There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided (...) a highly convincing argument for CTT by analyzing the processes carried out by a human computer. I then contend that if the Gandy–Sieg account is correct, then the notion of effective computability has changed after 1936. Today computer scientists view effective computability in terms of finite machine computation. My contention is supported by the current formulations of CTT, which always refer to machine computation, and by the current argumentation for CTT, which is different from the main arguments advanced by Turing and Church. I finally turn to discuss Robin Gandy's characterization of machine computation. I suggest that there is an ambiguity regarding the types of machines Gandy was postulating. I offer three interpretations, which differ in their scope and limitations, and conclude that none provides the basis for claiming that Gandy characterized finite machine computation. (shrink)

We analyse Kreisel’s notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church’s thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.

People recognize faces of their own race more accurately than faces of other races. The “contact” hypothesis suggests that this “other‐race effect” occurs as a result of the greater experience we have with own‐ versus other‐race faces. The computational mechanisms that may underlie different versions of the contact hypothesis were explored in this study. We replicated the other‐race effect with human participants and evaluated four classes of computational face recognition algorithms for the presence of an other‐race effect. Consistent with the (...) predictions of a developmental contact hypothesis, “experience‐based models” demonstrated an other‐race effect only when the representational system was developed through experience that warped the perceptual space in a way that was sensitive to the overall structure of the model's experience with faces of different races. When the model's representation relied on a feature set optimized to encode the information in the learned faces, experience‐based algorithms recognized minority‐race faces more accurately than majority‐race faces. The results suggest a developmental learning process that warps the perceptual space to enhance the encoding of distinctions relevant for own‐race faces. This feature space limits the quality of face representations for other‐race faces. (shrink)

Recent studies have shown that self‐explanation is an effective metacognitive strategy, but how can it be leveraged to improve students' learning in actual classrooms? How do instructional treatments that emphasizes self‐explanation affect students' learning, as compared to other instructional treatments? We investigated whether self‐explanation can be scaffolded effectively in a classroom environment using a Cognitive Tutor, which is intelligent instructional software that supports guided learning by doing. In two classroom experiments, we found that students who explained their steps during (...) problem‐solving practice with a Cognitive Tutor learned with greater understanding compared to students who did not explain steps. The explainers better explained their solutions steps and were more successful on transfer problems. We interpret these results as follows: By engaging in explanation, students acquired better‐integrated visual and verbal declarative knowledge and acquired less shallow procedural knowledge. The research demonstrates that the benefits of self‐explanation can be achieved in a relatively simple computer‐based approach that scales well for classroom use. (shrink)

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain choice (...) principles such as co-finite choice, discrete choice, interval choice, compact choice and closed choice, which are cornerstones among Weihrauch degrees and it turns out that certain core theorems in analysis can be classified naturally in this structure. In particular, we study theorems such as the Intermediate Value Theorem, the Baire Category Theorem, the Banach Inverse Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem. We also explore how existing classifications of the Hahn—Banach Theorem and Weak Kőnig's Lemma fit into this picture. Well-known omniscience principles from constructive mathematics such as LPO and LLPO can also naturally be considered as Weihrauch degrees and they play an important role in our classification. Based on this we compare the results of our classification with existing classifications in constructive and reverse mathematics and we claim that in a certain sense our classification is finer and sheds some new light on the computational content of the respective theorems. Our classification scheme does not require any particular logical framework or axiomatic setting, but it can be carried out in the framework of classical mathematics using tools of topology, computability theory and computable analysis. We develop a number of separation techniques based on a new parallelization principle, on certain invariance properties of Weihrauch reducibility, on the Low Basis Theorem of Jockusch and Soare and based on the Baire Category Theorem. Finally, we present a number of metatheorems that allow to derive upper bounds for the classification of the Weihrauch degree of many theorems and we discuss the Brouwer Fixed Point Theorem as an example. (shrink)

