Building a Math Brain


In 1992, American psychologist Karen Wynn surprised the psychological community by reporting that infants as young as five months could perform basic addition and subtraction problems.  Specifically, Wynn claimed to have demonstrated the following:

  • Babies can differentiate between one object, two objects, and a “collection” of more than two objects.
  • Babies can recognize the exact numerosities of sets within the subitizing range. In other words, babies understand that if one object is placed with another object, the resulting set is exactly two. Conversely, babies understand that if someone has two objects and removes one, they are left with exactly one.

Wynn reported that these “number sense” relationships are stable and reliable across preverbal humans. Prior to Wynn’s discovery, most developmental psychologists assumed, as Piaget believed, that children construct number through successive and hierarchically integrated interactions (ie., experimentation) with the environment. It was also assumed that “number sense” developed after children learned to count. Not surprisingly, Wynn’s findings sparked a number of replication studies.

Wynn used a violation of expectations paradigm to test her hypothesis. When babies encounter something that is inconsistent with their model of the world, they will attend to it. So, Wynn measured infant subjects’ look time during manipulations of small sets of objects. Infants were placed in front of a puppet theater when the stage was empty. During each trial, an experimenter placed a puppet onto the stage. Then, a screen was lowered, and the experimenter showed the baby that she was placing another puppet on the stage behind the screen. The screen was then lifted to reveal the puppets. Trials were repeated several times with combinations of one, two, or three puppets. On some occasions, puppets were added or removed out of view, revealing incorrect equations. On “incorrect” trials, babies looked longer. Similar results were found for addition and subtraction trials. Combinations, operations, and correct/incorrect situations were randomized across trials.

Wynn

 

Wynn’s findings have been replicated on numerous occasions (Hespos & Rochat, 1995) and remain consistent when puppets are in motion (Koechlin, et al, 1998), or when the color or type of puppet is changed (Simon, et al., 2006). In fact, babies only increase look time when the arithmetic is incorrect. There is, however, still debate as to whether infants are tracking objects spatially or showing preference for familiarity (Cohen, 2002); and there is debate as to whether “look time” is an accurate measure of expectation violation.

Berger and colleagues (2006) decided to use EEG and Wynn’s paradigm to test whether 6-9 month old infants’ increased look time on incorrect trials results in a similar brain pattern to that of adults when they observe correct and incorrect equations. In adults, error detection results in a specific pattern of brain activity in the middle-frontal area (Berger, et al., 2006). In this study, babies’ brain activity was measured concurrently with behavioral data via video recording during presentation of Wynn trials. Inter-rater reliability on coding of look time/attention data was at 92%, and look time data replicated Wynn’s findings. Mean look time for correct vs. incorrect trials was shorter and significant. Brain activity was calibrated to look time data on video recordings, and the frequency and topography of infant brain activity during incorrect trials was identical (though onset was slower) to that of adults. Berger et. al (2006) conclude that in 5-9 month olds, effects of expectation violation were evident in the frontal lobe structures associated with the executive functions of error detection and resolution. For an example trial, see the slide below from PNAS:

Berger, et al.

This study supports the use of look time as a measure of expectation violation in infants. It is also interesting to note that sub-structures of higher-ordered executive functions via “early warning systems” are present in infants, as this type of brain activity is often associated with later stages of development. This is the first study that directly links look time on error presentation to brain structures known to be associated with error detection and resolution. It has been commonly accepted in the empiricist view that we “construct” our sense of number through interaction with the environment. However, current evidence suggests that we are born with a concept of numerosity, pre-loaded and ready for verbal mapping.

Berger, A. , Tzur, G., Posner, M. (2006). Infant brains detect arithmetic errors. PNAS, 103(33). 12649-12653.

 

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