Complex Working Memory

Operation Span - Complex Working Memory

Solve simple math, then memorize a letter, repeat. Then recall the letters in order. The gold-standard complex span task.

Operation Span

About this exercise

Operation span (OSpan) was developed by Turner & Engle (1989) and remains the gold-standard complex working memory measure.

Unlike simple span tasks, OSpan forces simultaneous processing AND storage - the realistic working memory of everyday life.

You alternate solving math equations (true/false) with memorizing letters. At the end, recall the letters in order.

Scores are often discussed in relation to reading comprehension, fluid reasoning, and academic performance.

The science

Engle's research group has shown OSpan correlates strongly with Gf (fluid intelligence) - far more than simple span tasks.

The math distractor prevents rehearsal, isolating true working memory capacity rather than rote storage.

What it measures

Your ability to hold letters in mind while your attention is hijacked by arithmetic.

This task isolates controlled attention under interference: the capacity to keep an ordered list of letters active in memory while the math equations actively compete for the same limited resource. A high span reflects efficient resilience to that competition, not just a large memory store. It measures how well you maintain and retrieve target items when processing repeatedly pulls focus away.

Unlike simple letter or digit span, which lets you rehearse undisturbed, the interleaved math blocks silent repetition, so the score taps capacity rather than rehearsal tricks. This same resistance to distraction predicts everyday performance such as following a conversation in a noisy room or holding a goal in mind while handling interruptions.

How to train it effectively

Treat the math as non-negotiable and let set size grow only when accuracy holds.

Start at short set sizes of two or three letters and answer every equation honestly before the deadline. Keep math accuracy high, around eighty-five percent or better, because rushing it inflates recall artificially. Only increase set size once you can reach near-perfect recall at the current length across several trials, then add one letter at a time.

The most common mistake is quietly skimping on the math to protect the letters, which defeats the purpose and trains the wrong skill. Resist sub-vocal rehearsal during the equation; instead, refresh the letter list in the brief gap right after you submit each answer. Recall strictly in presented order, never easiest-first.

Interpreting your score

Read your span as letters recalled in order while math stayed accurate.

Your meaningful result is the number of letters recalled in correct position on trials where you also kept the math accurate; the two must be read together. A score earned with sloppy equations is not a real span. Rather than chasing an absolute number, track your own trend across sessions at a fixed math-accuracy threshold to see genuine change.

Span is highly state-dependent: fatigue, stress, caffeine, and sleep loss can swing it noticeably from day to day, so judge it over many sessions, not one. It also says nothing about long-term memory, vocabulary, or reasoning content; it captures only how much you can juggle under interference at that moment.

How to play

  1. Each round shows a math equation - say True or False fast.
  2. Then a single letter flashes - memorize it.
  3. After all letters in the round, type them back in order.
  4. The next round adds one letter. Two consecutive failures end the session.