High school mathematics teachers’ learning experiences, during a professional development intervention to improve their understanding of linear and quadratic functions using GeoGebra

Thesis (PhD)--Stellenbosch University, 2021.ENGLISH SUMMARY : Mathematics is a compulsory subject at all levels of pre-tertiary Namibian education and mathematical functions are key concepts of the mathematics curriculum. Personal experience has shown that teaching and understanding functions is a challenge in the Namibian high school curriculum. There are several difficulties in learning algebra due to misconceptions and errors such as misunderstanding the meaning of numerical and literal symbols, the shift from numerical data or language representation to variables or parameters with functional rules or patterns, and their cognition. Hence, there is a need to integrate the use of information and communication technologies (ICTs) in order to improve the understanding and teaching of mathematical functions. However, successful integration depends on providing teachers with learning opportunities in using ICTs. The focus of this research was to investigate a selected number of high school mathematics teachers‟ learning experiences during a professional development intervention aimed at improving the understanding of functions using GeoGebra. This study provides answers to the following questions: (1) What are high school mathematics teachers‟ learning experiences, during a professional development intervention to improve their understanding of linear and quadratic functions using GeoGebra? (2) What does research have to say about the potential of GeoGebra in aiding the understanding functions? The study was conducted in the Ohangwena region in Namibia and grounded on the interpretive paradigm. The sample population consisted of ten high school mathematics teachers. Sampling of the participants was guided by convenience sampling procedures. Five workshops of 2-3 hours were organised with the selected teachers. During these workshops, guidance and time were given to the teachers to explore different activities related to multiple representations of mathematical functions. The teachers were interviewed while they interacted with a set of GeoGebra activities. A group discussion was held to explore and develop an understanding of the concept of functions, the nature of GeoGebra and its possible pedagogical affordances. Multiple methods were used to collect data, namely semi-structured interviews; focus group interviews; audiotaped discussions; observations; and field notes. Based on a qualitative analysis of the data generated, the findings indicated that teachers benefited significantly from the use of GeoGebra as mathematical digital software in various ways, ranging from personal mathematics exploration, attitudes toward mathematics and mathematics teaching of functions to pedagogical reflections, including the nature of mathematics and teachers interactions. These changes are well aligned with the emphases of the ongoing mathematics education reforms in Namibia, including the integration of technology into education. The research findings also revealed that in its design GeoGebra affords fast and consistent feedback and that teachers need more opportunities where they learn to experience relations between the pragmatic and epistemic dimensions of GeoGebra use, when it comes to linear and quadratic functions, for example.AFRIKAANSE OPSOMMING : Wiskunde is „n verpligte vak in al die fases van voortersiêre onderwys in Namibië en wiskundige funksies is van die kernkonsepte in die wiskundekurrikulum. Persoonlike ervaring wys daarop dat die onderrig en verstaan van funksies „n uitdaging in die Namibiese hoërskoolkurrikulum blyk te wees. Daar is verskeie struikelblokke in die leer van algebra. Dit kan te wyte wees aan wanopvattings en foute soos die misverstaan van numeriese en lettersimbole, die skuif van numeriese data of taalverteenwoordiging na veranderlikes of grense met funksionele reëls of patrone en die herkenning daarvan. Vandaar die behoefte om die gebruik van inligting- en kommunikasietegnologieë (IKTs) te integreer ten einde die verstaan en die onderrig van wiskundige funksies te verbeter. Die sukses van hierdie insluiting hang egter af van die mate waartoe ondewysers toegang tot leergeleenthede in die gebruik van IKTs gegun word. Met hierdie navorsing is daar gefokus op die ondersoek na „n gekose aantal hoërskool-wiskundeonderwysers se leerervarings tydens „n professionele ontwikkelingsintervensie, wat daarop gemik was om die verstaan van wiskundige funksies te bevorder deur die gebruik van GeoGebra. Met hierdie studie is daar gepoog om antwoorde op die volgende vrae te vind: (1) Wat is hoërskool-wiskundeonderwysers se leerervarings gedurende die bywoning van „n professionele ontwikkelingsintervensie wat daarop gemik is om die verstaan van wiskundige funksies te bevorder deur die gebruik van GeoGebra? (2) Wat is die bevindings van navorsing oor die moontlikhede van GeoGebra in die ontwikkeling van „n beter begrip van funksies? Die ondersoek is onderneem in die Ohangwena-distrik in Namibië en dit is gegrond op die interpretatiewe paradigma. Die deelnemers vir die steekproef bestaan uit tien hoërskool-wiskundeonderwysers. Die keuse van deelnemers is gelei deur doelbewuste steekproefprosedures. Vyf werkswinkels van 2 tot 3 ure elk is vir die gekose onderwysers gereël. Gedurende hierdie werkswinkels is die onderwysers begelei en daar is tyd gegee om verskillende aktiwiteite met betrekking tot die veelvuldige voorstellings van wiskundige funksies te ondersoek. Onderhoude is met die onderwysers gevoer, terwyl hulle besig was met „n stel GeoGebra-aktiwiteite. „n Groepsbespreking het plaasgevind oor die begrip wiskundige funksies om die verstaan daarvan te ontwikkel. Die aard van GeoGebra is ook bespreek en die moontlikhede daarvan as „n pedagogiese hulpmiddel is ondersoek. „n Verskeidenheid metodes is aangewend om data in te win, soos die voer van deelsgestruktureerde onderhoude, fokusgroeponderhoude, die maak van oudio-opnames van gesprekke, deur waarneming en met die byhou van veldnotas. Gebaseer op die kwalitatiewe ontleding van die gegenereerde data is daar bevind dat onderwysers beduidend kan baat vind by die gebruik van GeoGebra as „n wiskundige, digitale grensobjek (WDGO). Dit kan op verskeie wyses aangewend word, soos byvoorbeeld tydens persoonlike ondersoeke na wiskunde, in die aanspreek van die houding jeens wiskunde, by die onderrig van wiskundige funksies of tydens pedagogiese refleksies oor die aard van wiskunde, asook tydens onderwyserinteraksies. Hierdie veranderinge klop met die volgehoue hervorming van wiskundeonderwys in Namibië wat ook die integrasie van tegnologie in opvoeding insluit. Die navorsingsbevindige bring voorts aan die lig dat GeoGebra, as „n WDGO, vinnige en deurlopende terugvoer toelaat en dat onderwysers meer geleenthede behoort te kry waartydens hulle die verhouding tussen die pragmatiese en die epistemiese dimensies van GeoGebra-gebruik kan ervaar, veral wanneer dit kom by liniêre en drievoudige funksies.Doctora

