FET Phase Research Articles

The relationship between a set of selected variables characterizing FET phase South African geography teachers and their self-directed learning abilities

ABSTRACT This study investigates the relationship between a set of selected variables of geography teachers and their self-directed learning abilities. A quantitative research method based on the Self-Directed Learning Abilities Instrument (SDLi) was used. Geography teachers (n = 130) in the Further Education and Training phase in two districts in North West province completed the SDLi. Most of the teachers held the perception that they possessed the necessary SDL abilities. The results show that these teachers’ perceptions of their preparedness to teach geography to learners had a moderate but significant correlation (r = 315; p = .000) with their perceptions of their SDL abilities, while satisfaction with their profession as geography teachers had a weak but significant correlation with their SDL abilities (r = 0.276; p = .001). The results show no relationship between the teachers’ teaching experience, school quintile or teaching qualifications and their SDL abilities. Geography teachers with a postgraduate degree held more positive perceptions of their SDL abilities in comparison to teachers with an undergraduate degree or a teaching diploma. Small practically significant differences between teachers teaching in no-fee schools (Quintiles 1 to 3) and geography teachers teaching in fee-paying schools (Quintiles 4 and 5) were reported, with the teachers in no-fee schools holding slightly more positive perceptions of their SDL abilities.

Ukuqonda kothisha mayelana nokufundiswa kwekhono lokufunda ngokuhlolisisa kanye nokuqondisisa imibhalo yesiZulu emabangeni aphezulu

This study explores teachers’ understanding of teaching critical reading and reading comprehension using isiZulu literary texts in FET phase. The study adopted interpritivist worldview and employed qualitative research methods to generate data. Semi-structured interviews, lesson observations and document anaysis were used to generate data from selected teachers. Purposive sampling was used to select teacher participants who are teachig isiZulu Home Language literary texts in the FET phase. This study used inductive approach to analyse data and it is supported by two theories; Piagets’ cognitive theory and Vygotskys’ social contsructivsm theory. Piaget (1983) emphasises cognitive developmental stages that learners undergo when reading lterary texts and learning language skills. On the other hand, Vygotsky (1978) puts emphasis on the role that social and cultural aspects play in understanding the world during learning. Vygotsky highlights the role of the knowledgable person (teacher, parents or peers) to facilitate learning experience during learning. Findings shows that teachers are using traditiona method of teaching literary texts. Traditional method focuses only on the structure and acquisition of textual information. Traditional method does not develop critical reading and comprehension because literary text is viewed as a complete and factual piece. Traditional method does not afford learners opportunities to create new meanings and interrogate authors perspectives. IQOQA Lolu cwaningo luphenya ngokuqonda kothisha mayelana nokufundiswa kwekhono lokufunda ngokuhlolisisa kanye nokuqondisisa imibhalo yesiZulu emabangeni asesigabeni sokuFunda okuQhubekayo nokuQeqesha. Ngokusebenzisa indlelakubuka yomhumusho kanye nezindlela zobunjalo botho, lolu cwaningo lukhiqize ulwazi ngezindlela zezinhlololwazi ezisakuhleleka, ukubukela othisha befundisa kanye nokuhlaziywa kwamadokhyumenti. Kulolu cwaningo kwalandelwa indlela yokuqoka ngenhloso othisha abafundisa imibhalo yesiZulu ulimi lwaseKhaya. Kwasetshenziswa isu lokuholela kokuthile; nohlaka lwemicabango kaPiaget (1983) kanye nekaVygotsky (1978) njengezinsizakuhlaziya okutholakele ocwaningweni. Injulalwazi kaPiaget (1983) ibalula ubumqoka bokuthuthukiswa kwengqondo yomfundi ukukwazi ukucabanga okufundwayo. Kanti-ke, injulalwazi kaVygotsky imayelana neqhaza lenhlalo kanye namasiko ekufundeni imibhalo. Indlela yokuhlaziya okutholakele ngezindikimba (thematic analysis) iye yaholela ekutheni kuhlaluke ukuthi othisha basasebenzisa indlela yendabuko yokufundisa ukuhluza isakhiwo kanye nohlaka kombhalo, nokwenza bangagxili ekuthuthukiseni amakhono elokuhlolisisa kanye nokuqondisisa imibhalo yesiZulu. Le ndlela yokuhluza imibhalo igxilisa ukuthola ulwazi lombhalo kanye nezimpawu ezisobala.

