Designing a web-based learning support system for flow-chart proving in school geometry

This is the final version of the article. Available from the publisher via the DOI in this record.As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed to enable students to access the study of proofs in geometry by tackling proof problems where they can ‘drag’ sides, angles and triangles from the figural diagram of the problem to on-screen cells within a flow-chart proof format. When doing so, the system automatically converts the figural elements to their symbolic form and identifies any of four kinds of errors in the learners’ proof attempts, providing relevant feedback on-screen. We use empirical examples from our pilot studies to illustrate how this combination of technological features and systematic feedback can support student understanding of the structure of proof and how to plan one. Finally, we point out some limitations to mathematical expression and the usage of the flow-chart format, and indicate the prospect of minimizing such limitations by adopting a learning progression for the introductory lessons concerning deductive proofs.This research is supported by the Daiwa Anglo-Japanese Foundation (No. 7599/8141) and the Grant-in-Aid for Scientific Research (No. 26590230, 15 K12375, 16H02068, 16H03057), Ministry of Education, Culture, Sports, Science, and Technology, Japan. Special thanks to Yoichi Murakami who programmed this web-based system

Designing a web-based learning support system for flow-chart proving in school geometry

This is the final version of the article. Available from the publisher via the DOI in this record.As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed to enable students to access the study of proofs in geometry by tackling proof problems where they can ‘drag’ sides, angles and triangles from the figural diagram of the problem to on-screen cells within a flow-chart proof format. When doing so, the system automatically converts the figural elements to their symbolic form and identifies any of four kinds of errors in the learners’ proof attempts, providing relevant feedback on-screen. We use empirical examples from our pilot studies to illustrate how this combination of technological features and systematic feedback can support student understanding of the structure of proof and how to plan one. Finally, we point out some limitations to mathematical expression and the usage of the flow-chart format, and indicate the prospect of minimizing such limitations by adopting a learning progression for the introductory lessons concerning deductive proofs.This research is supported by the Daiwa Anglo-Japanese Foundation (No. 7599/8141) and the Grant-in-Aid for Scientific Research (No. 26590230, 15 K12375, 16H02068, 16H03057), Ministry of Education, Culture, Sports, Science, and Technology, Japan. Special thanks to Yoichi Murakami who programmed this web-based system

A rare case of dual origin of the left vertebral artery without convergence

A case of dual origin of the left vertebral artery was encountered in a dissection course for medical students in 2014. Two vertebral arteries were observed on the left side. One arose from the aortic arch between the origin of the left common carotid artery and the left subclavian artery, entered the transverse foramen of the 4th cervical vertebra, and coursed upward into the transverse foramen. The other arose from the left subclavian artery as expected, divided into two branches anterior to the cervical vertebrae, and entered the transverse foramina of the 6th and 7th cervical vertebrae. Both branches flowed into the anterior spinal artery. Moreover, as seen in other anomalies, 3 arterial fenestrations were observed in the cranial arteries. This case is extremely unique with respect to the following points: the 2 ipsilateral vertebral arteries did not combine to form 1 vertebral artery, the vertebral artery of subclavian artery origin entered the transverse foramen of the 7th cervical vertebra, and 3 fenestrations were observed in the intracranial arteries. This is a very suggestive case for neurosurgeons and radiologists who perform treatments involving the vertebral artery

Nanoscale Weibull Statistics

In this paper a modification of the classical Weibull Statistics is developed for nanoscale applications. It is called Nanoscale Weibull Statistics. A comparison between Nanoscale and classical Weibull Statistics applied to experimental results on fracture strength of carbon nanotubes clearly shows the effectiveness of the proposed modification. A Weibull's modulus around 3 is, for the first time, deduced for nanotubes. The approach can treat (also) a small number of structural defects, as required for nearly defect free structures (e.g., nanotubes) as well as a quantized crack propagation (e.g., as a consequence of the discrete nature of matter), allowing to remove the paradoxes caused by the presence of stress-intensifications

The Role of High Molecular Weight Kininogen (Fitzgerald Factor) in the Activation of Various Plasma Proteolytic Enzyme Systems

Bovine high molecular weight kininogen (bHMWK) partially corrects the aPTT of Fitzgerald-trait plasma, which is congenitally deficient in HMWK. The relationship between the structure and activity of HMWK was clarified by studying the effects of different fragments of bHMWK on the aPTT of Fitzgerald-trait plasma. The peptides studied, all in equimolar concentrations, were lys-bradykinin-free HMWK, bradyk In In-fragment 1-2-tree HMWK, heavy chain, fragment 1 -2-Hght chain, and light chain. Bradykinin- fragment 1-2-free HMWK, heavy chain, and light chain have little or no correcting activity upon Eitzgeraldtrait plasma aPTT. Fragment 1-2 light chain has the same correcting activity as intact bHMWK, while that of lysbradykinin-free HMWK appears to be higher. Both fragment 1-2 and fragment 2 inhibit the clotting time of normal human plasma. On a molar basis, fragment 2 is a more active inhibitor than fragment 1-2. Bovine plasma kallikrein released kinins from both bHMWK and hHMWK; however, while the correcting activity of bHMWK was completely destroyed after sixty minutes of incubation, that of hHMWK was fully retained. These data suggest that: (1) the active part of bHMWK is comprised of the fragment 1-2 light chain portion; (2) fragment 1-2 or fragment 2 is the binding site to negatively charged surfaces, while the light chain interacts with other components of the surface-mediated reactions; and (3) bovine plasma kallikrein releases kinins but probably does not cause the release of fragment 1-2 from hHMWK

Beta-glucan reflects liver injury after preservation and transplantation in dogs.

