In reviewing the six articles within this "Instructional Science" special issue, we are reminded of Schoenfeld's ("Educ Res" 45(2):105-111, 2016) review of American Educational Research Association president-authored papers for the centennial celebration of AERA. There, he succinctly unveiled the content focus of AERA research…

Scaling up educational interventions in the STEM (Science, Technology, Engineering, and Mathematics) field is critical but under-researched. We review and draw implications from a series of studies investigating the long-range impact of an implementation of an early mathematics scale-up model based on learning trajectories. Lasting effectiveness…

For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and…

In recent years, there has been increased interest in improving early mathematics curricula and instruction. Subsequently, there has also been a rise in demand for better early mathematics assessments, as most current measures are limited in their content and/or their sensitivity to detect differences in early mathematics development among young…

We examined children's development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching. We checked the hierarchical…

How learning about learning trajectories has helped a teacher develop goals and objectives for her preschool children's mathematical knowledge, identify children's developmental levels in specific mathematical topics, and chart paths for instruction that will guide their learning of mathematics. Participating in research encouraged her to develop…

Describes young children's thinking about geometric shapes and discusses implications for teaching and learning. (KHR)

Reviews research involving the LOGO computer programming language and its effect on children's achievement in mathematics, language arts, and problem solving, as well as social-emotional development. Identifies some of the unique characteristics of LOGO that may contribute to student learning. (MDM)

Describes several studies that challenge conventional wisdom regarding the teaching and learning of nonstandard and standard unit, rulers, and measurement sense. Discusses the educational implications of their results. (Author/CCM)

Provides suggestions for implementing the geometry standards in an elementary curriculum by including all aspects of geometry. (KHR)

Defines spatial structuring as the mental operation of constructing an organization or form for an object/set of objects. Examines in detail students' structuring and enumeration of two-dimensional rectangular arrays of squares. Concludes that many students do not see row-by-column structure. Describes various levels of sophistication in students'…

Although geometry and spatial reasoning are important as a way to interpret and reflect on the physical environment and also form the foundation for learning mathematics and other subjects, many early childhood and primary school teachers spend little time instructing their students in these areas. This paper examines how young children learn…

This chapter discusses the way that mathematics curricula are developed in the United States. It suggests that curriculum development in mathematics education makes little progress because it fails to adhere to scientific methodology. Weaknesses in the current development process, how such development can become scientific, how curriculum…

Investigates, by conducting individual clinical interviews of 97 children ages 3 to 6, the criteria preschool children use to distinguish members of a class of shapes from other figures, emphasizing identification and descriptions of shapes and reasons for these identifications. Concludes that young children initially form schemas on the basis of…

Describes the design principles behind a set of research-based software microworlds included in the "Building Blocks" program, a pre-kindergarten to grade 2 software-based mathematics curriculum. Discusses how to help children extend and mathematize their everyday activities and presents the nine-step design process model used.…