Problem solving can be learned and taught through various disciplines. Pure problem solving is a process that is best learned when applied to problems relevant to the learner's long-term goals. Math and science deal with both content and problem solving process. In fact, math and science offer a unique perspective to the skills involved in understanding, approaching, and solving problems. Combining the math and science approach to problem solving with math and science content that is relevant to IT content would strengthen student preparation for computer careers.
What are the elements of mathematical and scientific thinking independent of content? Table 1 lists elements of math and science thinking that are process skills. These entries are the result of research from a variety of sources including the Web, a collection of reports/findings from research and professional groups, and data panels consisting of faculty and professionals. This is not to say that only math and science teach these outcomes, but that rigorous study in math and science uniquely prepares students with these skills.
|
Math/Science
Element
|
Description
|
|
Analytical Thinking
|
Ability to use reasoning involving truths that are logically consistent.
|
|
Precise Language
|
Ability to define terms unambiguously; ability to make statements in terms of observable and quantifiable data; ability to question statements and conclusions for clarification of ambiguous terms.
|
|
Logical Thinking
|
Ability to use reasoning based on relationships among propositions in terms of implication and contradiction; looks for consistency and inconsistency; ability to make logical connections between hypotheses and data, and develop appropriate experiments; able to sustain a consistent approach in complex, multi-step problems; ability to classify problems.
|
|
Problem-solving
|
Ability to approach problems in a systematic way, to look for patterns, to recognize elements that meet consistency and inconsistency with past experience and knowledge; includes the ability to break problems down into smaller components, restructure them, develop new approaches, challenge assumptions, suspend judgment, and brainstorm.
|
|
Conceptualization
|
Ability to ask the right questions; how a person approaches a problem; ability to answer the question asked, not a different question.
|
|
Data Gathering
|
Ability to identify needed data; ability to observe, organize and record data; ability to recognize unexpected evidence.
|
|
Data Analysis
|
Ability to organize and evaluate data in a way that leads to conclusions and decisions consistent with the data; knowledge of when there is sufficient or insufficient data; ability to judge reasonableness of result.
|
|
Computation
|
Ability to accurately perform mathematical operations. |
|
Estimation
|
Ability to estimate results; ability to evaluate results for reasonableness and recognize when a result does not seem probable. |
|
Prediction
|
Ability to predict probabilities and outcomes with degrees of certainties; understanding of cause and effect. |
|
Hypothesis Development
|
Ability to construct a falsifiable hypothesis from which an experiment can be designed; ability to specify that data that would support or contradict a hypothesis. |
|
Modeling
|
Ability to represent relationships and data in another way, using a model such as an equation, diagram, or graph; ability to abstract from specific situations to general situations; ability to apply general models to specific instances. |
|
Experimentation
|
Ability to design an experiment or observation to test a hypothesis, duplicate results, understand control factors, use experience form other situations, learn how to eliminate variables. |
|
Simplification
|
Ability to take complex relationships and problems and reduce them to related simpler problems with fewer variables; ability to work with parts of a problem and apply the results to more complex problems. |
|
Pattern recognition
|
Ability to recognize patterns from discrete instances; ability to question universality of generalization; ability to generalize specific instances into formulas and make conclusions. |