A comprehensive understanding of biological functions requires new systemic perspectives, such as those provided by systems biology. Systems biology approaches are hypothesis-driven and involve iterative rounds of model building, prediction, experimentation, model refinement, and development. Developments in computer science are allowing for ever…

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

Our work is inspired by the book "Imagining Numbers (particularly the square root of minus fifteen)," by Harvard University mathematics professor Barry Mazur ("Imagining numbers (particularly the square root of minus fifteen)," Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of…

This paper promotes the use of adapted primary literature as a curriculum and instruction innovation for use in high school. Adapted primary literature is useful for promoting an understanding of scientific and mathematical reasoning and argument and for introducing modern science into the schools. We describe a prototype adapted from a published…

This documentary account situates teacher educator, prospective teacher, and elementary students' mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill--creating and analyzing representations. The author examines responses of prospective…

In longitudinal studies data is collected in a series of waves. Each wave after the first suffers from attrition. Therefore it can be difficult to discriminate between changes in sample parameters due to a longitudinal process (e.g. ageing) and changes due to attrition. The problem is particularly vexing if one of the purposes is to compare…

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Electricity is regarded as one of the most challenging topics for students of all ages. Several researchers have suggested that naive misconceptions about electricity stem from a deep incommensurability (Slotta and Chi 2006; Chi 2005) or incompatibility (Chi et al. 1994) between naive and expert knowledge structures. In this paper we argue that…

Introduction: We present some aspects of a wider investigation (Canadas, 2007), whose main objective is to describe and characterize inductive reasoning used by Spanish students in years 9 and 10 when they work on problems that involved linear and quadratic sequences. Method: We produced a test composed of six problems with different…

Achievement gap language has become associated with the observed disparities on a number of educational measures between the academic performances of Black and White students. This theoretical lens is problematic because it sends an unintended message that Black students are not worthy of study in their own right. Using a mixed-methodological…

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

The mathematical model used to describe independence between two events in probability has a non-intuitive consequence called dependent spaces. The paper begins with a very brief history of the development of probability, then defines dependent spaces, and reviews what is known about finite spaces with uniform probability. The study of finite…

The purpose of this study was to identify determinants of transfer. Accounting for variables in several domains (background, academic, social, environmental), this research was particularly interested in the effect of environment on transfer. Data employed in this study was derived from the Beginning Postsecondary Students Longitudinal Study (BPS:…

Smaller universities may produce research which is on a par with larger, elite establishments. This is confirmed by a recently developed mathematical model, supported by data from British and French higher education research-evaluation exercises. The detailed nature of the UK system, in particular, allows quantification of the notion of critical…