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Experience Report on Using WeBWorK in Teaching Discrete Mathematics
... Their insights reveal not just heightened student engagement but also superior conceptual clarity. Echoing this trend, Cao and Grabchak (2023) integrated the WebWorK online homework system in their discrete math syllabus, reporting substantial improvements in foundational skills and a shift towards personalized learning trajectories. Wang et al. (2023) brought in innovation by amalgamating blended learning with the interactive "rain classroom" framework, observing enhanced student enthusiasm and academic performance. ...
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, content, tools, and methods tailored for aspiring computer science teachers. The study draws from both a comprehensive review of relevant literature and the synthesis of the authors’ pedagogical experiences. Methodology: The research utilized a system-activity approach and aligned with the State Educational Standard. It further integrated the theory of continuous education as its psychological and pedagogical foundation. Contribution: A unique model for instructing discrete mathematics elements to future computer science educators has been proposed. This model is underpinned by informative, technological, and personal competencies, intertwined with the mathematical bedrock of computer science. Findings: The study revealed the importance of holistic teaching of discrete mathematics elements for computer science teacher aspirants in line with the Informatics educational programs. An elective course, “Elements of Discrete Mathematics in Computer Science”, comprising three modules, was outlined. Practical examples spotlighting elements of mathematical logic and graph theory of discrete mathematics in programming and computer science were showcased. Recommendations for Practitioners: Future computer science educators should deeply integrate discrete mathematics elements in their teaching methodologies, especially when aligning with professional disciplines of the Informatics educational program. Recommendation for Researchers: Further exploration is recommended on the seamless integration of discrete mathematics elements in diverse computer science curricula, optimizing for varied learning outcomes and student profiles. Impact on Society: Enhancing the quality of teaching discrete mathematics to future computer science teachers can lead to better-educated professionals, driving advancements in the tech industry and contributing to societal progress. Future Research: There is scope to explore the wider applications of the discrete mathematics elements model in varied computer science sub-disciplines, and its adaptability across different educational frameworks.
The state of emergency caused by the covid-19 pandemic has shown that teaching at this time is not easy. Teachers have to make more use of distance education and students have to adapt to that. Classic face-to-face study is not possible but asymmetric communication between the teacher and his students may be replaced by greater student independence and greater student effort. Within the subject theory of probability and statistics, a questionnaire was created to find how students manage distance education. It has been found out that they use the prepared tutorial videos and online assignments (in WeBWork platform) the most. They expressed that distance education prepared by the teacher can replace face-to-face study, but this form of learning is much more demanding and therefore they prefer classic face-to-face study.
Contribution: This article compares the predictive performance of the scores on WeBWorK homework (online) with those of standard handwritten homework. The comparison is done across six undergraduate electrical engineering classes where each of the nine instructors have used both homework modalities. Background: Online homework systems have been used for many years, but analysis of their effectiveness is mixed. Previous work has been limited to a small number of classes in a wide variety of disciplines. This article has a larger number of classes and instructors than previous studies. The classes cover many basic topic areas in electrical and computer engineering, so is directly applicable to the audience of these transactions. Research Question: What is the effect of online homework compared to traditional handwritten homework on the performance of the students on the final exams in selected ECE classes? Methodology: Mixed-effects analysis of variance models are used to determine the predictive ability of performance on homework of the two modalities on the performance on the final exams. The data are limited to classes where the instructors have taught the class using both modalities. These models incorporate the effect of modalities for each instructor and the effect of the modalities across all classes. Findings: The result is that there is no significant statistical difference in the two modalities to predict final exam scores. This indicates that the advantages of using the automated online system can be obtained with no detrimental effect on the students' learning.
The basic principles of a flipped classroom teaching method are to deliver content outside of the class and to move active learning into the classroom. There are many strategies for delivering the content online, such as having instructors prepare online lectures, wrapping the course around a MOOC, and curating online videos from various sources. There are also many strategies for including active learning in the classroom that go beyond providing programming labs, and can include various forms of peer instruction. In this paper we describe our experiences flipping four different computer science classes across multiple semesters over two years. This breadth of experience with classroom flipping has enabled us to compare strategies and approaches and develop an understanding of which approaches appear to work under which circumstances. We discuss how we structured out-of-class preparatory work, how we created or sourced online videos, how we used active learning activities in-class to scaffold skills development and identify students' misconceptions, and how we structured teams for in class activities. This paper contributes a set of flexible strategies to consider for provision of curricular content out-of-class, structuring students' preparatory work, applying active learning of skills and concepts, and leveraging social interaction and peer instruction for CS education. We present the impact of our approaches based upon leading indicators of course evaluations and student surveys. We discuss lessons learned and students' responses to our strategies.
