In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

In this study it was aimed to evaluate the effects of various factors such as sample sizes, percentage of misfit items in the test and item quality (item discrimination) on item and model fit in case of misspecification of Q matrix. Data were generated in accordance with DINA model. Q matrix was specified for 4 attributes and 15 items. While data…

Detection of students' ability levels is one of the common aims in educational studies. Cognitive Diagnosis Modeling approach has been used recently for the purpose of ability level detection by defined Q-matrices. To evaluate students' strengths and weaknesses, determine their mastery skills, and design instructions and interventions in learning…

This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

This paper discusses a talent management and career planning system designed based on the performance and qualifications of a group of interns working for an emerging social media company located in Istanbul. The proposed model is dynamic, comparative, and perceptional in constructing a talent pool for an organization. This system was developed…

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

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…

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,…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

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…

Presents mathematical games that involve a problem-solving matrix, multicolored cubes, and three-dimensional dominoes. The work of Alexander MacMahon is highlighted. (MA)

Provides a summary of a series of research and development projects which investigated the reasons for failure in educational technology-based systems of instruction. Develops a new approach to the design of such systems and their subsequent implementation and control. A 17-item bibliography is included. (Author/CHC)