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Determine Percentages from Varied Component Criteria

download_pdf_smWhen creating assessments, many teachers have difficulty deciding how to score them and then be able to turn that score into a percentage. When creating outcome assessments, all components must be represented; however, it’s possible they will not all be equal in terms of the number of questions posed and/or points awarded. For example, posing two problems and requiring at least one to be correct may be sufficient to indicate mastery of one algebra component; but, for another component it may take five questions with a criterion of at least four correct to ascertain mastery. As a result of such differences, teachers often struggle with the problem of how to score each component on an assessment, since the point values and number of questions are not uniform. Typically, the decision is made simply to average the component scores in order to obtain the final percentage teachers feel they must enter in a grade book or program. Unfortunately, this type of average may indicate students have successfully demonstrated the full outcome when, in fact, some have not.

Let’s suppose an outcome contains seven components and the last component is a real-world application that the assessment authors determined to be a “gatekeeper” type of component. In other words, unless students are reasonably successful on the last component, they have not truly demonstrated success. In the following example, the assessment authors decided what scores were required for mastery of each component:

Component scores required for mastery:
Component 1 = 6/8
Component 2 = 7/9
Component 3 = 5/6
Component 4 = 3/4
Component 5 = 9/12
Component 6 = 6/9
Component 7 = 15/20

This is where many assessment authors stop. Instead of considering the number of questions and points related to each component, they merely add up the earned points and divide by the total to come up with an overall percentage score for the outcome assessment:

Total = 51/68 or 75%

If we look more carefully, though, it is easy to understand why using the above method is a mistake. Remember when we said component seven is our “gatekeeper?” Using the above formula, it doesn’t matter which points are missed; therefore, the student could conceivably miss up to 17 points on component seven and still achieve the required 75% on the assessment as long as s/he didn’t miss any other points. (See below)

Component scores earned:
Component 1 = 8/8
Component 2 = 9/9
Component 3 = 6/6
Component 4 = 4/4
Component 5 = 12/12
Component 6 = 9/9
Component 7 = 3/20

Total = 51/68 or 75%

So, even though the student obviously did not master the “gatekeeper” component, s/he did earn enough total points to show an overall passing percentage grade due to the averaging formula used. Some might argue that in most cases, students would not get perfect scores on all the first components and then do so poorly on the last one. But here’s another example of what could – and often does – happen.

Component scores earned:
Component 1 = 8/8
Component 2 = 8/9
Component 3 = 5/6
Component 4 = 4/4
Component 5 = 10/12
Component 6 = 7/9
Component 7 = 9/20

Total = 51/68 or 75%

Notice this student missed some questions on components two, three, five, and six – and also missed more than half of the questions for most-important component seven. Yet, this student still achieved the required 51 points and 75%. These examples point out why, unfortunately, numerous students are promoted and/or allowed to move on without truly mastering the material. We must rethink how we score assessments! We can still use the component requirements in the first example to create a functional rubric that will better represent what the student has truly mastered AND allow us to record a percentage score. Creating the rubric will take some thought and require the assessment authors to make some tough decisions about the definition of mastery for the given assessment. These authors have already determined an acceptable performance on each component…now they must go one step further and describe how to use those performances to determine a total percentage for the outcome score.

Here’s how it works. The following rubric shows an example of how one district translates component scores into a percentage grade for an outcome assessment. This is the same example used earlier, where there are seven components, and the seventh one is the important “gatekeeper component.” The overall score a student must achieve is at least a 75% using the following rubric:


Using this method, students are required to demonstrate skills for each component and the teacher will also have a more accurate percentage score to record.

Note: Each scoring level addresses the fact that students must pass component seven, the “gatekeeper” component. The percentages were discussed and agreed upon by the authors who obviously felt that 75% was a “passing” score…not the typical 70%. These are decisions made by the authors; however, they can also be dictated by district policy. For example, a district may decide that 70% is mastery and require all outcome assessments to follow suit. If that were the case here, the rubric would need to be changed a bit. The 75% may change to a 70% and the other numbers may also be adjusted accordingly. There is no exact “formula” for creating these rubrics. Each district must make local scoring decisions, which often require trial and error and feedback through validation forms before they are fully refined. However, this process is essential in showing a more accurate picture of student mastery and should be used in conjunction with the required component scores.