Mary's Apples and Physics

The example below shows that the problem solving process is the same for puzzles (story problems) and for problems based on subject matter. Using a unified approach to problem solving that is valid across the curriculum removes an important barrier to learning and using mathematics efficiently and effectively.

The same linear process is used for solving the puzzle as is used to solve the physics problem. The Mary's Apples structure occurs as a part of a wide variety of problems. The problem solving skills learned in introductory algebra story problems form the basis for problem solving in more advanced courses. If the principles of solving story problems are learned well in middle school and high school, they will serve the student well in later subject matter courses in college and beyond. The words change and the symbols change, but the problem solving process remains the same. Sound problem solving skills make possible the understanding and use of concepts expressed in mathematical form.

Solving word problems in any subject that uses mathematical methods consists of satisfying several conditions simultaneously. Doing this consists of using elementary methods of solving simultaneous equations. As the solution comparison shown above demonstrates, this basic process is independent of subject. Common sense, reliable problem solving based on basic concepts inherent in mathematics, introduced at the pre-algebra level, would solve the important objectives expressed in the NCTM standards and those advanced by AAAS in project 2061, Bench Marks for Science Literacy.

The problem solution was developed using SureMath