Mathematics Education Communities: Crossing Virtual Boundaries

The growth of social media has yielded a range of virtual communities focused on issues related to education (Carpenter & Krutka, 2014; Hur & Brush, 2009). These communities, which operate across a range of different platforms, create an evolving landscape for users to navigate. Moreover, interactions within and across virtual communities has become a norm within society at large as well as within mathematics education. The Math Twitter Blog-o-Sphere (MTBoS), Mathematics Stack Exchange, specialized Facebook groups, and myNCTM are just a few examples of communities that are currently popular with mathematics teachers and educators in North America. Similarly, students of mathematics use virtual communities to make records of information that, in earlier times, would have been available through more informal channels. For example, solution clearinghouse sites (e.g., Chegg. com) allow students to request or post answers to problems sets and teacher-rating sites (e.g., RateMyProfessor.com) offer a platform where students can trade information about their instructors. With the ubiquity of internet-enabled devices, negotiating virtual communities has become a norm within mathematics teaching and learning. Consequently, educators, both new and old, who participate in these communities are encountering issues and ideas that they likely have limited experience with. This raises a number of questions for mathematics teacher educators seeking to help themselves, preservice teachers (PSTs), and current teachers understand these virtual communities. For example: How can the differences, similarities, and affordances of communities be highlighted? How can the boundaries that define and separate these communities be made clear? Within this chapter, we seek to address these and related questions by providing a framework for understanding these communities. We then use this framework to examine several communities currently popular within North America

What Does It Take to Be a Fox? New Horizons for Communities of Practice

In this theoretical research report we reflect on the challenges of becoming more fox-like in mathematics education work. Using a communities of practice motivating theoretical lens, we compare and discuss the differences in defining, creating, and accessing knowledge between virtual and scholarly communities of practice in mathematics education. We present four claims that virtual communities of practice in mathematics education are inherently foxy work. As part of our claims, we discuss how scholarly communities of practices are inherently hedgehog work. We conclude with a list of recommendations of those within the scholarly communities of practice in mathematics education. These recommendations include looking toward the successful fox-like attributes of the virtual communities in mathematics education

Cystic lymphangioma of the lesser sac presenting as acute appendicitis: A case report

Intra-abdominal lymphangiomas usually present by 2 years of age and are uncommon in adults. Cystic lymphagiomas arising from the lesser sac are even more uncommon. We report an unusual case of a lesser sac cystic lymphangioma presenting as acute appendicitis. A 21 year old female was admitted with pyrexia, right iliac fossa tenderness and an elevated C-reactive protein (CRP). At laparotomy, a large fluid filled cystic lesion was observed occupying the right side of the abdominal cavity. The lesion was excised in its entirety and histological diagnosis confirmed lymphangioma. The patient remains well with no evidence of recurrence 1 year post resection

Alveolar soft-part sarcoma responding to interferon alpha-2b

A 23-year-old woman with an alveolar soft-part sarcoma of her calf with pulmonary metastases unresponsive to chemotherapy is described. Interferon (IFN) alpha-2b induced an impressive tumour response still ongoing after IFN treatment had to be stopped because of a psychosis. An explanation of this effect is still speculativ

Epithelioid sarcoma in the thoracic spine

Epithelioid sarcoma is a rare and highly malignant soft tissue tumor that is commonly found in the extremities and rarely in the trunk area. This malignant tumor often mimics granuloma or nodular fasciitis, which causes a delay in establishing the diagnosis. This type of cancer has a high recurrence rate. Surgical treatment requires wide radical resection. The objective of this case report is to highlight the unique location of a rare neoplasm and to illustrate the relentless course of epithelioid sarcoma despite initial radical resection. A 14-year-old boy was admitted to our facility with a soft tissue mass on the right lower thoracic spine. The large tumor mass had deeply penetrated into the muscles, infiltrated the neuroforamen of T9–T10 level, and compressed the dural sac. Immunohistological study of the biopsy was highly consistent with an epithelioid sarcoma. Wide excision of the mass, laminectomy and spine fusion with instrumentation was performed. The patient received chemotherapy and irradiation. The first recurrence of the neoplasm was seen as a contralateral metastasis 21 months after the resection. On the last follow-up, 3 years postoperatively, the patient was in a good general condition. However, further progression of the sarcoma had to be recognized. Our case encompasses multiple features that represent negative prognostic factors. Initial wide excision of the neoplasm and adjuvant therapy including chemotherapy and irradiation seem to slow down the relentless course of epithelioid sarcoma in the trunk

