The authors describe a Modeling Instruction program that places an emphasis on the construction and application of conceptual models of physical phenomena as a central aspect of learning and doing science. (Contains 1 table.)

The utility of an "ecologically rational" recognition-based decision rule in multichoice decision problems is analyzed, varying the type of judgment required (greater or lesser). The maximum size and range of a counterintuitive advantage associated with recognition-based judgment (the "less-is-more effect") is identified for a range of cue…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…

This study brings together two lines of research on teachers' affective responses toward mathematics curriculum reforms: their concerns and their efficacy beliefs. Using structural equation modeling to analyze data on 151 elementary mathematics teachers' concerns and efficacy beliefs 5 years into a mandated curriculum reform on problem solving,…

Self-efficacy and mathematics anxiety have been identified as predictors of mathematics achievement. In the present study, secondary analyses on matrix summaries available from prior published studies were utilized to investigate the contribution that self-efficacy and mathematics anxiety made in mathematics performance. Commonality analyses were…

The purpose of this article is to clarify conceptions, definitions, and applications of learning and problem-solving efficiency. Conceptions of efficiency vary within the field of educational psychology, and there is little consensus as to how to define, measure, and interpret the efficiency construct. We compare three diverse models that differ…

Intelligent tutors have become increasingly accurate at detecting whether a student knows a skill, or knowledge component (KC), at a given time. However, current student models do not tell us exactly at which point a KC is learned. In this paper, we present a machine-learned model that assesses the probability that a student learned a KC at a…

Background: A federally-funded program at the University of Texas at San Antonio adopted a holistic problem solving mentoring approach for novice teachers participating in an accelerated teacher certification program. Aims/focus of discussion: To investigate a novice teacher's problem-solving activity through self-expression of challenges and…

Response to Intervention (RtI) has promise for helping students, particularly ones with disabilities, achieve higher levels of academic and behavioral success in the general education classroom. What does it mean for gifted students or for those who are gifted and have a learning disability, such as twice-exceptional students? How might current…

The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

This article describes a psychoanalytic consultation model to an independent grade 7-12 school that offers a practical and efficient approach to improve school climate. This model may stand alone or complement other approaches, and it can be implemented in both independent and public school settings. It focuses not only on "at risk" students,…

How do we model and improve technical problem solving, such as network subnetting? This paper reports an experimental study that tested several hypotheses derived from Kolb's experiential learning cycle and Huber's problem solving model. As subjects solved a network subnetting problem, they mapped their mental processes according to Huber's…

The teacher leaders and school administrators at Nipher Middle School in Kirkwood, Missouri, have recently embraced a new set of strategies for supporting learning for all students. During the weekly problem-solving conversations that are a part of their response-to-intervention model, it became evident that clusters of students with unique and…

The objective of this research was to better understand the transfer of learning between different variations of pre-algebra problems. While the authors could have addressed a specific variation that might address transfer, they were interested in developing a general model of transfer, so we gathered data from multiple problem types and their…