TITLE:
From Marbles to Numbers—Estimation Influences Looking Patterns on Arithmetic Problems
AUTHORS:
Claudia Godau, Maria Wirth, Sonja Hansen, Hilde Haider, Robert Gaschler
KEYWORDS:
Mental Arithmetic; Estimation; Fixation Pattern; Transfer; Commutativity Principle
JOURNAL NAME:
Psychology,
Vol.5 No.2,
February
26,
2014
ABSTRACT: Flexibly spotting and applying shortcut options in arithmetic is often a
major challenge for children as well as adults. Recent work has suggests that
children benefit in terms of such flexibility from tasks requiring estimation
or other operations with quantities that they cannot easily enumerate. Such
tasks often require comparison of quantities by fixation and as such
necessitate long-range eye movements, e.g. across the whole screen. We tested
whether fixation patterns account for transfer from estimation to arithmetic
tasks. Conceivably, participants who first solve estimation tasks are more
flexible in spotting and applying shortcuts on later arithmetic tasks, because
they stick to scanning the screen with long-range eye movements (which were
necessary for solving the estimation task). To test this account, we manipulated
the location of the marbles in an estimation task so that one group of
participants had to make long-range eye movement, whereas another group did not
need long-range eye movements to solve the task. Afterwards participants of
both groups solved addition problems that contained a shortcut option based on
the commutativity principle. We tested whether shortcut usage and fixation
patterns in the arithmetic problems were influenced by the variant of the
estimation task provided beforehand. The experiment allowed us to explore
whether flexibility in spotting and using arithmetic shortcuts can be fostered
by applying a prior task that induces flexible looking patterns. The results
suggest that estimation tasks can indeed influence fixation patterns in a later
arithmetic task. While shortcut search and application is reflected in fixation
patterns, we did not obtain evidence for the reverse influence. Changed
fixation patterns did not lead to higher shortcut usage. Thus, the results are
in line with top-down accounts of strategy change: fixation patterns reflect
rather than elicit strategy change.