Layered Structures of Ti-6Al-4V Alloy and Metal Matrix Composites on Its Base Joint by Diffusion Bonding and Friction Welding

Metallic layered structures demonstrate an advanced set of characteristics that combine different properties not found within homogenous bulk materials. Powder metallurgy (PM) is proven to be the most efficient way of fabrication of layered structures, including highly rated structures of Ti alloys. Residual porosity, however, remains one of the biggest problems of titanium-based PM products and this can adversely affect the mechanical properties and performance of the structural parts. Post-sintering hot deformation is a common way to control the porosity of metallic materials. Traditional thermomechanical processing like hot rolling, however, could not be applied on multi-layered structures due to the disparity of the different layers’ plastic flow. Separate processing of high performance individual layers to reach their best parameters, followed by post processing bonding of the mating subcomponents is a credible pathway for fabrication of the layered materials with highly optimized properties of each individual layer. In this study we used diffusion bonding (DB) and friction welding to join the parts made of Ti-6Al-4V alloy and metal matrix composites on the base of this alloy reinforced with 10% of either TiB or TiC. Parts were fabricated using blended elemental PM. Different protocols were used to join the materials: DB welding via rotational friction (RFW) and linear friction (LFW) as well as different geometries of mating subcomponents were tested. Structure characterization of the joints using light optical microscopy, SEM, EDS, EBSD as well as mechanical tests were performed. All used protocols were generally successful in bonding the parts made of Ti-64 alloy and composites on its base. The potential of DB, RFW and LFW of Ti-6Al-4V alloy and its MMC are discussed

Hemangiopericytoma of the Greater Omentum

A 41-year-old Chinese woman was admitted to our hospital with epigastric pain. Computed tomography detected a heterogeneous enhancement tumor fed by the left gastroepiploic artery in the left lower quadrant and cholelithiasis. Excision of the tumor in the greater omentum and cholecystectomy were performed laparoscopically. Histological findings confirmed a diagnosis of hemangiopericytoma with low-grade malignancy. To our knowledge, hemangiopericytoma of the greater omentum is very rare, and only 12 cases were reported in English literature. We report a case of hemangiopericytoma arising in the greater omentum and review the literature

The role of pontine lesion location in differentiating multiple sclerosis from vascular risk factor-related small vessel disease

Background: Differentiating multiple sclerosis (MS) from vascular risk factor (VRF)-small vessel disease (SVD) can be challenging. Objective and Methods: In order to determine whether or not pontine lesion location is a useful discriminator of MS and VRF-SVD, we classified pontine lesions on brain magnetic resonance imaging (MRI) as central or peripheral in 93 MS cases without VRF, 108 MS patients with VRF and 43 non-MS cases with VRF. Results: MS without VRF were more likely to have peripheral pons lesions (31.2%, 29/93) than non-MS with VRF (0%, 0/43) (Exp(B) = 29.8; 95% confidence interval (CI) = (1.98, 448.3); p = 0.014) but there were no significant differences regarding central pons lesions between MS without VRF (5.4%, 5/93) and non-MS with VRF patients (16.3%, 7/43) (Exp(B) = 0.89; 95% CI = (0.2, 3.94); p = 0.87). The presence of peripheral pons lesions discriminated between MS and VRF-SVD with 100% (95% CI = (91.8, 100)) specificity. The proportion of peripheral pons lesions in MS with VRF (30.5%, 33/108) was similar to that seen in MS without VRF (31.2%, 29/93, p = 0.99). Central lesions occurred in similar frequency in MS with VRF (8.3%, 9/108) and non-MS with VRF (16.3%, 7/43, p = 0.15). Conclusion: Peripheral pons lesion location is a good discriminator of MS from vascular lesions