We present a comprehensive empirical evaluation of the ACT‐R–based model of sentence processing developed by Lewis and Vasishth (2005) (LV05). The predictions of the model are compared with the results of a recent meta‐analysis of published reading studies on retrieval interference in reflexive‐/reciprocal‐antecedent and subject–verb dependencies (Jäger, Engelmann, & Vasishth, 2017). The comparison shows that the model has only partial success in explaining the data; and we propose that its prediction space is restricted by oversimplifying assumptions. We then implement a (...) revised model that takes into account differences between individual experimental designs in terms of the prominence of the target and the distractor in memory‐ and context‐dependent cue‐feature associations. The predictions of the original and the revised model are quantitatively compared with the results of the meta‐analysis. Our simulations show that, compared to the original LV05 model, the revised model accounts for the data better. The results suggest that effects of prominence and variable cue‐feature associations need to be considered in the interpretation of existing empirical results and in the design and planning of future experiments. With regard to retrieval interference in sentence processing and to the broader field of psycholinguistic studies, we conclude that well‐specified models in tandem with high‐powered experiments are needed in order to uncover the underlying cognitive processes. (shrink)

Horsten and Roelants have raised a number of important questions about my analysis of effective procedures and my evaluation of the Church-Turing thesis. They suggest that, on my account, effective procedures cannot enter the mathematical world because they have a built-in component of causality, and, hence, that my arguments against the Church-Turing thesis miss the mark. Unfortunately, however, their reasoning is based upon a number of misunderstandings. Effective mundane procedures do not, on my view, provide an analysis (...) of ourgeneral concept of an effective procedure; mundane procedures and Turing machine procedures are different kinds of procedure. Moreover, the same sequence ofparticular physical action can realize both a mundane procedure and a Turing machine procedure; it is sequences of particular physical actions, not mundane procedures, which enter the world of mathematics. I conclude by discussing whether genuinely continuous physical processes can enter the world of real numbers and compute real-valued functions. I argue that the same kind of correspondence assumptions that are made between non-numerical structures and the natural numbers, in the case of Turing machines and personal computers, can be made in the case of genuinely continuous, physical processes and the real numbers. (shrink)

278 non-freshman university students taking a l2-week critical thinking course in a large single-section class, with computer-assisted guided practice as a replacement for small-group discussion, and all testing in machine-scored multiple-choice format, improved their critical thinking skills, as measured by the California Critical Thinking Skills Test, by half a standard deviation, a moderate improvement. The improvement was more than that reported with a traditional format without computer-assisted instruction, but less than that reported with a format using both computer-assisted instruction and (...) essay-type assignments. Further studies are needed to test hypotheses suggested by these results. (shrink)

Motor imagery-based brain-computer interfaces have been studied without controlling subjects’ gaze fixation position previously. The effect of gaze fixation and covert attention on the behavioral performance of BCI is still unknown. This study designed a gaze fixation controlled experiment. Subjects were required to conduct a secondary task of gaze fixation when performing the primary task of motor imagination. Subjects’ performance was analyzed according to the relationship between motor imagery target and the gaze fixation position, resulting in three BCI control conditions, (...) i.e., congruent, incongruent, and center cross trials. A group of fourteen subjects was recruited. The average group performances of three different conditions did not show statistically significant differences in terms of BCI control accuracy, feedback duration, and trajectory length. Further analysis of gaze shift response time revealed a significantly shorter response time for congruent trials compared to incongruent trials. Meanwhile, the parietal occipital cortex also showed active neural activities for congruent and incongruent trials, and this was revealed by a contrast analysis of R-square values and lateralization index. However, the lateralization index computed from the parietal and occipital areas was not correlated with the BCI behavioral performance. Subjects’ BCI behavioral performance was not affected by the position of gaze fixation and covert attention. This indicated that motor imagery-based BCI could be used freely in robotic arm control without sacrificing performance. (shrink)

We introduce the computable FS-jump, an analog of the classical Friedman–Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

Embedding ethics modules within computer science courses has become a popular response to the growing recognition that CS programs need to better equip their students to navigate the ethical dimensions of computing technologies like AI, machine learning, and big data analytics. However, the popularity of this approach has outpaced the evidence of its positive outcomes. To help close that gap, this empirical study reports positive results from Northeastern’s program that embeds values analysis modules into CS courses. The resulting data suggest (...) that such modules have a positive effect on students’ moral attitudes and that students leave the modules believing they are more prepared to navigate the ethical dimensions they’ll likely face in their eventual careers. Importantly, these gains were accomplished at an institution without a philosophy doctoral program, suggesting this strategy can be effectively employed by a wider range of institutions than many have thought. (shrink)

