When working memory works with ⺙x – 2 = ⻂: Effects of prior training on performance

“Working memory” is a broad term that describes what we do with information that is consciously accessible. For instance, when students take notes in class, they are hearing the lecturer’s sentences, placing them in the context of what they know about the topic, and synthesizing both to form the note they ultimately write on the page. This may require no manipulation — if, say, they write down exactly what was said — or substantial manipulation, if they are building a mindmap on the fly.

Working memory and long-term memory interact with one another; things you’ve previously learned help you understand and structure the information you’re currently working with. One of the most common examples is “chunking”, in which items are combined into meaningful groups to be remembered. The eight-digit number sequence 31412718 is easier to remember if you know it is the first four digits of π and the first four digits of e. Eight numbers become two — but only if you already know π and e.

The connection between working memory and long-term memory is a matter of debate, but it is typically assumed that well-learned material from long-term memory can be manipulated with considerable and equal ease in working memory. This is consistent with working memory and long-term being conceptualized as, in some sense, separate.

In their article “Item strength affects working memory capacity”, published recently in the Psychonomic Society’s journal Memory & Cognition, Shen, Popov, Delahay, and Reder challenge this view. They show that the ability of participants to remember associations between Chinese characters and numbers — and then use those associations — depends on how often participants have previously seen those Chinese characters, in spite of the fact that all the characters were well-learned.

This is difficult to reconcile with well-known conceptions of working memory, such as those by Atkinson and Shiffrin or by Baddeley and Hitch, that depend on long-term and working memory being separate, with abstract representations of items in memory being “transferred” between them.

When we learn new things — such as words in new language, or mathematical symbols — the frequency of different words or symbols will vary. For instance, in English some words are common (“the”) and others rare (“qat”). Shen and colleagues wanted to explore the effect of this variability on working memory, but they did not want to depend on natural variability in already learned items, because this is often confounded with other variables; for instance, the most common words in English are functional words like “the”, with nouns and verbs being less common. Any differences between common words and uncommon words might be attributed to factors other than how often they’re seen. To get around this, Shen and colleagues used Chinese characters that were unfamiliar to the research participants. These Chinese characters were randomly assigned to be “high frequency” or “low frequency”, with high-frequency characters being shown twenty times more often than low-frequency items.

To teach the Chinese characters to the participants, the authors used a visual search task (see the figure below). Participants were shown a target Chinese character (high or low frequency) for one second and then shown a group of four similar characters that might, or might not, contain the target character. Participants were then asked to indicate whether the target character was present. In nine sessions across several weeks, the participants performed over 6,000 such trials, gradually improving to about 95% accuracy, on average.

Shen and colleague’s visual search task Participants performed over 6000 trials over several weeks.

Consider how long-term memory supports such a task. If an English reader were to perform the same task with Latin letters (say, a) they would only need to remember the identity of the letter, and hunt for it in the search group. This is due to the fact that a is known to English readers. However, this is not possible with characters that are not previously known. With the visual search task, the authors’ purpose was to induce long-term learning of the Chinese characters.

After weeks of training in the visual search task, the participants were then asked to perform a combined memory and algebra task. In this new task, on each trial participants were asked to remember associations between two of the Chinese characters and two digits. Participants were then immediately asked to solve an algebraic equation such as x/2 – 2 = 1, in which x=6. Notice that this equation takes two steps to solve: adding 2 to both sides, then multiplying both sides by 2. An equation like x-3=5, on the other hand, requires only one step to solve. Participants were presented with some of both.

In an additional twist, participants might also be provided with equations in which two of the numbers were replaced by the Chinese characters they were asked to remember: for instance, ⺙x – 2 = ⻂. In order to solve this equation, one would have to remember both associations between Chinese characters and digits, mentally substitute the digits into the equation, and then solve for x.

An equation could thus be one of four types: one step or two steps, and requiring substitution (from Chinese) or not. After solving the equation, the participants were tested on their memory for the Chinese characters and digits. Participants were asked to indicate which of the several Chinese characters was presented, and what digits were associated with them.

Shen and colleague’s combined memory and algebra task. Participants were asked to solve an equation while simultaneously remembering digits associated with two Chinese characters.

Let’s stop to consider what we’d predict will happen. The algebra task is taxing for working memory already; when we add mental substitution of Chinese characters, it seems reasonable to predict that the task will be even harder. Also, increasing the number of steps in the algebra task should make it harder. As the figure below shows, that’s exactly what Shen and colleagues found; increasing the number of steps and requiring substitution both decreased performance.

Average performance on the algebra task.

What Shen and colleagues were really after, though, was a potential effect of whether the Chinese characters were high frequency or low frequency during the initial training. As long as the Chinese characters were well-learned, there’s no particular reason why their frequency during training would affect how well you can juggle them during the algebra task. You can see from the figure above, however, that when two algebra steps were required, substitution of a low frequency character caused a performance decrease of over 10%, compared to high frequency characters.

Shen and colleagues call this an effect of “item strength” on working memory, although it should be noted that “item strength” is a metaphor rather than a measured quantity (and even granted the metaphor, an item’s representation could be “strong” but the item might still be low in frequency relative to other items). The reason for the effect of high vs. low frequency Chinese characters is not understood, but it seems clear any conception of working memory that considers long-term memory as a separate system that simply feeds into working memory is inadequate.

Interestingly, Shen and colleagues also discuss the implications of their findings for the debate about whether working memory capacity is best thought of as made up of discrete “slots” or a continuous resource. Is your memory limited by the number of discrete things you try to remember — say, four digits — or is it more flexible? Could you remember, say, ten simple things, but only two complex things? Shen and colleagues believe that their results rule out discrete working memory models, because in these models an item is simply that: an item. There does not seem to be any room for learned frequency to affect performance.

I suspect that advocates of “slot” models will object that 1) only the strongest of such models would fail, and 2) resource models benefit from being extremely flexible and making no prediction at all, which is not much of a win in scientific terms. It isn’t clear why learned frequency would affect the resources an item requires, either. One thing is certain, though: Shen and colleagues’ results provide fertile ground for further debate over the relationship of working memory to long-term memory.

Psychonomics article discussed in this post:

Shen, Z., Popov, V., Delahay, A. B., & Reder, L. M. (2017). Item strength affects working memory capacity. Memory & Cognition. DOI: 10.3758/s13421-017-0758-4.


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