Helping Your Student with Math and Science Problems
As a part of giving back to the community, I serve as an adjunct professor at Grand Canyon University’s Colangelo College of Business teaching statistics as well as in the College of Doctoral Studies teaching methodology. Even at the collegiate level, students sometimes struggle with how to approach a math problem. As a result, I have had to teach my students first how to approach a problem, and then how to solve it. Although this approach works best for problems with scenarios (word problems), it also works for practice problems that are less complex in which the student is given an equation and asked to find the solution.
- Read the full question. As the learner is reading, highlight any key words or phrases that may influence the student’s approach to the problem. Key words might include less than, greater than, or provide a ratio, or the problem may use differing units (e.g., cm vs inches) and require the learner to standardize the units.
- Determine what the question is asking. Do you expect the answer to be a number, a percentage, a ratio, or a value with units, or do you expect the value to be bounded between two values. For example, a probability must be 0 ≤ X ≤ 1. Knowing this ahead of time helps the learner to identify mistakes.
- Identify the variables. The scenario (story problem) provides the variables and parameters necessary to solve the problem. Occasionally, standard parameters and constants, such as pi, the speed of light, or the acceleration due to gravity, will be necessary to solve the problem, but will not be provided as they are understood as part of the science or mathematics. On occasion, the information given will provide data that requires an intermediate calculation to solve the final problem. An example is to convert centimeters to meters, ounces to liters, or calculating the radius of a circle given other parameters, such as the diameter or circumference of the circle.
- Determine the best approach to find the solution for which you are looking. In most cases, the student is practicing the use of an equation that is suited for the situation, or the student must choose from a variety of equations or procedures to arrive at the solution.
- Determine the solution. Use the equation determined in step 4 and the variables from step 3. Once the learner has achieved a solution, check that the solution fits with the expected solution from step 2.
- Read the question again and ensure that the solution completely answers the problem asked. In probability and statistics, for example, formulas are designed to determine probabilities for values less than a given value. However, the question may ask for the learner to determine the probability for values greater than a given value, or between two values. This is also a good time to make sure that the solution is properly labeled, such as X = 5, y = 10 cm, or 7 < z ≤ 20. In mathematics, all the symbols and labels are important!
The last piece of advice I would offer is to use a pencil to solve the problems on paper, especially in primary and secondary school. Doing so allows the student to see the problem develop and to catch any errors along the way. Use scratch paper, if necessary, but keep the work organized and work from top to bottom. My students have had great success with this process; hopefully, your student will, too.
Dr. Alex Casteel