Object-oriented Schema Research Articles

Acting on Totalities of infinite Processes: constructing facets of an Object conception

AbstractWe offer a new angle to explain the comprehension of mathematical infinity. We use Action—Process—Object—Schema (APOS) theory to explore the construction of different aspects of the cognitive Object related to this notion. We focus our attention on different ways of interacting with infinity, and how to act on infinite entities. Our aim is to shed light on the nature of mental constructions that take place when individuals deal with mathematical infinity. An infinite union of finite subsets of $${\mathbb{N}}$$ N provides the context for our theoretical analysis and the design of interviews conducted with graduate students and instructors. In this study we identify three types of Actions with different complexity levels. When these Actions are performed, they lead to the construction of different facets of the associated Object. We question the construction of an Object conception in infinity-related situations and offer an explanation that might change the way we think about the learning of certain mathematical concepts. We discuss the implications of our research for the advancement of APOS theory. We also offer pedagogical suggestions related to the comprehension of mathematical infinity.

Exploring Effectiveness of ACE Cycle of Instruction on Teaching area and Volume of Cylinder

This article aimed to explore the effectiveness of the application of activities, classroom discussion and exercise (ACE) cycle in mathematics instruction and investigate students' perceptions of the ACE cycle of teaching. The study focused on the area and volume of cylinders and was conducted among 20 students in grade nine selected for the intervention. The study adopted the APOS (Action, Process, and Object Schema) theory as the guiding theory and the ACE teaching cycle for intervention and implemented it over only one week. The study's results revealed that the well-planned three phases of the ACE cycle of instruction were effective in promoting students' activeness, developing their understanding of the area and volume of the cylinder, enhancing their motivation and improving their achievement.

Simple querying service for OpenAPI descriptions with semantic extensions

We introduce OpenAPI Query Language 2 (OAQL2), an SQL-like language for querying OpenAPI documents. OpenAPI is a standard format for the description of REST services, based on JSON (or YAML). A Web service capable of executing OAQL2 queries is implemented. The service stores metadata for each OpenAPI document and executes the queries on metadata to avoid the overhead of expensive join operations. It builds indexes to speed up queries, handles composite schema objects, and uses reasoning to support searching on semantic models referred to by OpenAPI properties. The run-time performance of OAQL2 has been assessed experimentally on a large database of 10,000 real service descriptions downloaded from SwaggerHub. Compared to the system implemented in our previous work, OAQL2 is proven to be faster and more complete in terms of syntax and compatibility with OpenAPI. To the best of our knowledge, there is nothing similar to SQL for OpenAPI. All other query methods are not designed for OpenAPI and require the user to be familiar with the peculiarities of OpenAPI syntax. This results in long complicated queries.

Thematic Roles in Image Schemas: A Missing Link Between Mind and Language

Abstract As early as 1968, Fillmore suggested that deep cases could be sets “of universal, presumably innate, concepts” human beings form to describe reality. Langacker’s (1991) role archetypes highlight the “primal status and nonlinguistic origin” of Thematic roles. I argue that Thematic roles have their “nonlinguistic” origin in image schemas and link the image schemas with language structures. The thesis is based on my description of the object schema (Szwedek, 2018), the definition of the image schema (Szwedek, 2019), and major works on Thematic roles. The object schema is fundamental in that all physical objects are experienceable by the senses (Szwedek, 2011, 2018). In contrast to relational schemas, it is also conceptually independent, while “[r]elations are conceptually dependent, i.e. one cannot conceptualize interconnections without conceptualizing the entities they interconnect” (Langacker, 1987). I posit that Thematic roles are a link between image schemas (mind) and language, constituting a stable scaffolding for various syntactic structures.

What’s new with APOS theory? A look into levels and Totality

This paper focusses on developments concerning transitional aspects of learning from the perspective of APOS (Action—Process—Object—Schema) theory. Recent investigations about levels between stages and Totality as a possible new structure are commented on, as well as offering related pedagogical suggestions and ideas for future research.

