My research addresses questions at the intersection of cognitive, developmental, and educational science: investigating how young learners build upon their intuitions to acquire formal symbolic reasoning abilities. Most of my work has been within the domain of proportional reasoning, which provides a particularly unique opportunity to investigate cognitively and educationally relevant questions from early childhood into adulthood. More recently, I've extended these questions about bridging nonsymbolic intuitions with symbolic thinking by investigating relational language more generally (e.g., more/less, bigger/smaller).

Young children's intuitions about proportion and probabiliy
Even before learning formal fractions, young children, and even infants, have fairly surprising intuitions about probability and proportion. Yet, 6yearold children also show systematic errors in how they use proportion information: when the number of items is inconsistent with the overall proportion (e.g., 3/4 vs. 5/9 where 3 < 5 but 3/4 > 5/9), children tend to make mistakes because they rely more on the number of items than the proportion (Hurst & Cordes, 2018; Dev Psych).
In order to better understand children's intuitions, and the limits of these intuitions, I have several studies investigating how flexible or malleable children's thinking is and, in particular, whether (and how!) we can prevent children from making this error. For example, giving children practice with continuous visual representations (where number is not available; Hurst & Cordes, 2018; Dev Psych) or labeling visual, equivalent proportions with a single category based label (Hurst & Cordes, 2019) helps children attend to proportion, instead of numerical information.
In ongoing work, we are looking at the role of gesture in children's attention to numerical versus proportional information, the relation between children's proportional reasoning ability and other numerical and domain general skills, and how children's attention to these different features may depend on the particular context.
In order to better understand children's intuitions, and the limits of these intuitions, I have several studies investigating how flexible or malleable children's thinking is and, in particular, whether (and how!) we can prevent children from making this error. For example, giving children practice with continuous visual representations (where number is not available; Hurst & Cordes, 2018; Dev Psych) or labeling visual, equivalent proportions with a single category based label (Hurst & Cordes, 2019) helps children attend to proportion, instead of numerical information.
In ongoing work, we are looking at the role of gesture in children's attention to numerical versus proportional information, the relation between children's proportional reasoning ability and other numerical and domain general skills, and how children's attention to these different features may depend on the particular context.
Different representations for formal, symbolic proportions
Learning fractions is extremely difficult for many children (and adults!), but recent work by me and by others suggests that learning fractions is extremely important for later math learning, especially algebra.
One of the things that makes learning about fractions so difficult is the many ways it can be talked about and represented. By investigating how these different representations impact people's thinking, we can learn more about how our minds mentally represent information and communicate it to others. Also, if we have a better understanding of how children and adults think about fractions, across different representations, we may be able to construct curricula that better match how children think and learn.
In my work in particular, I'm interested in how different aspects of fraction information (for example: ratio, proportion, partwhole relationships, magnitude information, etc.) are understood using different notations and representations (for example: fractions, decimals, pie charts, number lines, discrete items, etc.). In particular, I'm interested in which notations/representations may be best matched for teaching specific types of fraction concepts, and not good for teaching other concepts. For example, some recent research suggests that fractions may be particularly difficult for magnitude information (Hurst & Cordes, 2016, JEP:HPP; 2018, JECP) and that people may be more likely to treat area models in a way that preserves partwhole information in addition to magnitude (Hurst, Santry, Relander, & Cordes, in prep).
In ongoing work, we're looking at the potential benefits of matching spatial and symbolic representations, context differences in the use of fraction vs. decimal notation, and how children use gesture to explain their thinking in different kinds of fraction concepts. I'm also very interested in taking what we learn about young children intuitions and using them in fraction lessons that take advantage of children's existing knowledge. For example, we're testing a card game that involves different kinds of continuous and discrete representations for teaching fraction symbols.
One of the things that makes learning about fractions so difficult is the many ways it can be talked about and represented. By investigating how these different representations impact people's thinking, we can learn more about how our minds mentally represent information and communicate it to others. Also, if we have a better understanding of how children and adults think about fractions, across different representations, we may be able to construct curricula that better match how children think and learn.
In my work in particular, I'm interested in how different aspects of fraction information (for example: ratio, proportion, partwhole relationships, magnitude information, etc.) are understood using different notations and representations (for example: fractions, decimals, pie charts, number lines, discrete items, etc.). In particular, I'm interested in which notations/representations may be best matched for teaching specific types of fraction concepts, and not good for teaching other concepts. For example, some recent research suggests that fractions may be particularly difficult for magnitude information (Hurst & Cordes, 2016, JEP:HPP; 2018, JECP) and that people may be more likely to treat area models in a way that preserves partwhole information in addition to magnitude (Hurst, Santry, Relander, & Cordes, in prep).
In ongoing work, we're looking at the potential benefits of matching spatial and symbolic representations, context differences in the use of fraction vs. decimal notation, and how children use gesture to explain their thinking in different kinds of fraction concepts. I'm also very interested in taking what we learn about young children intuitions and using them in fraction lessons that take advantage of children's existing knowledge. For example, we're testing a card game that involves different kinds of continuous and discrete representations for teaching fraction symbols.
Using relational language to engage in math thinking
In another line of work, I have extended my research on proportional reasoning to investigate how young children think about other kinds of mathematical and spatial relations. Most of this work has focused on parents and children’s use of relational language, including words like before/after and more/less.
I am interested in exploring the link between relational language and mathematical understanding by investigating when children choose to use relational language and what this might tell us about their relational thinking. For example, when a child refers to six as being “bigger” than, “more” than, or “after” five, what does this tell us about that child’s understanding of the relation between five and six? 