An investigation into the opportunity to learn that is available to Grade 12 mathematics learners

This study investigated the opportunity to learn (OTL) that is available to Grade 12 mathematics learners. Learner workbooks were analysed in terms of time on task, curriculum coverage, curriculum coherence, and cognitive demand. Based on these elements, experienced mathematics teachers judged the opportunity that the learners have to achieve more than 60% for each topic. According to the workbooks, the average number of active learning days in this sample was 54.1 days per annum. This resulted in limited curriculum coverage in almost all sections in 16 of the 18 under-performing schools. In these schools, learners spent most of their time practising routine procedures. The high correlation of 0.95 (p < 0.001) between the experts’ prediction about the opportunity to learn in the different schools (based on the learner workbooks) and learners’ actual performance in the Grade 12 exam shows that the number, the coverage, the cognitive level, and the coherence of activities play a major role in understanding learner performance..http://www.sajournalofeducation.co.zaam2013gv201

The state of mathematics education in Afrikaans schools

Hoërordedenkvaardighede is noodsaaklike basiese vaardighede vir die een-en-twintigste eeu aangesien rekenaars berekeninge en algoritmes baie vinniger en akkurater kan doen as mense. Dit beteken dat skole leerders moet toerus om logies te dink, patrone te ontdek, bewyse te lewer, asook om nieroetineprobleme op te los. Hierdie fasette wat as hoërordedenke geklassifiseer word, is die kern van wiskundige denke en ontwikkeling. Suid-Afrika neem aan verskeie internasionaal vergelykende studies deel. Met behulp van hierdie vergelykende studies kan bepaal word hoe die Afrikaanse wiskundeleerders in Suid-Afrika se prestasie met dié van leerders in ander lande vergelyk en ook wat die tekortkominge in die wiskundeonderwys is. Volgens die 2003-TIMSS-uitslae is die probleem in Afrikaanse skole juis dié vrae wat hoërordedenke vereis. Dit beteken dat die Afrikaanse skole ’n doelbewuste poging sal moet aanwend om hoërordedenke te ontwikkel. Die 1999-TIMSS-videostudie toon dat die lande wat die beste presteer, soos Japan, tydens onderrig meer tyd wy aan die ontwikkeling van begripsvorming en aan die oplos van moeiliker probleme. Die fokus in die presterende lande is op die ontwikkeling van hoërordedenke deur probleemoplossing. Daar word dus minder tyd afgestaan aan herhaling van roetine- of soortgelyke oefeninge wat ’n rekenaar ook kan doen. Die omgekeerde hiervan is ’n tipiese verskynsel in Afrikaanse skole, waar ’n onderwyser byvoorbeeld een of meer voorbeelde op die bord doen waarna die leerders ’n hele aantal soortgelyke roetine-oefeninge doen.Higher-order thinking skills are essential basic skills for the 21st century as computers can do calculations and algorithms faster and more accurately than people. This means that schools should equip students to think logically, search for patterns, do proofs and solve non-routine problems. These activities are part of higher-order thinking, which is the essence of mathematical thinking and development. South Africa participates in several international comparative studies. Using these comparative studies, it has been possible to determine how the performance of Afrikaans mathematics learners in South Africa compares to that of learners of other countries and also to highlight possible deficiencies in mathematics education. According to the TIMSS 2003 results, Afrikaans learners perform poorly in the TIMSS advanced level questions, where higher-order thinking is required. This means that Afrikaans schools should purposely develop higher-order thinking. The TIMSS 1999 Video Study shows that the best performing countries like Japan spend more time in class on the development of conceptual understanding and working on complex problems. High-performing countries are focused on the development of higher-order thinking through problem solving. They also spend less time on doing routine or repetition exercises which can rather be done by a computer. The contrary is typically the case in Afrikaans schools where a teacher will for example do one or more examples on the blackboard and the students will follow and do a number of similar routine exercises.http://www.satnt.ac.zaam2013gv201

Does the use of technology make a difference in the geometric cognitive growth of pre-service mathematics teachers?

This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements. In order to investigate this, a quasi-experimental non-equivalent comparison group design was used. Similar course content was used for both the control and experimental groups. The students worked through a series of geometry activities and problems. The difference between the groups was that dynamic geometry software was integrated into the teaching of the experimental group. The Cognitive Development and Achievement in Secondary School Geometry (CDASSG) Van Hiele geometry test was used to determine all the students’ level of geometric thinking before and after the course. The study found that the use of dynamic geometry software enhanced student teachers’ geometric visualisation, analysis and deduction, but not their ability to informally justify their reasoning and to understand the formal aspects of deduction.The Research and Development grant from the University of Pretoriahttp://www.ascilite.org.au/ajet/ajet28/stols.htm

Why don't all maths teachers use dynamic geometry software in their classrooms?