Transitional points in constructing the preimage concept in linear algebra

From an APOS (Action–Process–Object–Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the learning of the concept of linear transformation in general, and the notion of preimage in particular. A questionnaire was designed and applied to 31 students from three different higher education institutions in Mexico, who were enrolled in an introductory linear algebra course. For the first time, transitional points known as levels are explicitly identified in the aforementioned context and empirical evidence is presented. Some difficulties resulting from the intervention of constructions related to the function concept are also pointed out. Discussion about the characteristics of levels in the APOS framework provides a theoretical contribution to the field.

Open-ended transitions to adulthood: Metaphorical thinking for times of stasis

In this article we engage critically with how metaphors have been used in sociological youth studies, including a turn to new metaphors that capture the foreclosure of futures and experiences of waiting, delay and non-institutional temporalities. Drawing on the resources of queer theory we challenge the developmentalism that underpins youth studies, employing notions of the impasse and growing sideways to capture the open-endedness of young adult lives. Working with data from a qualitative longitudinal study of Danish youth, we focus on how 47 young people responded to an invitation to talk about and through an object that represented the last three years of their lives. These rich accounts can be understood as examples of Paul Riceour’s ‘metaphoric discourse’, characterised by the simultaneity of ‘is’ and ‘is not’. The article first offers a schema of the biographical objects (trophies, hobbies, mortal, connective and protest) that captures the work of ‘being in time’ for young adults, mapping this onto the formal and informal markers of adulthood. We then engage with participants’ own metaphorical thinking in greater depth – suggesting that the paradoxical metaphors that emerge from their talk can expand how we understand the struggle for maturity. The metaphor of open-endedness is offered as a hybrid term, allowing us to look in two directions at once: capturing and comparing transitions as part of a project of social justice, while also recognising the limits of such frameworks for understanding the experiences of a new generation.

Formulating a Modified Genetic Decomposition for the Concept of ‘Limit of a Sequence’

In this paper we focused on university mathematics students’ mental constructions on the concept limit of a sequence. The aim was to explore the nature of the mental constructions and to contribute to Action–Process–Object–Schema (APOS) theory in terms of instructional strategy for teaching limit of sequences. The belief that understanding students’ mental constructions in learning mathematics leads to improved instructional strategy guided this study. Maple software was applied in the learning of limit of sequences to foster students’ understanding of the topic. Thirty university students took part in this study. The data was collected through the test questions and interviews. The results revealed that in most cases, the preliminary genetic decomposition could be used to appropriately describe students’ constructions of their responses. Furthermore, many students operated at an action/process/object level with the exception of a few students who were not able to operate at these levels. It was also revealed that few students carried out procedures effectively without the conceptual understanding of the concept limit of a sequence. It is recommended that the preliminary genetic decomposition be extended to include aspects necessary for conceptual understanding of the limit of sequences in modified genetic decomposition, such as prerequisites, concepts which include rules of inequalities and properties of the modulus function. These concepts are required for the understanding of proving or disproving the given limits of a sequence.

Construction of the concept of pairability in comparing infinite sets in the individuals’ mind: an APOS approach

Abstract This study focuses on the concept of pairability as a fundamental metaphorical concept in the Cantorian set theory regarding comparison of infinite sets. In this theory, pairability appears in a hierarchical manner of generating and developing as a one-to-one correspondence by arrows in finite, and then in infinite states, a bijection map through an explicit formula and the concept of cardinality. Adapting these hierarchical components of pairability and the APOS theory, about description of constructing and understanding a mathematical concept in a hierarchical manner, this study examines the construction of the concept of pairability in the individuals’ mind. In this way, their imaginations of pairability and practical performances in different situations will also be surveyed. In so doing, a total of 20 mathematics teachers and university lecturers holding at least an M.Sc. degree in mathematics were chosen. To collect the data, interviews were conducted in which the participants not only answered questions about the concept of the various types of pairability but also compared infinite countable sets in different situations. Our findings revealed that a bijection map via an explicit formula was the individuals’ dominant conception of pairability and most of the incorrect answers were related to unsuccessful attempts to recall a formula or method as the only possible way, and the encapsulated concept of cardinality was used less frequently in practice. Therefore, there was not a total schema of actions, processes and objects of the concept of pairability in the individuals’ mind.

