zenexfoundation.org.zazenexfoundation.org.za/images/stories/Zenex_Foundation... · Web view2016-07-13 · There is a plethora of mathematics related interventions in South Africa

Zenex Foundation Landscape Review of

Mathematics Interventions in South African Schools

Nicky Roberts, Ingrid Mostert and Thulelah Takane

Kelello Consulting

April 2016

SUMMARY

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Zenex Foundation Landscape Review of Mathematics Interventions in South African Schools [1]

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Contents

1.Introduction..................................................................................................2.Methodology.................................................................................................3.Findings........................................................................................................

3.1 Frameworks for describing interventions and their theories of change................................................4

3.2 Government strategy in mathematics in South African schools..............................................................7

3.3 Summary of interventions in mathematics in South African schools.................................................11

3.4 Lessons emerging relating to mathematics interventions in South African schools........................16

3.5 Expert opinion on priority investments for mathematics interventions in South African schools. .21

4.Emerging recommendations.....................................................................5.Concluding remarks..................................................................................

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1. Introduction

This landscape review is intended to inform the design of the new Zenex Mathematics Programme. The proposed programme is aimed at interventions that support Maths education (teaching and learning) in the Senior Phase (Grades 7 – 9). However, as the Zenex team was not certain that selection of the Senior Phase was most appropriate, they commissioned a landscape review to guide the development of a programme and the selection of a phase, as well as to make recommendations regarding areas of need in the mathematics terrain. Zenex Foundation wanted to make sure that, before investing in any new mathematics intervention, the landscape of existing mathematics education interventions in South Africa was understood. Therefore, expert opinion on areas of greatest need in terms of phases and project inputs was sought.

There is a plethora of mathematics related interventions in South Africa which share a common ‘hoped for’ output of improving school-level mathematics teaching and learning. This landscape review however did not set out to document all interventions but rather to capture major and larger scale initiatives. It therefore sought to document the main interventions which have a scale of at least ten schools or a district wide reach. Where small-scale interventions (at one or two schools) were brought to bear through expert input, or because they figured in the literature, these were also included. The review was undertaken with the chief aim of collecting evidence about mathematics intervention programmes in South Africa. Consideration was given to:

● The phase (Foundation, Intermediate, Senior Phase, FET) targeted in the intervention;● The scale and geographic reach of interventions;● The beneficiaries of the intervention (learners, parents, teachers, district officials);● The lessons learnt from the interventions; ● The approach to or focus on the Mathematics which features in their professional

development/ teacher support options; and● Explicit or implied theories of change underpinning the intervention.

Various interventions offered particular input variables in different combinations, and the review of the interventions reports on the presence or absence of the following kinds of intervention inputs:

1. Resources inputs: What kinds of teaching and learning materials are provided through the intervention for supporting mathematics teaching and learning, with a particular focus on Open Educational Resources?

2. Teacher development and/or support inputs: There are various pre-service and post-graduate training offerings being provided by universities. What are teacher development and/or teacher support offerings which are being integrated into the mathematics interventions?

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3. Learner-focused inputs: Which initiatives work directly with learners relating to mathematics learning, and what kinds of in-school and out-of-school offerings are provided?

4. Parent and community inputs: The extent to which interventions engage parents and communities as part of their intervention inputs was sought. Where particular examples of this kind of intervention can be found they will be described in some detail.

2. Methodology

The landscape review was undertaken as desk research study where there were several phases of enquiry and data collection:

Firstly, we reviewed existing reports and documentation relating to mathematics interventions in South African schools.

Secondly we reviewed government plans, progress reports and mathematics related strategies.

Thirdly, to ensure that we had a wide selection of types of mathematics interventions in South African schools, we also compiled lists of registered training providers offering mathematics related courses for educators and lists of the accredited courses.

Using the above sources to draw on the interventions cited in the literature, and from the review of project documentation, a list of experts engaged in mathematics education interventions in schools was compiled. Draft project snapshots were developed from available grey literature and circulated to the expert (frequently the programme manager) for their review. The experts were also requested to complete additional information in the project snapshots and requested to respond to a few questions relating to their opinions on priority investments for Zenex Foundation. There are three main sections to the project snapshot descriptions: intervention focus and reach; project inputs; and theoretical basis, evaluations and intervention learnings.

Using the project snapshots an overall summary of the South African landscape in relation to mathematics intervention programmes at school level was developed. Finally, the expert network was consulted to provide their opinions on national priorities for mathematics education, which were intended to guide the Zenex Foundation planning process. A draft report was developed and circulated back to the expert network for their comment and review.

3. Findings

3.1 Frameworks for describing interventions and their theories of changeVarious frameworks for considering factors that influence learning outcomes were found through the review of literature and the project snapshots: The Zenex implementation framework; Taylor 2007; Hattie 2012 meta evaluation of effect sizes; the WCED 2015 mathematics strategy, and a conceptual framework relating to mathematical proficiency (Kilpatrick 2015) which was used by

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several experts in their descriptions of how they approached mathematics in their interventions. The Kilpatrick five-strands of mathematical proficiency were used to describe approaches and relative weighting of desired changes in relation to mathematics by several of the experts. For this executive summary we provide a synopsis of how each source was mapped against the Zenex implementation framework:

Figure 1: Mappings of factors influencing learning outcomes against implementation framework target groups

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3.1.1 Which phase is most suitable for interventions?

