The cognitive challenge in mental calculation: Is it hard to remember or hard to forget?
Read Ligal’s full dissertation (in Hebrew)
Working memory (WM) is essential to our everyday functioning. It allows us to process, store, and maintain information for short periods of time, thereby allowing to run complex tasks in real time. The WM capacity is strictly limited; exceeding this capacity creates interference between items and consequently obstructs memory. Therefore, it is crucial to retain in memory only the information most relevant to the task at hand. To this end, there exists a removal mechanism that discards no-longer-relevant information and makes room for new, relevant information.
In academic tasks, WM plays a central role in solving math problems, specifically in performing arithmetic calculations — a fundamental math ability. When we need to execute a multi-step algorithm mentally, WM allows storing and processing intermediate results. Still, to date, only very few studies have attempted to understand the precise role of WM in mental arithmetic algorithms, and to describe how WM difficulties affect mental arithmetic.
To help bridge this gap, the present study examined how removal from WM and interference in WM affect the performance in arithmetic procedures. Participants performed a simple arithmetic procedure in which they were required, in each trial, to remember several values, retrieve them from WM in several steps, and perform calculations on them. In Experiment 1, in some steps they were asked to retrieve a value they have already retrieved in a previous step (“recurring retrieval”), whereas in other steps they retrieved a value that was not retrieved earlier (“first retrieval”). The error rate was higher in first-retrieval steps than in recurring-retrieval steps. We propose that this is an effect of interference: when a value remains in active memory without being used, in each step it is subject to interference from the other values being activated. In our experimental setup, the values in the first-retrieval steps were retained passively in WM more steps than the values in the recurring-retrieval steps, and consequently the values in first-retrieval steps suffered more interference. Experiment 2 imposed higher WM load, thereby increasing the likelihood of a value being removed from WM after each step. The “recurring-retrieval advantage”, observed in Experiment 1, diminished — consistent with the idea that the removal process (which occurrs more frequently in Experiment 2) damaged the memory representation of the specific value removed, and thus it disrupted the recurring-retrieval steps more than the first-retrieval steps. Additional analyses, which examined random fluctuations within each experiment, reinforced these conclusions. Moreover, a theoretical analysis of the task allowed us to identify the specific WM representation levels wherein removal was the most difficult, and to propose several concrete mechanisms explaining how removal and interference may disrupt memory representations and consequently impede the mental execution of arithmetic procedures.
The study strongly suggests that math difficulties can stem not only from math-specific mechanisms, but also from domain-general mechanisms such as WM. Hence, it is important to understand math difficulties not only in the context of ‘mathematical’ cognitive processes but also in the broader context of general cognitive processing. The study also indicates that WM comprises several distinct sub-processes, each of which can create specific difficulties in predictable mathematical operations. We saw these difficulties in typically-developing individuals; presumably, they might be even more severe in individuals with learning disorders or specific cognitive deficits.