Science and technology education

The purpose of this chapter is to discuss how the idea of a Pedagogy of Hope is perceived,
interpreted and realised at the Institute for Mathematics and Science Teaching of the
University of Stellenbosch (IMSTUS). First some background information is given about
the impact of the programmes which, it is argued, cannot be pinned to one Millennium
Development Goal (MDG) theme. The focus then shifts to how IMSTUS adopts a
pragmatic rather than theoretical interpretation of the University’s vision of a pedagogy
of hope by engaging in reflection-in-action to bring about redress in mathematics
and science education to historically disadvantaged learners. It is concluded that the
impact of the innovative interventions at the Institute turns despair into hope for learners
who would otherwise have had no opportunity to realize their hopes and dreams in
participating fully, as democratic citizens, in the socio-economic development of the
country.

My purpose in this paper is to situate a university-school mathematics and science
education partnership within a social justice perspective in education. The focus of
the systemic intervention endeavour was school-based teacher professional development
in which university-based facilitators embarked on class visits with the aim of
identifying teacher needs, co-teaching and offering professional support over a
three-year period. This was in contrast to evaluation (inspection visits) often undertaken
by the subject advisors under the auspices of the Department of Education
which, for historical reasons, tend to be viewed with suspicion by teachers and teacher
unions. Five historically disadvantaged secondary schools and their 10 feeder
primary schools were involved in this study with a view to providing equal opportunities
to learners from marginalized communities in the Cape Winelands
district of the Western Cape. Initial results suggest that an intervention programme
that is responsive to local needs can go a long way in bringing about collaborative
teacher professional development that leads to reflective practice in professional
learning communities and can add value to the quality of student achievement in the
gateway subjects of mathematics and science.
Keywords: disadvantaged schools; learning communities; mathematics and science
education; reflective practitioner; SMILES; social justice; teacher professional
development; university-school partnerships

The purpose of this study was to determine in-service students’ perceptions of the
effectiveness of the Advanced Certificate in Education (ACE) programme offered by
Stellenbosch University, South Africa, in preparing them to be confident teachers of
Mathematical Literacy, Life Sciences or Physical Sciences in the Further Education and
Training (FET) phase. An open-ended questionnaire was administered at the end of the
first year of the two-year mixed-mode part-time study. The university’s standard student
feedback questionnaire was administered during contact sessions. A Likert-type 5-point
scale version of the initial open-ended questionnaire was designed and administered to
the cohort after graduation. Findings were that there were process, content, contextual
and outcomes aspects of the programme which were consistently positive and needed to
be maintained. There were aspects that were initially perceived negatively or positively
but sentiment changed after graduation. There were also aspects that were consistently
perceived negatively and needed improvement.

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.

The role of proof in school geometry has been a subject of intense debate throughout the
twentieth century and that debate persists even today. This study aims to identify and
analyse deductive geometric proof difficulties encountered by Bachelor of Education
(BEd) in-service student teachers and to propose possible ways of remediating them.
The authors conducted a content analysis of responses to a circle geometry item in an
achievement test taken by 170 students. Although 78% of the students performed well
in the deductive proof item, 22% evidenced misunderstandings or misconceptions
which varied in complexity. The misconceptions were analysed into four categories
and implications for pedagogy proffered to turn the misconceptions into critical
teaching and learning opportunities.

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.

"The purpose of this paper is to critically analyse and discuss the views of constructivism, on the teaching and learning of mathematics. I provide a background to the learning of mathematics as constructing and reconstructing knowledge in the form of new conceptual networks; the nature, role and possibilities of constructivism as a learning theoretical framework in Mathematics Education. I look at the major criticisms and conclude that it passes the test of a learning theoretical framework but there is still a gap between theory and mathematics classroom practice.
KEY WORDS: constructivism, construction and reconstruction, radical/cognitive constructivism, social/realist constructivism, epistemological relativism, theoretical framework."