In this exploratory study, we sought to examine the influence of mathematics teachers’ beliefs on their intended and actual usage of dynamic mathematics software in their classrooms. The theory of planned behaviour (TPB), the technology acceptance model (TAM) and the innovation diffusion theory (IDT) were used to examine the influence of teachers’ attitudes, subjective norms and perceived behavioural control on their intention to use dynamic mathematics software in their classrooms. The study adopted the co-relational research design, with both correlation statistics and regression analysis used to analyse the data. By using stepwise regression analysis, it was possible to identify the most important belief predictors and their weights for the different constructs. The results were verified by the use of partial least squares. This study found that beliefs about the perceived usefulness and beliefs about their level of technological proficiency are the most important predictors of teachers’ intended and actual usage of the software. In this preliminary study the suggested simplified model sufficiently explains 15 (83.3%) of the 18 teachers adaption and use of dynamic mathematics software in their classrooms.Funding for this research was provided by the National Research Foundation of South Africa.http://www.ascilite.org.au/ajet/ajet.htm

Can behavioral intentions predict domestic electricity consumer's actual behavior towards energy efficiency?

To reduce domestic electricity consumers consumption of electricity is a global concern. This pilot study investigates the extent to which domestic electricity consumers intend to use and use energy efficiently. A co-relational research design was used to investigate the relationship between the predictor variables and the independent variables in the constructs of the Theory of Planned Behavior which was selected as theoretical framework. A convenience stratified sample of 61 domestic electricity consumers was selected. A questionnaire and telephone response log was used to collect data. Simple linear regression analysis indicates significant statistical evidence of a linear relation between the predictor variables and the independent variables. The participants intended to save between 2% and 35% of their electricity consumption and the actual electricity consumption savings were between 2% and 30%.http://www.sherpa.ac.uk/romeo/issn/1308-7711/am2016Science, Mathematics and Technology Educatio

An application of the Rasch measurement theory to an assessment of geometric thinking levels

The purpose of this study is to apply the Rasch model to investigate both the Van Hiele theory for geometric development and an associated test. In terms of the test, the objective is to investigate the functioning of a classic 25-item instrument designed to identify levels of geometric proficiency. The data set consists of responses by 244 students (106 for a pre-test and 138 for a post-test) of which 76 students sat both the pre-test and the post-test. The summary item statistics do not show statistically discernible differences between observed and expected scores under the Rasch model (Chi-square statistic). The Rasch analysis confirms to some strong extent the Van Hiele theory of geometric development. The study identifies some problematic test items as they only require knowledge of a specific aspect of geometry instead of testing geometric reasoning. In terms of the Van Hiele theory, the Rasch analyses identified as problematic some items about class inclusion, an issue which has also been raised in other studies.http://www.tandfonline.com/loi/rmse202016-01-31hb201

Mathematical literacy teachers : can anyone be one?

In this case study, Mathematical Literacy teachers were interviewed and observed in the classroom in order to provide insight into the way this subject, relatively new in South African schools, is handled. The focus of this research was the instructional practice of these teachers specifically in terms of their mathematical knowledge regarding the subject and its learners. The idea that this subject is inferior to other subjects in general, but to mathematics in particular, was alluded to by some participants, alongside of the notion that it was infra dig to teach it. The study revealed that a working knowledge of mathematics as well as teaching-and-learning skills are necessary for this subject to achieve what it was meant to do when it was introduced into South African high schools in 2006.http://www.perspectives-in-education.comam2014gv201

What constitutes effective mathematics teaching? Perceptions of teachers

Beliefs help shape how teachers perceive effective mathematics teaching. Providers of professional development, be they local or from other countries, need to be cognisant of such perceptions. This paper seeks to answer the question, ‘What do South African teachers perceive as effective and ineffective teaching for developing conceptual understanding of mathematics?’ A sample of 46 mathematics teachers was shown vignettes from eight different classrooms where the lesson dealt with some aspect of teaching fractions, and were then asked to comment on the strengths and weakness of what they observed. The comments were classified into seven themes with 18 sub-themes or categories. The majority of the comments focused on two themes, use of materials and modes of instruction. The various mathematical approaches for developing the concept of fractions received little attention. Perceptions of which vignette was considered to be the most effective approach to teaching mathematics resulted in a wide variety of responses. Finally implications for professional development are explored. It is suggested that in-service courses should be geared to what teachers themselves consider best practice, and that reflection on practice should play a more significant role in professional development.Japan Society for the Promotion of Science (Grant number 22653108).http://www.tandfonline.com/loi/rmse202016-09-30hb201

