Manipulating the ratio of known to unknown items has been shown to improve student on-task behavior and increase the desirability of schoolwork. Although many intervention protocols manipulate ratios of known to unknown items, these frequently require extensive adult cuing. School psychologists recommending such interventions may face resistance…

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One,…

Functions provide powerful tools for describing change, but research has shown that students find difficulty in using functions to create and interpret models of changing phenomena. In this study, we drew on a models and modeling perspective to design an instructional approach to develop students' abilities to describe and interpret rates of…

Many students encounter difficulties in science and mathematics. Earlier research suggested that although intuitions are often needed to gain new ideas and concepts and to solve problems in science and mathematics, some of students' difficulties could stem from the interference of intuitive reasoning. The literature suggests that overcoming…

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: "language of generalisation," "language of comparison," "language of proportional reasoning," and…

The purpose of the study reported in this paper is to evaluate the effectiveness of an implementation of teaching rounds as a practice-based approach to pre-service teacher education in mathematics. The teaching rounds implemented in the study utilised the NSW Quality Teaching model pedagogical framework as a tool for learning about and reflecting…

Professional development (PD) is key to improving mathematics teaching and learning in the middle grades. Many PD projects and initiatives have been undertaken across the United States. Yet, we know very little about what teachers learn in and through such PD, nor about what those who conduct the PD might be learning as well. This knowledge gap…

Mathematical tasks embedded in real-life contexts have received increased attention by educators, in part due to the considerable levels of student engagement often triggered by their motivational features. Nevertheless, it is often challenging for teachers to implement high-level (i.e., cognitively demanding), real-life tasks in ways that exploit…

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…

[Slides] presented at the annual conference of the National Council of Supervisors of Math.

The results of the study reported in this article found that primary-aged students used context knowledge in three broad ways: (1) to rationalise the data or their interpretations; (2) in taking a critical stance toward the data; and (3) in ways that were not necessarily productive or pertinent in addressing the task at hand. When teaching…

A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of…

Uses two studies to examine developmental and task effects in estimation problems. Results are discussed in terms of student and task characteristics and the implications of such variables on information processing model of learning. Implications for science teaching, learning problem diagnostics, and science curricula are also discussed. (TW)