Caitlin Tenison

Modeling the distinct phases of skill acquisition.

A focus of early mathematics education is to build fluency through practice. Several models of skill acquisition have sought to explain the increase in fluency because of practice by modeling both the learning mechanisms driving this speedup and the changes in cognitive processes involved in executing the skill (such as transitioning from calculation to retrieval). In the current study, we use hidden Markov modeling to identify transitions in the learning process. This method accounts for the gradual speedup in problem solving and also uncovers abrupt changes in reaction time, which reflect changes in the cognitive processes that participants are using to solve math problems. We find that as participants practice solving math problems they transition through 3 distinct learning states. Each learning state shows some speedup with practice, but the major speedups are produced by transitions between learning states. In examining and comparing the behavioral and neurological profiles of each of these states, we find parallels with the 3 phases of skill acquisition proposed by Fitts and Posner (1967): a cognitive, an associative, and an autonomous phase. (PsycINFO Database Record

Modeling Strategy Use in an Intelligent Tutoring System: Implications for Strategic Flexibility

Education research has identified strategic flexibility as an important aspect of math proficiency and learning. This aspect of student learning has been largely ignored by Intelligent Tutoring Systems (ITSs). In the current study, we demonstrate how Hidden Markov Modeling can be used to identify groups of students who use similar strategies during tutoring and relate these findings to a measure of strategic flexibility. We use these results to explore how strategy use is expressed in an ITS and consider how tutoring systems could integrate a measure of strategy use to improve learning.

The Common Time Course of Memory Processes Revealed

Magnetoencephalography (MEG) was used to compare memory processes in two experiments, one involving recognition of word pairs and the other involving recall of newly learned arithmetic facts. A combination of hidden semi-Markov models and multivariate pattern analysis was used to locate brief “bumps” in the sensor data that marked the onset of different stages of cognitive processing. These bumps identified a separation between a retrieval stage that identified relevant information in memory and a decision stage that determined what response was implied by that information. The encoding, retrieval, decision, and response stages displayed striking similarities across the two experiments in their duration and brain activation patterns. Retrieval and decision processes involve distinct brain activation patterns. We conclude that memory processes for two different tasks, associative recognition versus arithmetic retrieval, follow a common spatiotemporal neural pattern and that both tasks have distinct retrieval and decision stages.

Inferential Pitfalls in Decoding Neural Representations.

A key challenge for cognitive neuroscience is to decipher the representational schemes of the brain. A recent class of decoding algorithms for fMRI data, stimulus-feature-based encoding models, is becoming increasingly popular for inferring the dimensions of neural representational spaces from stimulus-feature spaces. We argue that such inferences are not always valid, because decoding can occur even if the neural representational space and the stimulus-feature space use different representational schemes. This can happen when there is a systematic mapping between them, as shown by two simulations. In one simulation, we successfully decoded the binary representation of numbers from their decimal features. Since binary and decimal number systems use different representations, we cannot conclude that the binary representation encodes decimal features. In the second simulation, we successfully decoded the HSV color representation from the RGB representation of colors, even though these color spaces have different geometries and their dimensions have different interpretations. Detailed analysis of the predicted colors showed systematic deviations from the ground truth despite the high decoding accuracy, indicating that decoding accuracy on its own is not sufficient for making representational inferences. The same argument applies to the decoding of neural patterns from stimulus-feature spaces and we urge caution in inferring the nature of the neural code from such methods. We discuss ways to overcome these inferential limitations.