Touch Together: Open-Ended Design of TouchCounts Shapes Parent―Child Affective Engagement in Family Mathematics

This qualitative study investigates how the open-ended design of TouchCounts (Sinclair & Jackiw, 2014), a multi-touch application for early numeracy, shapes affective dynamics during parent―child interactions in family math activities. Drawing on inclusive materialism (de Freitas & Sinclair, 2014) and affect theory in mathematics education (de Freitas et al., 2019), the study conceptualizes affect as a relational, provisional force that circulates among parent, child, and technology, and is entangled with their interaction. It focuses on how TouchCounts elicits distinct affective dynamics through its open-ended and multimodal features (e.g., without prescribed or level-driven tasks, gesture-responsive multi-touch screen, full-screen math-object generation space, and support for explorative individual and collaborative use). Through micro-scale analysis of two excerpts from a parent-child dyad's interaction video-recordings, selected from five participating pairs in Canada, the study captures affective dynamics—expressed through gestures, embodied actions, and verbal output—as they emerge and unfold differently in each sub-environment (i.e., Enumerating World and Operating World). Findings show that the distinct affordances of each World give rise to nuanced, affect-rich interactions that embody diverse ways of mathematical thinking and communication. This research underscores the potential of open-ended digital technologies to shape the affective dimensions of early math learning in family contexts.