Counting and school grades #rhizo15


Lot of confusion about grades and counting.

Teachers do not understand grading.
Grading is measurement on a nominal/ordinal scale.
Both scales are qualitative scales.
A student with grade A (or a 10) and a student with grade B (or a 8) and a student with grade C (or 6) have different grades. The median, i.e. middle-ranked, item is allowed as the measure of central tendency; however, the mean (or average) as the measure of central tendency is not allowed.
The average grade of these three students is not B. The average grade does not exist.
Student A did a better job than student B and C, but we cannot say student A is twice better or 20 % better.
In ordinal scales the grades or numbers are not real counting but it is labeling. (the pedagogical error of labeling a test outcome with a B-label, or a 8-label and applying the label to the student as well)
In ordinal scales a real, arithmetical zero does not exist.

Some people are still writing about these scales and which operations are allowed.

I’m thinking the question isn’t what can we measure, but how can we get the instruments we have to help us measure and evidence the developmental changes we know are occurring and need to be recognised and valued?

What information is in a ordinal scale?
In an ordinal scale the A’s and C’s and 10’s and 4’s try to place items in a meaningful order. The A and 10 are tags or labels. In schools the scale tells us the order of having no mistakes in a test and having more errors in a test.

Of course the diagram is impossible. Ordinal grades cannot make a graph like that. (


2 thoughts on “Counting and school grades #rhizo15

  1. At my Uni we mark and grade like this:

    A1: 22
    A2: 21

    G2: 0

    (we have 5 A grades to try to persuade markers to use the full range).

    I wondered your opinion about this?

  2. Human teachers do not use the full range of the available scale. That is the first disturbance of the fair grading of student performance. This is one reason to look upon grades and points as ordinal figures.
    If A1 is a grade for performance in a course, and 22 are the course points or grade points than the school errs in viewing the course points as interval scale numbers or as ratio scale. These numbers are a translation of a ordinal scale in letters to an ordinal scale in numerals. The average of the ordinal numerals is a not allowed operation. The grades-to-course-point operation is a confusing way to evaluate the overall performance of a student.

    And if all courses are as heavy and difficult one could argue that the grades could be regarded as interval scale. I would not agree with that. Because how do we weigh the difficulty of a course?

    So ‘clever’ students will read some easy courses to collect course points to lift up their average course points.

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