Combining Exploratory Learning With Structured Practice to Foster Conceptual and Procedural Fractions Knowledge

Robust domain knowledge consists of conceptual and procedural knowledge. The two types of knowledge develop together, but are fostered by different learning tasks. Exploratory tasks enable students to manipulate representations and discover the underlying concepts. Structured tasks let students practice problem-solving procedures step-by-step. Educational technology has mostly relied on providing only either task type, with a majority of learning environments focusing on structured tasks. We investigated in two quasi-experimental studies with 8-10 years old students from UK (N = 121) and 10-12 years old students from Germany (N = 151) whether a combination of both task types fosters robust knowledge more than structured tasks alone. Results confirmed this hypothesis and indicate that students learning with a combination of tasks gained more conceptual knowledge and equal procedural knowledge compared to students learning with structured tasks only. The results illustrate the efficacy of combining both task types for fostering robust fractions knowledge

Artificial Intelligence And Big Data Technologies To Close The Achievement Gap.

We observe achievement gaps even in rich western countries, such as the UK, which in principle have the resources as well as the social and technical infrastructure to provide a better deal for all learners. The reasons for such gaps are complex and include the social and material poverty of some learners with their resulting other deficits, as well as failure by government to allocate sufficient resources to remedy the situation. On the supply side of the equation, a single teacher or university lecturer, even helped by a classroom assistant or tutorial assistant, cannot give each learner the kind of one-to-one attention that would really help to boost both their motivation and their attainment in ways that might mitigate the achievement gap. In this chapter Benedict du Boulay, Alexandra Poulovassilis, Wayne Holmes, and Manolis Mavrikis argue that we now have the technologies to assist both educators and learners, most commonly in science, technology, engineering and mathematics subjects (STEM), at least some of the time. We present case studies from the fields of Artificial Intelligence in Education (AIED) and Big Data. We look at how they can be used to provide personalised support for students and demonstrate that they are not designed to replace the teacher. In addition, we also describe tools for teachers to increase their awareness and, ultimately, free up time for them to provide nuanced, individualised support even in large cohorts

Embodied Artificial Intelligence through Distributed Adaptive Control: An Integrated Framework

In this paper, we argue that the future of Artificial Intelligence research resides in two keywords: integration and embodiment. We support this claim by analyzing the recent advances of the field. Regarding integration, we note that the most impactful recent contributions have been made possible through the integration of recent Machine Learning methods (based in particular on Deep Learning and Recurrent Neural Networks) with more traditional ones (e.g. Monte-Carlo tree search, goal babbling exploration or addressable memory systems). Regarding embodiment, we note that the traditional benchmark tasks (e.g. visual classification or board games) are becoming obsolete as state-of-the-art learning algorithms approach or even surpass human performance in most of them, having recently encouraged the development of first-person 3D game platforms embedding realistic physics. Building upon this analysis, we first propose an embodied cognitive architecture integrating heterogenous sub-fields of Artificial Intelligence into a unified framework. We demonstrate the utility of our approach by showing how major contributions of the field can be expressed within the proposed framework. We then claim that benchmarking environments need to reproduce ecologically-valid conditions for bootstrapping the acquisition of increasingly complex cognitive skills through the concept of a cognitive arms race between embodied agents.Comment: Updated version of the paper accepted to the ICDL-Epirob 2017 conference (Lisbon, Portugal

Coin.AI: A Proof-of-Useful-Work Scheme for Blockchain-based Distributed Deep Learning