There is a strong research and evidence-based rationale for intervention to be in Foundation Phase. Besharati (2015) conducted a meta-evaluation of 15 years of school interventions in South Africa, and found that the school phase is statistically and substantially significant in predicting the impact of the interventions. The lower the phase in which the intervention occurs the higher the impact. This is consistent also with the general child development literature and some of the international meta-analytical work done in education (Hill et al, 2008, Bloom et al, 2008, Lipsey et al, 2012).

This aligns with the Hattie (2011) finding that prior cognitive ability has a significant effect size, which suggests the need for early intervention to ensure that learners have the cognitive foundations on which future learning can build. For example, one of the conclusions of the van der Berg (2008) study was that policy interventions are required earlier rather than later in the education process.

3.1.2 Does the introduction of LTSMs make a difference?

Besharati (2015) conducted a meta-evaluation of 15 years of school interventions in South Africa, and found that contrary to popular belief and too much of the international education impact evaluations (Hanushek, 2002, Kremer, Brannen & Glennerster, 2013, Glewwe et al, 2007), evidence from South Africa demonstrates that simple provision of effective learning and teaching material (see for instance Scholar, 2013, Taylor, 2013, Botes & Mji, 2010) can yield similar impact on learning outcomes as the more complex and expensive whole school development programmes (Mouton et al, 2014, Bloch, 2009), (Besharati and Tsotsotso 2015). However, it is important to note that access to Learning and Teaching Support Materials (LTSM) seems to have a greater impact on reading that it does on mathematics, with accessing to reading textbooks being a higher priority than access to mathematic textbooks. Van der Berg (2008) found that socio-economic differentials play a major role in education outcomes, but showed that more resources did not necessarily (or without qualification) improve school performance. He therefore argues that resources mattered only conditionally. This is supported by the findings of Slavin and Lake’s (2008) (cited in Fleish et al. (2011)). This places the role of the district and higher levels as well as the school in ensuring adequate provision of learning materials; but also makes clear the centrality of instructional leadership (from the school management team, as supported by the district) which places the focus squarely back on teachers and their use of the learning materials in the classroom, as the central role players in the improvement of learning attainment. In addition, homework frequency is also identified as a potential intervention with the argument appealing to the cost-effective nature of such an intervention.

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3.1.3 What of teachers their knowledge and skills?

Almost all of the expert’s place emphasis on the subject matter knowledge and pedagogic content knowledge of teacher. The centrality of the teacher and the instructional leadership support from their school principals (or school management team) is therefore a critical factor. It is people and changes in people’s attitudes, beliefs, knowledge and behaviour which are necessary for impact on learning attainment.

3.1.4 Are there any common ways of describing mathematical profiency?

Kilpatrick, Swafford et al’s (2001) five strands of mathematical proficiency were invoked in the Olico theory of change and were also referenced by two oh the other expert respondents. As these strands of mathematical proficiency have emerged from different projects in this landscape review, and as they offer a finer grained detail on what is meant by mathematics which then has implications for how people development, reflection, resourcing and productive pedagogy for mathematics, we elaborate on each strand briefly:

1. Conceptual understanding refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] to learn new ideas by connecting those ideas to what they already know.” A few of the benefits of building conceptual understanding are that it supports retention, and prevents common errors.

2. Procedural fluency is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

3. Strategic competence is the ability to formulate, represent, and solve mathematical problems.

4. Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification.

5. Productive disposition is the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

The five strands are mutually supportive and interconnected (hence the metaphor of strands in a rope). Yet different mathematics interventions place different emphasis on particular strands, and focusing on these different levels of emphasis in relation to an approach to mathematics teaching and learning can be informative. As such we use these fives strands to classify some of the respondents articulated approach to mathematics. This provides an addition level of detail for reflecting on the emphasis places on particular strands of mathematical proficiency which emerged from the projects in the South African landscape review.

3.2 Government strategy in mathematics in South African schoolsIn this section we provide a synopsis of the government strategy and related government-lead interventions for mathematics in South African schools.

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The national department of education is aware of the poor performance relating to mathematics which is evident across the levels in the schooling system. (National Planning Commission 2011) ((NEEDU) 2014)

The NPC diagnostic report further demonstrates South Africa’s awareness of the factors contributing to the problems within the education system:

Research evidence highlights the significance of factors or problems within the education system itself. These include the ongoing changes and amendments to curricula, the type of teacher training, inadequate support to teachers, teaching time compared to other activities and the availability of learning and teaching materials such as text books. Several other complex issues play a role in the quality of education. Curriculum design; language issues; the use of technology; the efficacy of the bureaucracy; the balance of power between parents, schools and the bureaucracy; and high levels of violence against women and children are all relevant factors. Without dismissing any of these factors, our conclusion is that the main problems lie in teacher performance and the quality of school leadership. (National Planning Commission 2011)

It is important to note that the main problems are thought to lie in teacher performance and quality of school leadership (people).

