Today’s guest post comes from Madison Hodson, an instructor at AcerPlacer who studies mathematics/statistics education at Utah State University. Here she exams what makes a “good” math question.
The validity of a knowledge measurement (a question on an assignment or exam) is broken up into two parts— relevance and reliability. For a question to be relevant, it must reflect the unit goal or objective and it must contain the correct mathematical content and learning levels. Reliable questions are those that when answered would give non-contradictory results.
If a measurement is relevant, then, once answered, proper evaluation can take place regarding the students knowledge and application of learned concepts. It is important for educators to clearly define their learning objectives ahead of time. This way, they can make sure their lessons cover all aspects of the objective. Having stated the objectives of each lesson also allows educators to draft relevant questions to homework and tests that cover and reinforce learned principles.
To aid in reliability, one of the most important qualities for each question is for it to be stated clearly. There must be no confusion as to what each question is asking and there are no ambiguous answers. This ensures that there are no discrepancies in the results from each question. Students either grasp the question and answer correctly or they don’t. The author personally thinks this aspect is important because she has felt confused by questions or answers on tests before.
Grading rubrics are imperative to ensure that scores are recorded based on fulfillment of the learning objective. For each question, there should be a rubric assigned that clearly designates the quantity of points that will be awarded for each answer. The rubric must be designed so that no matter who is scoring the question— there should be no controversy as to what answer(s) merit any specific amount of points. Having a rubric of this type will not allow any discrepancies between scores and will aid in the validity of each test score.
The purpose of knowledge measurements is stated in it’s name. Questions are posed to test the students knowledge and measure what they have learned and retained. By having clear objectives, relevant and reliable questions, and a precise grading rubric— educators, specially mathematics and statistics educators, are able to accurately determine their students knowledge, understanding, and application of concepts that have been taught. By taking time to generate relevant questions and watching for discrepancies within the students responses, educators will have valid results to base evaluations off of.