Neural Correlates of Mathematical Problem Solving

This study explores electroencephalography (EEG) brain dynamics associated with mathematical problem solving. EEG and solution latencies (SLs) were recorded as 11 neurologically healthy volunteers worked on intellectually challenging math puzzles that involved combining four single-digit numbers through basic arithmetic operators (addition, subtraction, division, multiplication) to create an arithmetic expression equaling 24. Estimates of EEG spectral power were computed in three frequency bands — θ (4–7 Hz), α (8–13 Hz) and β (14–30 Hz) — over a widely distributed montage of scalp electrode sites. The magnitude of power estimates was found to change in a linear fashion with SLs — that is, relative to a base of power spectrum, theta power increased with longer SLs, while alpha and beta power tended to decrease. Further, the topographic distribution of spectral fluctuations was characterized by more pronounced asymmetries along the left–right and anterior–posterior axes for solutions that involved a longer search phase. These findings reveal for the first time the topography and dynamics of EEG spectral activities important for sustained solution search during arithmetical problem solving.

Tangible Self-Consequation and Arithmetical Problem-Solving: An Exploratory Comparison of Four Strategies

In an exploratory investigation, 25 volunteer postgraduate students were exposed to a control and four self-consequation conditions of positive and negative reward and positive and negative punishment. The experimental tasks were arithmetic problems matched for difficulty. Generally, the results indicated that, when subjects were operating under the two self-reward conditions whereby they self-reinforced correct responses, they attempted more items and produced more correct responses. Conversely, as predicted, participants in the two self-punishment conditions were more accurate.

Arithmetical Problem Solving: A Demonstration with the Mentally Handicapped

In line with the thesis that the ultimate goal of an arithmetic program with the mentally handicapped is to facilitate problem solving, the investigators field tested an 18 week demonstration program. The groups taught by trained teachers showed significant gains in the 2 problem solving areas. Gains among retarded and average controls were not as consistent.