What do we want? Passing average or competency always?

I’m at the Australasian Computer Science Week at the moment and I’m dividing my time between attending amazing talks, asking difficult questions, catching up with friends and colleagues and doing my own usual work in the cracks.  I’ve talked to a lot of people about my ideas on assessment (and beauty) and, as always, the responses have been thoughtful, challenging and helpful.

I think I know what the basis of my problem with assessment is, taking into account all of the roles that it can take. In an earlier post, I discussed Wolff’s classification of assessment tasks into criticism, evaluation and ranking. I’ve also made earlier (grumpy) notes about ranking systems and their arbitrary nature. One of the interesting talks I attended yesterday talked about the fragility and questionable accuracy of post-University exit surveys, which are used extensively in formal and informal rankings of Universities, yet don’t actually seem to meet many of the statistical or sensible guidelines for efficacy we already have.

But let’s put aside ranking for a moment and return to criticism and evaluation. I’ve already argued (successfully I hope) for a separation of feedback and grades from the criticism perspective. While they are often tied to each other, they can be separated and the feedback can still be useful. Now let’s focus on evaluation.

Remind me why we’re evaluating our students? Well, we’re looking to see if they can perform the task, apply the skill or knowledge, and reach some defined standard. So we’re evaluating our students to guide their learning. We’re also evaluating our students to indirectly measure the efficacy of our learning environment and us as educators. (Otherwise, why is it that there are ‘triggers’ in grading patterns to bring more scrutiny on a course if everyone fails?) We’re also, often accidentally, carrying out an assessment of the innate success of each class and socio-economic grouping present in our class, among other things, but let’s drill down to evaluating the student and evaluating the learning environment. Time for another thought experiment.

Thought Experiment 2

There are twenty tasks aligned with a particularly learning outcome. It’s an important task and we evaluate it in different ways but the core knowledge or skill is the same. Each of these tasks can receive a ‘grade’ of 0, 0.5 or 1. 0 means unsuccessful, 0.5 is acceptable, 1 is excellent. Student A attempts all tasks and is acceptable in 19, unsuccessful in 1. Student B attempts the first 10 tasks, receives excellent in all of them and stops. Student C sets up a pattern of excellent,unsuccessful, excellent, unsuccessful.. and so on to receive 10 “Excellent”s and 10 “unsuccessful”s. When we form an aggregate grade, A receives 47.5%, B receives 50% and C also receives 50%. Which of these students is the most likely to successfully complete the task?

This framing allows us to look at the evaluation of the student in a meaningful way. “Who will pass the course?” is not the question we should be asking, it’s “Who will be able to reliably demonstrate mastery of the skills or knowledge that we are imparting.” Passing the course has a naturally discrete attention focus: focus on n assignments and m exams and pass. Continual demonstration of mastery is a different goal. This framing also allows us to examine the learning environment because, without looking at the design, I can’t tell you if B and C’s behaviour is problematic or not.

A has undertaken the most tasks to an acceptable level but an artefact of grading (or bad luck) has dropped the mark below 50%, which would be a fail (aggregate less than acceptable) in many systems. B has performed excellently on every task attempted but, being aware of the marking scheme, optimising and strategic behaviour allows this student to walk away. (Many students who perform at this level wouldn’t, I’m aware, but we’re looking at the implications of this.) C has a troublesome pattern that provides the same outcome as B but with half the success rate.

Before we answer the original question (which is most likely to succeed), I can nominate C as the most likely to struggle because C has the most “unsuccessful”s. From a simple probabilistic argument, 10/20 success is worse than 19/20. It’s a bit tricker comparing 10/10 and 10/20 (because of confidence intervals) but 10/20 has an Adjusted Wald range of +/- 20% and 10/10 is -14%, so the highest possible ‘real’ measure for C is 14/20 and the lowest possible ‘real’ measure for B is (scaled) 15/20, so they don’t overlap and we can say that B appears to be more successful than C as well.

From a learning design perspective, do our evaluation artefacts have an implicit design that explains C’s pattern? Is there a difference we’re not seeing? Taking apart any ranking of likeliness to pass our evaluatory framework, C’s pattern is so unusual (high success/lack of any progress) that we learn something immediately from the pattern, whether it’s that C is struggling or that we need to review mechanisms we thought to be equivalent!

But who is more likely to succeed out of A and B? 19/20 and 10/10 are barely distinguishable in statistical terms! The question for us now is how many evaluations of a given skill or knowledge mastery are required for us to be confident of competence. This totally breaks the discrete cramming for exams and focus on assignment model because all of our science is built on the notion that evidence is accumulated through observation and the analysis of what occurred, in order to be able to construct models to predict future behaviour. In this case, our goal is to see if our students are competent.

I can never be 100% sure that my students will be able to perform a task but what is the level I’m happy with? How many times do I have to evaluate them at a skill so that I can say that x successes in y attempts constitutes a reliable outcome?

If we say that a student has to reliably succeed 90% of the time, we face the problem that just testing them ten times isn’t enough for us to be sure that they’re hitting 90%.

But the level of performance we need to be confident is quite daunting. By looking at some statistics, we can see that if we provide a student with 150 opportunities to demonstrate knowledge and they succeed at this 143 times, then it is very likely that their real success level is at least 90%.

If we say that competency is measured by a success rate that is greater than 75%, a student who achieves 10/10 has immediately met that but even succeeding at 9/9 doesn’t meet that level.

What this tells us (and reminds us) is that our learning environment design is incredibly important and it must start from a clear articulation of what success actually means, what our goals are and how we will know when our students have reached that point.

There is a grade separation between A and B but it’s artificial. I noted that it was hard to distinguish A and B statistically but there is one important difference in the lower bound of their confidence interval. A is less than 75%, B is slightly above.

Now we have to deal with the fact that A and B were both competent (if not the same) for the first ten tests and A was actually more competent than B until the 20th failed test. This has enormous implications for we structure evaluation, how many successful repetitions define success and how many ‘failures’ we can tolerate and still say that A and B are competent.

Confused? I hope not but I hope that this is making you think about evaluation in ways that you may not have done so before.