Stuck on convention: a story of derivative relationships

In this article, we explore the responses of a group of undergraduate mathematics students to tasks that deal with areas, perimeters, volumes, and derivatives. The tasks challenge the conventional representations of formulas that students are used to from their schooling. Our analysis attends to the specific mathematical ideas and ways of reasoning raised by students, which supported or hindered their appreciation of an unconventional representation. We identify themes that emerged in these responses and analyze those via different theoretical lenses—the lens of transfer and the lens of aesthetics. We conclude with pedagogical recommendations to help learners appreciate the structure of mathematics and challenge the resilience of certain conventions.     

Early social communication development in infants with autism spectrum disorder

Social-communication differences are a robust and defining feature of autism spectrum disorder (ASD) but identifying early points of divergence in infancy has been a challenge. The current study examines social communication in 9- to 12-month-old infants who develop ASD (N = 30; 23% female; 70% white) compared to typically developing (TD) infants (N = 94, 38% female; 88% white). Results demonstrate that infants later diagnosed with ASD were already exhibiting fewer social-communication skills using eye gaze, facial expression, gestures, and sounds at 9 months (effect size: 0.42–0.89). Moreover, three unique patterns of change across distinct social-communication skills were observed within the ASD group. This study documents that observable social-communication differences for infants with ASD are unfolding by 9 months, pointing to a critical window for targeted intervention.