Assessment — when the numbers don’t add up
ASSESSMENT and numbers don’t go together, they’re not like terms.
Yet numbers are still at the heart of most grading done by teachers, even math teachers.
Numbers in assessment do only harm.
For a start they are grossly inaccurate, offering only spurious objectivity. But mostly they divert students from focussing on their learning. Ditto if you replace the numbers with letters.
In short, alpha-numeric grades suck.Students focus on their learning when they no longer feel the need to focus on grades. Shift the feedback from numbers and letters to descriptive feedback, and you shift the focus from grades to learning. Focus on the learning and forget the grades.Let’s look at the accuracy.
A teacher scores assignments on a range of 0 to 4. He, or rather his percentage-based grading software, converts the number to a percentage.Say he has a student who mostly scores threes. Except on some days it is raining and our teacher is grumpy and gives a two. Or, on sunny days he is happy and feeling generous and gives a full 4.
Over, say, 12 assignments the average score would be 36. If it was always raining, the score would be 24. If always sunny the score would be 48. That’s plus or minus 12 out of a total possible score of 48, plus or minus 25 per cent.Now, let’s assume our teacher only swings 0.5 either way. If it always rains, the score would be 30, or if it shines as high as 36. That’s plus or minus six out of 48, or plus or minus 12.5 per cent.
Now let’s assume our teacher is obsessive. He scores directly as a percentage, a number out of 100. Presumably he must have have 100 criteria on which he is making the decision… 1 per cent per criteria.
Well, let’s assume the plus or minus on the average grade of 75 per cent is between say 70 per cent at its lowest on a rainy day and 80 per cent for sunny days. Then that’s plus or minus 5 per cent.
At the end of the semester is the student grade C, B or A? Well, the student could have gotten some 4s on sunny days, so on some days the student was grade A. On rainy days, the student was struggling to get a C.In percentage terms the student was probably a secure B. Or, maybe not. What if in percentage terms the student was plus or minus 5 per cent on an average of 85 per cent, or even a little higher. A or B?
But on what basis was the teacher scoring? How to define a score down to one point out of 100, or even five points out of 100? Against what is the score, percentage, defined? After all, mathematically a percentage must be out of something. What is the something? Does the student know. Indeed, does the teacher know?
Some teachers are confident they do. I’ve watched as a student, eyes full of tears (of anger or frustration?) appealed an 89 per cent and seen the teacher abdicate their professional judgement and refuse to budge from the magic computer-generated number and concede the A. She must have been confident her grading was consistently well within a margin of error of less than one in 100.I’ve seen a teacher post percentages to three decimal places… presumably the teacher had a rubric defining their grading down to 100,000 criteria!
As Alfie Kohn has pointed out in his inspirational The Schools our Children Deserve “what grades offer is spurious precision — a subjective rating masquerading as an objective evaluation.”
Research, Kohn says, has long been available confirming what all teachers know: any given assignment may well be given two different grades by two equally-qualified teachers. “It may even be given two different grades by a single teacher who reads it at two different times,” says Kohn.
Quoting Paul Dressel’s 1957 article Facts and fancy in assigning grades, Kohn says a grade “is an inadequate report of an inaccurate judgement by a biased and variable judge of the extent to which a student has attained an undefined mastery of an unknown proportion of an indefinite amount of material.”
As Kohn says: “A teacher can meticulously record scores for one test or assignment after another, eventually calculating averages down to a hundredth of a percentage point, but that doesn’t change the arbitrariness of each individual mark.”
But what if a teacher counts right answers, surely that must give an objective assessment?
What about the student who clearly understands the concept, but made a silly computational error? What about the student who gets the right answer by successfully repeating the steps of an algorithm, but who cannot explain why the algorithm works or what it means?
Does that assessment say much about either student’s learning? More to the point, does the assessment do anything to help either student achieve learning?
So, what about numbers, points, percentages, letters… and focus on learning?
As the Assessment Reform Group has concluded: “Feedback that emphasises relative performance, for example marks or grades which are formally or informally compared with those of others, encourages pupils to concentrate on getting better grades rather than on deeper understanding.”
Alan Blankstein in Failure is NOT an Option, arguing that “grades and test scores do not reflect what children are really learning,” points to an example of a child whose “intrinsic motivation to learn and do well has been replaced by an external motivator: grades”.
As Alfie Kohn concludes: “Research has found three consistent effects of traditional grades: students think less creatively, they lose interest in what they’re learning, and they try to avoid challenging tasks.
“Thus, rather than trying to improve techniques for grading, we should be looking for alternatives − and rather than complaining that too many students are getting A’s, we should be worried that too many students think that getting A’s is the point of education”
Entry filed under: Assessment + Grading, Thoughts from the classroom, What's on the PiFactory blog.... Tags: alpha-numeric grades, alphanumeric grades, Assessment + Grading, assessment for learning, descriptive feedback, education, formative assessment, grades, grading, math, percentage based grading, summerative assessment.