Operation Span Task

Version: v1 (current)

A complex span task measuring working memory capacity through concurrent processing and storage demands.

Overview

The Operation Span (OSPAN) task is one of the most widely used measures of working memory capacity. Unlike simple span tasks (e.g., digit span) that only require storage, complex span tasks like OSPAN require participants to simultaneously process information (solve simple math problems) while remembering items (letters or words) for later recall.

This dual-task design taps into the core executive functions of working memory: maintaining goal-relevant information while performing concurrent processing. Individual differences in OSPAN scores correlate with reading comprehension, fluid intelligence, and academic performance, making it a powerful cognitive assessment tool.

The task is extensively used in cognitive psychology, educational research, and clinical neuropsychology to measure working memory capacity and executive function.

Scientific Background

Classic Findings:

• Capacity Limits: Most adults recall 3-5 items correctly under dual-task conditions
• Storage-Processing Trade-off: More complex processing reduces storage capacity
• Individual Differences: OSPAN scores predict fluid intelligence (r ~ 0.5)
• Age Effects: Working memory capacity declines with aging, evident in OSPAN
• Training Effects: Working memory training can improve OSPAN scores (though transfer is debated)

Key Mechanisms:

• Controlled Attention: Ability to maintain task goals in the face of interference
• Dual-Task Coordination: Switching between processing and storage operations
• Interference Resistance: Protecting memory traces from overwriting during processing

Seminal Papers:

• Turner & Engle (1989): Original OSPAN development
• Engle, Tuholski, Laughlin, & Conway (1999): Working memory, short-term memory, and fluid intelligence
• Unsworth, Heitz, Schrock, & Engle (2005): Automated OSPAN version

Why Researchers Use This Task

1. Working Memory Assessment: Gold-standard measure of complex working memory capacity
2. Intelligence Research: Strong predictor of fluid intelligence and reasoning
3. Educational Studies: Correlates with reading comprehension and academic achievement
4. Clinical Assessment: Sensitive to ADHD, schizophrenia, and frontal lobe dysfunction
5. Cognitive Training: Baseline and outcome measure for working memory interventions

Current Implementation Status

Fully Implemented:

• ✅ Math operation verification (processing component)
• ✅ Letter/word recall (storage component)
• ✅ Adaptive set sizes (2-6 items)
• ✅ Practice trials for both components
• ✅ Partial credit scoring (correct items in correct positions)
• ✅ Processing speed and accuracy tracking

Partially Implemented:

• ⚠️ Limited to letters as to-be-remembered items (not words or spatial locations)
• ⚠️ Fixed math operations (addition/subtraction only)

Not Yet Implemented:

• ❌ Spatial OSPAN variant (locations instead of letters)
• ❌ Adaptive difficulty adjustment based on performance
• ❌ Running span variant

Configuration Parameters

Options

Parameter	Type	Default	Description
operation_span_font_size_px	number	48	Display font size in pixels (min 8, max 400)
operation_span_practice_enabled	boolean	true	Whether the practice phase runs before the main trials
ospan_show_recall_count_cue	boolean	false	Show neutral placeholder slots indicating how many letters to recall

Instructions

Rich-text (HTML) instruction editors: main_instructions, hint_instructions, and — when practice is enabled — practice_instructions and trials_instructions.

Trials and Practice Trials

There are no separate "set size", "timing", or "operation type" parameters. Instead, the trial structure is defined directly in two editable spreadsheets (one for main trials, one for practice trials when enabled). Each row defines one set:

Column	Type	Description
Letters (comma-separated)	text	Letters to remember, e.g. F,H,Q
Operations (semicolon-separated equation=answer,T/F)	text	The operations to verify before each letter, e.g. (2*3)+1=7,(4-1)*2=6
Block	text	Block label for grouping/analysis

The set size of a trial is derived from the number of letters/operations in the row (not a configured number). Per-trial timing and accuracy values (math_duration_ms default 5000, letter_duration_ms default 1000, isi_ms default 500, response_timeout_ms default 30000, math_accuracy_criterion default 0.85) are read from each trial object when present and otherwise fall back to these defaults; they are not exposed as form fields in the configuration UI.

