Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

A well-known lesson taught by many upper-elementary and early-middle-school teachers at the beginning of the school year asks students to compare how arm span relates to height. Students measure their height and arm span and compare their measurements to those of their classmates. This lesson gets students measuring, graphing, and practicing…

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…

Stochastic accumulator models account for response time in perceptual decision-making tasks by assuming that perceptual evidence accumulates to a threshold. The present investigation mapped the firing rate of frontal eye field (FEF) visual neurons onto perceptual evidence and the firing rate of FEF movement neurons onto evidence accumulation to…

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity…

Human visual perception is a fundamentally relational process: Lightness perception depends on luminance ratios, and depth perception depends on occlusion (difference of depth) cues. Neurons in low-level visual cortex are sensitive to the difference (but not the value itself) of signals, and these differences have to be used to reconstruct the…

Radical reform in science and mathematics education is needed to prepare citizens for challenges of the emerging knowledge-based global economy. We consider definite proposals to establish: (1) "Standards of science and math literacy" for all students. (2) "Integration of the science curriculum" with structure of matter,…

This article presents the authors' response to Asha K. Jitendra's Response to Xin and Zhang ("The Journal of Educational Research," 2009, Vol. 102, No. 6). The claim of "factual errors, including inappropriate quotes, misrepresentation of information, and inadequate scholarship in Xin and Zhang's text" are not justified. In this rejoinder, the…

A recent resurgence in logical-rule theories of categorization has motivated the development of a class of models that predict not only choice probabilities but also categorization response times (RTs; Fific, Little, & Nosofsky, 2010). The new models combine mental-architecture and random-walk approaches within an integrated framework and…

This research describes technical drawing techniques applied in a project involving digitizing of existing hard copy subsurface mapping for the preparation of three dimensional graphic and mathematical models. The intent of this research was to identify work flows that would support the project, ensure the accuracy of the digital data obtained,…

This article describes a project designed to extend sixth-form pupils looking to further their knowledge and skill base in physics. This project involves a quantitative analysis of the decaying amplitude of a metal plate oscillating in a strong magnetic field; the decay of the amplitude is used to make estimates of the strength of the magnetic…

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

This study lies at an intersection between advancing educational data mining methods for detecting students' knowledge-in-action and the broader question of how conceptual and mathematical forms of knowing interact in exploring complex chemical systems. More specifically, it investigates students' inquiry actions in three computer-based models of…

Product assessment is widely applied in creative studies, typically as an important dependent measure. Within this context, this study had 2 purposes. First, the focus of this research was on methods for investigating possible rater effects, an issue that has not received a great deal of attention in past creativity studies. Second, the…

Early in 2010, a group of year 11 students (age 15-16) studying GCSE (General Certificate of Secondary Education) Astronomy at The Radclyffe School, Oldham, in the UK, teamed up with a similar age group from Tianyi High School, Wuxi City, in China, to undertake a joint astronomy investigation. This article outlines the outcome of the first stage…