One decade ago, Bitcoin was introduced, becoming the first cryptocurrency and establishing the concept of "blockchain" as a distributed ledger. As of today, there are many different implementations of cryptocurrencies working over a blockchain, with different approaches and philosophies. However, many of them share one common feature: they require proof-of-work to support the generation of blocks (mining) and, eventually, the generation of money. This proof-of-work scheme often consists in the resolution of a cryptography problem, most commonly breaking a hash value, which can only be achieved through brute-force. The main drawback of proof-of-work is that it requires ridiculously large amounts of energy which do not have any useful outcome beyond supporting the currency. In this paper, we present a theoretical proposal that introduces a proof-of-useful-work scheme to support a cryptocurrency running over a blockchain, which we named Coin.AI. In this system, the mining scheme requires training deep learning models, and a block is only mined when the performance of such model exceeds a threshold. The distributed system allows for nodes to verify the models delivered by miners in an easy way (certainly much more efficiently than the mining process itself), determining when a block is to be generated. Additionally, this paper presents a proof-of-storage scheme for rewarding users that provide storage for the deep learning models, as well as a theoretical dissertation on how the mechanics of the system could be articulated with the ultimate goal of democratizing access to artificial intelligence.Comment: 17 pages, 5 figure

Teaching and learning in virtual worlds: is it worth the effort?

Educators have been quick to spot the enormous potential afforded by virtual worlds for situated and authentic learning, practising tasks with potentially serious consequences in the real world and for bringing geographically dispersed faculty and students together in the same space (Gee, 2007; Johnson and Levine, 2008). Though this potential has largely been realised, it generally isn’t without cost in terms of lack of institutional buy-in, steep learning curves for all participants, and lack of a sound theoretical framework to support learning activities (Campbell, 2009; Cheal, 2007; Kluge & Riley, 2008). This symposium will explore the affordances and issues associated with teaching and learning in virtual worlds, all the time considering the question: is it worth the effort

Transforming pre-service teacher curriculum: observation through a TPACK lens

This paper will discuss an international online collaborative learning experience through the lens of the Technological Pedagogical Content Knowledge (TPACK) framework. The teacher knowledge required to effectively provide transformative learning experiences for 21st century learners in a digital world is complex, situated and changing. The discussion looks beyond the opportunity for knowledge development of content, pedagogy and technology as components of TPACK towards the interaction between those three components. Implications for practice are also discussed. In today’s technology infused classrooms it is within the realms of teacher educators, practising teaching and pre-service teachers explore and address effective practices using technology to enhance learning

Combining exploratory learning with structured practice educational technologies to foster both conceptual and procedural fractions knowledge

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two quasi-experimental studies whether a combination of an exploratory learning environment, providing exploratory tasks, and an intelligent tutoring system, providing structured tasks, fosters procedural and conceptual knowledge more than the intelligent tutoring system alone. Participants were 121 students from the UK (aged 8–10 years old) and 151 students from Germany (aged 10–12 years old) who were studying equivalent fractions. Results confirmed that students learning with a combination of exploratory and structured tasks gained more conceptual knowledge and equal procedural knowledge compared to students learning with structured tasks only. This supports the use of different but complementary educational technologies, interleaving exploratory and structured tasks, to achieve a “combination effect” that fosters robust fractions knowledge

¿When is it the Gesture that Counts: Telling Stories that cut to the [Cyber]chase – or, gest get to the po¡nt!