Keyboard Shortcuts

Researchers can customize the keyboard bindings used during the task:

Parameter	Type	Default	Description
Show keyboard hint	boolean	True	Display an on-screen hint showing the configured keys
Letter key	key	Any letter (A-Z)	Key accepted for letter recall input
Letter action label	text	"to recall letters"	Label shown in the keyboard hint
Submit key	key	Enter	Key to submit the recalled sequence
Submit action label	text	"to submit"	Label shown in the keyboard hint

The default "Any letter" setting accepts any letter key A-Z for the recall phase.

Data Output

Markers and Responses

The task records high-resolution timestamps via several marker types tracking the complex trial structure. The trial onset marker is prefixed with the task slug (e.g. operation_span_trial_start, or operation_span_practice_trial_start during practice).

Markers:

Marker	Data fields	Description
operation_span_trial_start / operation_span_practice_trial_start	trial_index (or practice_trial_index), stimulus_id, set_size, operations, letters, block	Onset of the present-then-recall sequence
stimulus_shown	trial_index, stimulus_id, item_index, set_size, block	Each math+letter pair onset within the sequence
math_problem_shown	trial_index, item_index, equation, correct_answer, block	A new math problem appears
math_response	trial_index, item_index, equation, correct_answer, user_answer, correct, latency_ms	Response to the math verification
letter_shown	trial_index, item_index, letter	Letter to remember displayed
recall_prompt_shown	trial_index, set_size, letters_count, block	Letter recall prompt appears
response_recorded	trial_index	Letter recall submitted
operation_span_trial_end / operation_span_practice_trial_end	trial_index (or practice_trial_index)	End of the sequence

math_response example payload:

{
  "trial_index": 1,
  "item_index": 0,
  "equation": "(2 * 3) + 1 = ?",
  "correct_answer": 7,
  "user_answer": 7,
  "correct": true,
  "latency_ms": 1420
}

Response Data (letter recall):

{
  "trial_index": 1,
  "stimulus_id": "operation_span_0_1",
  "source": "keyboard",
  "set_size": 3,
  "operations_presented": [{"equation": "(2 * 3) + 1 = ?", "correct_answer": 7, "user_answer_expected": 7}],
  "letters_presented": ["F", "H", "Q"],
  "math_responses": [{"equation": "(2 * 3) + 1 = ?", "user_answer": 7, "correct": true, "latency_ms": 1420}],
  "letter_response": ["F", "H", "Q"],
  "letter_response_correct": true,
  "partial_credit_unit_score": 3,
  "absolute_score": true,
  "responded": true,
  "math_accuracy": 1.0,
  "meets_math_criterion": true,
  "block": "main",
  "is_practice": false,
  "recall_latency_ms": 4500
}

source is one of keyboard, timeout, or moderator_advance. When the recall is not answered (timeout or moderator advance), letter_response_correct and absolute_score are recorded as null (not false), and responded is false.

Summary Artifact

A JSON file (operation_span_summary_<taskIndex>.json) with aggregated statistics:

{
  "task_kind": "operation_span",
  "task_index": 0,
  "total_trials": 15,
  "overall": {
    "total": 15,
    "valid_responses": 14,
    "correct_recall": 9,
    "recall_accuracy": 0.64,
    "meets_math_threshold": 12,
    "math_threshold_rate": 0.86,
    "total_pcu_score": 47,
    "absolute_span": 9,
    "average_math_accuracy": 0.89,
    "timeouts": 1
  },
  "breakdowns": {
    "set_size": {
      "size_3": { /* statistics */ },
      "size_4": { /* statistics */ },
      "size_5": { /* statistics */ }
    }
  },
  "trials": [ /* per-trial data */ ],
  "practice": {
    "total_trials": 3,
    "overall": { /* same stats shape */ },
    "breakdowns": { "set_size": { /* ... */ } },
    "trials": [ /* per-trial practice data */ ]
  }
}

The per-set-size breakdown is built dynamically over the set sizes actually present in the data (size_<n> keys). The practice block is included only when practice was enabled and produced results.

