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Elaborating on threshold concepts
Abstract
We propose an expanded definition of Threshold Concepts (TCs) that requires the successful acquisition and internalisation not only of knowledge, but also its practical elaboration in the domains of applied strategies and mental models. This richer definition allows us to clarify the relationship between TCs and Fundamental Ideas, and to account for both the important and the problematic characteristics of TCs in terms of the Knowledge/Strategies/Mental Models Framework defined in previous work.
... Mathematical concepts are presented only as tools, with little or no discussion of their analyses, rigorous proofs for their essential properties, and the abstract ideas behind them. As a result, even though students are provided with the means to acquire knowledge of the relevant concepts, and strategies for applying the knowledge in practice, there is little emphasis on developing effective mental models, which is crucial for passing through the liminal state in learning the threshold concepts of a subject [24]. A similar problem can be found in some schools of mathematics, where computer science related courses are confined to a few basic programming ones. ...
... The reference educational theory will be Threshold Concepts. Although the original account-introduced by Meyer and Land [17]-was criticized for lacking a practical definition [25], the theory has evolved following the contribution of many scholars, including Rountree et al. [24], who elaborated on one of their main features, i. e., being transformative. It is indeed this account of threshold concepts that will be used as the framework for the current paper. ...
... Obtaining accuracies comparable to the ones reported in [14] requires symbolic differentiation. This demonstrated the importance of knowing the differences between various differentiation schemes, which is crucial for entering the transliminal state and constructing effective mental models of neural networks [24]. ...
Contribution: Using threshold concepts as the framework for curriculum design, a project on neural network methods for solving differential equations is presented, with a rich set of transformative concepts from mathematics and computer science. Projects of this kind complement a typical curriculum with expertise that is crucial for critique and fundamental development of modern machine learning. Background: The curricula of many schools of mathematics and computer science present a relatively shallow introduction to the other subject. Student projects, on the other hand, provide an effective environment for interdisciplinary research between the two disciplines. Intended Outcomes: Providing students from computer science and mathematics the opportunity to obtain a deeper understanding and appreciation of the other subject, beyond the confines of the school curriculum. Application Design: The project contains tasks that require acquisition, not just of knowledge, but also of effective strategies and mental models, relevant to a set of transformative concepts from both disciplines. The tasks require a spectrum of activities, ranging from rigorous theoretical work to coding. Findings: Although the theory of threshold concepts needs further development, the existing paradigms provide a helpful framework for curriculum design. The continuous formative assessment proved effective in monitoring the participants’ journeys through the liminal state.
... 13 The method has also been modified and recognized as a form of object facilitation, used to support reflection on, and ultimately better understanding of, difficult or 'threshold' concepts in HE. 14 Through the use of metaphor, object facilitation such as LSP facilitates successful application of strategies and mental models after knowledge acquisition and internalization has taken place, strengthening learning. 14,15 Therefore, LSP is ideally placed as a tool to support consolidation of learning for example, in revision tutorials. ...
... Threshold concepts are those troublesome aspects of a discipline that, when crossed, are transformative for learning. 15 They are integrative, irreversible, bounded and troublesome in nature, although not all troublesome concepts are threshold concepts. 14 In Biology, language, scale, hypothesis building, variation, randomness, uncertainty and energy transformation have been put forward as threshold concepts, with energy transformation and scale being particularly relevant to this application. ...
A Lego Serious Play (LSP) ‐ based exercise was developed to support student engagement with learning consolidation at the end of a first‐year undergraduate cell biology course. The exercise was offered in addition to a regular revision session in preparation for the summative exam. Students were studying four‐year BSc (Hons) degrees in: Animal Biology, Environmental Biology, Marine and Freshwater Biology, Biological Sciences, Biomedical Sciences, Microbiology & Biotechnology in Scotland, UK. Although many students studied Human Biology at High School, in‐depth cell biology was studied for the first time by the majority of students during this course. The LSP process was adapted for use in the classroom. Core concepts were identified from the twelve‐week cell biology course as the basis for LSP build challenges and incorporated into LSP build – share – reflect cycles by students individually and then joined together by the group to explore the interconnected nature of cell biology processes. Student and lecturer evaluations were thematically analyzed to explore the impact of the technique on student engagement. Results indicate that the method supports student cognitive and affective engagement who report improved and understanding of the topic, and enjoyment and interest. In addition, behavioral engagement such as learner interaction, independence, and empowerment were revealed by the lecturer interview. Identified barriers to the adoption of LSP include perceived issues around creativity, play and exploration and scientific identity, together with a lack of evidence of efficacy. This study seeks to remedy that gap.
... A key component of CT is the process of abstraction. Indeed, abstraction is recognized as a threshold concept [14]: a generative idea that once learned provides "a qualitatively different view of subject matter within a discipline. " The process of creating abstractions interleaves multiple problem solving phases: planning, building, and monitoring. ...
... Increasingly, other researchers have studied CT teaching and learning from a situated perspective [3,4,9,10]. Specifically, our framework connects with prior work on how problem solving involves a balancing act between exploration, building, and monitoring [1,14]. In addition, we recognize that developing abstractions requires a gradual process of specifying and prioritizing goals and subgoals, including refactoring a previous route by developing new subgoals [1]. ...
