EXD.5:5 - Archetypal Grounding

The fixed task asks for the mean across all individuals. Group A has two values with mean 3; group B has six values with mean 8. The learner’s first product is “(3 + 8) / 2 = 5.5, because there are two averages.”

Preserve that response. Ask, “Which things receive equal weight in this calculation?” The learner says, “The two groups.” Ask, “Which things should have equal weight in the question?” If the learner identifies the individuals, guide the mismatch: the denominator two counts groups, while the target contains eight people.

The corrected explanation should state: “Each mean summarizes a different number of people. The group sums are 2 × 3 = 6 and 6 × 8 = 48. Divide 54 by the total count eight to get 6.75.” If the learner cannot reconstruct a group sum, supply that relation explicitly and retain it as help.

A retry uses three values with mean 4 and nine values with mean 8. Ask for the pooled mean and why its denominator has that value. The correct result is (3 × 4 + 9 × 8) / 12 = 7. A response that uses the total count and reconstructs both sums meets the stated criterion under the available assistance. It does not yet establish independent performance after a delay.

For a contrasting target, ask for equal influence of the two group means. The result is then 6. The learner should preserve the target-dependent rule, not replace one memorized shortcut with a claim that group means must always receive count weights.

These are constructed prompts and answer criteria. The actual learner’s responses determine which help and further work are warranted.