The purpose of this article is to report on a formative evaluation research study of a
university-school partnership for mathematics and science education within a community
engagement and social justice perspective in higher education in order to inform redesign
and replicability. The partnership involved the school-based systemic intervention
through teacher professional development in which university-based facilitators
embarked on class visits with the aim of identifying teacher needs, co-teaching and
offering professional support over a four-year period. This was in contrast to traditional
inspection visits which teachers and teacher unions are not comfortable with. Five
historically disadvantaged secondary schools and their ten feeder primary schools were
involved in this study with a view of providing equal opportunities to learners from
marginalized communities in the Stellenbosch region of the Western Cape. That the
schools were located in socio-economically disadvantaged communities added a social
justice perspective to the partnership goals. Initial results of the study suggest that an
intervention programme that is collaborative and responsive to local needs can achieve
greater impact if sufficiently funded and efficiently facilitated. Teachers can open up
to the change initiative and build self-reflective professional communities of practice
that enrich their practice and ultimately impact positively on learner achievement in the
gateway subjects of mathematics and science.

In this paper we discuss the pedagogical role that the dynamic mathematics properties of the Geometer's Sketchpad can play in modeling and simulating the derivative concept and related notions in introductory calculus. The paper suggests that in an approach of modeling and simulation experiences in Sketchpad students' concept images of the derivative can be enriched qualitatively by the multiple representations afforded and the connections made between them. In a study carried out by the first author (Ndlovy 2008) involving first year non-mathematics major undergraduate science students at a university in Zimbabwe, six forms of representation were identified. In this paper we describe the nature of these representations and possibilities of translating from one to the otehr. We further examine how the students' conceptual understanding of the derivative evolved fter going through a sequence of sketchpad model-eliciting activities within a hypothesised learning trajectory. The design of the learning trajectory was informed by the historical development of the derivative as synthesized from the literature on the history of the calculus. The models and modeling approach proposaed by Lesh and Doerr (2000) influenced the selection and sequencing of problems and test items to develop and to assess students' qualitative understanding of the derivative. Teh findings of the study suggested that, as a result of the students' experience with the Sketchpad acativities, there was a statistically significant improvement in the post-test scores, even in non-routine problems.

"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."

Background: South Africa is a developing country whose education system is experiencing a
transformation constrained by a legacy of apartheid. The latest TIMSS results confirm the uneven
distribution of achievement in mathematics and science. Chief among the problems is that there is a
dearth of suitably qualified and experienced teachers to teach the subjects effectively. Moreover the
many teachers are unfamiliar with learner-centred pedagogies espoused in the curriculum. Continuing
teach professional development (CPD) in subject matter knowledge (SMK) and learner-centred
pedagogical content knowledge (PCK) is acknowledged to be a viable solution. However, for it to be
relevant, CPD must be constantly informed by teacher needs and perceptions of self-efficacy.
Aims: This study sought to compile teachers’ reflections on the effectiveness or otherwise of their inservice
training and to seek feedback on how regularly they perceived themselves to be applying
learner-centred constructivist pedagogy in their mathematics and science classrooms. The research
questions which guided the study included: What were the teachers’ perceptions about their CPD
programme in relation to the relevance of the content to the curriculum and the pedagogical
approaches? To what extent did the teachers perceive themselves to be applying learner-centred
constructivist approaches in their classrooms at the commencement of the 3-year CPD programme?
Methodology: Eighty-nine teachers attending a CPD programme in early 2013 were asked to complete
reflection journals on a daily basis for the duration of a two-week contact session. The reflection
journals, as a participant-observer record of thinking critically and analytically about one’s learning
experiences constituted the qualitative data sources for this study. The same teachers completed a 5-
point Likert scale Constructivist Learning Environments Survey (CLES) questionnaire to evaluate the
frequency with which they perceived themselves to be implementing constructivist teaching and
learning approaches in their science and mathematics classrooms. The CLES results constituted a
quantitative data source making the study a mixed-methods approach.
Results of the Study: Teacher reflections on the suitability of their in-service showed an awareness of
the need for a paradigm shift in the way mathematics and science are taught. They appreciated the
usefulness of the workshop in enriching their SMK and PCK and showed a willingness to change their
teaching practices to emulate the learner-centred approaches modelled by CPD facilitators.
Questionnaire results showed that teachers perceived their learners to be only moderately interested
in learning mathematics and science (a mean of 3.47), to moderately experience their learning as
personally relevant to their out-of-school life (mean of 3.61) but showing a rather lacklustre interest in
taking responsibility for their own learning (a mean of 2.65). They further perceived themselves to be
offering high levels of support to learners (a mean of 4.31). A recommendation emanating from this
study is to extend the CLES survey to learners’ perspectives for a more complete picture.
Keywords: continuing professional development, pedagogical content knowledge, subject matter
knowledge, mathematics and science education, constructivist learning.