Educational researchers have increasingly drawn attention to how students develop computational thinking (CT) skills, including in science, math, and literacy contexts. A key component of CT is the process of abstraction, a particularly challenging concept for novice programmers, but one vital to problem solving. We propose a framework based on situated cognition that can be used to document how instructors and students communicate about abstractions during the problem solving process. We develop this framework in a multimodal interaction analysis of a 32-minute long excerpt of a middle school student working in the PixelBots JavaScript programming environment at a two-week summer programming workshop taught by undergraduate CS majors. Through a microgenetic analysis of the process of teaching and learning about abstraction in this excerpt, we document the extemporaneous prioritization of subgoals and the back-and-forth coordination of problem solving phases. In our case study, we identify that (a) problem solving phases are nested with several instances of context-switching within a single phase; (b) the introduction of new ideas and information create bridges or opportunities to move between different problem solving phases; (c) planning to solve a problem is a non-linear process; and (d) pedagogical moves such as modeling and prompting highlight situated resources and advance problem solving. Future research should address how to help students structure subgoals and reflect on connections between problem solving phases, and how to help instructors reflect on their routes to supporting students in the problem solving process.
... Furthermore, understanding recursion goes beyond memorizing definitions; it encompasses the ability to apply, test, and utilize the concept in realworld scenarios, thereby opening up new avenues for mental models and program design. The intricacies of recursion include both theoretical significance and substantial practical application, making it a transformative element of computing education [23]. ...
... Sien & Chong (2012) analyse object-oriented modelling from a TCs angle and conclude that classes, generalisation-specialisation hierarchies, and object interaction should be added to the list of computer science TCs. Rountree et al. (2013) contend that any successful crossing of the liminal space requires not only the acquisition and internalisation of the knowledge, but also "its practical elaboration in the domains of applied strategies and mental models". Shinners-Kennedy & Fincher (2013) summarised the work of a group of researchers who had to identify and report TCs in computer science education. ...
... Furthermore, understanding recursion goes beyond memorizing definitions; it encompasses the ability to apply, test, and utilize the concept in real-world scenarios, thereby opening up new avenues for mental models and program design. The intricacies of recursion include both theoretical significance and substantial practical application, making it a transformative element of computing education [22]. ...
Grasping complex computing concepts often poses a challenge for students who struggle to anchor these new ideas to familiar experiences and understandings. To help with this, a good analogy can bridge the gap between unfamiliar concepts and familiar ones, providing an engaging way to aid understanding. However, creating effective educational analogies is difficult even for experienced instructors. We investigate to what extent large language models (LLMs), specifically ChatGPT, can provide access to personally relevant analogies on demand. Focusing on recursion, a challenging threshold concept, we conducted an investigation analyzing the analogies generated by more than 350 first-year computing students. They were provided with a code snippet and tasked to generate their own recursion-based analogies using ChatGPT, optionally including personally relevant topics in their prompts. We observed a great deal of diversity in the analogies produced with student-prescribed topics, in contrast to the otherwise generic analogies, highlighting the value of student creativity when working with LLMs. Not only did students enjoy the activity and report an improved understanding of recursion, but they described more easily remembering analogies that were personally and culturally relevant.
... Boustedt [15] Two phenomenographical outcome spaces describing programming students' understanding of the Java interface and software system 9 Robins [142] Learning edge momentum effect: theory to explain learning progression in introductory programming 221 Thompson and Kinshuk [179] Phenomenographical outcome space describing practioners' understandings of the nature of an object-oriented program 4 Sanders et al. [153] Notion of 'threshold skills ' 36 Rountree et al. [149] Extension to the definition of threshold concepts to capture strategies and mental models 15 Seiter and Foreman [156] Progression of early computational thinking (PECT) model: framework for understanding and assessing computational thinking in primary school 193 Lewis [87] Initial taxonomy for describing how students understand recursion 20 ...
Use of theory within a field of research provides the foundation for designing effective research programs and establishing a deeper understanding of the results obtained. This, together with the emergence of domain-specific theory, is often taken as an indicator of the maturity of any research area. This paper explores the development and subsequent usage of domain-specific theories and theoretical constructs (TCs) in computing education research (CER). All TCs found in 878 papers published in three major CER publication venues over the period 2005–2020 were identified and assessed to determine the nature and purpose of the constructs found. We focused more closely on areas related to learning, studying, and progression, where our analysis found 80 new TCs that had been developed, based on multiple epistemological perspectives. Several existing frameworks were used to categorize the areas of CER focus in which TCs were found, the methodology by which they were developed, and the nature and purpose of the TCs. A citation analysis was undertaken, with 1727 citing papers accessed to determine to what extent and in what ways TCs had been used and developed to inform subsequent work, also considering whether these aspects vary according to different focus areas within computing education. We noted which TCs were used most often and least often, and we present several brief case studies that demonstrate progressive development of domain-specific theory. The exploration provides insights into trends in theory development and suggests areas in which further work might be called for. Our findings indicate a general interest in the development of TCs during the period studied, and we show examples of how different approaches to theory development have been used. We present a framework suggesting how strategies for developing new TCs in CER might be structured, and discuss the nature of theory development in relation to the field of CER.
