Instructional explanation

Use this profile when a learner needs to reconstruct and use a relation that a learning task requires. A lesson, example or demonstration is insufficient when the learner can imitate its surface but cannot make the required connection. Start from the target performance and its criterion, including the help permitted. A learner who already performs the relevant task, or someone seeking only a sufficient immediate answer, may need no additional explanatory exercise.

Human Capability Development supplies the task through HCD.6, feedback tied to the task criterion and retry through HCD.9, task-specific assistance through HCD.10, and instructional-material evaluation through HCD.19. Explanation Design constructs the relation-bearing account, example, expression and recipient contribution within that work. It neither infers a capability deficit from every failed explanation nor treats today’s assisted correction as a durable capability result.

For the pooled-mean task, suppose the learner can add and divide and initially writes “(3 + 8)/2 = 5.5, because there are two averages.” The required question is equal weight per individual. EXD.1 preserves that target; EXD.2 shows why count multiplied by mean recovers each group sum. EXD.3 can place count, mean and sum together, while retaining the same subject claims.

EXD.5 asks what the denominator should count under this target. Preserve the initial explanation. If needed, point to the eight individual observations and ask the learner to reconstruct the total sum and count. Record the corrected calculation, 54/8 = 6.75, with the help supplied. A retry with three observations of mean 4 and nine of mean 8 requires (12 + 72)/12 = 7. The product criterion is the reconstructed relation between group sums, group counts and the individual mean; a correct number alone can result from copying.

A changed target remains a changed target in instruction. If the learner now asks for equal weight per group, the corresponding mean is 6 in the retry, and EXD.4 returns to the selected question. The instructor can separately decide whether the original learning objective still requires the individual-weighting task.

Recognition concerns a particular learning obstacle and a plausible constructive move. Assurance concerns the product actually obtained at the stated help conditions. An unaided changed task can support a claim about that performance; retention needs a later opportunity, and broader transfer needs a task that tests the intended changed relation or context. Observations on one learner or a constructed example do not establish a population effect.

Guidance can reduce an irrelevant search burden while concealing what the learner can do independently. An initial contribution can reveal a missing relation while imposing unnecessary effort on an unprepared learner. Choose the opportunity and assistance by the task and preparation; compulsory initial failure, repeated self-explanation and automatic fading are poor substitutes for that decision.

Fiorella’s differentiated explaining, visualizing and enacting contributions, the 2023 relational-mapping study, Zhang and Fiorella’s error-focused feedback, and Tetzlaff and colleagues’ assistance synthesis inform EXD.2/.5 at their stated limits. Mayer’s multimedia principles and Cromley and Chen’s synthesis inform EXD.3’s conditional form choices. These sources support candidate instructional moves and relevant distinctions; they do not certify this particular lesson. The practical gain is a repair directed at the needed relation with interpretable assistance and retry evidence. EXD.6 and HCD.19 decide whether changing the material is worth its burden or whether a different task or support question owns the next action.