Mathematical Logic and Deduction in Computer Science Education

Background & Context Continuously developing teachers’ knowledge, practice, and professional identity is one of the key standards for effective computer science (CS) teachers. Objective This study aims to understand the landscape of CS teachers in the United States, the professional identity they hold, and how their background and teaching context are associated with their CS teacher identity. Method Using data of 3540 teachers, we performed a two-step cluster analysis to reveal homogeneous subgroups of CS teachers. The relationship between teachers’ backgrounds and their CS teacher identity was also assessed. Findings This study identified four profiles of CS teachers based on their professional identity. . CS teacher identity is strongly associated with teachers’ Computer Science Teachers Association membership, teaching responsibility, teaching experience, and their exposure to CS coursework. Implications More professional support is needed for CS teachers, especially for early-career CS teachers, elementary school teachers, and teachers with multiple responsibilities and little CS background.

The essence of the concept “educational and methodical task” in the context of professional training of future teachers is revealed, the expediency of application of tasks in the process of obtaining qualification by students under the educational and professional program 014 “Secondary education (Informatics)” is substantiated. The teacher's ability to effectively solve methodological problems, which are reflected in the stages of understanding, design and implementation of methodological activities, is identified with methodological competence, as the processes of eliminating contradictions involve the use of methodological knowledge and methods of mastering professionally significant personal qualities. The expediency of distinguishing between methodical and educational-methodical problem is proved. The educational-methodical task is described as a task in which the content of the methodical activity of the teacher in a specific pedagogical situation is modeled, search of a way out of which assumes imitation of educational process during studying a school course of computer science in the conditions as close as possible to real. Competent problem solving requires fundamental knowledge of computer science and knowledge of computer science teaching methods, implementation of methodological actions that combine knowledge from different fields. The educational and methodical task is a multifaceted phenomenon and its content corresponds to the goals of the methodical activity and the characteristics of the educational-professional program according to which a student acquires the qualification “computer science teacher”. Considerable attention is paid to the analysis of classification of methodical and educational-methodical tasks. It is offered to use the following criteria: structural components of the methodical activity; functions of methodical activity; the level of complexity of the activity. The conclusions emphasize that the educational and methodical task is an important tool and method of preparing students for future professional activities, the systematic solution of various types of such tasks contributes to the acquisition of pedagogical experience, the formation of methodological competence of computer science teachers.

This manual provides any interested educator - formal or not - with the necessary framework, material and guidance for implementing a location-based game design course to promote physical activity and social interaction in urban open spaces. The first section presents materials and concepts that help introduce, structure and carry out a course for various target groups. The second section of the manual presents in detail examples of four courses tailored for different target groups: PART 1. Secondary education - describes a course for second stage pupils, PART 2. Higher education – imparted to architecture and urban design students, but previous experience shows that it is also appropriate in an interdisciplinary setup, PART 3. Adult learners - introduces a self-learning package and presents the topics and chapters that are covered by the learning material, and PART 4. Chronically ill children – an example that contains information for both students in higher education (computer science) and chronically ill children. Each part of the second section presents conclusions and recommendations as well as further material adapted to the needs of the presented target groups.

In the quest to study and deliver Computer Science (CS) education reform, attention to gate-keeping teacher characteristics is imperative. Broad research in teacher education has demonstrated that teacher dispositions are an important driver of teacher motivation, professional choices, and classroom practices. Identification and measurements of teacher dispositions enables further analysis of how teacher beliefs may support or hinder effective practice in CS instruction, how teacher populations may differ, and how identified dispositions may change with exposure to various CS learning experiences. We analyzed 17 key documents produced by 12 national CS organizations using a grounded theory methodology to identify desirable attitudes and beliefs associated with CS and the CS education reform movement. The documents included standards, corporate research reports, advocacy tools for CS education, and organizational documents of professional associations for CS and CS Education. The analysis yielded several important dispositional targets for description and measurement in the area of teacher attitudes and beliefs. An analysis of 98 coded segments related to dispositions yielded consensus attitudes and beliefs. Professional documents in CS highlight an equity orientation, a teacher growth mindset, and identify key beliefs regarding (career) outcomes and epistemology of CS. It is possible, based on this analysis, to create a profile of a teacher who demonstrates the attitudes and beliefs of a reform-aligned CS teacher, the CS "Champion''. Instrument development along these factors is an important next step towards unlocking the analytical power of teacher attitudes and beliefs.