... Why do students report that they just come to understand everything in an instant, overnight? A substantial amount of research has gone into the area of threshold concepts in computer science education (Boustedt et al., 2007;Eckerdal et al., 2006;Rountree et al., 2013;Sanders & McCartney, 2016;Thomas et al., 2010). The idea of threshold concepts originated from Meyer and Land (2005) and aims at identifying particular concepts that function as thresholds in different subject areas, like keys to the subject. ...
Background and Context
Research in programming education seems to show that hands-on writing at the keyboard is beneficial for learning, but we lack an explanation of why that is and an underlying theory to anchor that explanation.
Objective
The first objective is to lay out a theoretical foundation for understanding the learning situation when novices first encounter programming in the computer lab. The second objective is to illustrate how this theoretical foundation can help give insight by applying it to an empirical study.
Method
Core concepts from Dewey’s pragmatic theory are combined with the thinking of Deleuze and the later Wittgenstein to form a theoretical framework. The main empirical data is seven student interviews, which were analyzed using a qualitative content analysis method in two steps, first analyzing the stated content and second through the lens of the theoretical framework.
Findings
Students’ learning processes can be understood as ‘come to agreement’ and habitual actions when doing programming as ‘practical thinking’.
Implications
Programming education can be reframed beyond the theory–practice dichotomy already rejected by pragmatism. This may have an impact on both course design and assessment, in that knowledge and measurement of knowledge have to be re-evaluated in a pragmatic light.
... In addition economics (O'Donnell, 2010;Shanahan, 2016;Shanahan, Foster, & Meyer, 2006;Woodward, 2011), other business-related disciplines are studying how applying threshold concepts to their fields can shape student learning and later professional performance. Examples include computer science (Rountree, Robins, Rountree, 2013), management (Dyer & Hurd, 2018;Hawkins & Edwards, 2015;Hibbert & Cunliffe, 2015;Nahavandi, 2016;Vidal, Smith, & Spetic, 2015), finance (Hoadley, Tickle, Wood, & Kyng, 2015); and entrepreneurship (Bollinger & Brown, 2015;Hatt, 2018). ...
In this article, the authors present the notion of perspective as a threshold concept in business communication. Using an SoTL framework, the researchers explore the effect of teaching threshold concepts in a summary writing assignment in a foundational business communication class. Working with a close reading methodology, the authors examine the context of perspective as a threshold concept by analyzing students’ summary samples for gender bias and explore how close reading can support further research into threshold concepts in business communication.
... 2013 Extending the definition of threshold concepts [73] literature + argumentation 10 2013 Zones of proximal flow pedagogical framework to promote intrinsic motivation and leverage student learning experiences [3] adapted an existing theory + empirical 36 2013 Progression of early computational thinking (PECT) model for understanding and assessing computational thinking of primary school students [77] argumentation + empirical 92 [69] investigates the model in a different context to determine whether it can be applied with BlueJ despite some clear differences between the two environments. Their work is still inconclusive with regard to the predictive power of NPSM, but it is important to investigate whether the initial reported success was tied to a specific context. ...
... 2013 Extending the definition of threshold concepts [73] literature + argumentation 10 2013 Zones of proximal flow pedagogical framework to promote intrinsic motivation and leverage student learning experiences [3] adapted an existing theory + empirical 36 2013 Progression of early computational thinking (PECT) model for understanding and assessing computational thinking of primary school students [77] argumentation + empirical 92 [69] investigates the model in a different context to determine whether it can be applied with BlueJ despite some clear differences between the two environments. Their work is still inconclusive with regard to the predictive power of NPSM, but it is important to investigate whether the initial reported success was tied to a specific context. ...
In order to mature as a research field, computing education research (CER) seeks to build a better theoretical understanding of how students learn computing concepts and processes. Progress in this area depends on the development of computing-specific theories of learning to complement the general theoretical understanding of learning processes. In this paper we analyze the CER literature in three central publication venues -- ICER, ACM Transactions of Computing Education, and Computer Science Education -- over the period 2005--2015. Our findings identify new theoretical constructs of learning computing that have been published, and the research approaches that have been used in formulating these constructs. We identify 65 novel theoretical constructs in areas such as learning/understanding, learning behaviour/strategies, study choice/orientation, and performance/progression/retention. The most common research methods used to devise new constructs include grounded theory, phenomenography, and various statistical models. We further analyze how a number of these constructs, which arose in computing education, have been used in subsequent research, and present several examples to illustrate how theoretical constructs can guide and enrich further research. We discuss the implications for the whole field.
... Fortune and Kennedy-Jones (2014) have suggested that if threshold concepts are to meet this characteristic then they should not exist in any other discipline, and they proposed occupation as the only threshold concept in OT. However, recent publications suggest that there are only two non-negotiable threshold concept characteristics, being transformation and integration (Quinlan et al. 2013, Rountree, Robins, andRountree 2013). In this study, participants suggested that although a number of the ten threshold concepts discussed may be shared with other disciplines, it is perhaps the integrated use of the threshold concepts, in an occupation-based context that defines the discipline of OT and differentiates it from other professions. ...