Exploring Challenges Hindering Teachers’ Implementation of Classroom Management Strategies in Gauteng High Schools, South Africa

This study explores challenges hindering teachers’ implementation of classroom management strategies in schools and suggests solutions thereafter. This study adopts the behaviourism theory, which aims to help learners unpack and emulate desirable behaviour, arguing that learning should lead to the adoption of constructive, observable conduct, such as what individuals say or do. The study is located within a qualitative approach using a case study design. The study consisted of purposively sampled participants comprised of twelve Grade 10 (FET Phase) educators from the three chosen high schools in Gauteng Province in the Ekurhuleni North District, South Africa. The collected data was analysed using content analysis. The findings highlighted large class sizes and insufficient parental involvement as key obstacles to effective classroom management. Setting clear expectations and fostering a positive environment were noted as crucial solutions. Recommendations include schools and educators actively promoting a supportive classroom atmosphere, establishing clear expectations, and encouraging parental participation in the learning process to overcome classroom management challenges and enhance high school teaching and learning experiences.

Undergraduate Students’ Perceptions of the Use of Online Examinations in an Open and Distance Learning Environment

This phenomenological study explored undergraduate students’ perceptions of the usefulness and ease of using online examinations in relation to the practicality and security of those who enrolled for Teaching Mathematics in the FET Phase. The perception theory, which outlines positive and negative perceptions, was used to underpin this study. An interpretive paradigm was also used as the study employed a phenomenological qualitative research design. The study generated data from 12 students who participated in semi-structured telephone interviews. The findings of the study revealed both positive and negative perceptions of online examinations. Positive perceptions that made online examination pleasurable were cost saving and saving on travel time, writing at one’s own pace and space, submitting answer sheets online, getting immediate feedback, and writing online and offline. On the other hand, negative perceptions included difficulties in using the Invigilator App, noise pollution, network connectivity, and load shedding. The study suggests that students identify spaces where they can easily access a stable internet network with no noise pollution.

Learning Support Strategies to Overcome the Effects of Promoting Condoned Senior Phase Mathematics Learners to the FET Phase

The study investigated the effects of condonation on the promotion of senior phase mathematics learners into the FET phase in a high school in KwaZulu-Natal. Condoned learners were assisted to progress, despite not meeting the pass requirements. The study suggests learning support strategies teachers could use to improve condoned FET mathematics learners' performance. An exploratory case study investigated the condonation policy and its effects thereof. Interviews were conducted with two mathematics teachers, and open-ended questions were posed. The data analysis entailed collating the data, followed by a thematic data analysis approach. The literature study was done on pertinent theories, prior studies, and pragmatic research. The findings suggest that condoned learners did not master the foundational knowledge and accumulated knowledge gaps. Consequently, learners struggle to achieve good performance in FET mathematics. This may lead to condoned learners failing FET mathematics, dropping mathematics in favour of more uncomplicated mathematical literacy or dropping out of school rather than completing Grade 12. The study recommends that condoned senior phase mathematics learners struggling to perform well in FET mathematics need to undergo an individualised learning support programme. Teachers will then employ various academic teaching and learning support strategies to help improve learners' FET mathematics performance. The success of learning support depends on a collaborative relationship between nurturing teachers and parents and positive discipline in group teaching within supplemental classes.