Key metrics:

• total_pcu_score: Partial credit unit score (letters recalled in correct positions)
• absolute_span: Number of perfectly recalled sets
• average_math_accuracy: Proportion of math problems answered correctly
• meets_math_criterion: Whether math accuracy meets the threshold (default 85%)

Example Research Configurations

Standard OSPAN (Unsworth et al., 2005)

Set Sizes: 3-7 items
Trials: 3 per set size (15 total)
Operations: Simple math (3-9 range)
Timeout: Self-paced operations, 800ms letter display
Scoring: Absolute (sum of perfectly recalled sets)

Short OSPAN (Clinical/Children)

Set Sizes: 2-4 items
Trials: 3 per set size (9 total)
Operations: Very simple math (1-5 range)
Timing: Generous timeouts
Scoring: Partial credit to reward progress

Research OSPAN (Maximum Sensitivity)

Set Sizes: 3-6 items
Trials: 4 per set size (16 total)
Operations: Adaptive difficulty
Analysis: Partial credit scoring for finer discrimination

Participant Experience

1. Instructions: Learn that you will solve math problems and remember letters
2. Practice (if enabled): Complete a few combined practice sets (math + letter recall) with correct/incorrect feedback, then read the pre-main instructions
3. Main Task: For each set:
   • Solve the math problem (type the numeric answer), then submit
   • See the letter to remember (e.g., "F")
   • Repeat operation-letter pairs for the set size
   • Recall all letters in order by typing on keyboard (default accepts any A-Z key -- configurable by researcher) or clicking from the letter grid
   • Press Enter to submit (default -- configurable by researcher)
4. Repeat: Complete all configured sets
5. Completion: Task ends and the summary artifact is emitted

All keyboard bindings are configurable by the researcher in the study configuration. The keys listed above are the defaults.

Design Recommendations

General Guidelines

• Set Sizes: Use range 3-6 for adults; 2-4 for children or clinical populations
• Processing Difficulty: Keep operations simple to avoid floor effects
• Processing Accuracy: Require ≥85% accuracy to ensure participants process operations
• Scoring: Absolute scoring (all-or-none) vs. partial credit depending on goals

Processing Task Design

• Use operations requiring 2-4 seconds to solve
• Balance true/false answers (50/50)
• Avoid patterns (e.g., alternating true/false)
• Ensure operations don't facilitate letter encoding (e.g., answers shouldn't spell letters)

Population-Specific Adaptations

Children (8-12 years):

• Set sizes: 2-3 items
• Simple operations: 1-digit addition/subtraction
• Generous timeouts
• Visual feedback and encouragement
• Partial credit scoring

Older Adults (65+):

• Set sizes: 2-5 items
• Slower pacing
• Larger font for operations and letters
• Allow self-paced operation verification
• Consider shorter session (fewer trials)

Clinical Populations:

• Adapt set sizes to functioning level
• May need simplified operations
• Extended practice
• Monitor processing accuracy carefully (may ignore math)

Common Issues and Solutions

Issue	Solution
Low processing accuracy (<80%)	Emphasize equal importance of both tasks; add practice; slow down
Participants ignore math	Implement minimum processing accuracy requirement; provide feedback
Floor effects (all recall errors)	Reduce set sizes, simplify operations, or add practice
Ceiling effects (perfect recall)	Increase set sizes, add more trials, or speed up operations
Participants write letters down	Emphasize no external aids; monitor if in-person

References

• Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28(2), 127-154.
• Engle, R. W., Tuholski, S. W., Laughlin, J. E., & Conway, A. R. A. (1999). Working memory, short-term memory, and general fluid intelligence: A latent-variable approach. Journal of Experimental Psychology: General, 128(3), 309-331.
• Unsworth, N., Heitz, R. P., Schrock, J. C., & Engle, R. W. (2005). An automated version of the operation span task. Behavior Research Methods, 37(3), 498-505.
• Conway, A. R. A., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R. W. (2005). Working memory span tasks: A methodological review and user's guide. Psychonomic Bulletin & Review, 12(5), 769-786.

See Also

• Digit Span - Simple span task without processing component
• N-Back Task - Alternative working memory updating task
• Visual Short-Term Memory - Visual capacity measure