The relationship between teachers' instructional practices and their learners' level of geometrical thinking

This case study describes and investigates the instructional practices of Grades 1 to 5 teachers and the levels of geometry thinking of the learners, according to the Van Hiele model, with a view to determining whether there is a match between the instructional practice and the learners’ level of thinking. The instructional practices of the teachers were observed and analysed, and their learners’ levels of geometry thinking were accessed through a Van Hiele test. The results suggest that there is not a simple relationship between the phases of learning, as described by Crowley in 1987, and geometric development in terms of the Van Hiele levels. It is, however, possible to explain the geometric development to a limited extent in terms of the Van Hiele levels of the observed teaching activities. Although the presence of activities on an appropriate level does not guarantee growth in terms of the Van Hiele model, the absence thereof results in stagnation. The instructional practices in primary schools in all Grades should span geometry experiences on all the levels, because the previsualisation level and Van Hiele Level 1 thinking are still evident up to Grade 5.http://journals.sabinet.co.za/ej/ejour_persed.htmlam2014gv201

Investigating the quality and content of five teachers’ reflection on their teaching of mathematics

In Suid-Afrika is beperkte navorsing gedoen oor onderwysers se reflektiewe klaskamerpraktyk. Die artikel het dus ten doel om die gehalte en inhoud van wiskundeonderwysers se refleksie of besinning oor ’n les binne die konteks van lesstudie te ondersoek. Die spesifieke doel van hierdie studie was om ondersoek in te stel na die gehalte en inhoud van vyf wiskundeonderwysers se besinning of refleksie voor, tydens en nadat ’n les aangebied is. Die vyf onderwysers (twee manlik en drie vroulik) het gesamentlik oor hul eie sowel as hul kollegas se wiskundeonderrig besin. Die onderwysers is doelbewus geselekteer om aan die studie deel te neem. Kwalitatiewe data is uit onderhoude, lesplanne, klaskamerwaarnemings en reflektiewe skryfwerk of geskrifte versamel. Daar is bevind dat al die wiskundeonderwysers agterna verbaal en skriftelik oor hul optrede besin het, terwyl drie van die onderwysers tydens optrede oor onderrig gereflekteer het. Die ontleding van hul lesplanne het geen bewyse van besinning vóór optrede (reflect-for-action) gelewer nie, met ander woorde die betrokke onderwysers het nie met die oog op toekomstige optrede besin nie. Twee onderwysers het wel krities oor hul leerders se verstaan van wiskunde en oor hul eie onderrig van begrippe besin. Aangesien hulle lede van die lesbestuderingsgroep was, het dit geblyk dat die hele ervaring ’n kontekstuele faktor is wat hierdie onderwysers se besinning op ’n positiewe wyse beïnvloed het. Die onderwysers se ontoereikende taalvaardighede en hul onvermoë om basiese wiskundige begrippe behoorlik te verbaliseer, het hul reflektiewe praktyk skynbaar egter negatief beïnvloed.Not much research has been done on mathematics teachers’ reflective practice in South Africa. This article reports on the quality and content of mathematics teachers’ reflections on a lesson within the context of lesson study. The aim of the study was to investigate the quality and content of five mathematics teachers’ reflections before, during and after teaching a lesson. The five teachers (two males, three females) reflected collaboratively on their own as well as on their colleagues’ teaching of mathematics. The teachers were selected purposely to participate in the study. Qualitative data were gathered using interviews, lesson plans, classroom observations and reflective writings. The findings indicated that whereas all the mathematics teachers reflected on-action verbally and in writing, three of the teachers reflected in-action while teaching. Based on lesson plan analysis, there was no evidence that these teachers reflected for-action. Two teachers reflected critically on their learners’ understanding of mathematics and their own teaching of concepts. Being a member of the lesson study group experience emerged as a contextual factor that seemed to influence these teachers’ reflections in a positive way. However, the teachers’ inadequate linguistic skills and inability to verbalise basic mathematical concepts properly seemed to influence their reflective practice negatively.http://www.satnt.ac.zaam2013gv201