The Effect of Computer Simulation on Grade 11 Learners’ Conceptualisation of Stoichiometric Chemistry

This study, titled <i>The Effect of Computer Simulation on Grade 11 Learners’ Conceptualisation of Stoichiometric Chemistry</i>, was carried out at a school in the Frances Baard District of the Northern Cape province of South Africa. Poor conceptualisation of stoichiometric chemistry by learners in Grades 10-12 in South Africa and, hence, their failure to apply the concepts to problem-solving in the same and other topics in chemistry, is a cause for concern. The study was conducted with the theoretical framework of activity theory. A mixed method design that consisted of a pre-test post-test experimental design, a questionnaire and interviews were used for the study. Two Grade 11 physical sciences classes which consisted of a control and experimental group were taught stoichiometric chemistry after the SCAT pre-test. The experimental group obtained an intervention comprising computer simulations during teaching, while the control group was taught using the lecture method. The ANOVA results showed that learners of the control and experimental groups were comparable in terms of prior knowledge of the topic of stoichiometric chemistry. The paired t-test showed that both groups improved their performance in stoichiometric chemistry. However, the ANCOVA results showed that the experimental group had a greater improvement in performance than the control group. The results of the SCAT post-test, observation of lessons, questionnaire and interviews showed that the experimental group conceptualised stoichiometric chemistry better than the control group. The quantitative and qualitative data was triangulated, and it also indicated that the experimental group conceptualised stoichiometric chemistry better than the control group. It is therefore suggested that using computer simulations for the teaching and learning of stoichiometric chemistry is a better method to improve its conceptualisation in the FET phase of schools in South Africa.

Mathematical Knowledge for Teaching in Further Education and Training Phase: Evidence from Entry Level Student Teachers’ Baseline Assessments

This paper investigates entry-level student teachers' mathematical knowledge for teaching in the Further Education and Training phase (FET) through Baseline Assessment. The study employed a quantitative research technique. The data collection instrument was a mathematics subject knowledge test (Baseline Assessment) for FET phase student teachers. Purposive and convenient sampling methods were employed in the study. The study enlisted the participation of 222 first-year mathematics education student teachers from a rural Higher Education Institution (HEI) specialising in FET phase mathematics teaching. One hundred and seventy-five (175) student teachers completed the Baseline Assessment for all grades in this study (10, 11, and 12). The Baseline Assessment findings were examined using descriptive statistics. The results revealed that student teachers have a moderate knowledge of mathematics topics in the FET phase at the entry-level. In addition, an adequate level of understanding for teaching Grades 10 and 12 Patterns, Functions, Algebra, Space and Shape (Geometry), and Functional Relationships. While the elementary level of understanding for teaching grade 10 Measurement, Grade 11 Patterns, Functions, Algebra, and Trigonometry and Grade 12 Space and Shape (Geometry). There is no level of understanding for teaching FET phase Data and Statistics and Probability. The paper suggests that student teachers must develop a comprehensive understanding of the mathematics curriculum with the assistance of teacher educators in HEIs.

Secondary teachers’ experiences of enacting financial literacy/accounting in a technology-rich environment

ABSTRACT South African accounting and Economic and Management Sciences (EMS) teachers draw from different levels of experience in the teaching of financial literacy. This leads to poor performance in financial literacy and accounting in the FET phase. Therefore, this qualitative study sought to explore the secondary teachers’ experiences of enacting financial literacy/accounting in a technology-rich environment. The interpretive paradigm is used as a world view in the presentation of findings framed by the TPACK theoretical framework. One-on-one semi-structured interviews, focus groups and reflective activities were used to generate data from the six teachers in distinct schools who were purposefully and conveniently selected. Data were thematically analysed through inductive and deductive processes. Findings revealed that the varying use of experiences reflects the lack of content knowledge, technological knowledge which affects the pedagogical knowledge and some of the curriculum concepts. The study recommends the combination of proficient (professional) and common (societal) experiences so that subjective (personal) experiences assist teachers in enacting and integrating technologies with the financial literacy/accounting curriculum in a way that improves learner performance in a technology-rich environment

