Search

The purpose of this study was to investigate preservice teachers’ (PSTs') beliefs about their intentions to integrate information and communication technologies (ICTs) in their future mathematics classrooms. The main research objective was to examine the extent to which PSTs’ beliefs predicted their intentions to integrate ICTs in their classrooms. We adopted a sequential mixed-methods design in which a survey questionnaire was the main data collection method followed by focus group and individual interviews. 147 secondary mathematics PST majors at two South African universities responded to the questionnaire. We purposefully selected eighteen of the preservice teachers for individual and focus group interviews. Quantitative results partly affirmed usefulness beliefs as the strongest predictor of attitude, which in turn was the strongest predictor of intentions to integrate mathematics teaching and learning ICTs. Although survey data showed that the influence of superiors and peers had the strongest influence on subjective norms, interview data contrastingly revealed that learners’ needs and societal expectations in the digital age pressured PSTs more to shift their professional identities. While quantitative results showed that self-efficacy beliefs had the strongest influence on PSTs’ control on ICT integration, the most recurrent self-efficacy theme from interviews was PST’s plea for training in the use of ICT tools. A wide range of ICT tools were identified as applicable to mathematics classrooms. This signified varying conceptions of which ICT tools were appropriate for mathematics teaching and learning. A recommendation is that mathematics teaching and learning ICT’s should be integrated as early as possible in initial teacher education curricula.

The purpose of this mixed methods study was to investigate the effect of a graphing calculator (GC) intervention on Grade 11 learners’ achievement in quadratic inequality problem solving. The quantitative aspects of the study involved an experimental and control group design in which the experimental group received instruction using the GC activities and the control group was taught without using the GC. The qualitative aspects of the study involved script analysis and task-based interviews. We used three data collection instruments: a quadratic inequality problem solving test used both as a pre- and a post-test administered to both the experimental and the control group learners, a written task analysis protocol and a task-based interview schedule. The results of the dependent samples t-test confirmed a statistically significant improvement in the quadratic inequality problem solving achievement of the experimental group with a Cohen’s d effect size of 1.3. The dependent t-test results for the control group were also a statistically significant improvement but with a smaller Cohen’s d of 1.2. The results of the independent t-test indicated that the experimental group achievement was significantly higher than that of the control group with a Cohen’s d effect size of 0.79. Script analysis of selected learners’ post-test solutions also showed that learners in the experimental group employed more problem-solving strategies (at least three – symbolic, numeric and graphical). Interview results of purposively selected learners also affirmed that experimental group participants perceived the GC intervention to have prepared them more effectively for multiple solution strategies of the quadratic inequality problem tasks. The researchers recommend the integration of GCs in the teaching and learning of mathematics in general and quadratic inequalities in particular. However, more research is needed in the integration of the GC in high-stakes assessment.

The subject of teacher competencies has been a key issue in mathematics education reform as the quality of an education system is fundamentally defined by the quality of its teachers. The study reported in this article attempted to identify and analyse displayed preservice teacher competencies and challenges encountered in early experiences with a Sketchpad-mediated learning of geometry. The instrumental approach to technology integration in the classroom as articulated by Trouche, Artigue and others was used as an analytical framework together with the van Hiele theory of geometrical thought development. A qualitative research approach was used to investigate preservice teachers’ emerging competencies. Data were gathered through worksheet productions, lesson observations, open-ended questionnaires and an exit focus group interview. Twenty third-year mathematics major preservice teachers participated in workshop and microteaching sessions involving the use of the Geometer’s Sketchpad dynamic geometry software in the teaching and learning of the geometry of quadrilaterals. The competencies displayed by the participants were described in terms of the instrumental theory for technology use and the van Hiele theory for geometric thought development. The competency levels showed that the preservice teachers had difficulties with computer hardware and software usage and the associated classroom organisation and management initially but gradually improved and gained confidence. The participants’ own evaluations of their competencies affirmed that early experiences were unpleasant for many and barriers could be overcome by early exposure to computer environments. More computer resources need to be availed for a day-to-day integration to be sustainable.