In the current higher education environment, there is a growing expectation that universities ensure students graduate with skills and attributes that enable them to be work-ready, particularly within the health and social care disciplines. One curriculum design approach that has been proposed as facilitating this transformation from student to professional is the threshold concepts framework. A recent study identified ten threshold concepts within the discipline of occupational therapy. These were: Understanding the models and theories of occupational therapy; Evidence-based practice; Clinical reasoning; Discipline-specific skills and knowledge; Practising in context; A client-centred approach; Occupation; The occupational therapist role; Reflective practice; and, A holistic approach. This study aimed to explore whether these threshold concepts were taught within an Australian occupational therapy program. Twelve occupational therapy educators participated in focus groups, and five themes emerged from the data. These were: professional identity; time; the impact of the learning environment; explicit versus implicit content and language; and, the value and understanding of the threshold concepts framework. The study found that the integrated use of threshold concepts may make them unique to the discipline. Findings also indicated that using the threshold concepts framework facilitates the transformation from student to occupational therapist. However, students may not acquire all of the threshold concepts prior to graduation. Practice-based learning was considered pivotal for threshold concept acquisition. This study explores the application of the threshold concepts framework, providing insights for educators who are seeking to produce graduates who are well-equipped for employment in complex healthcare environments.
Purpose - Although the literature is clear on what comprises effective project stakeholder management, communication between key stakeholders and project managers is often ineffective. Research is silent on stakeholders’ insufficient knowledge of project management terminology, which is a barrier for such effective communication. This paper identifies the project management concepts that key stakeholders should understand to improve effective communication.
Methodology - This paper employs a three-step research design. In the first step, based on Threshold Concept theory we identify the key project management concepts through interviews with 20 project management practitioners, trainers and trainees. In the second step, we confirm the findings from the first step and identify effective approaches to enhance project stakeholders’ communication through seven additional interviews with project stakeholders. In the third step, we construct a functional model of the research findings by employing a system-level modeling tool.
Findings - This research identifies five project management threshold concepts that are challenging for project stakeholders to understand: (1) project benefits, (2) the iron triangle, (3) the critical path, (4) uncertainty, and (5) project leadership. Following these knowledge barriers, the paper proposes unique approaches to develop effective project stakeholder communication.
Originality/value - This paper advances project stakeholder management research by identifying knowledge barriers and providing project managers with more effective approaches to better engage with their stakeholders.
Cambridge Core - Education, History, Theory - The Cambridge Handbook of Computing Education Research - edited by Sally A. Fincher
The Cambridge Handbook of Computing Education Research - edited by Sally A. Fincher February 2019
In this paper, we survey the work that has been done in threshold concepts in computing since they were first discussed in 2005: concepts that have been identified, methodologies used, and issues discussed. Based on this survey, we then identify some promising unexplored areas for future work.
Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as ‘The Mathematics Problem’, with students not demonstrating understanding of the subject. This paper will suggest that students are constructing different concept images in engineering and mathematics, based on their perception of either the use or exchange-value for the topics. Using a mixed methods approach, the paper compares 10 different types of concept image constructed by students, which suggests that familiar procedural images are preferred in mathematics. In contrast strategic and conceptual images develop for mechanics throughout the years of the programme, implying that different forms of competence are being constructed by students between the two subjects. The paper argues that this difference is attributed to the perceived use-value of mechanics in the career of the engineer, compared to the exchange-value associated with mathematics. Questions are raised about the relevance of current definitions of competence given that some routine mathematical operations previously performed by engineers are now being replaced by technology, in the new world of work.
Background/aim:
Understanding and facilitating the transformation from occupational therapy student to practitioner is central to the development of competent and work-ready graduates. However, the pivotal concepts and capabilities that need to be taught and learnt in occupational therapy are not necessarily explicit. The threshold concepts theory of teaching and learning proposes that every discipline has a set of transformational concepts that students must acquire in order to progress. As students acquire the threshold concepts, they develop a transformed way of understanding content related to their course of study which contributes to their developing expertise. The aim of this study was to identify the threshold concepts of occupational therapy.
Method:
The Delphi technique, a data collection method that aims to demonstrate consensus in relation to important questions, was used with three groups comprising final year occupational therapy students (n = 11), occupational therapy clinicians (n = 21) and academics teaching occupational therapy (n = 10) in Victoria, Australia.
Results:
Participants reached consensus regarding 10 threshold concepts for the occupational therapy discipline. These are: understanding and applying the models and theories of occupational therapy; occupation; evidence-based practice; clinical reasoning; discipline specific skills and knowledge; practising in context; a client-centred approach; the occupational therapist role; reflective practice and; a holistic approach.
Conclusion:
The threshold concepts identified provide valuable information for the discipline. They can potentially inform the development of competencies for occupational therapy and provide guidance for teaching and learning activities to facilitate the transformation to competent practitioner.