3.2.1 National DBE Initiatives

There have been several interventions from the national department level which support the priority goals outlined in the Action Plan to 2019. These include the following:

1. The extension of public education to include a compulsory Grade R year attached to public primary schools. The Grade R year includes a formal curriculum for mathematics.

2. The provision of quality learning and teaching material for every learner 3. Initiative pertaining to initial teacher education and continuing professional development

of educators. 4. The introduction of standardised assessments. 5. Ongoing investments in 500 Dinaledi high schools which focus on mathematics and

science.

We have mapped these governments lead interventions in relation to mathematics education to the dimensions and elements of the WCED mathematics strategy to give a visual depiction of the various elements.

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Figure 2: Mapping national government interventions to elements of WCED strategy

3.2.2 Provincial Initiatives

Provincial Education Departments (PDEs) are tasked with implementing the policies and strategies developed by the DBE. Two notable examples of such strategies are

● the National Strategy for Learner Attainment Framework (NSLA) which a comprehensive transversal strategy to coordinate provincial improvement plans and steer them towards the optimal performance of all learners, and

● the Integrated National Literacy and Numeracy Strategy (INLNS) which aims to integrate all the provincial initiatives pertaining to numeracy and literacy.

In this section initiatives driven by these two strategies are reported on. Annually PDEs produce Learner Attainment Improvement Strategies (LAIS) or Provincial Strategy of Learner Attainment (PSLA), which are aligned with the provincial and national vision for It is against these plans that the province reports on its progress, and budget allocations are made for each district and the related provincial activities for the year. These plans commonly include mathematics as a priority subject, and various interventions are outlined. Schools in the province are categorised

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depending on their historic performance, and targeted interventions for different types of schools are then implemented. The interventions range from the development of individual Schools Improvement Plans (SIPS) or Academic Performance Improvement Plans (APIP) to teacher development and support initiatives’; from improving access to high quality learning and teaching support materials (LTSMs) to direct learner support and the tracking of learner progress. Learner attainment interventions from a selection of provinces are reported on below.

The Integrated National Literacy and Numeracy Strategy (INLNS) appears to be stimulating and directing provincial activity (NEEDU, 2013). A number of provinces (Gauteng, KZN, WC, FS and Mpumalanga) have developed and implemented Literacy and Numeracy Strategies (LNSs). We reported on the

1. Eastern Cape Learner Attainment Improvement Strategy2. Western Cape Lit/Num Strategy and Telematics project3. Gauteng Primary Language and Mathematics Strategy4. Free State Provincial Strategy of Learner Attainment

GPLMS programme, the Eastern Cape LAIS and the Free State

Figure 3: Mapping provincial government interventions to the elements of the WCED mathematics strategy

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While our review of LAIS and LNS documents has been partial, it seems that such plans are important drivers of the discretionary funding which provinces have to support the schooling system, through the work of district subject advisors, and making use of teacher resource centres. While some provinces monitor and evaluate the impact of their particular interventions; for other provinces no such monitoring or evaluation is apparent. Based on the partial information we were able to obtain from each province (and the difficulties we had in accessing such information for all provinces) it is clear that the provincial implementation of mathematics strategies differs widely from one province to the next. There does not appear to be a common theory of change of priority investments in relation to mathematics improvement to which provinces must adhere.

3.3 Summary of interventions in mathematics in South African schoolsThrough this landscape review we consulted a network of experts and obtained verified project descriptions from approximately 50 interventions in South African schools. Projects that we described from secondary sources, but that were not expert verified were classified as ‘unverified projects’ and excluded from the data analysis. We nevertheless included these descriptions from secondary sources in Annexure 5.

3.3.1 Project inputs (The intervention modes and target groups)

While the initial expectation was to classify projects accordingly to Component 2: The intervention modes in the Zenex intervention design framework, it was acknowledged that each project was likely to include several complementary elements of programme theory. This was confirmed in the responses from project experts as each project indicated that it had multiple project inputs.

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Figure 4: Verified project descriptions showing spread of project inputs (n=47)

Project nameResource

inputs

Teacher training

/ develop

ment inputs

School management / school functionality inputs

Assessment

inputs

Learner-focused inputs

Targeted

remediation

Parent/ commu

nity inputs

Total 45 43 20 37 40 20 23

There is considerable investment in resources (with 45 projects indicating resource inputs) and in people development (teacher and school management development inputs). Most projects include both resource inputs and teacher development, and only three projects couple resource inputs with learner-focused inputs. There is a relatively even spread of teacher training / professional development inputs (43 projects) and learner-focused inputs (40 projects). This is likely a result of engagement with teachers including expectations that the work with teachers would impact on learner attainment. All of the projects that referred to school management / school functionality inputs couple these with teacher training and professional development inputs. Most projects offer a cluster of project inputs which cohere in relation to their particular project aims. There are fewer projects which include targeted remediation, or parent/community inputs (although several projects have these as part of the cluster of project inputs).

3.3.2 Geographic spread

The projects included in this landscape review revealed that while the majority of projects have a national reach, there are far more projects in Gauteng and the Western Cape compared to the other provinces.

