Why Hard Courses Are Hard

Difficulty has more than one source

A hard course is not simply a course with a lot of material. We find it useful to separate three things: how complex the content is, how the teaching is designed, and what the learner already knows. Cognitive load theory gives these names. As the Learning Scientists describe it, intrinsic load is the working memory taken up by the task itself, while extraneous load is working memory spent on things outside the task's core demands, such as poor design or distraction.

The key idea inside intrinsic load is element interactivity. When elements are largely unrelated, as with foreign-language vocabulary, each can be learned alone. When they must be held together, as with the slope-intercept equation, the same source says, "the more elements that interact, the more working memory is needed". Background knowledge helps because it lets learners chunk elements together, as experienced readers process phrases and not single words.

Why the limit is working memory

The limit is small. A 2006 paper in Educational Psychologist summarises research showing that almost all unrehearsed information in working memory is lost within about 30 seconds. It cites an estimate of about seven items that may be as low as four, plus or minus one, and notes that when items are actively processed the number may be only two or three. These limits apply mainly to novel material. Long-term memory is where instruction aims to make a difference, and the authors state that the aim of all instruction is to alter it.

This explains a familiar pattern. An expert and a novice can look at the same page, yet the expert sees a few chunks and the novice sees dozens of loose elements.

A worked illustration

Here is a simple model of our own, illustrative, not real data, and not taken from the sources above. If every element in a task must be related to every other, the number of pairwise relations is:

• Relations = n x (n - 1) / 2

Four interacting elements give 4 x 3 / 2 = 6 relations. Eight give 8 x 7 / 2 = 28. Doubling the elements more than quadruples the relations. A novice who has not chunked the material faces something closer to the second number, while an expert who treats four of those elements as one unit faces something closer to the first. The model is crude, since real material is rarely fully interconnected, but it shows why a topic can feel several times harder after a modest increase in scope.

Difficulty that helps and difficulty that does not

Not all difficulty is a defect. In a chapter on desirable difficulties, two UCLA researchers argue that current performance can be "a highly unreliable index of whether learning has occurred". Cramming supports short-term performance, whereas spacing, interleaving, generating answers and using tests as study events support long-term retention. In one interleaving result they describe, 63 percent of new problems were solved correctly a week later, against 20 percent under blocked instruction.

A 2013 review of ten learning techniques, summarised by the Association for Psychological Science, rated practice testing and distributed practice highest, and rated summarisation, highlighting and underlining, and rereading low. The full report appeared in Psychological Science in the Public Interest in 2013. A press report on the review quotes its lead author as saying the techniques "will not be a panacea" and will benefit only students who are motivated and capable of using them.

What the evidence does not show

These sources are not new, and we have not found a single current release that settles the matter, so we state their dates. The 2006 paper argues for extensive guidance for novices, and says worked examples are superior for them. That is one position in a continuing debate, and we think the right balance depends on the learner and the material. An article in Instructional Science also notes that intrinsic load depends on more than element count, including prior knowledge and the learner's need to change categories of thought. Nothing here tells a teacher how much difficulty is right for a particular student.

Going deeper

Three ideas take the topic further. First, the three load types: intrinsic, extraneous and, in some accounts, germane. The Learning Scientists note that the intrinsic and extraneous labels depend on the goal of the task, so the same feature can be either.

Second, retrieval strength and storage strength. The UCLA chapter links current performance to retrieval strength and long-term learning to storage strength, which is why a condition that raises today's score may not raise next month's.

Third, how to read the primary reports. Check which students, materials and tasks the evidence covers, whether the outcome was a delayed test or an immediate one, and whether the comparison used the same study time. The 2013 report runs to pages 4 to 58 of volume 14 and rewards a slow read.

We would like to be corrected where we are wrong. Each link above points to the page we read, and we invite you to check it.