Lakoff and Nuñez (2000) argue that the origins of mathematical thinking arise from the progressive development of the human sensorium and experience. Cognitive science research in in education plays a big role in developing new pedagogies, especially those that leverage new “Cyberlearning” technologies. The current study employs two principle frameworks for creating pedagogy for learning mathematical fractions: (1) grounded and embodied cognition (Varela, Thompson & Rosch, 1991; Glenberg, 1997; 2003; Barsalou, 1999; 2008), (2) situated cognition (Lesh, 1981; Lave 1988, Greeno, 1998; Roth, 2002). Grounded and embodied cognition was operationalized through the gesture. Although gesture is traditionally discussed as a spontaneous co-articulation of speech (Kendon, 1972; McNeill & Levy, 1980; 1992; Goldin-Meadow, 1986) it is taking on a new role with the advent of 21st century technologies that utilize gestural interface. Using gestures as simulated action (Hostetter and Alibali, 2008), we developed two sets of gestural mechanics based on an exploratory study on the gestures elementary students used to explain mathematical fractions (Swart, 2014): (1) iconic gestures (I) – i.e., enactive of the processes to create objects, (2) deictic gestures (D) – i.e., index pointing to ground or identify objects or locations. Situated cognition was operationalized through narrative (Black and Bower, 1980; Graesser, Hauft-Smith, Cohen, and Pyles 1980; Graesser, Singer, Trabasso, 1994). Researchers crafted two types of narratives in order to create a situated learning environment (Hennessy, 1993): (1) strong narrative (S) – with a setting, characters and plot (based on the popular PBS Kids television show, Cyberchase, (2) weak narrative (W) – without an explicit setting, characters or plot. Combining these two factors together, the research team designed and developed Mobile Mathematics Movement (M3). Using the two independent variables, gesture (I vs. D) and narrative (S vs. W), M3 was crafted into 4 different versions: SI, SD, WI, WD. The first two iterations, M3:i1 and M3:i2, were tested in randomized factorial experiments in afterschool programs with high-needs populations. After completing these studies employing a design-based research (DBR) methodology, the tutor-game developed into its latest iteration, M3:i3. The curriculum of M3 had students employing a splitting objects (i.e., parts-to-whole) schema (Steffe, 2004) and was divided into two parts: (Part 1) object fracturing (x5 per level): estimating, denominating, numerating, re-estimating; (Part 2) object equivalency (comparing 5 fractions): comparing, ordering, verifying magnitudes, verifying positions on vertical number line. In the final dissertation study, 131 students (x̄age = 8.78 yrs, 52.6% Female; 39.7% Hispanic; 32.8% African-American; 19.9% South-East Asian; 3.8% Caucasian; 3.8% South Asian (Indian); 97.7 % received free/reduced lunch) from the Harlem and Lower East Side neighborhoods of New York City were consented and assented and completed the study. Students were randomly assigned to 1 of the 4 conditions, completed a direct pre-assessment of the curriculum as well as a transfer pre-assessment, played all seven levels of the tutor-game, completed an exit survey (free response and 5-point likert – motivation, self-efficacy, engagement, learning), completed a direct post-assessment of the curriculum as well as a transfer post-assessment (parallel forms) and a 7 minute semi-structured clinical interview. Factorial ANOVAs indicated a significant interaction between gesture and narrative (though all groups showed significant learning pre to post) on the direct assessment. Both the SI and WD groups significantly outperformed the other two groups, though were not different from each other. Though there was not a significant interaction between gesture and narrative on for the transfer assessment, pair-wise comparisons and planned contrasts showed that the SI group outperformed all the other groups. Follow up hierarchical linear regressions (HLR) showed that game play significantly mediated students’ learning. Specifically, students’ performances estimating and denominating were predictive of direct learning of the curriculum while estimating, denomination and numeration were all predictive of transfer. Further HLRs also found that students’ learning was moderated by their existing proficiencies for fractions. This finding helped clarify the nature of the narrative-gesture interaction, such that low-proficiency students improved more in the WD condition and high-proficiency students improved more in the SI condition. An exploratory factor analysis of the 5-point likert exit survey showed loaded on four factors as anticipated, with significant loadings for engagement and learning, but revealed no significant differences between the conditions. The significant interaction revealed that both a weak narrative (non-contextualized) environments using deictic (identity) gestures as well as strong narrative (contextualized) environments using iconic (enactive) gestures are differentially beneficial for learning. Contrary to our interaction hypothesis, learning for novices benefitted from a more abstract environment, supporting the work of (Kaminski, Sloutsky, Heckler, 2008) and learning for those with higher proficiencies at fractions was better in the more concrete environment (e.g., Moreno, Ozogul, & Reisslein (2011). The likert data supports research suggesting that students find digital platforms engaging and empowering, regardless of learning or not (for review see Wouters, van Nimwegen, van Oostendorp, & van der Spek, 2013). Together, these results have important implications for the design of learning environments and a digital pedagogy and follow-up work is necessary for expounding on the interactions between gestures and narratives as well as the possible mediation by task complexity