Figure 5: Verified project descriptions showing geographic spread of projects (n=47)

National GP EC FS KZN L NC NW MP WC

18 15 7 4 10 3 2 3 3 18

3.3.3 Phases and schools

The data from the verified project snapshots revealed that there are more projects at high school level than there are at primary school level participating in this landscape review:

Figure 6: Verified project descriptions showing spread of targeted phases (n=47)

Foundation Intermediate Senior FET13


Phase Phase Phase18 16 29 28

Several projects work across phases with the most common grouping of phases reflecting the primary-secondary school divide (with projects working on Foundation phase and Intermediate phase; or on Senior Phase and FET level). More information about the type of schools targeted was obtained from the expert respondents’ selection of the types of schools targeted by their intervention.

Figure 7: Verified project descriptions showing spread of targeted schools (n=46)

Primary schools

Combined schools

Secondary schools

Urban schools

Small town schools

Rural schools

Underperforming schools

High performing schools

21 6 30 23 15 17 16 7

This landscape review included projects where there were more interventions targeting secondary schools than primary schools, fewer interventions in rural schools compared to urban schools; and a greater focus on underperforming than on high performing schools.

3.3.4 Theoretical frameworks

The experts were asked to describe their explicit or articulated approach to mathematics within their project. They were also asked to describe their theory of change. There were several overlaps in how experts explained their approach to their programmes in response to these questions. We therefore considered their response to these two questions together, and separated the responses as follows:

● Theories of change related to an underlying theoretical rationale for the choice of project inputs to attain their envisaged outputs (this was at the macro level of project design; and used to inform the overall intervention design);

● Approaches to mathematics related to underlying theoretical rationales for focuses on particular aspects or approaches to mathematics learning and teaching (this was at the micro design level and specific to the treatment of mathematics).

The overall approach to theories of change relating to mathematics interventions in South African schools sees experts appealing to the importance of quality passes in Science, Technology, Engineering and Mathematics (STEM) subjects for access into higher education and into STEM related careers.

For some experts their approach to mathematics is defined in relation to the national curriculum statements or standards for mathematics. In these cases, their approach is defined by the

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Curriculum and Assessment Policy Standard (CAPS). It is notable that ideas of ‘number sense’ and ‘flexibly working with numbers and number relationships’ was a common refrain across expert respondents. In the Foundation Phase counting, number sense and flexibility were thought to be the necessary mathematical focus (with far less mention and attention to geometry, measurement and data handling, for example). References to number sense in Intermediate phase were also commonly made in response to a variety of questions in the questionnaire. By the Senior Phase the lament was that the absence of ‘number sense’ (amongst teachers and learners), was a significant hindrance to the transition from arithmetic to algebra which is required at Senior Phase.

A few of the expert respondents described their theory of change in terms of holistic chain of instructional leadership support from district, to school management to teachers and to learners themselves. While these experts mentioned teachers as important points of intervention; their engagement with teachers was considered alongside engagement with instructional leadership support from the district and School Management Teams (SMTs) and extended to the changing expectations of learners from passive recipients of teaching; to learners being active participants in their own learning

For some experts’ the starting point of their interventions is the teacher; while for others the starting point is the learner. This reflects a global contrast between mathematics educators who approach mathematics from a primarily pedagogic perspective and those who approach mathematics from a primarily cognitive perspective. It is important to recognise that both approaches are considered in the South African landscape – although there are far more projects and experts approaching mathematics pedagogically, than there are those who adopt a cognitive perspective.

3.3.5 Focusing on teachers: Mathematical knowledge for teaching (SMK, PCK and MDI)

For the majority of expert respondents, the primary theory of change was to focus on supporting and developing teachers. This reflects a belief that the most strategic investment is focusing on teachers, with a particular focus on their knowledge of mathematics for teaching (which encompasses their subject matter knowledge (SMK) and their pedagogical content knowledge (PCK)).

Several experts referred to the importance of addressing both theory and practice; and there was clear advocacy for the use of professional learning communities which included on-site supports, mentoring and coaching for teachers in their professional work space (the classroom) as a promising mechanism for providing such professional development support.

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Reflecting across the respondents who focus on teacher development, the five strands of mathematical proficiency are necessary but not sufficient. There are particular proficiencies which are specific to teaching mathematics which go beyond the mathematical proficiency defined for learning of mathematics. These include reflective practice; pedagogical content knowledge and what is being termed by colleagues at the University of Witwatersrand as ‘mathematics for teaching’ (where mathematical discourse for instruction is considered).

For those focusing on pedagogy the emphasis tends to be placed on supporting the development of subject matter knowledge (SMK) and pedagogical content knowledge (PCK) for mathematics. Commonly this includes approaches to extending teachers’ content knowledge and modelling or developing pedagogical approaches for mathematics teaching. A number of experts referred to the use of formative and diagnostic assessment data from learners as a key mean in which to engage teachers on areas requiring their pedagogic intervention.