Graft failure and extrahepatic organ complications, which frequently develop after transplantation, may be related to inflammatory mediators stimulated by endotoxin (ET). The role of endotoxemia after liver transplantation is controversial and may depend upon differences in the ET assay method used in the various contradicting studies. While the standard Limulus amebocyte lysate (LAL) is reactive for ET and beta-glucan, a novel turbidimetric assay method enables separate determinations of ET and beta-glucan. Beagle dogs undergoing orthotopic liver transplantation were divided into two groups. In Group I (n = 6) the grafts were transplanted immediately and in Group II (n = 6) grafts were preserved for 48 h in University of Wisconsin (UW) solution. Animals received cyclosporine immunosuppression and were followed for 14 days. Daily measurements of aspartate aminotransferase (AST), alanine aminotransferase (ALT), and lactate dehydrogenase (LDH) were performed. Samples for ET and beta-glucan measurement were collected serially and processed using the turbidimetric assay method. While no graft failure was seen in Group I, three of six Group II animals died from graft failure within 1 day after transplantation. Preservation and reperfusion injury was much more severe in the Group II grafts than in Group I grafts. While endotoxemia could not be detected, postoperative beta-glucan levels (undetectable pretransplant) were seen in both groups. Beta-glucan levels were much higher in Group II grafts than in Group I grafts, and correlated with the severity of liver damage. In conclusion, this study shows that beta-glucan, instead of ET, appears during the early posttransplant period. We believe that posttransplant elevation of beta-glucan is related to liver damage, especially endothelial damage by preservation and reperfusion

Anthracycline-Induced Cardiotoxicity: Cardiac Monitoring by Continuous Wave-Doppler Ultrasound Cardiac Output Monitoring and Correlation to Echocardiography

Background: Anthracyclines are agents with a well-known cardiotoxicity. The study sought to evaluate the hemodynamic response to an anthracycline using real-time continuous-wave (CW)-Doppler ultrasound cardiac output monitoring (USCOM) and echocardiography in combination with serum biomarkers. Methods: 50 patients (26 male, 24 female, median age 59 years) suffering from various types of cancer received an anthracycline-based regimen. Patients' responses were measured at different time points (T0 prior to infusion, T1 6 h post infusion, T2 after 1 day, T3 after 7 days, and T4 after 3 months) with CW-Doppler ultrasound (T0-T4) and echocardiography (T1, T4) for hemodynamic parameters such as stroke volume (SV; SVUSCOM ml) and ejection fraction (EF; EFechocardiography%) and with NT-pro-BNP and hs-Troponin T (T0-T4). Results: During the 3-month observation period, the relative decrease in the EF determined by echocardiography was -2.1% (Delta T0-T4, T0 71 +/- 7.8%, T4 69.5 +/- 7%, p = 0.04), whereas the decrease in SV observed using CW-Doppler was -6.5% (Delta T0-T4, T0 54 +/- 19.2 ml, T4 50.5 +/- 20.6 ml, p = 0.14). The kinetics for serum biomarkers were inversely correlated. Conclusions: Combining real-time CW-Doppler USCOM and serum biomarkers is feasible for monitoring the immediate and chronic hemodynamic changes during an anthracycline-based regimen; the results obtained were comparable to those from echocardiography

Centromere Plasmid: A New Genetic Tool for the Study of Plasmodium falciparum

The introduction of transgenes into Plasmodium falciparum, a highly virulent human malaria parasite, has been conducted either by single crossover recombination or by using episomal plasmids. However, these techniques remain insufficient because of the low transfection efficiency and the low frequency of recombination. To improve the genetic manipulation of P. falciparum, we developed the centromere plasmid as a new genetic tool. First, we attempted to clone all of the predicted centromeres from P. falciparum into E. coli cells but failed because of the high A/T contents of these sequences. To overcome this difficulty, we identified the common sequence features of the centromere of Plasmodium spp. and designed a small centromere that retained those features. The centromere plasmid constructed with the small centromere sequence, pFCEN, segregated into daughter parasites with approximately 99% efficiency, resulting in the stable maintenance of this plasmid in P. falciparum even in the absence of drug selection. This result demonstrated that the small centromere sequence harboured in pFCEN could function as an actual centromere in P. falciparum. In addition, transgenic parasites were more rapidly generated when using pFCEN than when using the control plasmid, which did not contain the centromere sequence. Furthermore, in contrast to the control plasmid, pFCEN did not form concatemers and, thus, was maintained as a single copy over multiple cell divisions. These unique properties of the pFCEN plasmid will solve the current technical limitations of the genetic manipulation of P. falciparum, and thus, this plasmid will become a standard genetic tool for the study of this parasite

Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories