The Neural Correlates of Control States in Algebra Problem Solving
msra(2013)
摘要
Algebra is a complex human activity that requires coordination of several cognitive abilities, including visual processing (for parsing the equation), declarative memory (for storing and retrieving arithmetic knowledge), and visual imagery (for updating and manipulating intermediate and partial representations of the equation). It is also a convenient experimental task, since the solution path can be perfectly characterized, and participants are extensively trained in solving algebraic problems with the same algorithm, repeating the same sequence of problem-solving steps. We took advantage of this paradigm, as well as previous results with algebraic tasks (Anderson, 2005; Qin et al., 2004), to look for the neural correlates of control states in ACT-R. Control states are those slot values in the goal chunk that hold a distinctive hallmark for the current state. They allow us to distinguish the current state from similar buffer configurations, allowing the correct sequence of productions to fire. Together with procedural knowledge, they constitute the main components of top-down control in ACT-R. In our experiment, participants were required to solve a set of 128 equations. In each of them, the unknown could be unwound in two steps, which consisted of first adding (or subtracting) the same quantity to both sides, and then multiplying (or dividing) both sides by the proper factor. Participants had to correctly indicate these two steps by pressing the corresponding finger in a data glove, and eventually choosing the result from a list of four alternatives. The equations were divided into four categories, obtained by varying two dimensions: whether the equations were Updated or not, and whether they contained Numbers or Parameters . In the Update condition, the software computed the intermediate state and displayed it on the screen. Under these conditions, participants did not have to perform mental manipulations of the equation, and the amount of control limited to the basic choice of the computational steps to carry on. On the contrary, in the No Update condition, the application did not update the equation on
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