From the teachers’ perspectives: resources used in teaching reading comprehension to English First Additional Language (EFAL) learners in the FET phase

ABSTRACT At most, schools in South Africa, the learners’ performances in English first additional language (EFAL) reading comprehension are a source of worry for stakeholders. The majority of these learners are EFAL speakers. To counteract this discomfort, effective and appropriate resources in the teaching of reading comprehension become handy. This study aimed to investigate the resources used in teaching reading comprehension to EFAL learners in the FET phase. The study employed a qualitative research design, semi-structured interview, to collect data. The sampling frame was six EFAL teachers in South Africa. The results of the study show that EFAL teachers in the FET phase use many resources to teach reading comprehension, which include the dictionary, textbooks, WhatsApp, the parents and videos. The challenges faced by learners in reading comprehension include overuse of the dictionary, a narrow vocabulary base and inability to skim and scan accordingly. It becomes imperative for EFAL to promote an enabling classroom environment so that learners’ reading comprehension skills are developed. Teachers need to understand that a deep comprehension is achieved when a reader progresses beyond literal comprehension to using the text combined with prior knowledge to construct understanding.

The educational research landscape on GIS integration and challenges – globally and in South Africa

As Geographic Information Systems (GIS) have only been included in the curriculum in the last decade, many educators globally struggle to integrate GIS practice into their teaching strategies. Following the global trend, South African educators might feel ill-equipped as they did not receive formal GIS training in a higher education institution. This paper highlights key global and South African challenges regarding GIS integration. To compare the challenges that South Africa faces with those experienced elsewhere, this mixed-method study gleaned data from student educators (n=78) who completed a questionnaire regarding their GIS FET Phase education, followed by in-depth interviews with FET Phase educators (n=10) and two provincial heads of Geography for the Department of Basic Education (DBE). Results from this study indicate a clear global and national pattern of barrier categories.

The educational research landscape on GIS integration and challenges – globally and in South Africa

As Geographic Information Systems (GIS) have only been included in the curriculum in the last decade, many educators globally struggle to integrate GIS practice into their teaching strategies. Following the global trend, South African educators might feel ill equipped as they did not receive formal GIS training in a higher education institution. This paper highlights key global and South African challenges regarding GIS integration. To compare the challenges that South Africa faces with those experienced elsewhere, this mixed method study gleaned data from student educators (n=78) who completed a questionnaire regarding their GIS FET Phase education, followed by in-depth interviews with FET Phase educators (n=10) and two provincial heads of Geography for the Department of Basic Education (DBE). Results from this study indicate a clear global and national pattern of barrier categories.

Writing approaches and strategies used by teachers in selected South African English First Additional Language classrooms

Background: The teaching of writing in English First Additional Language (EFAL) classrooms remains less explored in the Further Education and Training Phase (FET) in South Africa. This is so despite research showing a decline in the writing skills of second language learners, especially at the FET phase, calling attention to how writing is taught. Objectives: The purpose of this study was to investigate writing approaches and teaching strategies used by teachers in teaching writing in selected EFAL FET classrooms in the Pinetown district. Method: A qualitative approach was adopted to observe five writing lessons across five schools using a video camera. Discourse analysis was used to analyse data. Results: The findings indicate that teachers mostly used a process approach to writing, which is in line with their curriculum. The study also found that teachers generally used a question and answer method to teach writing, which entails teachers controlling the interactions in the classrooms through a nomination-response cycle. Analyses of lessons also suggest that teachers creatively employed code-switching to explain writing concepts better. Conclusion: The study concludes that the effectiveness of any pedagogy depends on the teachers’ knowledge and understanding of writing and approaches to writing. For effective development of learners’ writing, the study recommends instruction methods that embrace collaborative writing activities in the learners’ Zone of Proximal Development (ZPD) and the recognition of learners’ home languages.

