Pre-service mathematics teachers’ mental constructions when using Cramer’s rule

This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer’s rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the role of parameters in the solution of equations with parametric coefficients. These mental constructions occur within the Action-Process-Object-Schema (APOS) theory. In this study, data was generated from 31 first year pre-service teachers by means of an activity sheet and interviews. The interviews were used to clarify pre-service teachers’ responses to tasks from the activity sheet. The findings revealed that many PMTs displayed procedural understanding of Cramer’s rule. It was also found that they understood what the solution of system of linear equations means. This meant that they were operating at the action stage, in terms of APOS. Additionally, it revealed that the lack of construction of related schemata negatively impacted the PMTs’ attempt to construct the necessary mental constructions. Therefore, the researchers provided the genetic decomposition (GD) for the use of Cramer’s rule to assist teacher educators to analyse the mental constructions of students. This study explored a new application of APOS theory. Analysing the mental constructions of students by means of research is intended to assist in designing alternative teaching strategies. In this way, this study makes a significant contribution to the solution of system of equations pedagogy.Keywords: APOS; Cramer’s rule; parametric coefficients; pre-service mathematics teachers; system of linear equation

Correctional education designed for female inmate rehabilitation : a qualitative analysis of a marginalised group within the Ethekwini municipality

English, Zulu and Xhosa abstractsA qualitative exploratory study developed on global literature and research investigates female inmates' perspectives concerning correctional education programmes presented whilst incarcerated. Worldwide studies have hypothesised some conclusions which add to the recognition and understanding of the development and implementation of correctional education. This study builds on such understandings to provide a unique insight into the life of South African female inmate learners. The study outcomes add to the framework of information on female correctional education, a topic that has garnered little attention globally and in South Africa. According to the White Paper on Corrections in South Africa (2005), the Department of Correctional Services is cognisant of gender dynamics and female inmates special needs. The study's primary research question is: what are the female inmate learners' perceptions relating to their learning experiences from correctional education programmes offered whilst incarcerated? The study is informed by three major theoretical frameworks: feminist theory, restorative justice theory, and rehabilitation theory. Semi-structured in-depth interviews were conducted with seventeen study participants (fourteen female inmate learners and three inmate facilitators) at the Durban Westville Correctional Centre, located within the EThekwini Municipality in the province of KwaZulu-Natal. Discussions extrapolate female inmate learner perspectives in a female correctional school and factors affecting the female correctional education experience. The findings demonstrate that international and national laws and guidelines are largely "written documents" without effective implementation. There is a pervasive lack of educational staff, resources, infrastructure, gender sensitivity, and efficient and adequate education programmes. The study recommendations include effective policy making to address rehabilitation, the need for financial support, key stakeholders working together, a female-centered educational and rehabilitation plan, a need for a feminist criminologist, and a call for qualified education personnel.Ucwaningo lokuhlola