3.3.6 Focusing on learners

In contrast to the above approaches which have a pedagogic focus, the academic experts who approach their interventions with the child as the starting point, appealed to theories of cognitive development and neuroscience; or to the practice and feedback possible when making use of ICTs.

The respondents reporting on the use of ICT-based interventions commonly appealed to a theory of change which put learner agency and learner ability to utilise independent study time out of school time at the centre.

3.3.7 Focusing on research, needs analyses and evidence-based interventions

Finally, there were a few theories of change which put research, data and identified needs at the core of their interventions. Rather than having a set intervention; these experts refer to a first step of a process which involves investing in research to define and then respond to needs

When asked explicitly about their approach to mathematics, the most common response – and cutting across both the focuses on teachers and on learners - was related to conceptual understanding (strand 1). Most respondents appealed to actively constructing meaning as their explicit approach to mathematics. Such approaches draw on constructivist theories of learning mathematics with the active involvement of learners in making sense of mathematics ideas is in focus. Some of the experts explicitly mentioned the model adopted and appeal to particular technologies to support their approach (blended learning or technology-based approaches)

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Procedural fluency (strand 2) was also used as basis for describing approaches to mathematics. This seems to be a particular motivation for the ICT interventions, where access to mathematics questions which provide immediate feedback on learner’s solutions is cited as a major theoretical rationale for using ICTs. Similar points were made above relating to more macro considerations of programme designs using ICTs. This appears to be a particularly strong rationale for ICT use in the subject domain of mathematics where a single correct solution is anticipated.

Other respondents emphasised the strategic competence (strand 3) where many expert respondents made mention of problem solving being at the heart of mathematics.

Related to the above, is a broader focus on reasoning, problem solving and meta-cognition or awareness. Closely related to mathematical problem solving was mathematical reasoning and thinking which is more related to the adaptive reasoning (strand 4) strand of mathematical proficiency.

The final strand of mathematical proficiency (strand 5: mathematical dispositions) was the focus for a few of the expert respondents in their interventions. In this regard the dispositions of both teachers and learners were highlighted.

The above provides a sense of the current South African landscape with regard to the articulated or explicit approaches to mathematics. As would be expected there are different ways of approaching the mathematics – and that these do not necessarily suggest conflicting approaches. However, the theoretical framing of the approach to mathematics, guides the kinds of interventions and those elements which they focus on (through the intervention and the research questions considered).

3.4 Lessons emerging relating to mathematics interventions in South African schools

We are starting to get more documentation of general lessons for development projects in schools, and districts (for example the NECT report provides lessons on intervention areas, systemic impact, going to scale, sustainability, monitoring and evaluation, collaboration and cost effectiveness). These lessons apply to different levels of the education system (in relation to the target levels in the intervention design framework). We list generic lessons and then follow these with lessons which are particular to mathematics interventions.

3.4.1 General lessons

In this section we present lessons that are relevant to school improvement initiatives in general. This is comprised of a consolidation of the lessons emerging from the review of secondary

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sources, as well as the lessons offered by the expert network in response to the questionnaire. In the case of the latter, we have included the source of the lesson by indicating the project name in brackets following the lesson.

Planning and programme design issues

1. Plans require appropriate detail, realistic timeframes and clarity in terms of allocation and responsibility and interventions need to be comprehensive (in terms of the services and inputs offered) and targeted (in terms of selecting schools and priority subjects appropriately).

2. Interventions need to be given time – as change is not easy is takes sustained investment and focus

3. Communication, consistent project reporting /data collection and responding to this feedback through the involvement of all stakeholders in the project design and implementation are valued

4. Project leadership and collaboration between partner organisations are considered key to programme success

5. Monitoring evaluation and research are key aspects of programme design and are necessary from the project conception stage. A coherent research, monitoring and evaluation component is required.

Provincial level lessons

6. The province is critical for the conceptualisation, coherence, alignment, monitoring, evaluation and accountability of Learner Attainment improvement plans and for high level political commitment to intervention.

7. There is some concern that provincial level reporting does not allow for sufficient detail to identify schools, and appropriate interventions:

8. Staff vacancies, insufficient staffing and lack of permanent positions impact negatively on intervention attempts.

9. The project intervention progress should be regularly reported on using standardised reports to appropriate management structures. The project progress reports need to be analysed to inform future action and to ensure accountability.

10. Lower grades and primary schools should not be neglected.

District level lessons

11. Districts play a key role in supporting the school management, getting schools functional, and providing instructional leadership for teachers through curriculum advisors.

12. The school-based mentoring needed to support change in teaching practice requires adequate staffing of curriculum advisors at district level.

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13. Prioritise district level accountability, where district roles include school cluster management as well as instructional leadership which supports extended reading and writing in English (over oral English).

14. The key to improved learner performance lies in improved district functionality (with respect to support of higher expectations of schools and school management and the development of a school development plan).

School level lessons

15. The culture and basic functioning of a school are critical to the interventions success. Working in dysfunctional schools is waste of time and money.

16. This implies working with the school principal and school management teams to attend to time management. The entry point to the schools much be the school management; preferably the principal. Organisation must start from the school, with clearly defined roles.

