The paper describes an implementation of research done over several years, by me and in some cases others, at Stanford University and elsewhere. The implementation comprised the design, building, testing, and marketing of a digital educational technology platform to provide a supplementary tool for explorative mathematics learning and assessment.

The present study explores approaches to teacher scaffolding in digital game-based learning in primary mathematics classrooms as well as the effects on students' perceptions of learning in a digital game in which scaffolding was provided. A total of 141 primary school students and four mathematics teachers participated in the experiment, and qualitative data were collected through classroom observations and student interviews. The results identified whole-class and one-to-one scaffolding strategies, both of which had an important effect on students' learning activities and perceptions of mathematics in the context of digital games in primary education.

Though mathematicians invented the modern computer as a theoretical entity, and a few of them helped build the first modern digital computers, mathematicians as a whole lagged far behind scientists, engineers, and other professionals in actually using them (In this article, unless noted to the contrary, I use the term “mathematician” to refer to pure mathematicians, who focus on formulating and proving statements about abstract mathematical structures.). Recognizing that the field was in danger of falling too far behind, in May 1988, the American Mathematical Society launched a new section in its newsletter Notices, sent out to all members ten times a year, titled “Computers and Mathematics”. Its aim was to promote the use of computers by mathematicians and provide them with information about the many new mathematical software systems being developed. The section was initially edited by the Stanford mathematician Jon Barwise, who ran it until February 1991, after which the AMS asked me to take it over. I held the reins from the March 1991 issue until the AMS and I decided to end the special section in December 1994. That six-and-a-half-year run achieved the intended goal. By the time the special section wound up, the computer had become a staple tool for mathematicians, both in teaching and research.

For thousands of years, mastering numerical and symbolic calculation techniques was essential to be able to do mathematics. By 1990, that requirement was eliminated by the introduction of digital technologies that can perform any formal procedure. Those technologies revolutionized mathematical praxis. For the professionals, doing and using mathematics today is a very different experience from any time in the past. This chapter describes how today’s mathematicians go about their daily work, and looks at the challenges of changing educational practice to prepare today’s students to enter this new mathematical world.

In Data Science, we are concerned with the integration of relevant sciences in observed and empirical contexts. This results in the unification of analytical methodologies, and of observed and empirical data contexts. Given the dynamic nature of convergence, the origins and many evolutions of the Data Science theme are described. The following are covered in this article: the rapidly growing post-graduate university course provisioning for Data Science; a preliminary study of employability requirements, and how past eminent work in the social sciences and other areas, certainly mathematics, can be of immediate and direct relevance and benefit for innovative methodology, and for facing and addressing the ethical aspect of Big Data analytics, relating to data aggregation and scale effects. Associated also with Data Science is how direct and indirect outcomes and consequences of Data Science include decision support and policy making, and both qualitative as well as quantitative outcomes. For such reasons, the importance is noted of how Data Science builds collaboratively on other domains, potentially with innovative methodologies and practice. Further sections point towards some of the most major current research issues.

In narrative and neurobiological processes, a common re- sponse to an unexpected event can be observed: retroactive reinterpretation . In this activity, an established state of knowledge is restructured so that its ability to interpret causal consequences changes. We present a new graphical knowledge modeling technique to track the stages of retroactive reinterpretation in both narrative and biological do- mains. This method is based on situation-theoretic founda-tions, which have been extended using narrative devices to capture elusive properties of everyday reasoning, such as context and causal anticipation. The method and its accompanying visual model enables us to experiment with repre-sentational reasoning about cause, shifts in influence be- tween distinct systems and implicit knowledge. This work-in-progress indicates that cross-system, multi-ontology intelligence processes can be modeled using narra- tive mechanisms. A future goal is to use this method to address problems in ontological interoperability for predictive, multi-system neurobiological modeling. Capturing implicit causal agency in biology using a narrative-based model is thus feasible but comes with challenges in graphical display, which are discussed.

Acquisition of mathematical skills is crucial for today’s society. Individuals who experience difficulties in learning basic mathematics can be at a great disadvantage in their professional lives. Nevertheless, fewer research efforts have been directed toward mathematical development and mathematical difficulties than toward some other areas of development, such as language and literacy. In fact, it has been argued that at an individual level, insufficient mathematical competencies may be even more harmful to career prospects than reading or spelling deficiencies. From a societal perspective, mathematical deficiencies can lead to significant costs. Thus, it is important to develop more engaging and effective methods that can be used to enhance children’s conceptual understanding of mathematics, develop mathematical thinking processes, and improve arithmetical skills. Digital games provide interesting possibilities to support and study mathematical development. Yes, whereas it is easy to find online mathematics training solutions, games, and apps, only a small fraction of existing mathematics learning games are founded on theoretically sound principles, integrate mathematics directly into the gameplay, rely on good pedagogical practices, and really utilize the possibilities that game technologies provide for learning.

We approach a well-known problem: how to relate component physical processes in biological systems to governing imperatives in multiple system levels. The intent is to further practical tools that can be used in the clinical context. An example proposes a formal type system that would support this kind of reasoning, including in machines. Our example is based on a model of the connection between a quality of mind associated with creativity and neuropsychiatric dynamics: constructing narrative as a form of conscious introspection, which allows the manipulation of one's own driving imperatives. In this context, general creativity is indicated by an ability to manage multiple heterogeneous worldviews simultaneously in a developing narrative. 'Narrative' in this context is framed as the organizing concept behind rational linearization that can be applied to metaphysics as well as modeling perceptive dynamics. Introspection is framed as the phenomenological 'tip' that allows a perceiver to be within experience or outside it, reflecting on and modifying it. What distinguishes the approach is the rooting in well founded but disparate disciplines: phenomenology, ontic virtuality, two-sorted geometric logics, functional reactive programming, multi-level ontologies and narrative cognition. This paper advances the work by proposing a type strategy within a two-sorted reasoning system that supports cross-ontology structure. The paper describes influences on this approach, and presents an example that involves phenotype classes and monitored creativity enhanced by both soft methods and transcranial direct-current stimulation. The proposed solution integrates pragmatic phenomenology, situation theory, narratology and functional programming in one framework.

International Educational performance measures, like the Programme for International Student Assessment (PISA), rank countries based on their educational system's performance. However, these activities require years of work for thousands of people to collect, analyze and report the data. Furthermore, the results are always two years old when published and there are tens of missing countries. In this study, a global game-based analytics was introduced and evaluated in a real world environment. The paper continues the study reported in ECGBL 2013. Real-time game-based assessments do have several advantages compared to traditional measures, but they are not yet ready to replace PISA. For example, sample collection has to be radically improved in order to minimize noise and bring out only the valid cases.