An APOS Analysis of University Students’ Understanding of Derivatives: A Lesotho Case Study

The derivative is a central concept in calculus and has applications in many disciplines. This study explored students’ understanding of derivatives with a particular focus on the graphical (geometric) representation. The participants were four Mathematics Honours students from a university in Lesotho. Data were generated from the written responses to five tasks and interviews, with all collection methods included. The Action–Process–Object–Schema (APOS) theory was used as the framework of analysis. The findings of the study show that the mental constructions that students developed in learning the derivative concept were mainly actions. The coordinated process conception of the derivative as the limit was evident with respect to algebraic representation but not in the graphical representation. Only one student showed that they had the process conception of the secant lines tending to the tangent line. It was also found that the process of tending to the limit operator was interpreted as tending to and landing on rather than being in the neighbourhood of by some students. These findings suggest that students should be made aware of the interpretation of tending to as implying staying in the neighbourhood rather than landing on. Students should also be given activities based on derivatives that require translation from one mode of representation to another (algebraic to graphical in this case).

Complex Image Schemas

In my earlier papers (Szwedek 2018 and 2019), I refuted the almost universal view (e.g. Clausner, Croft 1999), that the image schema cannot be defined. I first proposed to follow Grady’s (2005) general recommendation that the image schemas which would be “too general to be associated with any particular type of perceptual experience, or too rich to count as fundamental dimensions of perceptual representation” (2005: 35) should be ruled out. I argued (Szwedek 2018) that the fundamental perception is that of density experienced only by touch and the only entities whose density is experienced by touch are physical objects. Following Johnson 1987 and Langacker 1987, I proposed that the only independent entities in this world are physical objects with innumerable relations among them. I argued that if there are conceptually dependent relations, they must be relations between or among independent entities. I then concluded that the only conceptually independent object schemas constitute the basis of the formulation of a definition of the image schema and against all the pessimistic views he proposed the following definition: “The IMAGE SCHEMA is a mental structure with at least one OBJECT image schema, which is a conceptually independent entity representing a physical object whose fundamental property is density experienceable by touch, with ensuing boundedness, shape, size, etc.” (Szwedek, 2019: 20). While my 2018 paper discusses simple image schemas, the present paper shows, on the example of ENABLEMENT, that they can also form complexes expressed by one word

The Story of Us: Constructing Creative Partnerships Through Collaboration

Drawing constructs and techniques from object relations, schema therapy, and narrative therapy, this article explored means for constructing successful partnerships in collaboration and mentoring. Selected psychodynamics account for the phases and stages in creative collaboration. The initially hierarchal relationship of mentoring is instigative for reparenting and co-constructing of new perspectives. Self-development and service to the community occur within the context of the bridge between you and me. Case studies of mutuality and collaboration were presented to emphasize key constructs and helpful practices. Recommendations were offered to fuel the creative process of collaboration.

