Guest Post: Valid Grading Measurements Continued

Today’s guest post comes from Madison Hodson, an instructor at AcerPlacer who studies mathematics/statistics education at Utah State University. This is a continuation of her previous article, which can be found here.

As described in my last article, I discussed the two principles necessary to produce a valid knowledge measurement (question on assignment or exam). This article will go into more detail and will provide examples for reference.

The validity of a measurement is broken up into two parts; one of those parts is measurement relevance. For a measurement to be relevant, it must reflect the unit goal or objective. That means for a question to be relevant it must pertain to the correct mathematical content and learning levels for each specific goal. If a measurement is relevant, then educated decisions and evaluations can take place based on the results.

In this example, let’s assume that the unit objective is, “When confronted with a real-life problem, the student determines whether or not computing the area of a surface will help solve the problem.” Listed below are three separate questions that could be included in the assignment. We need to determine which question is the most relevant.


Question 1.
Computing a surface area will help you solve one of the following three problems. Which one is it? (Circle the letter in front of your answer.)

  1. We have a large bookcase we want to bring into our classroom. Our problem is to determine if the bookcase can fit through the doorway.
  2. As part of a project to fix up our classroom, we want to put stripping along the crack where the walls meet the floor. Our problem is to decide how much stripping to buy.
  3. As part of a project to fix up our classroom, we want to install new carpet on the floor. Our problem is to decide how much carpet to buy.

Question 2.
What is the surface area of one side of the sheet of paper from which you are now reading? Use your ruler and calculator to help answer the question. (Circle the letter in front of your answer.)

  1. 93.5 square inches
  2. 93.5 inches
  3. 20.5 square inches
  4. 20.5 inches
  5. 41.0 square inches
  6. 41.0 inches

Question 3.
As part of our project for fixing up the classroom, we need to buy some paint for the walls. The paint we want comes in two different size cans. A 5-liter can costs $16.85, and a 2-liter can costs $6.55. Which one of the following would help us decide which size can is the better buy? (Circle the letter in front of your answer.)

  1. Compare 5 x $16.85 to 2 x $6.55
  2. Compare $16.85/5 to $6.55/2
  3. Compare $16.85 – $6.55 to 2/5

In the example given only the first question is relevant to the objective of, “When confronted with a real-life problem, the student determines whether or not computing the area of a surface will help solve the problem.” It is relevant because the students were faced with various real-life problems and had to determine when finding the surface area would actually be helpful. Based on the class’ answers to this question, the teacher could make an informed decision on whether or not the students achieved the objective.

The other two questions were focused on calculations that were not relevant to surface area. The results from these measurements would provide no feedback on whether or not the students had achieved the objective regarding when to calculate surface area.

As math instructors it is important for us to not only teach how compute numbers and algorithms but to teach logic and reasoning. Many individuals today struggle with the application of mathematics in real life. Perhaps had they experienced relevant math questions (to unit objectives and to life), these feelings would decrease. Creating mathematic contact that is both relevant and reliable takes a large time investment— however, as educators, it is worth our time to properly educate and evaluate our students.

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