The purpose of this study was to compare students’ perceptions of their experiences of scientific
inquiry in science fair projects with their experiences of scientific inquiry in scientific investigations in
the classroom. A mixed-methods approach was used involving a questionnaire survey with closed and
open-ended items. A convenient sample of grades 7-12 learners from 34 Stellenbosch Region schools
in South Africa responded to an adapted Principles of Scientific Investigation (PSI-S) questionnaire
designed and validated by Campbell et al. The questionnaire sought to determine the extent to which
learners experienced science fair projects and classroom based scientific investigations to be
conforming to scientific inquiry principles. That is, the extent of open-endedness with respect to how
much information or direction was given to learners in a) the formulation of research questions, b) the
design of the investigation procedure c) the conduct of the investigation procedure, d) collection of
data and e) drawing of conclusions in the solution process. Bell et al’s four-levels of inquiry were used
to analyse the extent of open-endedness and teacher-directedness. Quantitative findings suggest that
the science fair project experience offered significantly greater opportunities for learners to experience
authentic scientific inquiry than classroom scientific investigations. Qualitative results suggest that
learners’ resourcefulness and quality out-of-school support played a pivotal role in science fair project
experience. However, neither the science fair nor the classroom offered perfect scientific inquiry. The
implications of the study are that since learners who participate in science fairs have an additional
opportunity to experience the true nature of science (NOS) science fair participation should be
decentralised to afford mass participation. Governments in developing countries should expand the
provision of school IT and science centre infrastructures to democratise Internet access and narrow
the gap between school and science fair experiences. In-service (and indeed pre-service) science
teacher education should be adequately resourced to support teachers in entrenching authentic
scientific inquiry in both in science classrooms and in science fair projects.
Keywords: Expo for Young Scientists, science fair, principles of scientific inquiry, practical work,
scientific investigations, creativity, out-of-school support.

This article reports on the qualitative aspects of a study that examined whether introducing a
Problem-based Learning (PBL) approach in a one-year foundation programme can create
conditions for learners to develop and sustain self-directed learning skills. This interpretiveconstructivist
case study was located in evaluation research. Data were collected by means of
classroom observations and interviews with 35 students and 14 former students. Findings
indicated that introducing students to a PBL approach did promote more meaningful learning
patterns, typified by processing the subject matter critically and self-regulating learning
processes. The sustainability of the meaning-directed learning skills was questionable if student
beliefs in the approach did not support the activities employed. Introducing PBL into a foundation
programme can develop self-directed learning skills in students and set in motion a
process of growth towards lifelong learning.

"Learners’ participation in science fairs has been encouraged for affording them experiences in
carrying out hands-on activities such as scientific investigations oriented towards inquiry science.
However, there has been some debate as to the viability of the Expo’s usefulness to ill-equipped
learners in disadvantaged schools as their cultural capital deficits appear to deny them opportunities
to compete on an even keel with learners from historically advantaged schools (where learners have
higher accumulations of all forms of capital) in South Africa. The purpose of this study was to
conduct an exploratory analysis of factors influencing student participation and success rate at 2010
Stellenbosch Regional Expo in South Africa’s annual science fair for learners – the Expo for Young
Scientists. Participation in the Expo is acknowledged to be one opportunity for learners to
experience the highest levels of scientific inquiry. The study was a quantitative analysis of a
convenient sample of 36 schools that participated in the Regional Expo in respect of variables such
as distance from the venue, school type (primary, intermediate, combined or high school) gender
equity, and poverty quintile categories. Findings were that only 5.1% of eligible schools in the
region participated and distance from the venue was a deterrent for many schools. Historically
advantaged schools in quintiles 4-5 (higher socio-economic status) did not only have a superior
participation rate as a measure of equity, but also had a higher success rate as a measure of the
quality of participation. However, not all schools in the so-called quintiles 4-5 category performed
well, suggesting that the neglect of scientific investigations or scientific inquiry could be more
pervasive than initially assumed. The study recommends democratisation of participation through
decentralisation, increased funding for infrastructure and logistics and increased technical support
for teachers in disadvantaged schools.
Keywords: Expo for Young Scientists, science fair, principles of scientific inquiry, scientific
investigations, the nature of science, cultural capital, school poverty quintile"

