The gold standard for identifying more effective pedagogical approaches is to perform an experiment. Unfortunately, frequently a hypothesized alternate way of teaching does not yield an improved effect. Given the expense and logistics of each experiment, and the enormous space of potential ways to improve teaching, it would be highly preferable if…

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

This article details the application of an economic theory to the fiscal operation of a small engineering consulting firm. Nobel Prize-winning economist Wassily Leontief developed his general input-output economic theory in the mid-twentieth century to describe the flow of goods and services in the U.S. economy. We use one mathematical model that…

Constructing a matrix model not only offers the teacher a theoretical and practical method for organizing his own knowledge about a topic, but provides a vehicle for the student to cope with contemporary knowledge explosion in a realistic and sophisticated manner. (Author)

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…

A variety of examples are given from different areas of biology to illustrate the general applicability of matrix algebra to discrete models. These models of biological systems are concerned with relations between processes occurring in discrete time intervals. Diffusion, ecosystems, and different types of cells are modeled. (KR/Author)

Explains a three-dimensional conceptual model designed to help outdoor educators plan and evaluate programs that provide primary and reflective experiences in, about, and for the outdoors and that bring about positive growth in the cognitive, affective, and psychomotor domains of learning. (JHZ)

Stressing the importance of systematic planning for field experiences in teacher education, the authors outline the appropriate functions and instructional modes of the school-based component of teacher training. They present a matrix design for integrating the functions and modes of university-based and school-based instruction. (SJL)

We evaluated an intervention package for teaching generative sociodramatic play activities to a young boy with an autism spectrum disorder. In Phase 1, the boy learned computer activity schedules that featured embedded video models of what to say and do. A 3 x 3 instructional matrix defined 9 activities to be performed involving combinations of 3…

The construct validity of 14 measures used in college faculty personnel decisions was evaluated through a multitrait-multimethod matrix for data from 89 faculty members in 7 departments. The three-pronged model of teaching, research, and service was not validated. Exploratory factor analysis identified five or six behavior domains for evaluation.…

Classroom activities for directing student inquiry into the role of the individual in the future are provided in this text. Activities are presented within a framework of respect for and understanding of the past and the present. A matrix for the study of the individual as a whole person is presented. The matrix is devised along the present, past,…

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics," provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, it is expected that the Addenda Series will…