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

Self-trapped states and the related luminescence in PbCl2_2 crystals

We have comprehensively investigated localized states of photoinduced electron-hole pairs with electron-spin-resonance technique and photoluminescence (PL) in a wide temperature range of 5-200 K. At low temperatures below 70 K, holes localize on Pb$^{2+}$ ions and form self-trapping hole centers of Pb$^{3+}$. The holes transfer to other trapping centers above 70 K. On the other hand, electrons localize on two Pb$^{2+}$ ions at higher than 50 K and form self-trapping electron centers of Pb$_2$$^{3+}$. From the thermal stability of the localized states and PL, we clarify that blue-green PL band at 2.50 eV is closely related to the self-trapped holes.Comment: 8 pages (10 figures), ReVTEX; removal of one figure, Fig. 3 in the version

Hematoma in the Bucco-Mandibular Space: First Case Report.

Our previous studies based on intraoral dissection of fresh cadavers revealed that the fissure and loose connective tissues deep to the mucosa between the incisivus labii inferioris muscle and buccinator muscle form the entrance of the newly discovered bucco-mandibular space. To support the clinical significance of this space, we report the finding of a hematoma within this space in an adult fresh cadaver. Such a finding lends credence to studying the bucco-mandibular space and might help better understand the spread of some infections in the oral region

Internal Hernia of the Greater Omentum: Cadaveric Findings of a Previously Unreported Variant.

Transomental hernias (TOHs) are a rare finding, constituting a fraction of all intestinal hernias. Here, we report the cadaveric discovery of a spontaneous TOH involving the sigmoid colon in an 82-year-old female and discuss the relevant literature. To our knowledge, a TOH involving the sigmoid colon has not been previously reported

Avoiding the Esophageal Branches of the Recurrent Laryngeal Nerve During Retractor Placement: Precluding Postoperative Dysphagia During Anterior Approaches to the Cervical Spine.

Study Design: Anatomical cadaver study. Objectives: Postoperative dysphagia is a significant complication following anterior approaches to the cervical spine and the etiology of this complication is poorly understood. Herein, we studied the esophageal branches of the recurrent laryngeal nerves to improve understanding of their anatomy and potential involvement in dysphagia. Methods: Ten fresh frozen cadaveric human specimens were dissected (20 sides). All specimens were adults with no evidence of prior surgery of the anterior neck. The recurrent laryngeal nerves were identified under a surgical microscope and observations and measurements of their esophageal branches made. Results: For each recurrent laryngeal nerve, 5-7 (mean 6.2) esophageal branches were identified. These branches ranged from 0.8 to 2.1 cm (mean 1.5 cm) in length and 0.5 to 2 mm (mean 1 mm) in diameter. They arose from the recurrent laryngeal nerves between vertebral levels T1 and C6. They all traveled to the anterior aspect of the esophagus. No statistical differences were seen between left and right sides or between sexes. Conclusion: The esophageal branches of the recurrent laryngeal nerve have been poorly described and could contribute to complications such as swallowing dysfunction following anterior cervical discectomy and fusion procedures. Therefore, a better understanding of their anatomy is important for spine surgeons. Our study revealed that these branches are always present on both sides and the anterior surface of the esophagus should be avoided while retracting it in order to minimize the risk of postoperative dysphagia

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