Recent technical and infrastructural developments posit flipped (or inverted) classroom approaches ripe for exploration. Flipped classroom approaches have students use technology to access the lecture and other instructional resources outside the classroom in order to engage them in active learning during in-class time. Scholars and educators have reported a variety of outcomes of a flipped approach to instruction; however, the lack of a summary from these empirical studies prevents stakeholders from having a clear view of the benefits and challenges of this style of instruction. The purpose of this article is to provide a review of the flipped classroom approach in order to summarize the findings, to guide future studies, and to reflect the major achievements in the area of Computer Science (CS) education. 32 peer-reviewed articles were collected from a systematic literature search and analyzed based on a categorization of their main elements. The results of this survey show the direction of flipped classroom research during recent years and summarize the benefits and challenges of adopting a flipped approach in the classroom. Suggestions for future research include: describing in-detail the flipped approach; performing controlled experiments; and triangulating data from diverse sources. These future research efforts will reveal which aspects of a flipped classroom work better and under which circumstances and student groups. The findings will ultimately allow us to form best practices and a unified framework for guiding/assisting educators who want to adopt this teaching style.
College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: WeBWorK, an open-source system for web-based homework, or traditional paper-and-pencil homework. We assessed learning for 439 students in 19 college algebra classes at a large public university in the United States. Twelve classes used WeBWorK and seven had traditional paper-and-pencil homework. Analysis of covariance revealed no significant differences in algebra performance or achievement gain by homework group, ethnicity or gender when statistically controlling for previous mathematics achievement. Results support the conjecture that WeBWorK is at least as effective as traditionally graded paper-and-pencil homework for students learning college algebra in moderately sized lecture-based classes.
Numerous (mostly commercial) Web-based systems for the assessment of programming assignments have emerged in the past few years to support the teaching and learning of programming fundamentals. WeBWorK, an initiative led by the University of Rochester to support Mathematics education, is unusual in that it is an open-source and extensible system. Since 2005, collaborators at Pace University and Cornell College have been working to adapt WeBWorK to extend its reach to Computer Science. This paper reports on a global experiment undertaken with Computer Science students and faculty from three continents based on the use of WeBWorK. Students in the US, Cambodia, India, Senegal and Thailand were presented with a set of programming exercises in a controlled environment. The intention was to explore the impact of diverse cultures, distinct first languages and differences in prior everyday exposure to the Internet and use of pedagogical tools on the usability and perceived value of such tools in Computer Science education. The study poses an important question with regard to the global uptake of everyday and typically US-centric educational technology. It provides findings likely to be of value to academic institutions interested in its adoption and companies interested in its commercialization.
This paper describes the development of a web-based programming and assessment environment for use in supporting programming fundamentals courses (CS1, CS2) taught in Java. This environment is currently linked with WeBWorK, an open source web-based system developed at the University of Rochester that is popular for administering and assessing mathematics and physics coursework, but is designed for the potential integration with other course management system (CMS) environments. In addition to the traditional multiple-choice and short answer questions that have been augmented with the extensive randomization and customization routines of WeBWorK, this new environment (called WeBWorK-JAG where JAG stands for Java Auto Grader) can automatically collect and grade free-form program fragments written in Java. Novel pedagogy has been developed based on the capabilities of this extension and preliminary classroom results are discussed in this paper. For example, when students contributed to WeBWorK by creating WeBWorK-JAG questions for their peers, they are exposed to the reality of creating comprehensive unit tests and to the wider quality assurance aspects of formulating questions and their solution sets. This work is described in the context of an emerging commercial market for web-based programming assistants and its unique contributions are summarized.
It has been long established that discrete structures is an important and foundational component of the computer science curriculum. However, the topics covered in this course tend to be more abstract than those covered in most other introductory computer science courses. This leads to additional challenges for instructors and students. To deal with these challenges, we introduce a new pedagogy for teaching this course. Our approach is based on a variant of the flipped classroom paradigm and is comprised of four main components: before class preparatory work, in-class mini lecture, in-class team based problem solving activities, and weekly individual assignments. In this paper, we discuss these components in detail. Our approach is informed by several cutting-edge teaching methodologies including active learning, light weight teams, and gamification. We conclude the paper by discussing the results of a survey taken by the students and a summary of the grades attained in the class. These show that our approach was well received by the students and has led to good learning outcomes.
In this study we examine the introduction of on-line homework to a Calculus II course as a replacement for ungraded pencil-and-paper homework assignments. We consider how this had an impact on students' performance in the course, on student behavior in completing the assigned work, and on student attitudes toward it. We find that students working homework on-line appear to do no worse in the course than those with pencil-and-paper homework, and may do better, and that including the homework in the course grade appears to increase students' attention to the homework. In addition, there is some evidence that this greater attention results in students having a better understanding of what they are doing on the homework and the benefit they accrue by completing it. There is also evidence that the on-line homework affords instructors greater flexibility in their management of in-class time.
As the use of web-based homework delivery and checking systems expands, we have greater need to evaluate how students engage with these systems and how changes in the systems influence student behavior. Reported here is the assessment of WeBWorK, an open-source web-based homework program used largely in postsecondary math and science courses, with recent extension to high school courses. WeBWorK draws from a large library of problems to generate individual assignments and provides immediate feedback about correctness of students’ answers. WeBWorK allows entries in multiple choice, formula and numerical formats. The entries recorded by the system create an extensive database of student interactions with the system.
WeBWorK: Generating, delivering, and checking math homework via the Internet
- Michael Gage
- Arnold Pizer
- Vicki Roth
- Gage Michael