olusezingeni eliphezulu olwenziwa ezincwadini zomhlaba wonke kanye nocwaningo luphenya imibono yeziboshwa zabesifazane mayelana nezinhlelo zemfundo yokuhlunyeleliswa kwezimilo ezethulwa ngesikhathi ziboshiwe. Izifundo zomhlaba wonke ziye zalinganisa iziphetho ezithile ezengeza ekuqashelweni nasekuqondeni ukuthuthukiswa nokuqaliswa kwemfundo yokuqondiswa kwezimilo. Lolu cwaningo lwakhela phezu kokuqonda okunjalo ukuze kunikeze ukuqonda okuyingqayizivele ngempilo yomfundi wesifazane oyisiboshwa waseNingizimu Afrika. Okutholwe yilolu cwaningo kwengeza olwazini olumayelana nemfundo yokuqondiswa kwezigwegwe kwabesifazane, okuyisihloko esinganakwa kakhulu emhlabeni naseNingizimu Afrika. NgokoMqulu Womthetho Wokuhlunyeleliswa Kwezimilo eNingizimu Afrika (2005), uMnyango Wezokuhlunyeleliswa kwezimilo uyaqaphela ukuguquguquka kobulili kanye nezidingo ezikhethekile zeziboshwa zesifazane. Umbuzo oyinhloko wocwaningo uthi: iyiphi imibono yabafundi besifazane ababoshiwe mayelana nolwazi lwabo lokufunda ezinhlelweni zemfundo yokuhlunyeleliswa kwezimilo ezihlinzekwa ngesikhathi beboshiwe? Ucwaningo lusekelwe yizinhlaka zetiyori ezintathu ezinkulu: ithiyori yabesifazane, ithiyori yokubuyisela ubulungiswa, kanye nethiyori yokuvuselela. Kwenziwa inhlolokhono ejulile nabayishumi nesikhombisa (abafundi besifazane abayishumi nane nabagqugquzeli abathathu) eDurban Westville Correctional Centre, engaphakathi kuMasipala weTheku esifundazweni saKwaZulu-Natali. Izingxoxo ziveza imibono yomfundi oyisiboshwa wesifazane esikoleni sokuqondisa izigwegwe kanye nezici ezithinta ulwazi lwemfundo yokuqondiswa kwezimilo. Okutholakele kubonisa ukuthi imithetho neziqondiso zamazwe ngamazwe kanye nezezwe ngokuyinhloko "ziyimibhalo ebhaliwe" ngaphandle kokuqaliswa ngempumelelo. Kunokuntuleka okukhulu kwabasebenzi bezemfundo, izinsiza, ingqalasizinda, ukuzwela ngokobulili, kanye nezinhlelo zemfundo eziphumelelayo nezanele.Uphononongo lophononongo olusemgangathweni oluphuhliswe kuncwadi lwehlabathi kunye nophando luphanda iimbono zamabanjwa abhinqileyo malunga neenkqubo zemfundo yoluleko eziboniswa ngelixa eseluvalelweni. Uphononongo lwehlabathi lonke luye lwaqikelela ezinye izigqibo eziye zongeza ukuqondwa nokuqonda uphuhliso nokuphunyezwa kwemfundo yoluleko. Olu phononongo lwakhela phezu kokuqonda okunjalo ukunika ingqiqo eyodwa kubomi bomfundi wasebanjwa obhinqileyo waseMzantsi Afrika. Iziphumo zolu phando zongeza kulwazi oluninzi ngemfundo yoluleko yabasetyhini, isihloko esithe safumana ingqwalasela encinci kwihlabathi jikelele naseMzantsi Afrika. NgokwePhepha leNgcaciso yoMgaqo-nkqubo woLuleko eMzantsi Afrika (ka-2005), iSebe leeNkonzo zoLuleko liyaziqonda iinguqu zesini kunye neemfuno ezikhethekileyo zamabanjwa angabasetyhini. Umbuzo ongundoqo wolu phando ngulo: zithini iimbono zabafundi ababhinqileyo abakwibanjwa elimalunga namava abo okufunda kwiiprogram zemfundo yoluleko abazifundiswayo ngelixa bevalelwe? Uphononongo lusekelwe kwizicwangciso ezintathu eziphambili zethiyori: ithiyori yobufazi, ithiyori yokubuyisela kwisimo sobulungisa, kunye nethiyori yokubuyisela kwisimo sangaphambili. Udliwano-ndlebe olunzulu olufanelekileyo lwaqhutywa kunye nabathathi-nxaxheba abalishumi elinesixhenxe (abafundi ababhinqileyo abalishumi elinesine nabaququzeleli abangamabanjwa abathathu) kwiZiko loLuleko laseDurban Westville, elingaphakathi kuMasipala we-EThekwini kwiphondo laKwaZulu-Natal. Iingxoxo zibalaselisa iimbono zabafundi abakwibanjwa elibhinqileyo kwisikolo soluleko esibhinqileyo kunye nemiba echaphazela amava emfundo yoluleko yabasetyhini. Iziphumo zibonisa ukuba imithetho yamazwe ngamazwe neyesizwe nezikhokelo ubukhulu becala "ngamaxwebhu abhaliweyo" ngaphandle kokuphunyezwa ngokufanelekileyo. Kukho ukunqongophala okugqugqisileyo kwabasebenzi bezemfundo, izibonelelo, iziseko zophuhliso, uvakalelo ngokwesini, kunye neenkqubo zemfundo ezifanelekileyo nezifanelekileyo.Criminology and Security SciencePh. D. (Criminal Justice

