In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

We present a detailed description of a Cryptography and Computer Security course that has been offered at Knox College for the last 15 years. While the course is roughly divided into two sections, Cryptology and Computer Security, our emphasis here is on the Cryptology section. The course puts the cryptologic material into its historical context…

Aim/Purpose: This study seeks to present a learning model of discrete mathematics elements, elucidate the content of teaching, and validate the effectiveness of this learning in a digital education context. Background: Teaching discrete mathematics in the realm of digital education poses challenges, particularly in crafting the optimal model,…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we…

In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…

Behavioral skills training (BST) is an evidence-based approach for training individuals to implement discrete-trial teaching procedures. Despite the effectiveness of this approach, implementing BST can be time and resource intensive, which may interfere with a clinical organization's adoption of this training format. We conducted a scoping review…

Discrete mathematics brings interesting problems for teaching and learning proof, with accessible objects such as integers (arithmetic), graphs (modeling, order) or polyominoes (geometry). Many problems that are still open can be explained to a large public. The objects can be manipulated by simple dynamic operations (removing, adding, 'gluing',…

Discrete trial training is a popular teaching method for individuals with autism, but it is not easily implemented with fidelity due to its complexity. This is the first meta-analysis of single-case experimental design studies to quantify the impact of behavioral skills training on individuals' ability to implement discrete trials with fidelity.…

Network analysis is a topic in secondary mathematics education of growing importance because it offers students an opportunity to understand how to model and solve many authentic technology and engineering problems. However, very little is known about how students make sense of the algorithms typically used in network analysis. In this study, I…

There are a variety of discrete facility location models that have practical relevance for operations management and management science courses. Integer linear programming (ILP) is the standard technique for solving such problems. An alternative approach that is often conceptually appealing to students is to pose the problem as one of finding the…

Discrete trial training is a popular teaching method for individuals with autism, but is not easily implemented with fidelity due to its complexity. This is the first meta-analysis of single-case experimental design studies to quantify the impact of behavioral skills training on individuals' ability to implement discrete trials with fidelity.…

The purpose of this study was to elicit preferences for the 'format' and 'content' of tobacco treatment among college student smokers, using an online discrete choice experiment (DCE) survey. A DCE survey, supplemented with a think-aloud method, was conducted among 54 college students who smoked combustible cigarettes and/or e-cigarettes.…

Procedural fidelity is the extent to which an intervention is implemented as designed and is an important component of research and practice. There are multiple ways to measure procedural fidelity, and few studies have explored how procedural fidelity varies based on the method of measurement. The current study compared adherence to discrete-trial…

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight…