Arithmetic Encoding in the Human Brain

• In Event: Navigating Number Concepts Across Development

Abstract

How are two numbers combined into a third? Arithmetic is one of the most important cultural inventions of humanity. However, progress in understanding the fast spatiotemporal dynamics of mental arithmetic in the brain is implemented the fact that most of previous studies either used static measures of behavior (e.g., RTs; Ashcraft, 1992) or low temporal resolution measures of brain activity (Menon, 2014). I will present a series of studies in which I used time-resolved measures of behavior and brain activity to track, parse and characterize the series of covert processing stages involved in mental calculation, as well as to better understand the neural architecture and dynamics of the underlying brain networks.

In the first study, we asked adults to point to the result of single-digit additions and subtractions on a number line, while their finger trajectory was constantly monitored via a tablet computer. Finger trajectories revealed that two operands are processed serially: the finger first points toward the larger operand, then slowly veers toward the correct result. This slow deviation unfolds proportionally to the size of the smaller operand, in both additions and subtractions. We also observed a transient operator effect: a plus sign attracted the finger to the right and a minus sign to the left and a transient activation of the absolute value of the subtrahend. These findings support a procedural model whereby addition and subtraction are computed by a stepwise displacement on the mental number line, starting with the larger number and incrementally adding or subtracting the smaller number. In the second study, we aim at characterizing the neuronal correlates of arithmetic processing, by recording intracranial electroencephalography (iEEG) signals from 100 subjects (58 implanted with grids and 42 with depth electrodes; total of 9,010 recording sites), while they performed a variety of arithmetic tasks. Corroborating previous fMRI studies (Arsalidou & Taylor, 2011), results showed a distinct network of regions selectively activated during arithmetic, that included four main hubs: posterior inferior temporal gyrus (pITG), intraparietal sulcus (IPS), superior parietal lobule (SPL) and dorsolateral prefrontal cortex (DLPFC), which dissociated from canonical regions selectively activated during the control conditions: memory retrieval and sentence reading. Moreover, responses to calculations were generally format independent (i.e. comparable for Arabic numbers and number words), suggesting that number manipulation is performed at an abstract level. Next, a response onset latency map revealed a cascade of partially overlapping activations from early visual areas to pITG, followed by IPS/SPL, then by DLPFC and lastly by motor regions, associated with the response. Finally, regression analysis revealed that the IPS activity increases as a function of arithmetic problem-size, suggesting its role in the calculation procedure. Overall, this talk provides contributions to our knowledge about how elementary mathematical concepts are implemented in the brain and shows that a multimethod approach can help us identify and characterize the mental algorithms of human cognition.

Author

• Pedro Pinheiro-Chagas, Stanford University
  Presenting Author