In this paper I argue that pedagogic research organised around the investigation of threshold concepts offers a fresh way of thinking about research collaboration with students, academics and educational developers. I will first introduce the basic ideas about threshold concepts, briefly contrasting it with the phenomenographic tradition. I suggest that threshold concept inquiry effects a turn from this tradition by: a) encouraging partnerships with educationalists, students and subject specialists; and b) by a focus on the difficulty of the subject rather than on general education theory.
Computer science is a complex, highly technical, and changing field. In addition, it is a new subject: we've had relatively few years to study the ways in which students learn and how to help them most effectively. The idea of threshold concepts has the potential to help us focus on those concepts that are most likely to block students' progress(2, 4). Our project is in a preliminary stage. First, we are examining the ques- tion of threshold concepts from the educators' point of view. Last summer in Portugal, at the Conference on Innovation and Technology in Computer Science Education, we interviewed 36 computer science educators from nine countries and asked for suggestions about concepts that met the criteria for a threshold concept. Our interviews were unstructured, done in a fairly conversational style with one researcher asking questions and another taking written notes. From these, we learned several interesting things. First, the idea of threshold con- cepts is compelling: nearly everyone we spoke with was immediately inter- ested. Thirty-three concepts were suggested, with the most popular being: levels of abstraction; pointers; the distinction between classes, objects, and instances; recursion and induction; procedural abstraction; and polymor- phism. Second, while some concepts came up again and again, there was no universal consensus, possibly reflecting the current state of computer science education. For example, the most recent guidelines for computer-science curricula suggest six possible approaches to the introductory sequence of courses, admitting that each was in use at a number of different institutions and there was no clear way to choose among them(5). We have since given a poster and had discussions with researchers at a conference in Finland (3) and are also using a questionnaire and interviews to gather data more systematically from faculty. Preliminary analysis indi- cates that these results are similar to those collected in Portugal, but more carefully tied to the defining characteristics of threshold concepts. Some
Yes, and Yes.We are currently undertaking an pirical investigation of "Threshold Concepts" in Computer Science, with input from both instructors and students. We have found good pirical evidence that at least two concepts---Object-oriented programming and pointers--are Threshold Concepts, and that there are potentially many more others.In this paper, we present results gathered using various experimental techniques, and discuss how Threshold Concepts can affect the learning process.
Proposes a framework for skill acquisition that includes 2 major stages in the development of a cognitive skill: (1) a declarative stage in which facts about the skill domain are interpreted and (2) a procedural stage in which the domain knowledge is directly embodied in procedures for performing the skill. This general framework has been instantiated in the ACT system in which facts are encoded in a propositional network and procedures are encoded as productions. Knowledge compilation is the process by which the skill transits from the declarative stage to the procedural stage. It consists of the subprocesses of composition, which collapses sequences of productions into single productions, and proceduralization, which embeds factual knowledge into productions. Once proceduralized, further learning processes operate on the skill to make the productions more selective in their range of applications. These processes include generalization, discrimination, and strengthening of productions. Comparisons are made to similar concepts from previous learning theories. How these learning mechanisms apply to produce the power law speedup in processing time with practice is discussed. (62 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Presents findings of a task force established by the American Psychological Association to report on the issues of what is known and unknown about intelligence. Significant conceptualizations of intelligence are reviewed, including the psychometric approach, theories of multiple forms of intelligence, cultural variations, theories of developmental progressions, and biological approaches. The meaning of intelligence test scores, what they predict, and how well they predict intelligence is discussed. Genetic factors and intelligence, focusing on individual differences, conventional IQ tests, and other tests intended to measure cognitive ability, are described. Environmental factors such as social and biological variables are discussed, and sex and ethnic group differences are addressed. Recommendations for future research are presented. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This paper shows that so-called ‘threshold concepts’ have been defined in a way that makes it impossible, even in principle, to empirically isolate them. It continues by proposing an alternative theoretical framework, and argues: (1) that concepts are not reducible to abilities; (2) that acquisition of a given concept can be necessary, but not sufficient, for the possession of an ability; and (3) that being ‘threshold’ is an extrinsic property, such that what is threshold for one person is not for another. It closes by outlining two resultant problems for related empirical research. First, how is it possible to test for concepts, rather than abilities? Second, how can we tell if there is more than one possible conceptual route to the same ability?
This paper is part of an ongoing series of projects in which we are investigating "threshold concepts": concepts that, among other things, transforms the way a student looks as the discipline and are often troublesome to learn. The word "threshold" might imply that students cross the threshold in a single "aha"moment, but often they seem to take longer. Meyer and Land introduce the term "liminal space" for the transitional period between beginning to learn a concept and fully mastering it. Based on in-depth interviews with graduating seniors, we found that the liminal space can provide a useful metaphor for the concept learning process. In addition to observing the standard features of liminal spaces, we have identified some that may be specific to computing, specifically those relating to levels of abstraction.
Presents findings of a task force established by the American Psychological Association to report on the issues of what is known and unknown about intelligence. Significant conceptualizations of intelligence are reviewed, including the psychometric approach, theories of multiple forms of intelligence, cultural variations, theories of developmental progressions, and biological approaches. The meaning of intelligence test scores, what they predict, and how well they predict intelligence is discussed. Genetic factors and intelligence, focusing on individual differences, conventional IQ tests, and other tests intended to measure cognitive ability, are described. Environmental factors such as social and biological variables are discussed, and sex and ethnic group differences are addressed. Recommendations for future research are presented.