17. Instructional leadership is required to support curriculum coverage, to ensure higher cognitive demand, and more specialised and less oral work with extended writing and problem solving tasks.

18. There need to be quality learning and teaching materials (LTSMs) in place and in use daily in classrooms. ICT infrastructure and resources can improve access to quality teaching and learning materials.

19. When working with a targeted school there is a need to engage the parents and surrounding community and ensure their support and commitment.

20. Schools are about people and so ‘people development’ needs to be at the core of interventions

Teacher level lessons

21. The documents all agree that teachers are the centre of any learning attainment improvement intervention. The priority investment should be in on-going professional development and school-based mentoring for teachers.

22. More recent studies refer to the assessment or testing of teachers in terms of their subject matter knowledge.

23. There are lessons emerging relating to the type of training and support given to teachers:

a. Ensure that the type of training or support meets the requirements and features of the target phase of the intervention

b. Offer accredited training towards improved qualifications. However, anticipate that will not necessarily be supported by teachers as ‘Workshops work better than short courses because teachers do not want to do assignments. However, certificated courses (ACT) yield the best results.’ (Grasslow Park)

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c. Offer subject-specific training in content or methodology, linked to core teaching practices

d. The timing of contact time with teachers has been raised as a challenge. e. Some projects offer highly structured and tightly scripted programmes which

emphasize curriculum coverage and are supported by good materials and resources.

f. Offer human resources support in the form of additional teachers (either to reduce class size or for team teaching) or in the form of a mentoring programme.

g. Set up Professional Learning Communities.

24. Teacher training and developing is not a once-off event but requires on-going reflection, feedback and on-site support of follow up:

25. There are several lessons relating to the selection of teachers in teacher development initiatives:

a. Include teachers and principals of participating schools in the initial stages of designing the project.

b. Select all teachers in a particular phase and subject area in a school.c. Select one teacher per school in a circuit or district.d. Ask for voluntary participation in an intervention.e. Be aware that it is not always possible to predetermine selection criteria for

teachers on a project, as the department may select teachers for the project. In this case, plan to (i) understand your target audience; and (ii) put some effort into ‘selling’ the intervention to the beneficiaries. (NECT (2015) Example Guidelines for Social Investors)

26. Profiling teachers and tracking their development over time is encouraged27. In relation to duration and dosage of training interventions the following lessons have

been documented:a. Teachers need sustained and regular engagement over a period of time in order

to internalise new knowledge and practices. b. An intervention should be sufficiently long to allow for meaningful change in

behaviour and in application to take place.c. Where possible, hold training workshops on site or in the area.d. Don’t overload individual training sessions with too much content.e. Always record attendance.f. Build in some kind of accountability, reflection process and record keeping for

participating teachers.28. Teachers expect incentives for participating in professional development option

3.4.2 Lessons that are particular to mathematics interventions

For this landscape review we are interested in the lessons that are specific to mathematics interventions. We organise these lessons in relation to the primary object which was in focus for mathematics interventions: mathematical knowledge for teaching (which includes SMK and

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PCK); building and supporting long term professional learning communities as a mechanism for engaging with teachers to improve their knowledge together with considerations relating to teacher and learner dispositions towards mathematics.

Mathematical knowledge for teaching (MKfT)

The discussion relating to general lessons has identified the central position of teachers in the mathematics education landscape, which is reflected in the government documentation in terms of both the NPC diagnostic reports and related national and provincial strategies. This builds on general lessons which stress that teacher development interventions should integrate theory and practice; should be long term and accredited. The mathematical components of this lesson pertain to the priority components of how subject matter knowledge and pedagogical content knowledge for mathematics are conceptualised.

Mathematics requires that teachers learn – or re-learn new ways of viewing – the mathematics which they teach. This seems to be something which is particularly acute in the subject of mathematics and which takes time.

This learning and re-learning of mathematics requires the accurate diagnosis of areas of particular weakness, with professional development intervention specifically designed to consider the mathematics in terms of what is required for the effective teaching of the identified concept. The need to strengthen teachers own problem solving and reasoning abilities cuts across the mathematics levels. However, there is a broad separation between the subject matter knowledge needs of primary and secondary teachers. While primary teachers require a basic number sense; secondary teachers require knowledge on how to remediate the absence of number sense when trying to induct learners into algebraic reasoning.

The main emphasis seemed to be on a shift away from procedures and facts driving calculations, towards the underlying problem solving and mathematics reasoning/thinking.

In contrast, there were several experts who identified particular mathematics topics which are areas of difficulty for teachers at the FET level.

Whatever level of mathematics is in focus – it is clear that mathematics is central to the teacher development: the mathematics content itself; ways of teaching this mathematics; as well as knowledge of children’s understanding of this mathematics.