This paper explores the potential of virtual education options to fulfill policies designed to broaden participation in computer science (CS) education. Virtual education platforms inherently offer access to a wider range of students than traditional brick-and-mortar schools. Access does not preclude the various socio-economic challenges to engaging these platforms, but this format could be used to mitigate barriers to reaching groups of students that have historically been marginalized in CS courses. In 2019, Georgia passed legislation that requires all middle and high schools to offer CS courses by 2025. The legislation also allowed for virtual courses to satisfy the requirement. While the legislation is intent on broadening participation in CS education, it specifically incorporates a virtual option, making it novel among similar legislative actions across the country. In this context, we examine whether virtual CS courses increase access for marginalized student populations. As such, we explore (1) to what extent do the disparities in CS education found in brick-and-mortar classrooms also appear in virtual settings and (2) to what extent is there an association between modality and rurality on CS course enrollment. Using district enrollment data from 2012 to 2019 for CS courses in Georgia, we calculated the percentage of students in marginalized groups that enrolled in physical courses across the state compared to the percentage enrolled in statewide virtual courses to illuminate existing disparities in enrollment. We conducted this analysis at the district level to highlight variability in representative disparity and the underlying structural differences that might contribute to these disparities. Our analysis provides insight that incorporates the different levels of representative disparity districts have overall. As an early adopter of virtual CS education, the Georgia model provides valuable information for states interested in policies to broaden participation in CS courses.

Justice-centered approaches to equitable computer science (CS) education\nframe CS learning as a means for advancing peace, antiracism, and social\njustice rather than war, empire, and corporations. However, most research in\njustice-centered approaches in CS education focus on K-12 learning\nenvironments. In this position paper, we review justice-centered approaches to\nCS education, problematize the lack of justice-centered approaches to CS in\nhigher education in particular, and describe a justice-centered approach for\nundergraduate Data Structures and Algorithms. Our approach emphasizes three\ncomponents: (1) ethics: critiques the sociopolitical values of data structure\nand algorithm design as well as the underlying logics of dominant computing\nculture; (2) identity: draws on culturally responsive-sustaining pedagogies to\nemphasize student identity as rooted in resistance to the dominant computing\nculture; and (3) political vision: ensures the rightful presence of political\nstruggles by reauthoring rights to frame CS learning as a force for social\njustice. Through a case study of this Critical Comparative Data Structures and\nAlgorithms pedagogy, we argue that justice-centered approaches to higher CS\neducation can help all computing students not only learn about the ethical\nimplications of nominally technical concepts, but also develop greater respect\nfor diverse epistemologies, cultures, and experiences surrounding computing\nthat are essential to creating the socially-just worlds we need.\n

Computer science is a higher education domain that still show a significant male dominance. Many research studies have highlighted the importance of diversity and gender balance in computer science related areas such as software engineering and system development. However, there is still a well-identified problem that university programmes and courses on computer science fail to attract the female audience. The objective of this study is to investigate the concept of gender-inclusive computer science (CS) education with the aim of broadening participation in CS courses and programs. This is conducted through a literature study, initially focusing on keywords and research areas, and subsequently searching into existing research. The research question that guided the study was: "What concepts can be found in literature to make computer science education more gender-inclusive?". Data were analysed thematically in a two-step analysis process inspired by the grounded theory methods of Open coding and Axial coding. Findings suggest that there is significant room for learning in this field, particularly from Critical CS education studies. The Open coding analysis showed that the findings can be categorised into eight main themes. In the Axial coding the themes were merged, refined, renamed, and centred around the main axial theme of 'Epistemological pluralism'. Other essential themes that all are related to the axial main theme were: 'Design and creativity', 'Bias awareness and ethics', 'Collaboration and communication', 'Self-regulated learning', 'Real-world applications', and 'Role models and mentorship'. The result of this study is presented through a visual model that illustrates essential aspects of inclusive computer science education. The paper also proposes various directions for future research.

Efforts in the United States to broaden the participation of racial and ethnic minorities in K12 computer science (CS) education often focus on the need for children to change themselves to meet the standards and norms of traditional computing education. Less attention has been paid to how CS education itself might change and adapt to cultural contexts and locations that children already participate in and find of value. In this paper, we describe efforts to change the shape and culture of CS education by designing and implementing it in and for a youth boxing gym in an African American community. We report findings from a boxing inspired CS curriculum that was designed in collaboration with boxing coaches, mentors, and academic staff members at the gym. It was piloted over the course of two six-hour workshops with 15 middle and high school age children. We focused on two issues that are relevant to broadening participation and reshaping the culture of CS education: (1) how the curriculum changed children's perceptions of CS and (2) the creative adaptations that children made to the curricular content and materials. An analysis of pre- and post-surveys using a nonparametric test showed significant positive changes in children's responses to the constructs of self-confidence and expression with CS. Vignettes of children appropriating and personalizing technologies from the workshops are used to unpack these findings. We end with a discussion about the implications of these findings for culture-based CS education in both school and community contexts.

