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Watch a participant in this study:
Children’s and adults’ judgments of equitable resource distribution

	This study explored the criteria that children and adults use when evaluating the goodness niceness of a character who is distributing resources. Four- and five-year-olds played the Giving Game, in which two puppets with different amounts of chips each gave some portion of these chips to the children. Adults played an analogous task that mimicked the situations presented to children in the giving gameGiving Game.  For all groups of participants, we manipulated the absolute amount and proportion of chips given away.  We found that children and adults use different cues to establish which puppet was nicer; the four-year-olds focused exclusively on absolute amount, the five-year-olds focused mostly on absolute amount but showed some sensitivity to proportion, and the adults focused exclusively on proportion.  These results are discussed in light of their implications for equity theory and for theories of the development of social evaluation. 

But they also think addition outcomes should be bigger than actual outcomes,
and subtraction outcomes should be smaller than actual outcomes. Subjects’ responses peak roughly around the correct answer... Subtraction:
x + x = y Addition:
24 + 8 = 26 Sample movies: Warning- they’re fast!... Moving Along the Number Line: Operational Momentum in Non-Symbolic Arithmetic

	Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial-numerical representation of numerical magnitude have on their responses?  We conducted a psychophysical study in which participants viewed several hundred short videos of sets of objects being added or subtracted from one another, and judged whether the final numerosity was correct or incorrect.  Over a wide range of possible outcomes, subjects’ responses peaked at the approximate location of the true numerical outcome, and gradually tapered off as a function of the ratio of the true and proposed outcomes (Weber’s law).  Furthermore, an operational momentum effect was observed, whereby addition problems were overestimated and subtraction problems were underestimated.  The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum.
(4:1 Ratio) Novel
(2:1 Ratio)
Ratio Familiar
Ratio Multiple examples of
4:1 ratio of pellets:pacmen The pacmen eat pellets Infants look longer to the new ratio during test trials. And habituated to this... When familiarized to this... Ratio Abstraction by 6-Month-Old Infants

Human infants appear to be capable of the rudimentary mathematical operations of addition, subtraction, and ordering.  To determine whether infants are capable of extracting ratios, we presented 6-month-old infants with multiple examples of a single ratio. After repeated presentations of this ratio, infants were presented with new examples of a new ratio as well as new examples of the previously habituated ratio.  Infants were able to successfully discriminate two ratios that differ by a factor of two, but failed to detect the difference between two numerical ratios that differ by a factor of 1.5.  We conclude that infants can extract a common ratio across test scenes and use this information while examining new displays.  The results support an approximate magnitude estimation system, which has also been found in animals and human adults.
5+5=10 5+5=5 10-5=10 10-5=5 Subtraction Condition:
Babies look longer to 10-5=10 Addition Condition:
Babies look longer to 5+5=5 Large-Number Addition and Subtraction by 9-Month-Old Infants

Do genuinely numerical computational abilities exist in infancy?  It has recently been argued that previous studies which putatively illustrated infants’ ability to add and subtract  (e.g., Wynn, 1992) were tapping into specialized object-tracking processes which apply only within the smaller number range.  This contrasts with the original interpretation that successful performance was achieved via a numerical system for estimating and calculating magnitudes.  Here, we report that 9-month-old infants successfully add and subtract over numbers of items that exceed object-tracking limits, with continuous variables (such as area and contour length) controlled.  These results support the theory that infants possess a magnitude-based estimation system for representing numerosities, which also supports procedures for numerical computation.