Lessons in Grading: Understanding Averaging Modes and Other Functionalities

There is an unspoken belief that grades are immutable and once students do the work and are fairly assessed then the final mark is a simple straight forward calculation yielding a single result. Nothing could be further from the truth.

Whether it is a class with different activities or a standardized assessment with different components how the scores on those activities or components are combined to produce a final score can result in a range of outcomes.

There are two important aspects of assessment that must be mentioned here: Reliability and Validity. To the extent that the same level of performance gets the same score irrespective of time, place, or space of testing, the reproducibility of the test-score is the measure of the reliability of the score. To the extent that all intended uses and interpretations of the scores have been clearly articulated and each use of the assessment score can be justified with specific forms of evidence then the scores are deemed valid for the intended use.

COVID-19 Impact

Unfortunately, the sudden impact of COVID-19 on grading and assessment of students did not allow many agencies a lot of leeway to gather specific forms of validation evidence and reset performance standards and performance metrics. Many bodies responsible for student assessment and evaluation decided to hold students harmless for the effects of COVID-19. Did everyone get it right? Probably not. Some jurisdictions strayed so far in students’ favor that neither parents nor students complained. Teachers? That is another matter.

My goal here is to share some of the complexity involved in student evaluation and to help teachers understand how to use electronic Gradebooks (eGBs) with greater efficacy.

Setting the Table

“Dr. Clarke, I am very confused. I have a student and I am totally perplexed by what is happening with their grade in my electronic gradebook.

My understanding is if an assignment is excluded it does not affect a student’s grade but if I give an assignment a zero it will lower the student’s grade. Here is the situation, if I exclude a particular assignment the student’s average is 57% but if I give it a zero then that student’s average is 116%. This makes no sense. Shouldn’t the average go down if the assignment gets a zero instead of being excluded? This makes no sense!”

The above is not a single actual conversation but is based on several actual conversations. An explanation is given at the end of this article, but to truly understand the explanation you will need to read the article carefully, sorry!!

The Scenario above occurs because School Districts mandate how grades should be entered into electronic gradebooks [eGBs]. These school systems come up with a recipe based on the behavioral expectations of someone in a senior leadership position, how that person (or persons) think students and teachers will behave. The problem is there will always be at least one teacher or student who will not follow the prescribed protocol. What happens then?

For those of you who want a recipe for teachers to follow that is not what I offer or support. My approach is to teach teachers how the electronic gradebooks [eGBs] function; suggest a set of reasonable outcomes; AND ALLOW THE TEACHERS TO MAKE CHOICES IN THE BEST INTERESTS OF THEIR STUDENTS AND THEIR INSTRUCTIONAL PROGRAM(S).

Using Electronic Gradebooks [eGBs]

With many school systems moving to electronic Gradebooks [eGB] there is a learning curve associated with electronic grading. Added to this use of eGBs, school systems are putting guardrails in place to ‘protect’ students from adverse or punitive grading practices. Understanding the consequences and effects of these guardrails present an important aspect of electronic grading that few district leaders seem to take into consideration. With Coivd-19 closures and conversions from brick and mortar to virtual and distance learning, additional guardrails have been added. These additional guardrails also bring with them additional consequences which may have their own unique set of impacts.

As I said, my approach is to ensure teachers understand the different grade averaging modes and how to use them effectively then allow the teachers to make choices in the best interests of their students and their instructional programs [yes, I said that before and I am likely to repeat it again because it is something I fervently believe].

Averaging Modes

This process is layered. At the highest level there are four type of averaging: Total Points Averaging, Unweighted Assignment Averaging, Weighted Assignment Averaging, and Categorical Averaging [also referred to as Averaging by Weighted Categories].

Weighting Categories

Most schools that use categories divide the categories into assessment (A), practice and application (PA), engagement or participation (E), and homework (H). Generally, the sentiment in most jurisdictions is that students often use additional resources for Homework and since the benefit of Homework is in doing the work, the Homework category often gets a low weighting [H= 10%]. A commonly shared sentiment is that Engagement/Participation is low hanging fruit and, as such, that category often also gets a low weighting [E = 10%]. Finally, it is generally felt that Practice and Application and Assessment are central aspects of instruction and they often get a more significant weighting [A = 40%, PA = 40%].

Examples

 For simplicity of comparison I will start with two students, each with two assignments in each category. One assignment a perfect score and the other receiving 50%. To further enhance observable differences one assignment will be out of 50 and the other out of 100. For all the examples presented, student scores will either be 50% or 100%. This should simplify the presentation and help demonstrate the range of possible outcomes for a single grade set.

To facilitate comparison, Student A will receive the perfect score in the 50-point assignment and Student B will receive the perfect score in the 100-point assignment.

Our example students therefore have the following grade sets, each containing two grades in each category:

Student A: [A, 50/50 and 50/100], [PA, 50/50 and 50/100], [E, 50/50 and 50/100], and [H, 50/50 and 50/100].

Student B: [A, 25/50 and 100/100], [PA, 25/50 and 100/100], [E, 25/50 and 100/100], and [H, 25/50 and 100/100].

