MarkBook Models of Assessment, Evaluation, Calculation & Recording

    MarkBook^Ž   Appendix  A - 4

Grade Calculation Algorithms

How does one value or weight assessment data when multiple assessment measures are combined into a single grade? Do all measures count equally? Or are their contributions adjusted in some way? Do the measures have to fit into a category system? If so, are there fixed values or weights for each category? If using a calculation, does your system require an average, a median, or a mode as the determiner of central tendency? Or does it require a professional judgment based on examination of all of these? This section discusses MarkBook's algorithm calculations and how to use MarkBook to best match your needs.

MarkBook has eleven separate calculation algorithms to come up with a determination of central tendency. To do that, assessment data in letters or levels is converted into a percentage to six decimal places. Then the user's selected weighting system is applied. The calculation method is next. The calculated number is rounded off to the nearest integer or a single decimal, if selected.

WEIGHTING SYSTEMS

The value or weight of each assessment entry must be controlled in one of three ways: Entry Weight, Equal Weight, or Category Weight.

The "Entry Weight" System
This is the calculation system employed by many teachers when calculating grades manually. It is also the calculation method that students will use when computing their own grades. To calculate an overall grade, the educator adds up the total number of marks earned by each student, divides by the total base, and converts this to a percentage. Experienced educators recognize the difficulties with this method as discussed in section 7-6. However, MarkBook will perform this calculation method if necessary when the following steps are taken.

section 7-1

In this system, MarkBook will treat each assessment's base mark as its weight.

The "Equal Weight" System
In this system, the evaluator wishes to have all assessment items count equally towards the final grade. In this case, enter "1" as the weight for every assessment. This is done in the Entry Heading screen section 7-2. These weights can be changed later. Or, click on the 'Equal Weight' option in the Weight screen, section 7-6.

An Equal Weight calculation method is applicable for courses that have a very regular major summative test with no other kinds of assessments. A bar admissions course is an example. Each new lawyer attends lectures all week and writes a Friday exam on that week's work. This repeats for sixteen weeks. Final grades are calculated with each exam counting for one sixteenth of the overall grade. One caveat: if more than two exams are failed, the student is out.

The "Category Weight" System
In this system, the educator classifies all assessment items into categories (also known as "strands"). Each category is given a "Target Weight" so that the whole category contributes a fixed percentage towards the overall final grade. Educators may have such categories mandated by their administration. Reporting requirements may also dictate the category names and the weights of each. See examples in Chapter 10 beginning with section 10-4. To set up a category weight system:

section 7-6

section 7-1

MarkBook's categories can be established at the beginning of the course as in the "Categories/Strands" part of section 1-3. OR, categories can be created "on-the-fly" whenever you enter data as in section 7-2 or section 7-3.

If a teacher has entered lots of assessment data as per the Entry or Equal weight systems, they can still convert to a category system. Click on Mark Set at the top of the main operating screen, section 3-1, select "Edit [course]" and create one or more categories as in section 1-3. Switch to the "Category" weighting method. Now, from the main operating screen, select each entry in turn and click on "Entry XX Heading". Edit the entry so that it is in an appropriate category. Click Save and select the next item to edit. When done, the weight system originally set up will have been converted to a Category weight system.

CALCULATION OF CENTRAL TENDENCY
There are three traditional mathematical measures of center, Mean (aka Average), Median, and Mode. Measures of central tendency are measures of the position of the center or middle of a distribution. Since students don't always get the same mark or score on each succeeding assessment, teachers look for a middle position that characterizes each student's overall performance across all measures. The definition of 'middle' or 'center' is vague so that the term 'central tendency' can refer to a wide variety of measures.