Schema development for the chain rule: A South African case study

This article reports on the use of the Action-Process-Objects-Schema (APOS) theory as a theoretical framework to investigate first-year students’ understanding of the chain rule at a University of Technology in South Africa. Instructional design as part of APOS, based on the genetic decomposition, was used to teach the first-year students differentiation involving the concept of the chain rule and its use. A questionnaire based on functions, the composition of functions, derivatives and the structure of the integrand was used to monitor the development of the chain rule schema. Later, worksheets based on the use and application of the chain rule were designed to foster collaborative learning. A sample of 30 students participated in the study. In this manner differentiation of each function in the composite function was accomplished. Students either operated in the Inter- or Trans-stage of the Triad. It was found that students who had inadequate understanding of the composition of functions, performed well in the application of the chain rule. The analysis led to a formulation of three techniques for using the chain rule, namely: (1) the straight form technique; (2) the link form technique; and (3) the Leibniz form technique.Mathematics Educatio

Single-chain Fv phage display propensity exhibits strong positive correlation with overall expression levels

<p>Abstract</p> <p>Background</p> <p>Single chain Fvs (scFvs) are widely applied in research, diagnostics and therapeutic settings. Display and selection from combinatorial libraries is the main route to their discovery and many factors influence the success of this process. They exhibit low thermodynamic stability, resulting in low levels of premature cytosolic folding or aggregation which facilitates <it>sec </it>YEG-mediated translocation and phage in <it>E. coli</it>. However, there is little data analysing how this is related to and influenced by scFv protein expression.</p> <p>Results</p> <p>We characterised the relationship between overall scFv expression and display propensity for a panel of 15 anti-tetanus toxin scFvs and found a strong positive correlation (Rho = 0.88, p < 0.005) between the two parameters. Display propensity, overall expression and soluble localisation to the periplasm and extracellular fractions were clone specific characteristics which varied despite high levels of sequence homology. There was no correlation between display of scFv or its expression in non-fused (free) form with soluble scFv localisation to the periplasm or culture supernatant. This suggests that divergence in the fate of scFv-pIII and non-fused scFv after translocation to the periplasm accounts for the observed disparity. Differential degrees of periplasmic aggregation of non-fused scFv between clones may affect the partitioning of scFv in the periplasm and culture supernatant abrogating any correlation. We suggest that these factors do not apply to the scFv-pIII fusion since it remains anchored to the bacterial inner membrane as part of the innate phage packaging and budding process.</p> <p>Conclusion</p> <p>We conclude that in the absence of premature cytosolic aggregation or folding, the propensity of a scFv to be displayed on phage is directly related to its overall expression level and is thus indirectly influenced by factors such as codon bias, mRNA abundance or putative DNA motifs affecting expression. This suggests that scFvs capable of high overall expression and display levels may not produce high yields of non phage-fused soluble protein in either the periplasmic or extracellular fractions of <it>E. coli</it>. This should be considered when screening clones selected from combinatorial libraries for further study.</p> <p>The nucleotide and amino acid sequences of the anti-tetanus toxin scFvs have been deposited in the EMBL data base: accession numbers-C1: <ext-link ext-link-type="embl" ext-link-id="AM749134">AM749134</ext-link>, C2: <ext-link ext-link-type="embl" ext-link-id="AM749135">AM749135</ext-link>, C3: <ext-link ext-link-type="embl" ext-link-id="AM749136">AM749136</ext-link>, C4: <ext-link ext-link-type="embl" ext-link-id="AM749137">AM749137</ext-link>, C5: <ext-link ext-link-type="embl" ext-link-id="AM749138">AM749138</ext-link>, N1: <ext-link ext-link-type="embl" ext-link-id="AM749139">AM749139</ext-link>, N2: <ext-link ext-link-type="embl" ext-link-id="AM749140">AM749140</ext-link>, N3: <ext-link ext-link-type="embl" ext-link-id="AM749141">AM749141</ext-link>, N4: <ext-link ext-link-type="embl" ext-link-id="AM749142">AM749142</ext-link>, N5: <ext-link ext-link-type="embl" ext-link-id="AM749143">AM749143</ext-link> J1; <ext-link ext-link-type="embl" ext-link-id="AM749144">AM749144</ext-link>, J2: <ext-link ext-link-type="embl" ext-link-id="AM749145">AM749145</ext-link>, J3: <ext-link ext-link-type="embl" ext-link-id="AM749146">AM749146</ext-link>, J4: <ext-link ext-link-type="embl" ext-link-id="AM749147">AM749147</ext-link>, J5: <ext-link ext-link-type="embl" ext-link-id="AM749148">AM749148</ext-link>.</p

