Providing all students with equitable treatment and access has been a cornerstone of mathematics education reform (Association of Mathematics Teacher Educators, 2015; National Council of Teachers of Mathematics, 2014). Studies in mathematics classrooms show that using hands-on and interactive materials (i.e., "manipulatives") support…

Background: Tinkering, an ad hoc approach to solving a problem, involves manipulating objects to characterize and build knowledge about a particular system in an exploratory way, often with the goal of getting some product/idea to produce desired behavior. Tinkering contrasts more deliberate activity toward understanding how a phenomenon works.…

The importance of culture and social interactions in disciplinary learning and language development within specific social practices and contexts is now an agreed-upon notion in the science education literature. In a pivotal article in 1990, Lemke introduced the idea of manual-technical operations as one of four modes making up the "hybrid…

STEM instruction often uses visual representations. To benefit from these, students need to understand how representations show domain-relevant concepts. Yet, this is difficult for students. Prior research shows that physical representations (objects that students manipulate by hand) and virtual representations (objects on a computer screen that…

We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem…