*Math for the Inquiring Mind
Featured Courses: Math for the Inquiring Mind
This is a course about using math to analyze and solve problems.
Many of the decisions we face in modern life require consideration of the data that informs the choices. For example:
- alternative methods of paying for college
- a cost/benefit analysis for the purchase of a digital camera
- comparisons of wages and cost of living factors in different locales
- whether to lease a car or buy one
the long term cost of borrowing money
- the meaning of “a confidence level of 95%” in reported poll results
- and so on…
In this course you’ll learn about and apply a general process for making decisions, and solving problems, through the analysis of numeric data. Using a well-defined problem solving process, and a spreadsheet, students taking this course tackle problems using data analysis, visual analysis (charting), and statistical analysis. We’ve created an extensive set of narrated spreadsheet tutorials for this course that you’ll watch to learn how a spreadsheet like Microsoft Excel can be used as a problem solving tool.
Individuals who excel at solving problems tend to use guidelines to organize their thinking and to reach creative insights. This does not imply rigidly following a prescribed set of steps, but rather the use of a combination of discipline and creativity. Problem solvers use a general approach that varies with each unique situation.
Often the most critical steps in the problem solving process are the steps that occur before we actually frame or state the problem. What information or data do we have? What assumptions are we following? Who’s perspective are we using? Is the problem stated as simply as possible?
Here are a few key points to consider when you are problem solving:
- Keep the problem statement simple
- Have a clear understanding of the current factors or circumstances (influencing the problem)
- Collect accurate information or data
- Use the right analytical tools and methods (to evaluate the problem, the roots cause(es), and identified the solution)
- State the solution(s) in terms that can to acted upon
- Identify how to evaluate or inspect whether the solution worked
Problem Statements: Be specific
Narrowing the scope of your problem will allow you to focus on the analysis that will get you to an appropriate solution.
Problem Statement Examples
- Poor: Won’t be able to attend college next semester
- Good: Not enough money to pay next semester’s tuition
- Poor: SUNY College football games have lower attendance
- Good: 20% fewer alumni attended SUNY College football games last year
If the problem statement is too broad you will spend unnecessary time determining specifically what you are trying to resolve.
Proposing Solutions: How Broad or Narrow is Appropriate
Studies of excellent problem solvers reveal that they seek the broadest possible solutions. They also consider all possible solutions, even those they believe may not be used. Considering all the options reduces the possibility of overlooking an effective solution. Example: Problem: Not enough money to pay next semester’s tuition. Possible Solutions:
- Drop out of school for a semester
- Borrow money to pay for school
- Find scholarship or other funding
- Find a part-time or second job to make extra money
- Start a business out of my home, for weekends and evening to make extra money
Each is a possible solution, yet none is merely the opposite of not enough money. Some solutions merely postpone the problem. Some solutions solve the problem on a temporary basis. Some solutions solve the problem now and in the future.
Learning Journal | top
Our philosophy for teaching and learning mathematics is based on the idea that learning happens best when you, the student, put new information into the context of what you already know. One technique we use to encourage this is called a learning journal. In this course you will keep a journal where you reflect on what you have learned and its meaning to you. The process of writing and reflecting is a good way to cement what you have learned into your memory, but it also serves a second purpose. Problem solving oftentimes requires the application of knowledge and techniques in new ways. In his book, The Reflective Practitioner, How Professionals Think In Action, Donald Schon  notes that standard educational practices often result in knowledge that is “specialized, firmly bounded, scientific and standardized.” He goes on to say that “practice is characterized by indeterminacy” and that professional artistry requires that the practitioner to “reflect in action.” In other words, professionals (problem solvers) take what they have learned in specialized, narrowly-bounded, contexts and apply that knowledge broadly by reflecting on their own thinking as they progress through the problem. You’ll be asked to do this very thing by keeping a learning journal throughout this course.
Spreadsheet Tutorials: Beyond the Basics | top
A modern spreadsheet –pick any one you like– is a technological wonder. Just a sampling of the uses to which a modern spreadsheet can be applied includes:
- as a data management tool
- for presenting and sharing data
- for data analysis
- for statistical analysis
- for graphing and visual analysis
- mathematical modeling
- keeping lists
- tracking progress on a project
Notice that the uses listed here are not things like “add columns” or “sort rows”. These are higher order uses, the kinds of things you do when you use a spreadsheet as a problem solving tool. We’ve created an extensive series of narrated tutorials to help you learn how to go beyond the basics and learn to use a spreadsheet as a problem solving power tool. References:  Schon, D. (1983). The Reflective Practitioner: How Professionals Think in Action. New York: Basic Books