Also, for ease of comparison I am going to use a typical grade scale where A is 90-100, B is 80-89, C is 70-79, D is 60-69, and F is 59 and below.

Before you proceed any further in this article it might be useful to stop at this point and discuss possible Final Grades for both students. This should be particularly useful if you are reading this with a group of other teachers or administrators.

Discussion Question 1: What Final Grade do you think each student should get?

Total Points Averaging

This is the technique that most of us are familiar with. All points are totaled up, all possible points are also totaled, and the final grade is a percentage of points earned out of total points possible.

Student A: This student has a total of 400 points of a possible 600 points. This calculates at 67% for a grade of D.

Student B: This student has a total of 500 points of a possible 600 points. This calculates at 83% for a grade of B.

Discussion Question 2: Since both students demonstrated Mastery [100%] on exactly half the assignments in each category and Failed [50%] exactly half the assignments in each category is it fair or equitable that one student gets a grade of B and the other student gets a grade of D?

Unweighted Assignment Averaging

In Unweighted Assignment averaging each assignment is given the same weight. So, the Percentage Points earned in each assignment are averaged out of the total percentage points possible.

Student A: This student has 4-assignments with 50% [total 200 percentage points] and 4-assignments with 100% [400 percentage points] from a total of 8-assignments [800 possible percentage points]. The average grade [(200+400)/800] = 75%] is a C.

Student B: This student has 4-assignments with 50% [total 200 percentage points] and 4-assignments with 100% [400 percentage points] from a total of 8-assignments [800 possible percentage points]. The average grade [(200+400)/800] = 75%] is a C.

Discussion Question 3: Student A only earned 400 points, but Student B earned 500 points. Is it fair or equitable that they both should get the same grade?

Weighted Assignment Averaging

With Weighted Assignment Averaging teachers may give assignments varying weights based on any criteria they desire. Because the approach can have widely different results based on the weights let me summarize by saying weighing assignments can result in a Final Mark as low as a student’s lowest grade or as high as a student’s highest grade. Because all of these students have grades of A and F the students in these examples can have Final Marks from A to F.

Categorical Averaging

There are three common ways of using categorical averaging: (1) Categories Only, (2) Categories Total Points, (3) Categories and Assignments.

For this section I will add two more students: Student C never does homework and Student D is really bad at testing. To accommodate a common perspective, I will use the minimum 50% approach. Let me be absolutely clear: I do not use minimum 50 in any class I teach. If you do nothing you get nothing. But I understand the approach and because many people use that approach, I am using it here. To avoid putting students into situations from which they cannot recover I often use letter grade entry judiciously, emphasis on often and not always [I discuss this in my article on the options to minimum 50].

Student C: [A, 50/50 and 50/100], [PA, 50/50 and 50/100], [E, 50/50 and 50/100], and [H, 25/50 and 50/100].

Student D: [A, 25/50 and 50/100], [PA, 50/50 and 100/100], [E, 25/50 and 100/100], and [H, 25/50 and 100/100].

Summary of Students

(1)  Categories Only

With Categories only all assignments are equally weighted within each category so a 50% and a 100% will average to 75%. Table 2A shows how assignments within categories will average to give category scores and Table 2B shows how those categorical scores roll up to Final Scores and Final Grades.

(2)  Categories Total Points

With Categories Total Points, the points earned on each assignment are totaled for the numerator of the calculated grade and the total possible points are totaled for the denominator. Table 3A shows how assignments within categories will average to give category scores and Table 3B shows how those categorical scores roll up to Final Scores and Final Grades.

(3)  Categories and Assignments

With Categories and Assignments factoring into the weighting of grades teachers may give assignments any weight they wish. To highlight how this may impact grades each student will get a relative weight of 5 for the lower point assignment. Note this is purely illustrative as with this method Teachers may give any weight they desire to any assignment. Table 4A shows one way assignments within categories may average to give category scores and Table 3B shows how those categorical scores could roll up to Final Scores and Final Grades.

Impact of Averaging Mode

From the limited number of examples presented here one can see that, for one set of Grades, depending on how the Averaging Mode is set, a student with that one set of grades can have a final grade from F to A provided that set of grades include at least one F and one A. The lowest overall grade can be the lowest grade a student got on any assignment, and the highest overall grade can also be the highest grade a student got on any assignment. However, once the averaging mode has been set it will work to some students’ advantage and other students’ disadvantage EXCEPT where a student gets all grades of A: there Final Grade will be an A. The other exception is where students get all grades of F, their Final Grade will be an F. Table 5 shows examples showing the different outcomes of different averaging protocols on a set of student grades.

As we can see in Table 5 the same set of Grades across different categories, depending on the Averaging Mode, can result in any grade from A to F for most students. I hope this helps teachers and administrators understand the significant role that the choice of the averaging mode plays in determining final student marks/grades.

This is where I get the question: What would you recommend?

