The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the…

How can research findings from cognitive and learning sciences be meaningfully applied in authentic settings to improve student learning outcomes in mathematics? Decades of basic research on how people learn has implications for the design of curriculum, instruction, and assessment. However, bringing research to practice involves simultaneously…

Research has found that elementary students face five main challenges in learning area measurement: (1) conserving area as a quantity, (2) understanding area units, (3) structuring rectangular space into composite units, (4) understanding area formulas, and (5) distinguishing area and perimeter. How well do elementary mathematics curricula address…

A problem-solving capstone course for mathematics and mathematics education majors can help majors synthesize material learned in the major, create a basis for lifelong learning in the discipline, develop confidence, and promote interest in graduate study. Such a course may also play a role in departmental assessment of the major. This article…

Sketches a theory for designing teaching based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. Reviews the main psychological principles underlying this theory, then considers some examples of teaching designs in light of…