"The purpose of this paper is to illustrate some of the obstacles or theoretical-computational conflicts
that the integration of technology in the geometry classrooms can potentially bring. The question is
whether we have to accept Euclidean definitions as immutable or we have to revisit them. The
traditional school geometry quadrilateral, for example, is understood to be convex and many school
syllabi present examples of these without counter-examples of alternative interpretations of the
definitions. Monaghan stresses that there is a connection between the perception and description of a
given geometrical figure. By allowing the user to manipulate, experiment and conjecture with shapes
through the dragging and animation capabilities Dynamic Geometry Environments or DGEs have the
potential to influence the perception of geometrical figures in new ways that challenge the legitimacy
of some of the traditionally accepted geometrical definitions. For example, a quadrilateral with a reflex
angle (concave quad) perceptually appears to be a triangle to many learners. However learners
exposed to DGEs can readily perceive the shape as a quadrilateral they have previously constructed.
Similarly, a crossed quadrilateral may be perceived not to be a quadrilateral at all by many learners
until its vertices are dragged experimentally and discovered to fulfill all the properties of its convex
counterpart. Varignon’s theorem on the other hand is similarly upheld when two of a quadrilateral’s
sides are dragged to be co-linear surprisingly permitting us to re-define a triangle as a quad with two
collinear vertices in direct contravention of this forbidden Euclidean condition.
Keywords: dynamic geometry environments, technology, geometry, quadrilateral, varignon’s theorem."

"The subject of teacher knowledge has been a key issue in mathematics education reform and the
advent of information technology to the mathematics classroom does not make it less topical. The
purpose of this survey design study was to determine pre-service mathematics major teachers’
understanding of geometrical definitions and class inclusion using the van Hiele level model prior to
their entry into a voluntary series of workshops designed to introduce them to activities involving the
educational use of Geometer’s Sketchpad, a dynamic geometry software package for mathematics
teaching. Sixteen out of the twenty pre-service teachers who were selected to take part in the
workshop series took the baseline test which focused on the geometry of triangles and quadrilaterals
that was going to be dealt with in the induction programme. The study reported here is therefore part
of a larger study reported in [1]. The results for thesurveyshowed that participants had a higher van
Hiele level of understanding geometrical definitions than class inclusion. These results were surprising
for the same cohort and suggested that the levels in the van Hiele model were not as discrete or
autonomous as assumed by the model. Overall, however, the participants’ understanding of the
geometry of triangles and quadrilaterals was below expectations suggesting that even though the
participants had passed their General Certificate in Education (GCE) Ordinary level (approximately
Grade 11) mathematics examinations, they had regressed in their understanding of the geometry in
question. The recommendation is made that any efforts to reintroduce or consolidate Euclidean
geometry in the school curriculum must take into consideration that many teachers might need to be
supported comprehensively.
Keywords: Geometric thought levels, geometrical definitions, class inclusion, preservice teachers."

In this paper we analyse the effect of using the Moodle platform as a learning management system to
support a blended learning in-service course for secondary school mathematics teachers in South
Africa. First we describe briefly the background necessitating the in-service programme for maths
teachers and then sketch out the theoretical frameworks that informed the blended learning course
design. The views of 71 teachers who participated in the course were solicited using a questionnaire
to determine the extent to which the Moodle platform complemented the face-to-face contact sessions,
hard copy course material and Interactive Telematic Education (ITE) broadcast sessions which were
combined to come up with a unique blended learning model. The survey results indicated that
although the Moodle platform had some limitations it facilitated synchronous discussions on
designated days and asynchronous discussions between students and lecturers. Both the student-tostudent
and the lecturer-student interactions were of academic value and helped to reduce the barriers
of physical and temporal separations. A major limitation in the integration of Moodle was the limited
accessibility of the Internet to some of the learners. Some learners had to travel to gain access to the
internet at internet cafes, experienced very slow internet, or simply could not afford the exorbitant
costs or gave up participation. Recommendations are made for the improvement of the ICT
infrastructure and connectivity to schools and remote parts of the country, lowering of internet tariffs
and mobile gadget costs so that remotely located teachers can be reached and supported speedily by
university in-service programmes such as the ACE. Lessons learnt from this study can inform the
design of future programmes offered in blended learning format