Average or Mean
An average or mean is the sum of all scores divided by the count of those scores. It has advantages and disadvantages in the determination of a student's grade. First advantage: almost everyone knows what an average is and how to calculate it. Secondly, it's a sensitive calculation. That is, if one new assessment is added to the distribution, the new calculated average will almost always move up or down from the previous one. However, average has some problems as a determiner of central tendency for grades and is strongly criticized. Anomalous or outlying scores have such an impact on average that a false impression can be made. See section 9-4. Secondly, since it's widely used, some educators that it's the only reliable measure and all other measures are clearly suspect.

MarkBook will calculate an average with any of the three weighting systems taken into account.

Median
A median is the middle number is a set of numbers. In the case of a tie, it's the average of the tied numbers. The usual presumption is that all numbers have equal significance in determining a median. In the determination of a student's grade, it's a reliable determiner of central tendency provided that all assessments are weighted equally. However, in most collections of student assessment data, the assessments are differentially weighted. In this case, it's necessary to take into account those weights in calculating a weighted median.

Suppose a student has seven assessment marks: 16, 45, 54, 72, 78, 83 and 91. The unweighted median is 72. Suppose that the first assessment has a contribution towards the overall grade of 5%, the second 10%, the third, 40%, the fourth 15%, the fifth 10%, the sixth 15% and the last 5%. For a weighted median, MarkBook adds up the percentage weights in mark order until it reaches 50%. The mark overlying the 50%-of-weight position is the weighted median. In this example, it's 54, much different from 72. By taking weights into account, this calculation correctly factors the significant instruments more heavily than others.

Mode
A mode is the most frequent number in a set of numbers. As a determiner of a student's grade, it's misleading and useless on a percentage scale. However, if the assessment data is scored in levels or ABC letter grades, then mode gives a very useful picture of consistency. For a more elaborate discussion of mode in levels, see section 8-9. See examples of mode compared to average in section 9-4. A view of Mode is always available in the Student Report / Modal Analysis screen.

Putting the weighting systems and the calculation methods together, MarkBook can calculate a grade using the combination of any filled cell in the following chart.

	Entry Weight	Equal Weight	Category Weight
Average or Mean
Mode
Median
Blended Median
Blended Mode

Blended Median

Blended median is a hybrid calculation combining the principles of two calculation methods. To calculate a Blended Median, MarkBook determines the weighted median in each category. Then, these medians are averaged with the category weights factored in. The resulting percentage is an average but it's an average of medians not an average of marks.

Blended Mode

Blended Mode is a similar hybrid in which MarkBook first determines the Mode by level within each category using the levels defined for Modal Analysis under Setup. See section 7-1. It then converts this 'most consistent level' to an equivalent percentage for each category. MarkBook then averages these percentages taking the category weights into account. Again, the resulting percentage grade is an average but it's an average of modes and not an average of marks. For some students, the Blended Mode may fluctuate significantly whenever the user switches to a new levels scheme.

For any weighting/calculation method, select it on the Mark Sets / Edit screen as below. Note that if Blended Mode or Blended Median is selected, the only allowed weighting system is by category.

USING PROFESSIONAL JUDGMENT

MarkBook will calculate positions of central tendency with the weighting and calculation methods above. However, each educator is expected to make a professional judgment after viewing these presentations. Have a look at the average, at the mode and at the weighted median. For examples, see section 9-4. What do the calculations say about each individual? When there is a conflict among the various best measures (there frequently IS a conflict), it's necessary to decide what grade to assign each learner. As long as there is a solid rationale for assigning a specific number, the process is valid. A teacher often has more information about each learner than just marks. Medical and social problems, language barriers, specific learning disabilities, evidence of most recent achievement, and other elements in each student's life should be factored into this decision. This is called evaluation.

No computer software is capable of making a professional judgment. Nor should it try! Similarly, an educator shouldn't blindly rely on a single measure of central tendency. MarkBook will provide a detailed analysis of each learner's results. It's up to the educator to make a final grade determination based on all available evidence.

Manual: Go to Appendix A-5 for a discussion of why a teacher should use Class Management Software.