The category Language Structures and Conventions in the CAPS for English First Additional Language: A critical analysis

The category Language Structures and Conventions in the Curriculum and Assessment Policy Statement (CAPS) for language teaching includes what teachers often refer to as ‘grammar’. This aspect of language teaching is approached from the perspective of the Communicative Approach to Language Teaching, where the distinction between ‘meaning’ and ‘form’ (or structure) is blurred so that the communicative function of language structures are emphasized. Since the CAPS for English First Additional Language in the FET phase emphasizes communicative language teaching, the implication is that the teaching of language structure occurs in the context of communication events. The questions that this article asks are (i) how language structures and conventions are organised in the CAPS document and (ii) how this organisation is aligned with the language teaching approach espoused by the CAPS document. Arguing from the language teaching approach espoused by the curriculum document, the CAPS for English First Additional Language in the FET phase is analysed from two requirements that have been derived from the Communicative Approach: firstly, the idea that language form is expressed in a context that shows its socially appropriate use and secondly, a whole-to-part orientation that implies understanding the way in which language form can function in a text. Some suggestions are made for a possible revision of this aspect of the curriculum.Key terms: curriculum, Communicative Approach, English first additional language, language structure, grammar.

Economics student teachers’ views on the usefulness of a flipped classroom pedagogical approach for an open distance eLearning environment

PurposeThe purpose of this paper is to explore to what extent a flipped classroom pedagogy (FCP) design as a digital pedagogical tool enhances student teachers’ learning in economics education at an open distance e-Learning (ODeL) university.Design/methodology/approachThis exploratory study used a quantitative approach and online survey design. The sample consisted of 214 Postgraduate Certificate in Education (PGCE) and 157 Baccalaureus Educationis (BEd) (senior and further education and training phase) student teachers. A closed structured online questionnaire, Flipped Classroom Pedagogy Questionnaire, designed on a four-point Likert scale, was used to collect data. Descriptive and inferential data were computed to explore student teachers’ learning to teach an economics education in a teacher education course. Ethical clearance was granted and therefore adheres to the policy on research ethics of the university.FindingsEmpirically, the findings of this paper revealed that the FCP digital pedagogy enhanced economics students’ academic performance and perceptions in an online open distance learning environment. Furthermore, student teachers perceived that the functionality of the FCP experience as an online strategy was useful and effective for their learning. Therefore, these findings confirmed and extended what is revealed by earlier research studies regarding the debate on the usefulness of the FCP approach as a powerful technology-integrated teaching design in teacher education courses.Research limitations/implicationsThe findings of this investigation could not be generalised because a small sample was selected. Further investigation is needed regarding comparing other similar modules of the PGCE/BEd (senior and FET phase) programmes over a longer investigative period in the college. Further research should be explored, employing a mixed-methods approach on how student teachers perceived academic support in the FCP strategy towards self-directed learning.Practical implicationsUltimately, several implications for using the FCP approach emerged, in particular for rethinking teacher education programmes to support and accommodate the digital learner. To implement this approach successfully, faculties should formulate clear intended outcomes for implementing the FCP pedagogical approach. In addition, faculties at higher education institutions should seriously consider the merits of the FCP approach in order to avoid becoming redundant. Therefore, lecturers who intend to use this strategy either through a contact, blended or ODeL mode of delivery, are compelled to provide consistent, ongoing constructive feedback and monitoring required learning tasks.Social implicationsThe paper empowers PGCE/BEd (senior and FET phase) students to teach the subject in a diverse society.Originality/valueThis research study has shown that student teachers perceived an FCP approach in an online platform as an empowering tool that is both effective and useful and that positively impacts on their lived experience in an ODeL context. It extends the epistemology (subject of knowledge) of the effectiveness of the FCP strategy as an enhancer for student learning in an ODeL environment, teacher education in particular. Furthermore, a noteworthy contribution is made towards the application of the FCP as one of the digital pedagogies in teaching economics in an ODeL context. This exploratory study also makes a methodological contribution to the validation of an online data collection instrument for use in future studies.

