Below are summaries of projects I have been involved with previously or continue to work on. Most recent work is at the top of the list. Feel free to get in touch with me if you have any questions or comments.

I was very fortunate to have been funded by an ITP Fellowship, which supported my interests in bridging the gap between academic research and real-world settings. I strongly believe that experimental behavioral research can benefit from adaptation into applied contexts, and the recent replication concerns in psychology suggest that these translational efforts are needed now more than ever.

Non-symbolic ratios & fraction learning

What makes fractions so difficult to learn? We know from prior research that both children and adults can understand ratio magnitudes when presented in forms outside of conventional symbolic expressions, but the ability to interpret the mappings between fraction expressions and the magnitude concepts they denote is more challenging. In this work, I explore differences in fraction understanding among adults and children, and investigate whether explicit training in mapping between non-symbolic to symbolic depictions of fractional magnitudes can help children understand fraction relationships more easily by changing the conceptual structures associated with errors in representing symbolic forms.

Number Concepts

Cognitive psychologists typically focus on magnitude as the semantic core of number knowledge. However, numbers have many other properties apart from their quantities. For instance, the number 3 can be prime, odd, or a factor of 27; it can call to mind a set of triplets, a bronze medal for third place, or a triangle. Little is known about whether and to what extent aspects of number knowledge beyond magnitude shapes the representation of number concepts. In this project, we investigate how the role of individual and experimental factors can drive sensitivity to non-magnitude properties of number, and how this can affect learning

Learning & transfer in arithmetic problem-solving

Educators frequently face the challenge of trying to help students apply knowledge acquired in classroom practices to novel contexts. In mathematics, this is a notorious stumbling block; learners often perform poorly when solving new problems, despite receiving substantial experience with practice problems. In this research, we explore how this difficulty may arise due to the mental models that learners form during practice experiences. Our goals are to understand how different forms of instruction influence learning, and how to maximize tradeoffs of different instructional models to support robust, transferable knowledge. Specifically we compare item-based models of arithmetic fact retrieval with predictive models that rely on distributional patterns within practice experience.

Natural language, representational similarity, and active learning

In brain-imaging studies which aim to predict neural representations associated with word meaning, corpus-based methods from natural language processing (NLP) are often used to estimate the semantic similarity structure among words. These models are based on the idea that words which occur in similar contexts are similar in meaning. In cognitive psychology, this is linked to the hypothesis that individual concepts are associated with patterns of activity in the brain, and concepts with similar neural patterns are similar in meaning. Ideally, a corpus model should be cognitively plausible—that is, capable of reproducing human performance on a semantic task such as synonym judgments. However, performance across models can be difficult to compare because models are trained on different corpora and often evaluated on different semantic tasks. Moreover, reliable (i.e., human-like) performance can be highly variable and prone to overfitting on a small number of concepts. We are interested in the advantages and challenges corpus models of semantics pose for cognitive psychology, such as in applications of MVPA in neural semantics.

In collaboration with the UW Department of Electrical and Computer Engineering, we are using a cloud-based active learning system called NEXT which can potentially support or improve upon other models of estimating similarity structure. The model learns semantic relations by querying human subjects in the form of forced-choice triads, avoiding redundancy by posing queries which most rapidly reduce the variance across judgments to achieve a stable solution. We anticipate that the NEXT system will help guide our understanding of how knowledge structures are represented in the mind.

Posters & Publications

Murphy, A., Cox C., Jain, L., Jamieson, K., Sievert, S., Nowak, R., Rogers, T. (2017). NEXT: Accelerating the pace of scientific discovery. Poster presented at the Psychonomic Society Leading Edge Workshop, Beyond the Lab: Using Big Data to Discover Principles of Cognition, Madison, WI.

Murphy, A., Cox C., Rogers, T. (2017). Using NEXT to estimate conceptual structure. Paper presented at the 1st Annual Conference hosted by LUCID, eLUCID8: Data Science and Human Behavior, Madison, WI.

Murphy, A.D., Young, A.G., Boncoddo, R.A., Alibali, M.W., Rogers, T.T., Kalish, C.W. (under review). Can models of learning in non-mathematical domains explain knowledge transfer in arithmetic?

Murphy, A., Rogers, T., Hubbard, E. Expertise and flexibility in number concept representation. (in prep)

Murphy, A., Cox, C., Rogers, T. Similarity triplets: A new method of acquiring human judgments for cognitive psychology. (in prep)

Boncoddo, R.A., Murphy, A.D., Jensen, C.A., Young, A.G., Kalish, C.W., Alibali, M.W., & Rogers, T.T. (2016). The Implications of Nominal and Continuous Presentations of Functions for Learning and Transfer. Poster presented at the 2016 Annual Meeting of the Association for Psychological Science, Chicago, IL.

Murphy, A., Rogers, T., Hubbard, E., Brower, A. (2015). Beyond Magnitude: How Math Expertise Guides Number Representation. In Proceedings of the 37th Annual Conference of the Cognitive Science Society.

Murphy, A., Boncoddo, R., Young, A. (2015). Practice makes imperfect: How problem distribution can lead to prototype formation. Poster presented at the Annual Math Cognition and Learning Conference, St. Louis, MO.

Boncoddo, R., Murphy, A., Young, A., Kalish, C., Rogers, T., & Alibali, M. (2015). The Impact of Frequency and Instructional Format on Mathematics Learning and Transfer. Poster presented at the Annual Convention of the Association for Psychological Science, New York, NY

Murphy, A., Cox, C., Jamieson, K., Nowak, R., Rogers, T. (2014). Comparing Natural Language and Adaptive Querying Approaches for Estimating Similarity Structure. Poster presented at the 21st Annual Meeting of the Cognitive Neuroscience Society, Boston, MA.

Curtin, S., Holt, L., Murphy, A., Hufnagle, D. (2012). Comparing distributional regularities in speech directed to infants and adults Poster presented at the 18th Biennial International Conference on Infant Studies, Minneapolis, Minnesota.