The effects of lexical context on phonological processing are pervasive and there have been indications that such effects may be modulated by attention. However, attentional modulation in speech processing is neither well documented nor well understood. Experiment 1 demonstrated attentional modulation of lexical facilitation of speech sound recognition when task and critical stimuli were identical across attention conditions. We propose modulation of lexical activation as a neurophysiologically plausible computational mechanism that can account for this type of modulation. Contrary to the (...) claims of critics, this mechanism can account for attentional modulation without violating the principle of interactive processing. Simulations of the interactive TRACE model extended to include two different ways of modulating lexical activation showed that each can account for attentional modulation of lexical feedback effects. Experiment 2 tested conflicting predictions from the two implementations and provided evidence that is consistent with bias input as the mechanism of attentional control of lexical activation. (shrink)

Electroencephalogram based Brain–Computer Interfaces enable stroke and motor neuron disease patients to communicate and control devices. Mindfulness meditation has been claimed to enhance metacognitive regulation. The current study explores whether mindfulness meditation training can thus improve the performance of BCI users. To eliminate the possibility of expectation of improvement influencing the results, we introduced a music training condition. A norming study found that both meditation and music interventions elicited clear expectations for improvement on the BCI task, with the strength of (...) expectation being closely matched. In the main 12 week intervention study, seventy-six healthy volunteers were randomly assigned to three groups: a meditation training group; a music training group; and a no treatment control group. The mindfulness meditation training group obtained a significantly higher BCI accuracy compared to both the music training and no-treatment control groups after the intervention, indicating effects of meditation above and beyond expectancy effects. (shrink)

Previous studies have confirmed that the temporal attentional control created by the repetition of stimulus-response compatibility (SRC) tasks was transferred to shooting skills in lacrosse players. In the current study, we investigated whether combining motor imagery training with SRC tasks could enhance the scoring ability of lacrosse players. We grouped 33 male lacrosse players into three groups: an SRC task and motor imagery group (referred as to SRC+Image), an SRC task group, and a control group. Players in the first two (...) groups underwent five sessions of 200 SRC task trials. In addition, the SRC+Image group completed five sessions of motor imagery training. The control group underwent no training interventions. All three groups performed a lacrosse shooting test and a Simon task before and after training sessions to assess the magnitude of the interference effects of the various types of training they underwent. The results of the Simon task showed that repetition of 1,000 trials was enough to create a short-term representation with the incompatible special mapping being transferred to a dynamic activity like lacrosse shooting. Moreover, combination of a computer-based Type 2 task and motor-imagery training could effectively increase players’ scoring ability in a field of large spatial conflict. (shrink)

The rapid development of computers and technology affects modern daily life. Individuals in the digital age need to develop computational thinking skills. Existing studies have shown that programming teaching is conducive to cultivating students’ CT, and various learning models have different effects on the cultivation of CT. This study proposed a problem-oriented learning model that is closely related to programming and computational thinking. In all, 60 eighth-grade students from a middle school in China were divided into an experimental group which (...) adopted the POL model, and a control group which adopted the lecture-and-practice learning model. The results showed that the students who were instructed using the POL model performed better than those who were instructed using the LAP model on CT concepts, CT practices, and CT perspectives. Significant differences were found for CT concepts and CT perspectives, but not for CT practices. Findings have implications for teachers who wish to apply new learning models to facilitate students’ CT skills, and the study provides a reference case for CT training and Python programming teaching. (shrink)

In response to concern over the numeracy skills deficit displayed by student nurses, an online computer programme, ?Authentic World??, which aims to simulate a real-life clinical environment and improve the medication dosage calculation skills of users, was developed (Founded in 2004 Authentic World Ltd is a spin out company of Glarmorgan and Cardiff Universities, Cardiff, Wales UK.). Two randomised controlled trials were conducted, each at a UK University, in order to investigate the impact of Authentic World? on student nurses? general (...) numeracy abilities. All first year nursing students who gave consent were randomised equally into an intervention or control group. The intervention group were given access to Authentic World?. The primary outcome measure was the students? scores on a general numeracy test. The Intention to Treat (ITT) analysis in both trials revealed a small negative effect of Authentic World? on general numeracy, which was statistically significant in one trial. However, compliance with the intervention was very low in both trials, with only 24 and 12% of students allocated to the intervention groups spending more than 15 minutes using the programme. Providing nursing students with access to Authentic World? is not an effective use of resources since use of the programme appears to be very low. (shrink)