Domain configuration evolution, dielectric, ferroelectric and piezoelectric properties of 0.32PIN–0.345PMN–0.335PT single crystals

Domain configuration evolution with temperature of the unpoled [001]C-oriented 0.32Pb(In1/2Nb1/2)O3–0.345Pb(Mg1/3Nb2/3)O3–0.335PbTiO3 (0.32PIN–0.345PMN–0.335PT) single crystals was studied by the polarized light microscopy (PLM). The optical observation of the domain structures reveals the coexistence of polymorphic ferroelectric phases with mainly ferroelectric monoclinic phase at room temperature and the irreversible domain evolution upon thermal cycling, which induce the high piezoelectric response in such relaxor-based ferroelectric single crystals with the morphotropic phase boundary compositions combined with polarization rotation. The temperature dependent domain evolution and dielectric behavior demonstrate the successive temperature-induced second-order ferroelectric M phase to ferroelectric tetragonal (T) phase (FEM–FET) and first-order ferroelectric T phase to paraelectric cubic (C) phase (FET–PC) ferroelectric phase transitions in the unpoled 0.32PIN–0.345PMN–0.335PT single crystals. Two dielectric loss anomalies were detected around the dielectric anomaly below 100 °C in the poled 0.32PIN–0.345PMN–0.335PT single crystals, indicating that the FEM–FET phase transition can be correlated with two different ferroelectric phase transitions, one is MA–MC, and the other is MC–T phase transition. The FEM–FET phase transition was confirmed further by the energy density measurement. The temperature dependent piezoelectric properties proved that the working temperature of the 0.32PIN–0.345PMN–0.335PT single crystals can reach 130 °C, higher around 50 °C than the Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystals, indicating their promising applications in transducers used at elevated temperatures.

Temperature-dependent Raman spectra and electrical properties of 0.69Pb(Mg1/3Nb2/3)O3–0.31PbTiO3 single crystals

The temperature-dependent Raman spectra and electrical properties of the 0.69Pb(Mg1/3Nb2/3)O3–0.31PbTiO3 (0.69PMN–0.31PT) single crystals were investigated. Based on the group theory, the poled 0.69PMN–0.31PT single crystals belong to the monoclinic crystal system, which was confirmed by the room-temperature Raman spectra. The 0.69PMN–0.31PT single crystals experience successive structural phase transitions, i.e., a monoclinic–tetragonal (FEM–FET) phase transition at TM–T and a tetragonal–cubic (FET–PC) phase transition at T m determined by the dielectric measurement. Due to the enhancement of long-range order, their FEM–FET phase transition becomes more obvious after the poling process. The wavenumbers and line widths of the 271, 502, 575, 795 cm−1 Raman modes, and the intensity ratios of $$ I_{{271{\text{cm}}^{ - 1} }} /I_{{795{\text{cm}}^{ - 1} }} $$ and $$ I_{{502{\text{cm}}^{ - 1} }} /I_{{575{\text{cm}}^{ - 1} }} $$ exhibit obvious anomalies around T M–T and T m, which are closely related to the FEM–FET and FET–PC phase transitions. The temperature and electric field (E)-induced phase transitions are observed in the unipolar strain–E (S–E) curves. The converse piezoelectric constant (d 33), maximum strain value (S max%) and longitudinal electrostrictive coefficient (Q) increase considerably around the ferroelectric phase transition temperature T M–T.