Feedback and assessment for learning (and teaching)

Like the lessons on learning dispositions, the lesson pertaining to feedback – and particularly the use of assessment in mathematics – related to both teachers and learners. There were clear

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arguments relating to lessons in the value of effectively utilising assessment data (from both teacher and learner assessments) to inform the professional development offerings. This also related to the broader project design need to research and reflect on intervention impact, where regular assessment of both teachers (in relation to KfMT) and learners progress in relation to the mathematics were valued

In relation to learner assessments, there was general acknowledgement of the systemically poor attainment of learners in relation to grade-level expectations of the CAPS. The lesson in this regard pertains to the importance of differentiated assessments and learning materials which consider the mathematical developmental trajectories for learners (in relation to particular mathematics topics). There were several lessons relating to the need for diagnostic assessments which would allow identification and remediation of conceptual gaps in the learners’ mathematics. This has implications for the KfMT which teachers require, as teacher awareness of these trajectories and related assessments and materials become necessary.

Models of professional development engagement with teachers

The expert network also provided lessons relating how professional development programmes for mathematics teachers could be approached. There was also reference to ways in which in-service teachers can be incentivised and persuaded to participate in long term (year-long or more) programmes, with some opportunity created for working with teachers and learners together: Another project which has also managed to engage teachers in long-term interventions cautions about the adoption of ‘superficial compliance’ amongst teachers as key lesson emerging. The need for sound mathematical knowledge and a clear notion of mathematical progression (in developmental - and not necessarily grade related - terms) was echoed by other experts engaging with teacher development for mathematics teaching. One of the promising mechanisms for promoting interaction between teachers, through the notion of “Professional Learning Communities (PLCs) as a way of helping teachers upgrade their knowledge and share working practice has gained traction” (NECT, 2015). The idea of using strong mentoring and making use of geographic clusters for the mathematics learning communities, where both theoretical conceptual development is supported through in-school mentoring and reflection emerged in the lessons put forward by the expert network. The DIPIP project at University of Witwatersrand has had professional learning communities as its object of research study. As such several lessons emerging from this project are relevant. There was also reference to researched teaching methods which have shown impact in developing and or remediating number sense at primary school level.

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Productive learning dispositions

Some of the lessons put forward by the expert network were relevant to the productive learning disposition strand of mathematical proficiency. This was relevant to both learners and teachers where lessons relating to empowerment, personal agency, and confidence emerged.

Language and mathematics

Language and mathematics emerged as an important factor (particularly in relation to primary mathematics learning). There were very few lessons pertaining to this theme which were put forward by the expert network.

Quality resources (LTSMs)

The use of quality learning and teaching resources has been highlighted in various points in this landscape review, and LTSMs – in both print and e-learning formats - were the focus of several of the lessons mentioned by the expert network. We have combined printed and technology-based learning materials as both serve the purpose of providing learners with opportunities to develop procedural fluency (strand 2 of mathematical proficiency). Although each format provides its own strengths, both require appropriate teacher mediation to ensure that they serve their purpose of providing independent learning opportunities and related individualised feedback on tasks.

It was clear that many of the lessons relating to LTSMs were about the need to differentiated resource packs (which were not grade specific to CAPS expectations, but rather developmentally appropriate for particular mathematics topics) were required. This was considered particularly important for the remediation required (and in response to research finding that most learners are two or more grades behind CAPS expectations).

While technology-based LTSMs have the benefit of providing individualised learning pathways and immediate feedback on correct responses, a clear lesson relating to reluctance on the part of teachers to make use of such resources emerged. The motivating effect of using ICT was also brought to light with learner enthusiasm for technology-based interventions highlighted.

3.5 Expert opinion on priority investments for mathematics interventions in South African schools

In this section we provide a synthesis of the document review and the expert opinions solicited through the questionnaire and interview process. We refer to lessons emerging with reference to project names, and to expert opinions with reference to a code (G=Government; U=University and CS= Civil Society including funders, not for profit organisations, trade unions, professional bodies).

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3.5.1 Phase

The experts were asked to indicate which was the most neglected phase and to provide reasons for this choice. It was of interest that the selections made with regard to phase were relatively evenly spread between foundation, intermediate and senior phase; and there were several acknowledgements that the historic priority had been on the FET phase.

Table 1: Number of expert respondents indicating that a particular phase was most neglected in terms of mathematics interventions in SA schools

PhaseFoundation phase (Grade R – 3) 14Intermediate Phase (Grade 4-6) 16Senior Phase (Grade 7-9) 17Further Education and Training Phase (Grade 10-12)

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We do not think that too much can be read into the slight differences between Foundation Phase, Intermediate Phase and Senior Phase (asking 10 more experts of the field, would shift these results). The main observation is that there is a relatively even spread across these phases, with far fewer experts considering FET to be neglected. Mention was made about the need to consider the transitions between phases as key points of intervention (as mentioned in the NECT 2015 report). The following contrasting appeals from the expert network – one for investment in the primary school level, and another for a focus at the Senior Phase level – highlight these different opinions:

I think that there continue to be too few interventions at primary level that have a specifically mathematical focus. This point is relevant at all levels of our system – from classrooms all the way into pre- and in-service teacher education and research. This issue reflects too, ongoing problems with capacity in terms of people who have both the mathematical knowledge base, and the competence and inclination to work in developmental ways on primary mathematics. (U4)

The largest areas of concern are grades 7-9. These grades are often taught by SGB teachers because qualified teachers of these grades are moved to FET phase. Teachers with subpar skill sets or no qualifications in mathematics are left. Another issue is that maths teachers are often assigned principal positions, which adds to the workload, and they are not properly trained to manage both teaching and administrative roles. (CS30)