Notebook: Customizable web forms for recording observations

’Notebook’ is one of the primary data management systems of the Finnish Biodiversity Information Facility (FinBIF). It is a web solution for recording opportunistic as well as sampling-event-based species observations. It is being used for systematic monitoring schemes, various citizen science projects, and platforms for species enthusiasts. Notebook's main software component is LajiForm, which is the engine that renders a given JSON Schema into a web form. LajiForm is a separate, reusable module that is fully independent from other FinBIF systems. Notebook as a whole, includes other features embedded in FinBIF, such as linking users' geographical data to observation documents, spreadsheet document importing and form templates. We will demonstrate how the Notebook system works as a whole and also focus on LajiForm's technical aspects. Fig. 1 All Notebook forms use FinBIF's ontological schema in JSON Schema format. Rendering user-friendly web forms based on a single schema is a difficult task, because the web form should be asking meaningful questions, instead of just rendering the schema fields according to the form description. We want to present questions in an interactive style. For instance, after drawing a geographical location on a map for a potential flying squirrel nesting tree, we would ask "did you see droppings at the nest?", and answering "yes" would update the document to include a flying squirrel taxon identification with fields "breeding" and "record basis" filled in but not rendered to the form. A simpler form engine without a user interface (UI) customization layer would just render the "taxon", "breeding" and "record basis" fields and the user would have no understanding why there are so many fields to answer and how they relate to their work or study. Some forms are complex, e.g., for experienced biology enthusiasts who need a form that is advanced, customizable, and compact. Some forms are simple, e.g., for elementary school children. To tackle these challenges, LajiForm uses a separate schema for UI that allows everything from simple customization like: defining widgets for fields (e.g., date widgets, taxon autocomplete widget, map widget), changing field order or customizing field labels; to more complex customization like transforming the schema object structure, defining conditions when certain fields are shown or if updating a field should have an effect on other fields. defining widgets for fields (e.g., date widgets, taxon autocomplete widget, map widget), changing field order or customizing field labels; to more complex customization like transforming the schema object structure, defining conditions when certain fields are shown or if updating a field should have an effect on other fields. All the functionality is split into a loosely coupled collection of components, which can be either used as standalone components or composed together in order to achieve more advanced customization. The programming philosophy has drawn inspiration from functional programming, which has been helpful in writing isolated, composable functionality. LajiForm is written with the JavaScript framework React. LajiForm is built on top of react-jsonschema-form (RJSF), which is an open source JSON schema web form library provided by Mozilla. RJSF handles only simple customization, but it is very flexible in design and allows us to build extensions with features that are more powerful. Some features and design proposals were submitted to Mozilla – FinBIF is the largest code contributor to RJSF outside of Mozilla, with a dozen pull requests merged.

ALGORITHMS FOR MANAGING THE LOGICAL STRUCTURE OF THE DATABASE USING A PARAMETRIC MODEL OF COMPETITIVE ACCESS TO QUERIES BASED ON THE RANDOM FOREST METHOD

In article discusses the approach to development of mathematical software for support the process of managing the data schema in relational DBMS in terms of processing of parallel queries stream that compete for data in the hierarchy of the DBMS core memory. The necessity of the formation of a parametric model of queries competitive access. Briefly discusses methods of machine learning, allowing to solve the problem of regression recovery. The use of the random forest method as the most universal method of approximation of arbitrary functions is substantiated. A method of forming a parametric model of competitive access based on the random forest method, as well as an approach with the ensemble of sets of decision trees, which allows to provide the required generalizing ability and stability of the model to partial features and diversity of all types of queries received at the input of the DBMS. The stages of the developed algorithms are presented: ranking query parameters by total execution time and automatic data distribution, allowing you to go from approximating the target system with linear-continuous functions to a set of logical data schema objects, ordered by their effect on time, total query execution time, reducing multi-criteria optimization task to a task optimization by one criterion.

The development of a linear algebra schema: learning as result of the use of a cognitive theory and models

Learning is a complex phenomenon. Analyzing its development can provide knowledge about regularities and differences in students’ progress, which is needed to better understand learning. The aim of this study is to examine the development of students’ Linear Algebra Schema through an introductory one semester course. For that purpose, Action Process Object Schema (APOS) theory’s notions of Schema and Schema development were used to analyze students’ constructions at three different times throughout the course. Results show how students’ Schema are progressively constructed. They illustrate differences and commonalities in different students’ Schema development. Some concepts and factors were found to play an important role in promoting Schema development.

Mental constructions in linear algebra

The aim of this paper is on the one hand to discuss from an APOS (Action–Process–Object–Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research instruments and implementation of didactic interviews are discussed, supported by empirical data. Detailed analysis of transcripts from an interview with a student focuses on strategies used in interviewing as well as the mental stages involved in the construction of some linear algebra concepts. Due to the strategies employed, during the interview it is possible to witness the transition between different conceptions. A discussion of the relationships and interactions between different mental structures and mechanisms that play a role in the development of knowledge is provided, including theoretical considerations on the matter. Recommendations about pedagogical strategies are included.