Exploring Habitus and Writer Identities: An ethnographic study of writer identity construction in the FET Phase at two schools in the Western Cape

Globalisation processes have resulted in increasingly pluralistic societies, a phenomenon with ripple effects in contexts such as universities, which now provide access to heterogeneous student populations with diverse rituals, beliefs, cultures and languages. For this reason, deficit discourses that frame students as underprepared for the demands of tertiary studies are a global phenomenon (Boughey, 2003; Lillis, 2003; Lea & Street, 1998). Furthermore, the different identities, histories and dispositions (Bourdieu, 1990) of students result in hybrid linguistic repertoires, with some repertoires being more powerful than others (Blommaert, 2001; Blommaert, Collins &Slembrouck, 2005; Rampton, 2003). Therefore, having access to the preferred linguistic repertoire - in most cases standard English - is an asset, because this repertoire is more closely aligned than others to tertiary education practices and discourses. As a result, the scholarly community can be daunting for many first-year students whose linguistic identities are not always aligned to institutional values, practices and discourses; students can easily be indexed as under-achieving or incompetent.

Analysis of South African Grade 10 learners' conceptual resources regarding the concept of energy in physics

More than a thousand Grade 10 Physical Science learners from four South African provinces participated in a study that probed their conceptions of energy. The purpose was to determine the learners' conceptual resources, i.e. their initial conceptions, and identify the potentially productive resources from which they may construct physics concepts. The conceptions revealed by the learners in their responses to a questionnaire were categorised as core intuitive, implicit, conscious or verbal-symbolic. Notwithstanding learning the curriculum theme Energy and Change in their preceding school years, the results show that many of the learners have not yet mastered the concept of energy and related concepts ontologically well enough for progression to formal physics in the FET phase. However, their initial conceptions contain resources that can be refined to the science concepts. Implications and recommendations for learning and teaching in the FET phase are discussed in the framework of the conceptual refinement model.

Eastern Cape teachers’ beliefs of the nature of mathematics: Implications for the introduction of in-service mathematical literacy programmes for teachers

Various studies have shown that what teachers consider to be optimal ways of teaching mathematics is influenced by their beliefs about the nature of mathematics, and that it is advantageous to determine teachers’ conceptions of the nature of mathematics before developing curriculum interventions. With the imminent introduction of Mathematical Literacy in the FET phase in South Africa this study provides a snapshot of beliefs of teachers in the Eastern Cape, South Africa. Various methods were employed to stimulate teachers to both reflect on their beliefs and to make them explicit. A questionnaire was administered to 339 in-service teachers in urban and rural areas of the Eastern Cape. A sample of ninety-five of these teachers completed a second questionnaire based on videotapes of lessons recorded during the TIMSS (1995) study that they had viewed. These teachers also ranked their own teaching on a continuum ranging from traditional to constructivist approaches and provided explanations for their ranking. A further sub-sample of thirty-six teachers participated in individual interviews, which explored their perceptions of the nature of mathematics and their own teaching practice. In order to investigate whether these beliefs were mirrored in practice, four teachers were observed and videotaped in their classrooms. The data generated by this study suggest that the participating teachers’ espoused beliefs of the nature of mathematics tended to be innovative, and correlated with innovative views of teaching and learning; however these views were often not reflected in their practice. The implications that the apparent inability of teachers to translate their beliefs into practice have for the introduction of a contextual, problem-based Mathematical Literacy curriculum for teachers is explored.

Polarization-Agile Microstrip Antenna Array Using a Single Phase-Shift Circuit

A novel polarization-agile microstrip antenna array is proposed, in which the polarization agility from linear to circular polarization for the whole array is realized easily by controlling a single phase-shift circuit. Using the corner-fed square patch element, a new 16 element dual-polarized array with high isolation and low cross-polarization is designed and analyzed by the extended multiport network method. A special FET phase shifter circuit is created, where 0/spl deg/ or 90/spl deg/ phase shift between dual ports is electrically switched. Experimental results are presented to verify the theory, and measured circularly-polarized radiation patterns show a boresight axial ratio of 0.5 dB. Another experiment that connects a low noise amplifier together with the phase-shift circuit is also introduced, realizing both polarization agility and power amplification with one active circuit.