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Here or There (HOT) instruction is a blended synchronous approach that enables students from on-campus (“here”) or a remote location (“there”) to participate together in class activities in real time. The purpose of this article is to share three different cases at two universities that illustrate different implementations of HOT instruction, explain the affordances of these varied approaches, provide best practices that are common to each, and share lessons learned along the way. Readers will gain a better understanding of how to implement a range of innovative HOT approaches, and in what context(s) they might choose one approach over another. The authors’ experience indicates that sound pedagogical principles along with pragmatic considerations, such as class size, available technology, and instructor’s skills, should guide decisions regarding use of these blended synchronous approaches. Future research should look towards what impact blended synchronous environments have on student outcomes.

In this chapter, we review research on mathematical difficulties and exceptionalities. Mathematical difficulties are distinguished from general learning difficulties, and include developmental dyscalculia and mathematical learning disabilities. We discuss research on cognitive processing associated with mathematical difficulties, including the approximate number system, or number sense, fact retrieval, delayed procedural development, fractions and proportional reasoning, visuospatial reasoning, working memory, and time estimation. We also present neuroscience research indicating specific effects related to mathematics for children with a diversity of neurodevelopmental disorders, syndromes, and conditions, including Autism spectrum disorder, Fragile X syndrome, Turner syndrome, 22q11.2 deletion syndrome, Williams syndrome, Spina Bifida, prenatal alcohol exposure, premature birth, developmental coordination disorder, attention deficit hyperactivity disorder, epilepsy, traumatic brain injury, schizophrenia, and depression. Neuroscience research related to individual differences in language and reading and giftedness, including synesthesia, is also discussed. We conclude by raising considerations and limitations for interpreting neuroscience research on mathematical difficulties and exceptionalities, including small sample sizes, group assignment, inferences from lesion and neuroimaging studies, and the disease model.