When 2 × 4 is meaningful: the N400 and P300 reveal operand format effects in multiplication verification

Abstract

Arithmetic problems share many surface-level features with typical sentences. They assert information about the world, and readers can evaluate this information for sensibility by consulting their memories as the statement unfolds. When people encounter the solution to the problem 3 × 4, the brain elicits a robust ERP effect as a function of answer expectancy (12 being the expected completion; 15 being unexpected). Initially, this was labeled an N400 effect, implying that semantic memory had been accessed. Subsequent work suggested instead that the effect was driven by a target P300 to the correct solutions. The current study manipulates operand format to differentially promote access to language-based semantic representations of arithmetic. Operands were presented either as spoken number words or as sequential Arabic numerals. The critical solution was always an Arabic numeral. In Experiment 1, the correctness of solutions preceded by spoken operands modulated N400 amplitude, whereas solutions preceded by Arabic numerals elicited a P300 for correct problems. In Experiment 2, using only spoken operands, the delay between the second operand and the Arabic numeral solution was manipulated to determine if additional processing time would result in a P300. With a longer delay, an earlier N400 and no distinct P300 were observed. In brief, highly familiar digit operands promoted target detection, whereas spoken numbers promoted semantic level processing-even when solution format itself was held constant. This provides evidence that the brain can process arithmetic fact information at different levels of representational meaningfulness as a function of symbolic format.

Keywords: ERPs; N400; P300; arithmetic; numerical cognition; spoken number words.

Figure 1

Trial structure in Experiment 1 for the task with digit operands (top) and for the task with spoken number word operands (bottom), from left to right across time.

Figure 2

Layout of electrode channels used in all recordings, oriented with the front of the head at the top of the figure. Darkened circles indicate electrodes utilized in distributional analyses.

Figure 3

Grand average ERPs measured to the onset of correct (black) and incorrect (red) solutions with a 100ms prestimulus baseline, at representative channels indicated on the scalp map with an X. Negative voltage is plotted up. Solutions preceded by Arabic digit operands are on the left and solutions preceded by spoken number words are on the right. A robust correctness effect is visible, featuring an N400 in the auditory context and a P300 in the digit context. At top, topographic maps of the correctness effect are plotted for digits and auditory formats using the analysis time windows for the P300 or N400, respectively. Note that for illustration purposes and consistency with our discussion we show the digit format effect as a positivity (correct minus incorrect solutions) and the auditory format effect as a negativity (incorrect minus correct solutions).

Figure 4

Difference ERPs (correct minus incorrect) are plotted for each operand context (auditory in black; digit in red). The time windows used for analyses of the N400/P300 and subsequent effects are indicated by their location above the plot and are similarly color-coded for each trial type. The late effect for auditory trials did not reach significance.

Figure 5

Trial structure in Experiment 2 for the task with auditory operands, from left to right across time. The critical manipulation is the length of delay after the second operand.

Figure 6

Grand average ERPs measured from the onset of correct (black) and incorrect (red) solutions with a 100ms prestimulus baseline, from representative channels indicated on the scalp map with an X. At left are the responses to solutions when there was a short delay (150ms) following the second operand. Corresponding plots for the response to solutions when there was a longer delay (1000ms) are plotted on the right. A robust N400 correctness effect is visible with both delays. At top, topographic maps of the correctness effect (incorrect minus correct solutions) are plotted using the analysis time window for the N400.

Figure 7

Grand average ERPs at a representative middle central electrode (MiCe) contrast the waveform componentry and timing across all experiments and critical conditions.