Computer programming learning/teaching has been an active research area in computer science and engineering. The difficulty level of the teaching/learning process that novices in computer programming report is three-fold, lack of problem solving strategies, misconceptions of code syntax and semantics, and inability to develop an adequate mental model of the machine. This paper examines major difficulties encountered by students taking introductory-level programming courses and it proposes a computer model that sets thresholds for defining basic programming concepts. The study's initial findings suggest that the adoption of the model succeeded significantly in improving students' academic achievement and perception of computer programming
In this paper, we present the results of an experiment in which we sought to elicit students' understanding of object-oriented (OO) concepts using concept maps. Our analysis confirmed earlier research indicating that students do not have a firm grasp on the distinction between "class" and "instance." Unlike earlier research, we found that our students generally connect classes with both data and behavior. Students rarely included any mention of the hardware/software context of programs, their users, or their real-world domains. Students do mention inheritance, but not encapsulation or abstraction. And the picture they draw of OO is a static one: we found nothing that could be construed as referring to interaction among objects in a program. We then discuss the implications for teaching introductory OO programming.
The experiments reported in this article flow from the following assumptions concerning our cognitive processes: (a) Schema acquisition and automation are major learning mechanisms when dealing with higher cognitive activities and are designed to circumvent our limited working memories and emphasize our highly effective long-term memories. (b) A limited working memory makes it difficult to assimilate multiple elements of information simultaneously. (c) Under conditions where multiple elements of information interact, they must be assimilated simultaneously. (d) As a consequence, a heavy cognitive load is imposed when dealing with material that has a high level of element interactivity. (e) High levels of element interactivity and their associated cognitive loads may be caused both by intrinsic nature of the material being learned and by the method of presentation. (f) If the intrinsic element interactivity and consequent cognitive load are low, the extraneous cognitive load is critical when dealing with intrinsically high element interactivity materials. These assumptions are the basic points of cognitive load theory. They were used to suggest that, when learning to use equipment such as computer applications, learning might be facilitated by not having the equipment present, if the material that needed to be learned had an intrinsically high degree of element interactivity. A series of four experiments supported this hypothesis. It was concluded that an analysis of both intrinsic and extraneous cognitive load can lead to instructional designs generating spectacular gains in learning efficiency.
This paper describes Threshold Concepts, a theory of learning that distinguishes core concepts whose characteristics can make them troublesome in learning. With an eye to applying this theory in computer science, we consider this notion in the context of related topics in computer science education.
This paper describes Threshold Concepts, a theory of learning that distinguishes core concepts whose characteristics can make them troublesome in learning. With an eye to applying this theory in computer science, we consider this notion in the context of related topics in computer science education.
Different students have different strengths. A classroom based on a multiple intelligences model meets the needs of all students and raises their awareness of their own strengths and self worth.<br /
This paper arises from ongoing research undertaken by the Economics team of the ESRC/ TLRP Project 'Enhancing Teaching and Learning Environments' (ETL) 1 . This forms part of the large scale ESRC Teaching and Learning Research Programme Phase 2. ETL is seeking to identify factors leading to high quality learning environments within five disciplinary contexts across a range of HE institutions. Meyer's notion of a threshold concept was introduced into project discussions on learning outcomes as a particular basis for differentiating between core learning outcomes that represent 'seeing things in a new way' and those that do not. A threshold concept is thus seen as something distinct within what university teachers would typically describe as 'core concepts'. Furthermore, threshold concepts may represent, or lead to, what Perkins (1999) describes as 'troublesome knowledge' — knowledge that is conceptually difficult, counter-intuitive or 'alien'. The paper attempts to define characteristics of threshold concepts and, in the light of Perkins' work, to indicate correspondences between the notion of threshold concepts and that of 'troublesome knowledge.'
Yes, and Yes.We are currently undertaking an pirical investigation of "Threshold Concepts" in Computer Science, with input from both instructors and students. We have found good pirical evidence that at least two concepts---Object-oriented programming and pointers--are Threshold Concepts, and that there are potentially many more others.In this paper, we present results gathered using various experimental techniques, and discuss how Threshold Concepts can affect the learning process.
We examine the transformations experienced by students during their study of computing. These transformations led to changes in the students' perceptions of computer science, in their sense of identity as computer scientists, their behavior and their confidence. The changes are caused by learning or using particular concepts, and often associated with writing computer programs, learning new programming languages, or interacting with peers.
Since they were first described by Meyer and Land [1] the classification of concepts as 'threshold' concepts has engaged many researchers, including a number of CS researchers. A variety of approaches have been employed to identify concepts that could be classified as threshold concepts, with varying success. Our own frustrations in identifying them led us to identify shortcomings in commonly-used approaches, and to the promising possibilities offered by a new direction. We describe that new direction here, and detail the path that led us to it.