Little is known about how K-12 Computer Science (CS) teachers use technology and problem-based learning (PBL) to teach CS content in the context of CS Principles curricula. Significantly, little qualitative research has been conducted in these areas in computer science education, so we lack an in-depth understanding of the complicated realities of CS teachers' experiences. This paper describes the practices and experiences of six teachers' use of technology that was implemented to support PBL in the context of a dual enrollment CS Principles course.

Teaching formal methods in software construction has often been a concern of several computer science educators. In our opinion, the origin of most of the difficulties in learning formal methods in computer science and software engineering does not lie in computer science courses but in the mathematical background of the students. Moreover, there are numerous obstacles to learning basic concepts noted by both computer science and mathematics educators. To change this situation it is necessary to integrate the work of mathematics and computer science educators. That is, the main focus should be the creation of new educational approachs nourished by two components: a theoretical one (formally introducing discrete mathematics concepts) and an experimental one (implementing those concepts in a suitable programming language). In this paper, using examples from a discrete mathematics course for high school teachers, we describe the main characteristics of our approach.

Guiding theme of the ongoing reformation movement of the education system in Germany catalyzed by the OECD Programme for International Student Assessment is standardization. Educational standards are developed for all grades of school up to university level with a focus on the core subjects, reading, mathematics and scientific literacy [1]. Starting basis for the elaboration of standards are competence models, where competence is conceived according to Weinert [2] as "a roughly specialized system of abilities, proficiencies, or individual dispositions to learn something successfully, to do something successfully, or to reach a specific goal." As for computer science education, most of the existing approaches to competence models are of pragmatical nature, based on years of teaching experience. Although plausible and well thought out most of these models neither are concerted nor verified. This research work introduces a methodology of constructing a competence model from exercise characteristics by means of empirical statistical analysis. Exemplified by theoretical computer science in secondary education, it is exposed how hypotheses on the dimensional structure of a competence model are theoretically founded and empirically verified. The proceeding roughly breaks down into five steps. First step is the identification and classification of the characterizing attributes of task difficulty. "Characteristics" may be the closeness to the student?s realm of experience, the level of abstraction or complexity of the content, the level of formalization or redundancy of the task setting, or the level of cognitive process. Second step is the generation of hypotheses on the dimensional structure of a competence model, based on classification of the characteristics. For this purpose, the attributes are bundled to theoretically homogeneous groups according to criteria like "concerning the task setting, the curricular content or the learner activity". It is postulated that each competence dimension is composed of one group of characteristics, just as spectral colors are combined from primary colors. Step three is the implementation of an empirical study to gather empirical data on students? abilities along the characteristics. Step four is a statistical data analysis in order to verify the dimensional structure. Factor analysis appears to be an appropriate statistical technique for analyzing the correlations between the characteristics and bundle them to a small number of underlying dimensions, called factors. Since a factor shows, e.g., large correlation with the characteristic level of formalization and medium correlation with the characteristic redundancy of the task setting, it may be interpreted as their common factor, describing the portion of task difficulty emerging from the task setting. As step five it is proposed to cluster the competence profiles, referring to the factors. Typical competence profiles resulting from cluster analysis may be expressed in terms of characteristics to provide an individual competence diagnosis that is both meaningful and comprehensible. The following two examples are profiles of minimum and maximum competence level, to be fulfilled by every student (a) and to be attained only by high performing students (b) respectively: (a) The learners model a course of action close to their realm of experience (e.g., traffic lights) by using automata. If textually specified, algorithms are recalled and properly applied. (b) The learners model a problem beyond their experience (e.g., syntax check of arithmetic expressions) by using automata. Even if formally specified, problems are analyzed and appropriate algorithms are created.

K-12 computer science education utilizes a variety of tools and resources that make significant contributions. Tools such as unplugged computer science tools, block-based computer science tools, text-based computer science tools, physical computer science tools, robotic kits, artificial intelligence, etc. have an important place in K-12 computer science education. It is crucial to incorporate computer science instruction into the basic courses of K-12 students, as well as to incorporate these tools into the curriculum. Worldwide resources have a significant impact on the enrichment and dissemination of K-12 computer science education. The content and resources created by platforms like Computer Science Teachers Association (CSTA), International Society for Technology in Education (ISTE), National Centre for Computing Education (NCCE), etc. contribute significantly to K-12 computer science education. Websites such as K-12 Computer Science, CS for ALL, Teach Computing, Code.org, Scratch, etc. are also important platforms that have become learning communities in computer science education.