There is no one size fits all answer. However, there is a concept in assessment and evaluation called ‘Fairness’ which would be applicable in any consideration of a recommendation. To quote from the 2014 edition of Standards for educational and Psychological Testing published by AERA, APA, and NCME p.49:

“The term fairness has no single technical meaning and is used in many different ways in public discourse. It is possible that individuals endorse fairness in testing as a desirable social goal, yet reach quite different conclusions about the fairness of a testing program. A full consideration of the topic would explore the multiple functions of testing in relation to its many goals, including the broad goal of achieving equality of opportunity in our society.”

What if a Category Contains No Assignments?

If a category contains no assignments, then the weight from that category is re-distributed to the other categories.

So, let us say it is early in the term and only one assessment has been given to date. This is usually when grades begin to fall. However, young Michael was away ill and did not take the assessment. The teacher leaves that cell blank on Michael’s record. Michael has no assessment grade. This is not the same thing as him having an assessment grade of zero, this means that the cell for that mark is empty. Michael’s calculated mark is not based on A-40, PA-40, E-10, H-10 but is based on PA-40, E-10, H-10 which is really PA-67%, E-17%, H-17%. Note, while the weights remain the same, because of reallocation of weights the percentages are different.

This is an important factor contributing to the scenario described at the beginning of this article.

Extra Credit Points versus Extra Credit Assignments

There is an important distinction between Extra Credit Points and Extra Credit Assignments. There is also an important similarity.

Similarity

Extra Credit only exists provided that Regular Credit does exist. Most eBGs will only calculate Extra Credit if there are Regular Credit Points. Grades come from ratios. For Regular grades, the numerator of the ratio is the number of points the student has earned and the denominator is the number of possible points. The way Extra Credit points work is that they add points to the numerator but do not add any points to the denominator of the ratio. If there are no Regular credit points, then the denominator is zero. Since division by zero is undefined mathematically no calculation of grades can be done unless there are Regular credit points recorded.

Similarly, Extra Credit Assignments add points to the numerator but no points to the denominator. Therefore, Extra Credit Assignments will only calculate into the Final Mark provided there are Regular Assignments

Often, I will get calls from teachers that they have given extra credit assignments, but those assignments are not reflected in students’ grades. Usually the cause is that there are no Regular Credit Assignments in the category containing the Extra Credit Assignments.

Exempting Assignments

Most eGBs will allow specific scores to be exempt from calculation. What occasionally will happen is that when a score is exempt the category score may disappear. This happens because there are no other Regular Credit points in that category, therefore no denominator for that category, so a score in that category will not calculate.

Summary: What are the range of Possible Final Scores for Students

For the student who consistently scores an A on every assignment the Final Mark will be an A.

For the student who consistently scores a grade of F on every assignment the Final Mark will be F.

For all other students in between, your highest possible grade is limited by the highest grade that you have gotten on any single assignment and your lowest possible grade is limited by the lowest grade that you have gotten on any single assignment.

Exactly how grades will factor into the calculation of the final mark depends on the Averaging Mode selected by the Teacher or the School District.

Some Districts use Categorical Averaging as a guardrail, a mechanism to protect students from ‘unbalanced’ grading. The idea being that a student who is otherwise a good student but poor at test taking can still earn 60% in class by doing everything else even if they score zero on every assessment. The smart student who is unable to get homework done can still earn a 90% in class if they do everything else correctly. These are valid and effective student protection mechanisms.

Caution: What caused our initial scenario? How can we avoid similar situations?

In the Scenario described initially the student had earned a 75% on class assessments [A-40], 42% on engagement [E-10], 0% on homework [H-10] and had not turned in any of the 10 required Practice and Application problems [PA-40] earning 0% on PA. However, the student, as many students are wont to do, came to the teacher to find out what they could do for extra Credit to bring up their grade. The teacher assigned 50 problems indicating the student would get ? a point for each problem done correctly, showing all calculations. The student completed 41 of the 50 problems with no errors and earned 20.5 extra credit points under PA. However, when the required problems column in PA was left blank, PA did not factor into the final mark calculation and the student’s score on A, E, and H was 34.2/60 or 57%. When zero was put in for the required PA problems the extra credit then factored in giving the student 20.5/10 [or 82/40 when weighting is considered] to get a grand total of 116%.

In this case, because leaving the Required PA column blank did not allow the extra credit under PA to factor in the student earned 57%, a grade of F. When the teacher put in the 0 in the required PA column it allowed the PA extra credit to factor in and the student earned 116%, a grade of A.

Conclusion:

I often say:

No matter how high we set the bar some students will find a way to get over it and no matter how low we set the bar some students will find a way to crawl under it.

It is important that students are clear on how their work is being assessed and how their grades are being calculated. It is equally important that teachers understand how grading protocols work and the possible effects of different averaging modes, assignment exemptions, extra credit points, and extra credit assignments. We should use our tools to help our students develop a growth mindset and good work habits. These are the lenses we need to use to examine what we do so that we create environments to support successes for our students, not only at their current educational level but to prepare them for success at the next level whether that be additional education opportunities or advancement in their chosen career pathways.