
How do different representations impact the way people think about formal proportion?
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 word to 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.
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 word to 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.
What are young children's intuitions about information proportion and how do they impact learning?
Even before learning formal fractions, young children, and even infants, have fairly surprising intuitions about probability and proportion. For example, young infants are surprised when a red ball is pulled out of a bin of mostly white balls and only a few red balls (Denison & Xu, 2012). However, 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, I've recently shown that 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, under review).
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, I've recently shown that 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, under review).
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.
How can we improve people's attitudes toward math problem solving and persistence?
The number of Science, Technology, Engineering, and Math graduates is staggeringly low, even though these fields are becoming more and more important.
In my work, I'm interested in what kind of subjective factors influence people's decisions to pursue math and computer science fields. In particular, we are looking at how people's ideas about problemsolving and "debugging" as normal aspects of their math and computer science activities impacts their persistence and interest in these fields more generally. 