While the study of threshold concepts is a growing area of research, their identification has not proven to be an easy process. However, identification matters because of the potential impact of threshold concepts on the learning experiences of students. A dialogue amongst lecturers and/or students is common to the literature on identification of threshold concepts. This dialogue, with the inclusion of educational developers, has been called ‘transactional curriculum inquiry’ (Cousin in Researching learning in higher education, Routledge, New York, 2009). Diverse methods across a variety of disciplines have explored the identification of threshold concepts, including semi-structured interviews, analysis of exam responses and observation of classroom behaviour. A selection of these methods and disciplines is discussed in order to highlight two main challenges inherent in the identification process: first, the involvement of the wider professional and/or public community, and second, a lack of agreement amongst research participants about the threshold concepts within disciplines. This paper proposes that the transactional curriculum inquiry process should be extended to involve parties beyond the educational realm (e.g. the professional community) and that the use of consensus methodology offers the potential to facilitate agreement across the transactional process.
The Threshold Capability Integrated Theoretical Framework (TCITF) is presented as a framework for the design of university curricula, aimed at developing graduates’ capability to deal with previously unseen situations in their professional, social, and personal lives. The TCITF is a new theoretical framework derived from, and heavily dependent upon, the ideas of the Threshold Concepts Framework (Meyer and Land 2003a; Land et al. 2006) and Capability Theory (Bowden and Marton 1998; Bowden et al. 2000; Bowden 2004). Capability theory is firmly based in phenomenography and variation theory, is concerned with the development of knowledge capability, but has had limited application in practice. The threshold concepts framework has enjoyed greater acceptance by a large range of academics in many fields. This acceptance has initially focussed on analytic studies of what constitutes a threshold concept—and the location and distribution of such concepts—in a given domain. In many instances subsequent attention has focussed on issues of pedagogy and assessment, including the design of curricula. We propose a merging of capability theory and the threshold concepts framework and argue that capability and variation theories provide the ideal mechanism for developing a strong pedagogical approach based on newly emerging knowledge of the critical features of threshold concepts within different domains.
Threshold concepts can be used to both organize disciplinary knowledge and explain why students have difficulties at certain points in the curriculum. Threshold concepts transform a student's view of the discipline; before being learned, they can block a student's progress.
In this paper, we propose that in computing, skills, in addition to concepts, can sometimes be thresholds. Some students report finding skills more difficult than concepts. We discuss some computing skills that may be thresholds and compare threshold skills and threshold concepts.
Efforts to explain learning as a constructive process run into the paradox of having to attribute to the learner prior knowledge that is at least as complex as the new learning to be explained. Although no full solution of this paradox is in sight, it is argued that progress is possible through examination of the wide range of mental resources available to human learners, only a limited range of which are taken account of in current theories. This paper considers 10 relatively neglected resources for the “bootstrapping” of cognitive growth, including chance plus selection, the affective boosting of relevant schemas, the operation of innate biases, and use of spare mental capacity. Implications for educational research are illustrated with reference to recent work on the development of complex composition strategies.
Both the special education and gifted education literature call for a differentiated curriculum to cater for the wide range of student differences in any classroom. Gardner's theory of multiple intelligences was integrated with the revised Bloom's taxonomy to provide a planning tool for curriculum differentiation. Teachers' progress in using the tool to plan and implement units of work through learning centers was documented over 18 months in two small elementary schools. They reported greater confidence in their ability to broaden their curriculum and cater for different students' strengths across the multiple intelligences and intellectually challenge their students using first the original and then the revised taxonomy. The teachers saw their students as more successful learners as a result of this curriculum differentiation.
The aim of this paper is to introduce and validate the concept of program working storage (PWS) as a) a means of smooth transition of students in introductory programming courses from the end-user stance to the programmer stance, and b) a system which can provide comprehensive understanding of certain difficult programming concepts. In this respect, the program-memory interaction is considered as a possible "threshold concept" [31, 33]. Based on constructivism [16, 23, 41, 42], the PWS is then discussed as a potential beginner's viable model, which can be, later on, refined to what Ben-Ari describes as a viable computer model [5]. The extent to which the PWS can be used as a conceptual framework, which will enable teachers and learners to focus on program-memory interaction across a variety of dimensions, and eventually relate them to form a coherent whole, is also examined. The exact implementation of the PWS in the context of the various programming languages is beyond the scope of this paper. Nevertheless, it constitutes a topic for detailed study and future research.
I comment on and extend prior work that searches for threshold concepts in computer programming. I argue that explicitly linking threshold concepts to Brunerian fundamental ideas gives structure to the ongoing debate on threshold concepts. Program dynamics, information hiding and object interaction appear three strong candidates for threshold concepts in introductory programming, while abstraction and state seem to qualify as fundamental ideas. I further propose that the threshold concepts debate could benefit from the notion of transliminal concepts -- concepts that require an understanding of a threshold concept and can 'lure' students to and across thresholds.
