to investing.
• Carefully explain the mathematics and dangers of consumer credit and how to plan properly for living within one’s means.
• Describe the marginal income tax brackets of our nation’s tax code and how calculations are made based upon deductions and exemptions.
• Calculate the FICA tax on wages, its history and impact on our retirement system.
• Describe the difference between a tax credit and a tax deduction using specific examples.
• Demonstrate an understanding of the difference between our national debt and deficit and the ramifications for the future.
5. Learn to competently evaluate logical arguments and resolve real-life problems that require quantitative reasoning.
Students will be able to:
• Identify propositions, negations, conditionals, converses, inverses, and contrapositives.
• Distinguish between deductive and inductive arguments.
• Assess the validity and soundness of arguments.
• Apply George Polyá’s four-step problem-solving guidelines to quantitatively-based problems.
• Gain facility in the selection of appropriate tools such as the calculator and spreadsheet in the solving of quantitative real-world problems.