The article discusses the problem of teaching computer science, mathematics and logic in modern education, in particular, in a secondary general education school as inherited from the problems of the existing relationships between the sciences of computer science and mathematics, as well as generated by the prevailing forms and practice of teaching in the system of general education. The methodological aspects of teaching computer science, mathematics and logic are considered inherent in them and applied to them in a differentiated form: - a meaningful approach inherent in computer science and applied in mathematics and logic; - a formal approach inherent in mathematics and used in computer science and logic; - a socio-cultural approach characteristic of the triad ”computer science-mathematics-logic”. Against the background of the existing correspondence of the selected approaches (or the measure of this correspondence) to each local and independent element of the triad, it is assumed that there is an identification of the regular relations between the subject and the subject of education, the principles of organizing the processes of implementing methodological knowledge based on these regularities. For our study, it is important that the methodology and methodology of each differentiated system of the triad should contain everything that is ”necessary and sufficient” for the functioning of the educational system of the corresponding level. In this aspect, the article notes that mathematics studies form, computer science - form and content. The study of objects only in form leads to formalism in the information sphere (which is unacceptable), therefore, possible integration must be combined with the necessary differentiation. Since the processes of the development of knowledge of science, its methodology and teachingmethods are interrelated and interdependent, it is unconditionally interesting to reveal the potential (possibilities) of intersubject and metasubject connections and relations of the triad under consideration as close, but not homogeneous educational systems that have their own subject. specificity of the content, methods and forms of training. In this perspective, possible ways of solving the problems that have arisen are proposed in the context of changes in the school curricula of the content of information and mathematics education under the influence of the requirements of the new federal state educational standards and the structure of subject teaching in computer science and mathematics, ensuring their efficiency and effectiveness.

Purpose of research. The purpose of the paper is to describe the possibilities of including tasks for the design, development, use and experimental evaluation of “inverted” educational resources in the professional training of future teachers of mathematics and computer science for the development of their subject-methodical readiness. The formation and development of subject-methodical readiness is the main goal of professional training of future lecturers at a pedagogical university. The process of creating “inverted” educational resources requires from their author quite serious subject and methodological training. Potentially, the inclusion of tasks for the design, development, expertise, practical use and evaluation of “inverted” educational resources in the professional training of future teachers of mathematics and computer science can create conditions conducive to the formation of competencies of future teachers to create a comprehensive educational process in a digital environment. Since, on the one hand, in such didactic means, the educational content should be presented systematized and structured, have logic and hierarchical connections. On the other hand, the problematic issues included in the resources should reflect specific subject educational results in accordance with a given taxonomic model in the curriculum.Materials and methods. Based on the analysis of theoretical and methodological sources, the article substantiates the relevance of the problem of finding new ways and means of implementing additional subject training in mathematics and computer science for both schoolchildren and future teachers in the context of digitalization of education. The analysis of examples of “inverted” educational resources, which are the results of the implementation of project tasks by undergraduate students of the Krasnoyarsk State Pedagogical University named after V.P. Astafiev, is presented. Through theoretical and methodological substantiation, the main possibilities of including tasks for working with such resources at different stages of professional training of future teachers of mathematics and computer science at a pedagogical university are synthesized.Results. In this study, the problems related to the possibility of including “inverted” educational resources as digital didactic tools in the training programs of future teachers of mathematics and computer science were updated. The authors’ position on the issue of the purpose of such teaching tools in the context of the digitalization of education is presented and substantiated. Examples of the results of the implementation of project tasks by senior students during the 2021-2022 academic year were demonstrated. The key didactic and information technology features, possible tools for creating “inverted” educational resources are given. The definition of the subject-methodical readiness of the future teacher of mathematics and computer science as an essential component of professional readiness is concretized. The possibilities of strengthening subject-methodical training by including tasks for work with “inverted” educational resources are described: analytical – in junior courses when mastering disciplines related to the use of digital technologies in education; project – in the middle courses when mastering methodological disciplines; experimental and expert - in the senior courses when passing industrial (pedagogical) practice and mastering the final disciplines of the professional educational program of higher pedagogical education.Conclusion. On a final note, the results and conclusions obtained in the paper are summarized; the key positions of the authors on the inclusion of “inverted” educational resources in the professional training of future teachers of mathematics and computer science are given. The materials of the article may be of interest to lecturers of pedagogical universities who train future teachers, representatives of schools cooperating with organizations of higher pedagogical education, researchers in the field of digitalization and digital transformation of education.

Researchers have been working to understand the high dropout rates in computer science (CS) education. Despite the great demand for CS professionals, little is known about what influences individuals to complete their CS studies. We identify gains of studying CS, the (learning) environment, degree’s usefulness, and barriers as important predictors of students’ intention to complete their studies in CS (retention). The framework aims to identify reasons that may contribute to dropout, using responses from 344 CS students. The eight-predictor model accounts for 39 % of the explained variance in student retention. A high level for degree’s usefulness has a positive effect on retention. Further, cognitive gains and supportive environment positively impact degree’s usefulness, while non-cognitive gains hinder it. Lastly, negative feelings (personal values) are found to reduce student retention. The overall outcomes are expected to contribute to theoretical development, in order to allow educators and policy makers to take appropriate measures to enhance students’ experience in CS studies and increase retention.