2001 — 2003 
Hubbard, Edward Michael 
F31Activity Code Description: To provide predoctoral individuals with supervised research training in specified health and healthrelated areas leading toward the research degree (e.g., Ph.D.). 
The Neural Basis of NumberColor Synesthesia @ University of California San Diego
Synesthesia is a fascinating condition in which stimulation of one sensory modality causes experiences in a second modality. For example, when presented with musical tones, some people report seeing colors in addition to hearing those tones. Estimates of the prevalence of synesthesia range from 1 in 20 (Galton, 1880/1997) to 1 in 20,000 (Cytowic, 1989; Cytowic, 1997). We will use a combination of perceptual experiments and functional magnetic resonance imaging (fMRI) to explore the neural basis of synesthesia. We propose that numbercolor synesthesia is a result of neural "miswiring" between areas of the fusiform gyrus involved with numberform processing (Richard, Romero, Basso, Wharton, Flitman, & Grafman, 2000; Pesenti, Thioux, Seron & De Volder, 2000) and more interior areas of the fusiform gyrus considered to be involved with processing of color (Lueck, Zeki, Friston, Deiber, Cope, Cunningham, Lammertsma, Kennard & Frackowiak, 1989; Zeki & Marini, 1998). Should this hypothesis be borne out, it would provide an existence proof of the neural miswiring hypothesis and could lead to further studies investigating other forms of synesthesia, including tonecolor synesthesia and Glaton's (1880/1997) "numberforms."

0.957 
2014 — 2017 
Hubbard, Edward (coPI) Matthews, Percival [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Using Nonsymbolic Ratios to Promote Fraction Knowledge: a Neurocognitive Approach @ University of WisconsinMadison
This project, to be conducted by researchers at the University of Wisconsin, Madison, will study knowledge of fractions in college students and eighthgraders. The project will use behavioral and brain imaging measures. The main hypothesis is that some kinds of visual perception ability (such as sensitivity to the ratio formed by the lengths of two lines) are related to fraction understanding. The project will develop a training method aimed at improving knowledge about fractions. This project will advance the work of the REAL (Research on Education and Learning) program in studying the cognitive and neural basis of STEM (science, technology, engineering, and mathematics) learning.
The project will use fMRI (functional magnetic resonance imaging) to study brain activity, focusing on brain regions including the PFC (prefrontal cortex) and IPS (intraparietal sulcus). In particular, the research will use an adaptation method, looking at activation recovery when a novel ratio is presented in a series of ratios. The project addresses a cognitive primitives account of fraction magnitude processing, which posits that perceptual sensitivity to nonsymbolic ratio magnitudes plays a major role in supporting the developing understanding of symbolic fraction magnitudes. This account implies that neurocognitive architectures tuned to the processing of nonsymbolic ratiosuch as the relative lengths of two lines or the relative areas of two figuresare present even before learners receive fractions instruction.

0.915 
2016 — 2020 
Hubbard, Edward Michael Matthews, Percival Grant (coPI) [⬀] 
R01Activity Code Description: To support a discrete, specified, circumscribed project to be performed by the named investigator(s) in an area representing his or her specific interest and competencies. 
Perceptual and Cognitive Mechanisms of Developing Fractions Knowledge: a CrossSequential Approach @ University of WisconsinMadison
Project Summary Mathematical competence is an important determinant of life chances in modern society, and knowledge of fractions is a foundational skill for establishing mathematical competence. Despite the importance of fraction knowledge, children and adults often encounter considerable difficulties understanding fractions. To explain these widespread difficulties, many researchers have argued for an innate constraints account. They propose that fractions are difficult because they do not correspond to any preexisting categories in our brain, unlike whole numbers, which correspond to sets of countable things. Thus, they argue fraction concepts are challenging because they do not benefit from existing cognitive abilities and instead must be learned through adapting children's whole number understanding. The study team proposes a competing hypothesis, the cognitive primitives account, which integrates previously unrelated findings from neuroscience, developmental psychology and education. We argue that a primitive ability that we dub the ratio processing system (RPS) is tuned to the processing of nonsymbolic fractions?such as the relative length of two lines or the relative area of two figures?and is present even before formal instruction. On this view, children are equipped with cognitive mechanisms that support fraction concepts in the same way that the ability to process countable sets equips them to learn about whole numbers. To test the predictions of these competing hypotheses, this project will follow two cohorts of children (2nd graders until 5th grade and 5th graders until 8th grade) using behavioral and brain imaging methods to (a) trace the development of nonsymbolic fraction processing abilities, (b) determine how symbolic fraction knowledge builds on these abilities and (c) investigate whether individual differences in the RPS predict later math achievement. To test whether the acuity or recruitment of these nonsymbolic architectures plays a role in fraction difficulties as well as general math learning difficulties, the study team will compare the behavioral performance and neural activity on a battery of cognitive tasks. This research has important implications for our understanding of number processing and for designing educational practices that are optimal for fraction learning. Improving fractions understanding would help children to clear a critical hurdle in the acquisition of higherorder mathematical competencies that impact educational, employment, and even health outcomes. If cognitive primitives for nonsymbolic fractions can provide a foundation for the acquisition of symbolic fraction ability, then instruction should attempt to recruit these primitives. If deficits in these primitives contribute to math learning difficulties, then screening should include measures of nonsymbolic abilities and interventions should be designed to address these abilities.

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