An Exploratory Study on the Understanding of the Vector Subspace Concept

This exploratory study investigated 10 pre-service mathematics students’ understanding of vector subspaces at a university in Zimbabwe. The study involved an in-depth document analysis of the students’ written responses to five items based on the vector subspace concept. An APOS (Action–Process–Object–Schema) approach was used to identify the difficulties associated with developing the mental constructions of the vector subspace concept. The responses revealed that most of these pre-service teachers used reasoning associated with Action, or not even Action, conceptions of the prerequisite concepts of binary operations and sets, which hampered their engagement with the higher-level concepts of checking axioms. It is recommended that students should work with different sets and different types of binary operations, allowing them to routinise the Action of carrying out the binary operations on the sets first before moving to abstract applications. The data also revealed that students had difficulties in making links within the embodied, symbolic and formal worlds of thinking. It is suggested that instructors ensure that these links form an explicit focus of tasks.

The ATLAS Wide-Range Database and Application Monitoring

In HEP experiments at LHC the database applications often become complex, reflecting the increasingly demanding requirements of the researchers. The ATLAS experiment has several Oracle DB clusters with over 216 database schemes each with its own set of database objects. To effectively monitor them, we designed a modern and portable application with exceptionally good characteristics. Some of them include: A concise view of the most important DB metrics; a list of top SQL statements based on CPU, executions, block reads, etc.; volume growth plots per schema and DB object type; a database jobs section with signalization for failures; and in-depth analysis in case of row-lock contention or DB sessions. This contribution also describes the technical aspects of the implementation. The project can be separated into three independent layers. The first layer consists in highly-optimized database objects hiding all complicated calculations. The second layer represents a server providing REST access to the underlying database backend. The third layer is a JavaScript/AngularJS web interface. In addition, we will summarize the continuous integration cycle of the application, which uses GitLab-ci pipelines for basic testing, containerization and deployment on the CERN Openshift infrastructure.

Pre-service primary Mathematics teachers’ understanding of fractions: An action–process–object–schema perspective

Background: The concept of rational numbers is one of the learner’s first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study was set up to apply Action–Process–Object–Schema theory to study primary teachers’ understanding of addition and subtraction of fractions. Setting: The participants of this study comprised 60 undergraduate full-time students, studying to become teachers. The participants were enrolled in a foundational course in Mathematics because they had not passed Mathematics at Grade 12 level. This course was intended to help deepen their understanding of basic numeracy, allowing them to continue with further courses if they wanted to specialise in teaching primary mathematics Methods: Data were collected using written responses of the pre-service students to two tasks that focused on operations with fractions. Ten students volunteered to be interviewed of which three are drawn upon in this article. Results: Many of the pre-service teachers coped well with addition and subtraction of common fractions with the same denominator. However, more than 52% struggled to carry out these operations on common fractions with different denominators, showing that their conceptions had not developed into object-level structures. Conclusion: It is evident that the incorrect procedures have become embedded in the students mental schema. It is crucial that programmes for upgrading pre-service teachers should include opportunities for teachers to interrogate their personal understandings of the basic mathematics concepts.

Praxis, symbol and language

AbstractThis article focuses on the interweaving of constructive praxis with communication inontogenesis, inphylogenesisand in biocultural niche evolution (ecogenesis), within anEvoDevoSocioframework. I begin by discussing the nature of symbolization, its evolution from communicative signaling and its elaboration into semantic systems. I distinguish between thesymbol-readyand thelanguage-readybrain, leading to a discussion of linguistic conceptualization and itsdual groundingin organism and language system. There follows an outline account of the interpenetration in the human biocultural niche-complex ofsemiosphereandtechnosphere,mediated by the evolution of the niche of infancy. Symbolization (the foundation of the semiosphere) is by definition normative; the normative character of the technosphere is demonstrated by the interrelations in human development between affordance, action schema and canonical functional object schema. A model of the neuro-computational implementation of dual grounding is proposed.