In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

The mathematical reasoning ability is one of the essential hard skills of a student, especially in solving everyday problems. In supporting the achievement of this mathematical reasoning ability, meaningful teaching materials are an essential part of keeping exciting and not dull a learning process. This study aimed to design and develop an…

This research paper aims to produce a mathematical module with a problem-solving approach to train student's reflective thinking. To find out how to develop modules, there are three criteria must be fulfilled, namely validity, practicality, and effectiveness. Development of module used four stages, namely the initial situation analysis, design…

STEM education in elementary school is guided by the understanding that engineering represents the application of science and math concepts to make life better for people. The Engineering Design Process (EDP) guides the application of creative solutions to problems. Helping teachers understand how to apply the EDP to create lessons develops a…

This study explored the effectiveness of online instructional modules for providing supplementary instruction in basic mathematics and physics concepts. The modules were developed in accordance with a cognitive apprenticeship model. Participants (N = 47) were students enrolled in a required Statics course at a midwestern university. Participants…

In a design experiment, the feedback from the teacher-implementer is crucial to the success of the innovation simply because the teacher is finally the one that brings the innovation to life in front of the students. We describe in this paper the feedback made by the teacher-implementer after teaching one cycle of the problem solving module in a…

As part of an integrative learning experience at the end of a sophomore Calculus II course at the United States Military Academy, this project served as a multidisciplinary problem-solving exercise that explored the connections among mathematics, biology, and other fields of study. During a seven-lesson block of instruction, this module was…

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

Teaching mathematics through Open Distance Learning (ODL) has been a challenge to educators due to the nature of communication with learners and material delivery during instruction. In this paper, as a case study, we look at one mathematics module offered through ODL and the performance in the course for the past four years. A sample of 50…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…

This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…

Previous research has shown that students construct equations for word problems in which many of the terms have no referents. Experiment 1 attempted to eliminate some of these errors by providing instruction on canceling units. The failure of this method was attributed to the cognitive overload (Sweller, 2003) imposed by adding units to the…

This document is designed to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. The approach used is to: (1) develop the material in terms of full-rank factorizations and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) include…

This set of three modules was designed for use primarily to help teach and reinforce the basic mathematics skills in drafting classes. The modules are based on the needs of drafting students in beginning courses as determined by a survey of teachers across North Carolina. Each module consists of basic information and examples and problem sheets…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)