Hoofprints in the sand:A study on domestic sheep (Ovis aries) from Iron Age southern Phoenicia using traditional biometric methods

The majority of research to date on the translocation of livestock in the premodern (before 1500 CE) Mediterranean Basin has focused on expansive movements out from geographic origins of domestication or from colonizer-to-colonized territories. Fewer zooarchaeological studies have investigated the lateral trajectories of distinct varieties of domesticated animals around the post-Neolithic eastern Mediterranean, partially due to the difficulty in detecting intra-species variation osteologically. The research conducted in the present study sought to improve understanding of the human-mediated mobility of domestic sheep (Ovis aries) from Iron Age settlements in the southern Levant. Variability in body size and a greater variety of morphotypes were expected from coastal flocks in southern Phoenicia in comparison to inland herds, possibly due to the dynamic influence of maritime trade. Biometric data analysis of zooarchaeological materials using log size index and astragalar dimension index methods revealed evidence for the possible optimization of coastal sheep for wool production and a potential introduction event in the Persian period. The Aegean region could be a source for this introduction; however, further research is needed to specify the geographic origin of this phenomenon.</p

Upregulation of mucin glycoprotein MUC1 in the progression to esophageal adenocarcinoma and therapeutic potential with a targeted photoactive antibody-drug conjugate

BACKGROUND: Mucin glycoprotein 1 (MUC1) is a glycosylated transmembrane protein on epithelial cells. We investigate MUC1 as a therapeutic target in Barrett's epithelium (BE) and esophageal adenocarcinoma (EA) and provide proof of concept for a light based therapy targeting MUC1. RESULTS: MUC1 was present in 21% and 30% of significantly enriched pathways comparing BE and EA to squamous epithelium respectively. MUC1 gene expression was x2.3 and x2.2 higher in BE (p=<0.001) and EA (p=0.03). MUC1 immunohistochemical expression increased during progression to EA and followed tumor invasion. HuHMFG1 based photosensitive antibody drug conjugates (ADC) showed cell internalization, MUC1 selective and light-dependent cytotoxicity (p=0.0006) and superior toxicity over photosensitizer alone (p=0.0022). METHODS: Gene set enrichment analysis (GSEA) evaluated pathways during BE and EA development and quantified MUC1 gene expression. Immunohistochemistry and flow cytometry evaluated the anti-MUC1 antibody HuHMFG1 in esophageal cells of varying pathological grade. Confocal microscopy examined HuHMFG1 internalization and HuHMFG1 ADCs were created to deliver a MUC1 targeted phototoxic payload. CONCLUSIONS: MUC1 is a promising target in EA. Molecular and light based targeting of MUC1 with a photosensitive ADC is effective in vitro and after development may enable treatment of locoregional tumors endoscopically