This paper investigates the idea of teaching programming language syntax before problem solving in Introductory Computer Programming (CS1). Theories of procedural skill acquisition imply that syntax should be taught with a pedagogy and curriculum quite different from that used in teaching problem solving. We draw from this literature to propose a practice-based pedagogy and curriculum to teach students syntax before they learn its application, something we call a "syntax-first" pedagogy, which uses skilled performance in syntax to scaffold learning of problem solving. We report results of a controlled study investigating whether learning syntax using pedagogy suitable for procedural skill acquisition (e.g. repetitive practice) prior to learning problem solving influences student performance. A syntax-first pedagogy is complementary to almost any other teaching approach: in our study, simply adding carefully designed syntax exercises to an existing CS1 course resulted in higher exam scores, lower student attrition, and evidence that plagiarism rates may be lower.

Recent, empirically supported theories of cognition indicate that human reasoning, including mathematical problem solving, is based in tacit spatial-temporal simulated action. Implications of these findings for the philosophy and design of instruction may be momentous. Here, we build on design-based research efforts centered on exploring the potential of embodied interaction (EI) for mathematics learning. We sketch two emerging, reciprocal contributions: (1) a sociocognitive view on the role of automated feedback in building the perceptuomotor schemes that undergird conceptual development; and (2) a heuristic EI design framework. We ground these ideas in vignettes of children engaging an EI design for proportion. Increasing ubiquity and access to mobile devices geared to avail of EI principles suggests the feasibility of mass-disseminating materials evolving from this line of research.

We introduce an embodied-interaction instructional design, the Mathematical Imagery Trainer (MIT), for helping young students develop grounded understanding of proportional equivalence (e.g., 2/3 = 4/6). Taking advantage of the low-cost availability of hand-motion tracking provided by the Nintendo Wii remote, the MIT applies cognitive-science findings that mathematical concepts are grounded in mental simulation of dynamic imagery, which is acquired through perceiving, planning, and performing actions with the body. We describe our rationale for and implementation of the MIT through a design-based research approach and report on clinical interviews with twenty-two 4th-6th grade students who engaged in problem-solving tasks with the MIT.

When instructional designers develop content-targeted pedagogical situations, their practice can be theorized as engineering students‘ development of conceptual schemes. To account for the contributions of students‘ prior schemes and situated experiences towards the development of conceptual schemes, we suggest a distinction between the evocation of schemes and enactment of situations. The former suggests that the design of an instructional situation can activate students‘ prior schemes. The latter suggests that the structure of students‘ activity in an instructional situation determines the nature of newly constructed schemes. We contextualize our views using empirical data from case studies involving students‘ interactions with educational technology designed for embodying and grounding the concept of proportionality.