Mixed Problem Set¶
Artifact — instantiates Interleaved Discrimination Practice
A curated set of practice problems spanning several confusable target types, so the solver must choose the method before working the problem.
A Mixed Problem Set is a written collection of practice problems deliberately drawn from several related target types and arranged so that no heading, section, or ordering tells the solver which method applies. It is defined by its contents — the span of confusable target types it curates — not by any shuffling procedure. The whole point is to reinstate the one act that a homogeneous chapter-end exercise block removes: deciding what kind of problem this is before doing anything else. A block of twenty momentum problems trains the arithmetic of momentum; a set that hides one momentum problem among energy, force-balance, and rotational ones trains the far scarcer skill of recognizing that momentum is what the situation calls for. The artifact carries a prompt that forces this recognition to happen out loud, and a feedback key that explains the discriminating cue when the solver picks wrong.
Example¶
A first-year physics instructor notices her students ace the end-of-chapter problems and then fail the same problems on the cumulative final. On the homework, the chapter title Conservation of Energy has already told them to write down the energy equation; on the exam, nothing does. So she builds a Mixed Problem Set: eighteen problems that silently rotate among four already-taught methods — energy conservation, momentum conservation, Newton's-second-law force balance, and rotational dynamics — with no method named and no two adjacent problems sharing one. Each problem carries a single instruction at the top: before you compute anything, write one sentence naming which principle applies and why, and name the principle you first considered and rejected. The answer key is not just worked solutions; beside each it prints the discriminating cue — "a collision with no external horizontal force, so momentum, not energy: the collision is inelastic and dissipates energy." A student who reaches for energy on an inelastic collision sees exactly which feature should have redirected her. Over three weeks her class stops asking "which formula?" and starts reading the situation for the cue.
How it works¶
What distinguishes this artifact from an ordinary worksheet is three deliberate design moves, not the mere fact of variety:
- Curate a confusable span, not a random grab-bag. The set includes only methods a competent solver could plausibly confuse in this domain; unrelated topics are excluded, because mixing unrelated targets produces attention-splitting, not discrimination.
- Strip the advance label. Section headings, worked-example proximity, and problem ordering are all scrubbed of anything that pre-announces the method. Adjacency is arranged so consecutive problems demand different methods.
- Require the naming act before the work. Each problem asks the solver to commit to a method — and to the nearest method they ruled out — in writing, before solving. This converts a silent, skippable judgment into a scorable one.
- Key the feedback to the cue, not the answer. The solution key foregrounds the feature that selects the method and the feature that rules out the tempting wrong one, so a miss becomes information about the boundary rather than just a red mark.
Tuning parameters¶
- Category count — how many distinct methods the set spans. More categories raise discrimination demand but can overwhelm a solver who has not yet reached fluency in each; fewer keep the load learnable but risk under-training the choice.
- Confusability of the span — whether the mixed methods are near-neighbors (energy vs. momentum) or far apart (kinematics vs. thermodynamics). Near-neighbor spans train fine discrimination; far spans are easier and mostly train recognition of gross type.
- Naming-prompt strictness — whether solvers merely pick a method or must also justify it and name the rejected alternative. Stricter prompts surface reasoning but slow the set down.
- Feedback grain — answer-only, worked-solution, or cue-explained keys. Cue-explained keys teach the boundary but cost more to author.
- Distractor density — the fraction of problems engineered to look like one method but require another. High density sharpens boundaries but frustrates; low density under-exercises the trap.
When it helps, and when it misleads¶
Its strength is that it rebuilds the specific competence high-fluency block practice hides: method selection under uncertainty. It is cheap — a set of problems and a good key — and it turns an invisible skill into a graded, improvable one. The productive difficulty it creates is a textbook case of a desirable difficulty, a manipulation that slows practice yet improves durable, transferable performance.[1]
Its failure mode is that a Mixed Problem Set assembled without a real contrast logic is just a harder worksheet. If the problems leak surface cues — a pulley in the diagram, a distinctive number — solvers learn to read the formatting instead of the physics, and the set silently reverts to blocked practice with extra steps. The classic misuse is deploying it on novices who have not yet acquired each method in isolation: mixing then produces flailing, not discrimination, and confirms the learner's fear that they "just can't do word problems." The guarding discipline is to confirm baseline per-method fluency first, and to audit the set so the only reliable predictor of the right method is the conceptual cue, never an incidental one.
How it implements the components¶
discrimination_target_set— the artifact is a curated target set: it fixes which confusable methods are in scope and excludes the unrelated, so every problem is a live choice among genuine near-alternatives.retrieval_or_performance_prompt— the per-problem instruction to name (and justify) the method before solving is the active-attempt prompt, forcing retrieval of the selection act rather than the mechanics.comparison_feedback_loop— the cue-explained answer key closes the loop by connecting each miss to the discriminating feature and the ruled-out alternative.
It does NOT implement the interleaving_schedule or load_and_scaffold_boundary — a Mixed Problem Set is a fixed content collection, not an ordering engine; the constraint-respecting sequencing of a reusable item pool is Shuffled Practice Deck's job. Nor does it run the graded transfer measurement, which is Mixed Diagnostic Quiz.
Related¶
- Instantiates: Interleaved Discrimination Practice — supplies the practice artifact in which the target-choice act is reinstated.
- Sibling mechanisms: Shuffled Practice Deck · Near-Miss Case Rotation · Interleaved Repertoire Practice · Adaptive Interleaving Scheduler · Mixed Diagnostic Quiz · Contrastive Example Sequence · Alternating Context Drill
Editorial Notes¶
Form Classification¶
Form family: Experiment, Test & Rehearsal
Rationale: The curated set deliberately interleaves confusable problem types without method labels so learners practice selecting and applying the right method under transfer conditions.
Nearest alternative: Representation, Specification & Plan — The problems are packaged in an artifact, but the operative form is the deliberate rehearsal the set elicits rather than static information alone.
Review outcome: Adjudicated after independent review; high confidence.
Origin Attribution¶
Primary origin: Education & Pedagogy
Origin pattern: Convergent development
Present-day reach: Multi-domain
Rationale: Interleaved problem sets are an established educational practice for forcing learners to select a method rather than merely repeat a blocked routine.
Related originating lineages:
- Psychology — Learning and memory research on desirable difficulties and discrimination materially established the mechanism's rationale.
Review resolution: Both independent reviews agree on primary origin education_pedagogy; reconciliation resolves secondary fields (origin_mode_disagreement, domain_reach_disagreement). Alternate origins retained (psychology) are the union of reviewer-supported formative lineages with explicit rationales, not a list of later application domains. Present-day breadth is represented separately as domain_reach=multi_domain; origin_mode=convergent records the historical relationship among lineages. Confidence is conservatively reconciled to high, and encyclopedia_synthesis=false preserves either reviewer's finding that the encyclopedia generalized the mechanism.
Review outcome: Reconciled after independent review; high confidence.
References¶
[1] Bjork, E. L., and Bjork, R. A. "Making Things Hard on Yourself, but in a Good Way: Creating Desirable Difficulties to Enhance Learning". In M. A. Gernsbacher, R. W. Pew, L. M. Hough, and J. R. Pomerantz (eds.), Psychology and the Real World, 56–64. Worth Publishers (2011). Identifies interleaved practice as a desirable difficulty that can slow apparent acquisition while improving long-term retention and transfer. registry ↩