The purpose of this article is to report on an investigation of the perceptions and performance of mathematics teachers in a teacher professional learning (TPL) programme based on realistic mathematics education (RME) principles, which included a topic on transformations, undertaken by the researcher. Forty-seven Senior Phase (Grade 7–9) teachers took part in the mixed-methods study in which they answered a questionnaire with both closed and open-ended items. Fifty teachers took an achievement test at the end of the programme. The TPL programme used the RME approach in the design and delivery of mathematical tasks intended to enhance teachers’ mathematical knowledge for teaching. The sessions were conducted in a manner that modelled one way in which RME principles can be adopted as a teacher professional development strategy. The significance of the study is that continuing TPL is acknowledged to contribute to improvement in teaching and learning to address the concern about unsatisfactory learner achievement in mathematics. The responses suggested that the majority of teachers experienced the sessions positively in relation to all but one of the six RME principles. The teachers reported that they took an active part both as individuals and in small groups and expressed their willingness to adopt the type of activities and materials for their classrooms, which is an essential first step in Guskey’s first level of evaluation of a teacher TPL programme. The teachers’ average performance in an achievement test at the end of the topic was 72% which was indicative of modest learning gains at Guskey’s second level of TPL effectiveness.

South Africa’s performance in international benchmark tests is a major cause for concern amongst educators and policymakers, raising questions about the effectiveness of the curriculum reform efforts of the democratic era. The purpose of the study reported in this article was to investigate the degree of alignment between the TIMSS 2003 Grade 8 Mathematics assessment frameworks and the Revised National Curriculum Statements (RNCS) assessment standards for Grade 8 Mathematics, later revised to become the Curriculum and Assessment Policy Statements (CAPS). Such an investigation could help to partly shed light on why South African learners do not perform well and point out discrepancies that need to be attended to. The methodology of document analysis was adopted for the study, with the RNCS and the TIMSS 2003 Grade 8 Mathematics frameworks forming the principal documents. Porter’s moderately complex index of alignment was adopted for its simplicity. The computed index of 0.751 for the alignment between the RNCS assessment standards and the TIMSS assessment objectives was found to be significantly statistically low, at the alpha level of 0.05, according to Fulmer’s critical values for 20 cells and 90 or 120 standard points. The study suggests that inadequate attention has been paid to the alignment of the South African mathematics curriculum to the successive TIMSS assessment frameworks in terms of the cognitive level descriptions. The study recommends that participation in TIMSS should rigorously and critically inform ongoing curriculum reform efforts.

Encouragement to integrate information and communication technologies into mathematics education curricula is an increasingly universal phenomenon. As a contribution to the discourse, this article discusses the potential use in the classroom of The Geometer’s Sketchpad® (Key Curriculum Press, Emeryville, CA, United States) mathematics software in modelling the derivative and related concepts in introductory calculus. In an empirical study involving first-year non-mathematics major undergraduate science students, a hypothetical learning trajectory (HLT) was conjectured and implemented for students to experience the visualisation and multiple representations of calculus concepts on the Cartesian plane with a computer graphic interface. The utilisation scheme is interpreted through the lens of the instrumental1 approach proposed by Trouche. The HLT was partly informed by the historical development of the derivative as synthesised from the literature on the history of calculus and partly by the affordances, enablements, constraints and potentialities of Sketchpad itself. The findings of the study suggest that when exposed to the capabilities of this software, learners can experience Geometer’s Sketchpad® as an effective visualisation tool or instrument for the representation and learning of the derivative and related concepts in introductory calculus. However, the effectiveness of this tool is not a given or a foregone conclusion − it is a product of the teacher’s instrumental orchestration, gradual learner mastery of the software syntax and careful resolution of theoretical-computational conflicts that can arise during early use of the instrument.