Computer-based training has attracted increasing attention from researchers in recent years. Several studies have found that computer-based training resulted in improved executive functions in adults. However, it remains controversial whether children can benefit from computer-based training and what moderator could influence the training effects. The focus of the present meta-analysis was to examine the effects of computer-based training on EFs in children: working memory, cognitive flexibility, and inhibitory control. A thorough search of published work yielded a sample of 36 studies (...) with 216 effect sizes. The results indicated that computer-based training showed moderate training effects on improving EFs in children, while training effects of working memory were significantly higher. Furthermore, we found near-transfer effects were marginally significantly higher than far-transfer effects. The standard training method was significantly more effective than training with game elements. In computer-based training, typically developing children had significantly better training effects than atypically developing children. Some additional factors, such as the number of training sessions and age, also modulated the training effects. In conclusion, the present study investigated the effects and moderators of computer-based training for children's EFs. The results provided evidence that computer-based training may serve as an efficient way to improve EFs in children. We also discussed some directions for future computer-based training studies. (shrink)

David Marr's (1982) three‐level analysis of computational cognition argues for three distinct levels of cognitive information processing—namely, the computational, representational, and implementational levels. But Marr's levels are—and were meant to be—descriptive, rather than interactive and dynamic. For this reason, we suggest that, had Marr been writing today, he might well have gone even farther in his analysis, including the emergence of structure—in particular, explicit structure at the conceptual level—from lower levels, and the effect of explicit emergent structures on the level (...) (or levels) that gave rise to them. The message is that today's cognitive scientists need not only to understand how emergent structures—in particular, explicit emergent structures at the cognitive level—develop but also to understand how they feed back on the sub‐structures from which they emerged. (shrink)

We consider how to represent the measurable sets in an infinite measure space. We use sequences of simple measurable sets converging under metrics to represent general measurable sets. Then we study the computability of the measure and the set operators of measurable sets with respect to such representations.

This study examined the effects of computer-assisted cognitive rehabilitation in a group of 16 brain-damaged patients. Therapeutic effectiveness was assessed by improvement on computer tasks, the results of neuropsychological tests and quality of life ratings. Participants suffered from mild to moderate attention and memory problems or aphasia. The procedure involved baseline assessment, a 15-week course of therapy conducted twice a week and posttest. Neuropsychological tests assessing attention, memory and language problems and quality of life ratings were administered twice: in pre- (...) and posttests. Twelve healthy controls were also examined twice using the same battery of neuropsychological tests. The RehaCom program and the Polish computer therapy program for aphasics called Afa-System were used for rehabilitation. The computer-assisted rehabilitation tasks were selected individually for each patient. The results showed significant improvement on computer-assisted tasks in all braindamaged subjects. However, none or very little improvement was observed on neuropsychological tests and quality of life ratings. The results of the study confirm the importance of using different types of measures to estimate the effectiveness of computer-assisted neuropsychological rehabilitation as well as the necessity of applying various kinds of therapy to improve cognitive, emotional and social functioning in brain-damaged patients. (shrink)

An effective method is a computational method that might, in principle, be executed by a human. In this paper, I argue that there are methods for computing that are not effective methods. The examples I consider are taken primarily from quantum computing, but these are only meant to be illustrative of a much wider class. Quantum inference and quantum parallelism involve steps that might be implemented in multiple physical systems, but cannot be implemented, or at least not at (...) will, by an idealised human. Recognising that not all computational methods are effective methods is important for at least two reasons. First, it is needed to correctly state the results of Turing and other founders of computation theory. Turing is sometimes said to have offered a replacement for the informal notion of an effective method with the formal notion of a Turing machine. I argue that such a view only holds under limited circumstances. Second, not distinguishing between computational methods and effective methods can lead to mistakes when quantifying over the class of all possible computational methods. Such quantification is common in philosophy of mind in the context of thought experiments that explore the limits of computational functionalism. I argue that these ‘homuncular’ thought experiments should not be treated as valid. (shrink)

We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations of the computable (...) topological spaces constructed. (shrink)

In the educational hypermedia domain, adaptive systems try to adapt educational materials according to the required properties of a user. The adaptability of these systems becomes more effective once the system has the knowledge about how a student can learn better. Studies suggest that, for effective personalization, one of the important features is to know precisely the learning style of a student. However, learning styles are dynamic and may vary domain-wise. To address such aspects of learning styles, we (...) have proposed a computationally efficient solution that considers the dynamic and nondeterministic nature of learning styles, effect of the subject domain, and nonstationary aspect during the learning process. The proposed model is novel, robust, and flexible to optimize students’ domain-wise learning style preferences for better content adaptation. We have developed a web-based experimental prototype for assessment and validation. The proposed model is compared with the existing available learning style-based model, and the experimental results show that personalization based on incorporating discipline-wise learning style variations becomes more effective. (shrink)

