James J. Kaput (1942–2005) imagineer and futurologist of mathematics education

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his ‘big ideas’ as he lived through the most amazing innovations in technology that have changed our lives more in a generation than in many centuries before. His vision continues as is exemplified by the collected papers in this tribute to his life and work

Two new ArrayTrack libraries for personalized biomedical research

<p>Abstract</p> <p>Background</p> <p>Recent advances in high-throughput genotyping technology are paving the way for research in personalized medicine and nutrition. However, most of the genetic markers identified from association studies account for a small contribution to the total risk/benefit of the studied phenotypic trait. Testing whether the candidate genes identified by association studies are causal is critically important to the development of personalized medicine and nutrition. An efficient data mining strategy and a set of sophisticated tools are necessary to help better understand and utilize the findings from genetic association studies. </p> <p>Description</p> <p>SNP (single nucleotide polymorphism) and QTL (quantitative trait locus) libraries were constructed and incorporated into ArrayTrack, with user-friendly interfaces and powerful search features. Data from several public repositories were collected in the SNP and QTL libraries and connected to other domain libraries (genes, proteins, metabolites, and pathways) in ArrayTrack. Linking the data sets within ArrayTrack allows searching of SNP and QTL data as well as their relationships to other biological molecules. The SNP library includes approximately 15 million human SNPs and their annotations, while the QTL library contains publically available QTLs identified in mouse, rat, and human. The QTL library was developed for finding the overlap between the map position of a candidate or metabolic gene and QTLs from these species. Two use cases were included to demonstrate the utility of these tools. The SNP and QTL libraries are freely available to the public through ArrayTrack at <url>http://www.fda.gov/ArrayTrack</url>. </p> <p>Conclusions</p> <p>These libraries developed in ArrayTrack contain comprehensive information on SNPs and QTLs and are further cross-linked to other libraries. Connecting domain specific knowledge is a cornerstone of systems biology strategies and allows for a better understanding of the genetic and biological context of the findings from genetic association studies. </p

Representing addition and subtraction : learning the formal conventions

The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation

A network analysis of cofactor-protein interactions for analyzing associations between human nutrition and diseases

The involvement of vitamins and other micronutrients in intermediary metabolism was elucidated in the mid 1900's at the level of individual biochemical reactions. Biochemical pathways remain the foundational knowledgebase for understanding how micronutrient adequacy modulates health in all life stages. Current daily recommended intakes were usually established on the basis of the association of a single nutrient to a single, most sensitive adverse effect and thus neglect interdependent and pleiotropic effects of micronutrients on biological systems. Hence, the understanding of the impact of overt or sub-clinical nutrient deficiencies on biological processes remains incomplete. Developing a more complete view of the role of micronutrients and their metabolic products in protein-mediated reactions is of importance. We thus integrated and represented cofactor-protein interaction data from multiple and diverse sources into a multi-layer network representation that links cofactors, cofactor-interacting proteins, biological processes, and diseases. Network representation of this information is a key feature of the present analysis and enables the integration of data from individual biochemical reactions and protein-protein interactions into a systems view, which may guide strategies for targeted nutritional interventions aimed at improving health and preventing diseases

Mathematics education and technology

Recent international surveys such as the Organisation for Economic Co-operation and Development (OECD) report Students, Computers and Learning ( 2015) highlight the wide gap in students’ access to, and use of, technology in secondary mathematics in participating countries. The OECD “snapshot” methodology in which 15-year-old students were asked if they (or their teachers) had performed a range of mathematical tasks using computers in the month preceding their completion of the Programme for International Student Assessment (PISA) survey revealed low levels of technology use (see Fig. 1)

Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic

Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed

DNA methylation during human adipogenesis and the impact of fructose

Background: Increased adipogenesis and altered adipocyte function contribute to the development of obesity and associated comorbidities. Fructose modified adipocyte metabolism compared to glucose, but the regulatory mechanisms and consequences for obesity are unknown. Genome-wide methylation and global transcriptomics in SGBS pre-adipocytes exposed to 0, 2.5, 5, and 10 mM fructose, added to a 5-mM glucose-containing medium, were analyzed at 0, 24, 48, 96, 192, and 384 h following the induction of adipogenesis. Results: Time-dependent changes in DNA methylation compared to baseline (0 h) occurred during the final maturation of adipocytes, between 192 and 384 h. Larger percentages (0.1% at 192 h, 3.2% at 384 h) of differentially methylated regions (DMRs) were found in adipocytes differentiated in the glucose-containing control media compared to adipocytes differentiated in fructose-supplemented media (0.0006% for 10 mM, 0.001% for 5 mM, and 0.005% for 2.5 mM at 384 h). A total of 1437 DMRs were identified in 5237 differentially expressed genes at 384 h post-induction in glucose-containing (5 mM) control media. The majority of them inversely correlated with the gene expression, but 666 regions were positively correlated to the gene expression. Conclusions: Our studies demonstrate that DNA methylation regulates or marks the transformation of morphologically differentiating adipocytes (seen at 192 h), to the more mature and metabolically robust adipocytes (as seen at 384 h) in a genome-wide manner. Lower (2.5 mM) concentrations of fructose have the most robust effects on methylation compared to higher concentrations (5 and 10 mM), suggesting that fructose may be playing a signaling/regulatory role at lower concentrations of fructose and as a substrate at higher concentrations

Systems view of adipogenesis via novel omics-driven and tissue-specific activity scoring of network functional modules

The investigation of the complex processes involved in cellular differentiation must be based on unbiased, high throughput data processing methods to identify relevant biological pathways. A number of bioinformatics tools are available that can generate lists of pathways ranked by statistical significance (i.e. by p-value), while ideally it would be desirable to functionally score the pathways relative to each other or to other interacting parts of the system or process. We describe a new computational method (Network Activity Score Finder - NASFinder) to identify tissue-specific, omicsdetermined sub-networks and the connections with their upstream regulator receptors to obtain a systems view of the differentiation of human adipocytes. Adipogenesis of human SBGS pre-adipocyte cells in vitro was monitored with a transcriptomic data set comprising six time points (0, 6, 48, 96, 192, 384 hours). To elucidate the mechanisms of adipogenesis, NASFinder was used to perform time-point analysis by comparing each time point against the control (0 h) and time-lapse analysis by comparing each time point with the previous one. NASFinder identified the coordinated activity of seemingly unrelated processes between each comparison, providing the first systems view of adipogenesis in culture. NASFinder has been implemented into a web-based, freely available resource associated with novel, easy to read visualization of omics data sets and network modules

Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

Interactive and multimedia contents associated with a system for computer-aided assessment

This paper presents a research study addressing the development, implementation, evaluation and use of Interactive Modules for Online Training (MITO) of mathematics in higher education. This work was carried out in the context of the MITO project, which combined several features of the learning and management system Moodle, the computer-aided assessment for mathematics STACK, the mathematical software GeoGebra, several packages from the type-setting program LaTeX, and tutorial videos. A total of 1962 students participated in this study. Two groups of students taking a Calculus course were selected for a deeper analysis. In regard to usability and functionality, the results indicate that MITO scored well in almost all aspects, which is fundamental for their introduction into formal university courses. The analysis of the data reveals that the use of MITO educational contents by students mainly occurs about one week and a half prior the evaluations. Moreover, there is a strong correlation between the results of online assessments on MITO in a continuous assessment model and the final grade on the course