Threshold Concepts deserve discussion and reflection in Computer Science Education; they provide a conceptual framework intended to re-empower tertiary educators. At this stage, the idea of Threshold Concepts raises plenty of questions, promises renewed learner and teacher engagement, and suggests a means of focusing on the key aspects of a discipline that will allow a learner to, for example, "think more like a computer scientist." But what precisely are threshold concepts? Can we identify them? Can we agree on which concepts are threshold concepts and which are not? Can we validate them? If threshold concepts do exist, and can be identified and agreed upon, then how would they alter what we teach, how we teach, and how we assess? Do threshold concepts represent anything new or unexpected? The purpose of this paper is to set out issues for the Threshold Concepts model in Computer Science Education and encourage on-going discussion.
‘Threshold concepts’ are concepts that, among other things, transform the way a student looks at a discipline. Although the term ‘threshold’ might suggest that the transformation occurs at a specific point in time, an ‘aha’ moment, it seems more common (at least in computing) that a longer time period is required. This time period is referred to as the ‘liminal space’. In this paper, we summarise our findings concerning how computing students experience the liminal space and discuss how this might affect teaching. Most of our findings so far relate to software engineering. As it is likely that similar liminal spaces occur in other engineering disciplines, these findings have relevance across engineering education.
We transfer J. S. Bruner’s principle of orienting education towards fundamental ideas to computer science and brought it up for discussion. According to the considerations so far this principle seems to be a useful approach to structure computer science education. In order to support this thesis several advanced investigations would be helpful: 1) Development of curricula and programs for computer science education that stress fundamental ideas. 2) Elaboration of suitable examples which highlight certain ideas. 3) Even if the presented catalog of ideas is based on an objective analysis of activities and methods, it is undoubtedly influenced by the author. Hence, further discussion is necessary in order to refine and substantiate the catalog within the scientific community.
The present study builds on earlier work by Meyer and Land (2003) which introduced the generative notion of threshold concepts within (and across) disciplines, in the sense of transforming the internal view of subject matter or part thereof. In this earlier work such concepts were further linked to forms of knowledge that are troublesome, after the work of Perkins (1999). It was argued that these twinned sets of ideas may define critical moments of irreversible conceptual transformation in the educational experiences of learners, and their teachers. The present study aims (a) to examine the extent to which such phenomena can be located within personal understandings of discipline-specific epistemological discourses, (b) to develop more extensively notions of liminality within learning that were raised in the first paper, and (c) to propose a conceptual framework within which teachers may advance their own reflective practice.
We examine the changes in the ways computing students view their field as they learn, as reported by the students themselves in short written biographies. In many ways, these changes result in students thinking and acting more like computer scientists and identifying more with the computing community. Most of the changes are associated with programming and software engineering, rather than theoretical computer science, however.
Students often "get stuck" when trying to learn new computing concepts and skills. In this paper, we present and categorize strategies that successful students found helpful in getting unstuck. We found that the students reported using a broad range of strategies, and that these strategies fall into a number of recognizably different categories.
The purpose of this paper is to review the cognitive literature regarding transfer in order to provide a context for the consideration of transfer in neural networks. We consider transfer under the three general headings of analogy, skill transfer and metaphor. The emphasis of the research in each of these areas is quite different and the literatures are largely distinct. Important common themes emerge, however, relating to the role of similarity, the importance of 'surface content' and the nature of the representations that are used. We will draw out these common themes and note ways of facilitating transfer. We also briefly note possible implications for the study of transfer in neural networks.
In this paper we review the literature relating to the psychological/educational study of programming. We identify general trends comparing novice and expert programmers, programming knowledge and strategies, program generation and comprehension, and objectoriented versus procedural programming. (We do not cover research relating specifically to other programming styles.) The main focus of the review is on novice programming and topics relating to novice teaching and learning. Various problems experienced by novices are identified, including issues relating to basic program design, to algorithmic complexity in certain language features, to the ‘‘fragility’ ’ of novice knowledge, and so on. We summarise this material and suggest some practical implications for teachers. We suggest that a key issue that emerges is the distinction between effective and ineffective novices. What characterises effective novices? Is it possible to identify the specific deficits of ineffective novices and help them to become effective learners of programming? 1.
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We propose ?threshold skills? as a complement to threshold concepts. The definition of threshold concepts assumes that theoretical knowledge is paramount: gaining the understanding of particular concepts irreversibly transforms the learners. Mastering computing, like many disciplines, requires, however, learning a combination of concepts and skills. Mathematicians learn to do proofs, musicians learn to play their instruments, and martial artists learn to make moves by doing these activities, not just intellectually understanding them. We propose some characteristics for threshold skills and outline implications for teaching and for future work.
Includes bibliographical references (leaf [111]). Carbon-copy of original thesis. Thesis--Cambridge University.
Taxonomy of educational objectives handbook 1: Cognitive domain Threshold concepts in computer science: Do they exist and are they useful?
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- Longman
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- A Eckerdal
- R Mccartney
- J E Moström
- M Ratcliffe
- K Sanders
- C Zander
Bloom, B. (1956). Taxonomy of educational objectives handbook 1: Cognitive domain. New York, NY: Longman. Boustedt, J., Eckerdal, A., McCartney, R., Moström, J. E., Ratcliffe, M., Sanders, K., & Zander, C. (2007). Threshold concepts in computer science: Do they exist and are they useful? SIGCSE Bulletin, 39, 504–508.