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5. Using Calculations > Calculating the course grade

Calculating the course grade

Calculating the course grade All graded activities that are added to the online course will automatically be added to the gradebook. The students can have a range of assessments for which they will be given a range of scores. Apart from storing these grades, the gradebook can also calculate a final grade based on a range of preset aggregation settings available within the course. Aggregation is bringing together all the scores and then doing a calculation to present a final score. Before this aggregation takes place, a normalization process occurs. Normalization is when the grade given to an individual assessment is converted into a percentage and then used as a decimal for the calculations. Why use normalization? Normalization is necessary to ensure that all the grades have the same base value so that they can be calculated fairly in relation to the maximum grade. For example, a grade of 20 out of 100 is a lower percentage score than 20 out of 20. So, using both scores as 20 would not represent the achievement by the learner. In order for the gradebook to calculate a fair total, we need both of the grades to be recalculated into a decimal so that they have the same base value prior to adding them together for the final course grade. The calculation for normalization is the grade awarded divided by the total grade possible, so that all the graded activities have a base value of 10. The following table shows this for the two activities in this example:


As you can see, the normalized grade now shows that the two awarded scores of 20 should not be treated the same when calculating the final course grade, as they have significantly different decimal scores. It is this score that is used in the aggregation process. We will see many more examples of how this normalization process is used as we complete examples throughout the chapter and see how the different aggregation types use the normalized grades. Aggregation types Moodle has a range of aggregation types available and these are outlined briefly as follows. These are shown in the order they are listed within Moodle. The ones shown in bold, which are some of the most popular or the more complex to understand, will be used as detailed examples later in the chapter, and the actual calculations will be explained in more detail. However, for each of the following aggregation types, quick examples will also be given to show the calculation that takes place. For all the examples, the normalized grades of 1.0 and 0.2, as shown in the previous example, will be used. Mean of grades: Following normalization, the average score is calculated as the final score by adding up the total grades awarded and dividing it by the total number of graded items. Quick example: (1.0 + 0.2)/2=0.6.Weighted mean of grades: Each graded item can be given a weight. The grade given for the assessed item is normalized and then multiplied by the items weight to create an increased item grade. The final grade is calculated by adding together the increased item grades and then dividing this by the total weights applied (for example, if two assessments are given a x2 weight, the total of the increased grades added together will be divided by four). Quick example: (using a weighting of x2 for graded item one, and x3 for graded item two): (1.0x2)+(0.2x3)/5=0.52.Weighted mean of grades: Each graded item can be given a weight. The grade given for the assessed item is normalized and then multiplied by the items weight to create an increased item grade. The final grade is calculated by adding together the increased item grades and then dividing this by the total weights applied (for example, if two assessments are given a x2 weight, the total of the increased grades added together will be divided by four). Quick example: (using a weighting of x2 for graded item one, and x3 for graded item two): (1.0x2)+(0.2x3)/5=0.52.Simple weighted mean of grades: In this version of the weighted mean type, the maximum grades of each assessed item are used as the weighting, instead of the teacher needing to apply separate weights to each graded activity. For example, one assessed activity could be graded out of 100 and another activity could be graded out of 50. The first graded item would be worth more to the final course total than the second. Again, the gradebook first normalizes the grade and then multiplies that grade by the total grade possible. These increased assessment activity grades are then divided by the total weight possible (that is, the total of all the maximum grades in the course). Quick example: (1.0x20)+(0.2x100)/120=0.333.Mean of grades (with extra credit): This aggregation type is only available in Moodle to enable upgraded courses that already use this aggregation type to continue to use it (that is, for backwards compatibility). The weighted and simple weighted means options should be used instead to prevent the use of an aggregation method that is no longer supported.Median of grades: All the normalized grades are put into numerical order from lowest to the highest, and the final grade will be the grade in the middle of this list. If there is no middle number (if the total number of grades is an even number), Moodle will take the two middle numbers and present the average grade of these two as the final grade. Quick example: As there are only two numbers in our example, the final course grade will be an average - (1.0+02)/2=0.6. To show as an example, an additional graded item will be included. This grade will be 30 out of 30 which will provide a normalized grade of 1.0. Therefore, there are now three grades for this example: 0.2. 1.0 and 1.0 which are shown in order from lowest to highest. The gradebook will present the final grade as 1.0 as this is the grade in the middle.Lowest grade: Reviews all the grades, after normalization, and presents the lowest score as the final grade. Quick example: The final grade will be 0.2.Highest grade: Reviews all the grades, after normalization, and presents the highest score as the final grade. Quick example: The final grade will be 1.0.Mode of grades: Following normalization, the gradebook reviews all the grades and the grade that is awarded most frequently is presented as the final grade. Quick example: 0.2, 1.0, and 1.0. Final grade = 1.0.Sum of grades: This is the only aggregation method that does not use normalization. In this aggregation type, the gradebook simply adds together each score awarded for each assessment. This maximum grade possible for the course is all the maximum grades possible for each individual assessment added together. Quick example: 20 + 20 = 40 out of a maximum grade of 120. Maximum grades It is possible to set a maximum score for the course which means that Moodle will calculate the final score based on that maximum grade. For example, ten assessments in a course, each with a maximum grade of 25, will have a course total of 250. However, the final course grade achievable may only be 100. Therefore, the aggregation process can also convert the final score so that it is graded out of 100 (rather than 250). Where a maximum score is applied, the gradebook will add an additional calculation after aggregation as shown in the following step 3. Therefore, the full aggregation process will be: Normalize grades.Aggregation calculation (for example, apply weights, add grades together, calculate average, and so on).Multiply the aggregated normalized grades by the course maximum grade. Note Maximum grades do not apply with the sum of grades aggregation. Confused? Let’s take a look at an example to see the normalization, aggregation, and maximum grade calculations in action! Take a look at the following table and note the formulas shown in brackets to see the processes that the gradebook is completing for us. In this example, there are five graded activities within the course, each with a different maximum grade possible. The gradebook aggregation is set as a mean of grades calculation (the average of the grades). The maximum grade possible for the whole course is 100. The shaded row is the information that the gradebook uses for the aggregation/calculations.


To calculate the normalized grade, the grade awarded is divided by the maximum grade for each assignment. The calculation used is shown in brackets in the shaded row for columns A1 to A5. The mean aggregation grade is calculated by adding together the normalized grade for each of the grade items (the calculation is shown in the shaded row for the column Usual total). This is then divided by the total number of grades awarded which, in this example, is 5. This calculation is shown in the shaded row in the Mean aggregation column. The final grade is 84. The mean aggregation grade is multiplied by 100 which is the course maximum (you can see the calculation in the Final grade shown in the gradebook column). If the course maximum was 30, the final grade would have been 25.2 (0.84*30=25.2). Let’s go into the gradebook and set up some examples to see the aggregation types in action, and learn some other things that we can do to customize the gradebook so that it can further meet our needs.

  

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