Evolution over Time of Ventilatory Management and Outcome of Patients with Neurologic Disease∗

OBJECTIVES: To describe the changes in ventilator management over time in patients with neurologic disease at ICU admission and to estimate factors associated with 28-day hospital mortality. DESIGN: Secondary analysis of three prospective, observational, multicenter studies. SETTING: Cohort studies conducted in 2004, 2010, and 2016. PATIENTS: Adult patients who received mechanical ventilation for more than 12 hours. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Among the 20,929 patients enrolled, we included 4,152 (20%) mechanically ventilated patients due to different neurologic diseases. Hemorrhagic stroke and brain trauma were the most common pathologies associated with the need for mechanical ventilation. Although volume-cycled ventilation remained the preferred ventilation mode, there was a significant (p < 0.001) increment in the use of pressure support ventilation. The proportion of patients receiving a protective lung ventilation strategy was increased over time: 47% in 2004, 63% in 2010, and 65% in 2016 (p < 0.001), as well as the duration of protective ventilation strategies: 406 days per 1,000 mechanical ventilation days in 2004, 523 days per 1,000 mechanical ventilation days in 2010, and 585 days per 1,000 mechanical ventilation days in 2016 (p < 0.001). There were no differences in the length of stay in the ICU, mortality in the ICU, and mortality in hospital from 2004 to 2016. Independent risk factors for 28-day mortality were age greater than 75 years, Simplified Acute Physiology Score II greater than 50, the occurrence of organ dysfunction within first 48 hours after brain injury, and specific neurologic diseases such as hemorrhagic stroke, ischemic stroke, and brain trauma. CONCLUSIONS: More lung-protective ventilatory strategies have been implemented over years in neurologic patients with no effect on pulmonary complications or on survival. We found several prognostic factors on mortality such as advanced age, the severity of the disease, organ dysfunctions, and the etiology of neurologic disease