Using educational robots to integrate computational thinking with cross-disciplinary content has gone beyond Science, Technology, Engineering, and Mathematics, to include foreign-language learning and further cross-context target-language acquisition. Such integration must not solely emphasise CT problem-solving skills. Rather, it must provide students with interactive learning to support their target-language interaction while reducing potential TL anxiety. This study aimed to validate the effects of the proposed method of pair programming along with question-and-response interaction in a board-game activity on young learners’ CT skills (...) and TL learning across contexts. Two Grade 6 classes, one with 16 students who were studying Chinese as a Second Language and the other with 16 students who were studying English as a Foreign Language, participated in the activity. A series of instruments on achievement assessment, questionnaires on CT skills and TL anxiety, and sequential learning behaviour analysis were used to critically examine the results. The main conclusion is that the EFL group showed better social skills of cooperation on CT and lower TL learning anxiety, while the CSL group demonstrated better problem-solving skills in CT, but presented more behaviours of trial-and-error loops. Results not only contribute suggestions for cross-disciplinary learning but also provide support for cross-context instruction beyond educational coursework. (shrink)

Basic Digital Education is already planned to be integrated with the forthcoming curriculum for Austrian primary schools as it was already implemented for lower secondary schools in 2018. BDE includes the most essential and novel developments of Computational Thinking, which are fundamentally responsible for nurturing students' problem-solving skills. Thus, evaluating teaching materials, scaffolding guidelines, and assessments is becoming increasingly important for the successful implementation of CT in Austrian classrooms. This study is a part of a longitudinal multi-cycle educational design research (...) project aiming to explore how to foster CT and to raise the awareness, importance, and confidence of teachers and students in applying CT for everyday uses. Our paper focuses on a sub-study in which teaching units for grade 3 and 4 students were designed by combining an Open Educational Resource textbook and Physical Computing with the micro:bit device. The designed learning environment consists of three units and was implemented in two classes over 3 weeks. The two classes were further split into two groups each, to ensure better support during implementation. The class teachers received upfront teacher training and conducted pre- and post-test assessments with the students. The resulting data was then analyzed to gain insights into the effects on CT skills of the young learners. Results showed that combining block-based programming and physical computing devices could become a promising approach to promote computational thinking skills in lower school grades. Furthermore, the observed direction of the designed units supports low-barrier access to increase the desired uses of CT in classrooms. (shrink)

An argument map visually represents the structure of an argument, outlining its informal logical connections and informing judgments as to its worthiness. Argument mapping can be augmented with dedicated software that aids the mapping process. Empirical evidence suggests that semester‐length subjects using argument mapping along with dedicated software can produce remarkable increases in students’ critical thinking abilities. Introducing such specialised subjects, however, is often practically and politically difficult. This study ascertains student perceptions of the use of argument mapping in two (...) large, regular, semester‐length classes in a Business and Economics Faculty at the University of Melbourne. Unlike the semester‐length expert‐led trials in prior research, in our study only one expert‐led session was conducted at the beginning of the semester and followed by class practice. Survey results conducted at the end of the semester, show that, with reservations, even this minimalist, ‘one‐shot inoculation’ of argument mapping is effective in terms of students’ perceptions of improvements in their critical thinking skills. (shrink)

If careers in the computer industry were viewed, it would be evident that there is a conspicuous gender gap between the number of male and female employees. The same gap can be observed at the college level where males are dominating females as to those who pursue and obtain a degree in computer science. The question that this research paper intends to show is: Why are males so dominant when it comes to computer related matter? I have traced this question (...) back to the computer game. Computer games are a fun medium and provide the means for an individual to become computer literate through the engagement of spatial learning and cognitive processing abilities. Since such games are marketed almost exclusively to males, females have a distinct disadvantage. Males are more computer literate through the playing of computer games, and are provided with an easy lead-in to more advanced utilization of computers such as programming. Females tend to be turned off due to the male stereotypes and marketing associated with games and thus begins the gender gap. (shrink)