It is therefore useful to consider the differing characteristics of each phase, and the reasons that experts provided for selecting a particular phase. Through our engagement with the expert

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network, Bridge shared a tabulation of various considerations relating to phase for mathematics interventions with schools with us. We adapted this tabulation drawing on own knowledge of mathematics in South African schools and to include more of the detail provided through the above discussion:

Figure 8: Tabulation of phase level considerations for mathematics intervention

Foundation Phase(Grades R-3)

Intermediate Phase (Grades 4-6)

Senior Phase (Grades 7-9)

FET Phase(Grades 10-12)

Rationale for focus

Most research evidence of this as a strategic priority (Besharati 2015, Hattie 2011, Hill Hill et al, 2008, Bloom et al, 2008, Lipsey et al, 2012, Taylor, van den Berg et al. 2011, Besharati and Tsotsotso (2015)

There is an economic rationale for early intervention (Van der Berg 2008, Spaull and Kotze 2015)Backlogs for low SES children identified from Grade 1, with widening gap by Grade 7. (Spaull & Kotse 2015)

Foundation Phase is where the conceptual difficulties with mathematics first start to emerge, and problems at this early grade stage significantly compound conceptual difficulties higher up in the schooling system.

Evidence of less intervention at primary level.

Reaction to historic focus at FET level.

Recognition of the need to intervene earlier (than FET)

Very low performance in Grade 9 linked back to conceptual difficulties at IP level.

Learners not meeting SP expectations of CAPS (very poor ANA results), hence DBE priority area.

Calls for diagnostic interventions to remediate earlier lack of number sense.

Senior Phase is a better starting point than the historical focus on FET.

Senior Phase straddles two schools: primary and secondary.

Subject selection and subject combinations are frequently overlooked at intervention areas

There are not sufficient quality mathematic passes for entrance to higher learning and STEM careers.

The teachers in this phase

The teachers are age not subject specialists. They

Lack of mathematics specialisation and

In general, teachers do not have the CK required to teach

In general teachers, do not have the CK required to teach

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teach all 4 subjects.

There are currently inadequacies relating to both pre-service and in-service training for Foundation Phase teachers in relation to mathematics (in terms of language fluency of Foundation Phase teacher; their generalist training, and their related lack of mathematics knowledge (subject matter knowledge, pedagogical content knowledge and mathematical knowledge for teaching)

In general, teachers have the CK required to teach this phase, but they had weak/negative mathematical identities and lack PCK. (Venkat and Graven)

inadequate training of Intermediate Phase teachers

In general, teachers do not have the CK required to teach this phase.

Need holistic intervention programmes which address literacy and mathematics in parallel.

this phase.

They also lack the PCK for remediation of backlogs from FP and IP.

this phase.

Teachers struggle particularly with data handling (statistics) probability and Euclidian geometry.

The changes at school in this phase

Learning of mathematics takes place in a range of vernacular languages

The focus is on learning to read and basic mathematics concepts,

There are only four subjects: literacy (first and first additional languages), mathematics and life orientation.

Learning of mathematics switches to English (or Afrikaans) in Grade 4.

This phase shifts from learning to read to reading to learn. New subject range is introduced (languages and mathematics still central).

In some schools there are subject

The phase is split: The Grade 7 year is in primary school, but Grade 8 and 9 are in secondary school.Mathematics is compulsory subject.

There are subject specialist teachers.

Learners choose their subjects: mathematics or mathematics literacy.

Major focus is on preparation for Grade 12 NSC examination and tertiary education.

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specialist teachers in this phase – in others one class teacher teachers all subjects.

The mathematics in this phase

Focus on sense making and number sense.Strong focus on number sense and number work (adding & subtracting; multiplying & dividing including both discrete objects and measurement contexts).

Should include progression from counting to calculating; but informal unit-counting strategies dominate

Should include the use of concrete apparatus to support conceptual development.

Should include early algebra work on underlying structure and pattern of number system

Continued focus on sense making and number sense with increasingly use of a range of written calculation methods and formal measurement contexts

Number range is too big to use unit-counting strategies, yet unit counting strategies dominate.

Concrete apparatus needed for formal measurement, fractions and multiplication & division contexts

Early algebra should be extended across all content for pattern, structure, variables and functions

Serious gaps/ lack of primary school number sense identified here.

Lack of remedial intervention options for meeting grade level expectations.

Sound grounding for FET phase necessary. Algebraic and spatial reasoning central.

Formal shift from arithmetic to algebra.

Greater focus on generalized structures and spatial reasoning.

Formal algebra, geometry, trigonometry, financial mathematics statistics and probability.

Mathematics procedural fluencies

Number bonds (addition and subtraction facts); doubling and halving

Addition and subtraction facts; timetables (multiplication and division facts)

Additive and multiplicative relations of integers; manipulating algebraic expressions and equations (including exponents)

Algebraic manipulations, coordinate systems, Euclidian geometry of plane surfaces including polygons and circle geometry.

Number types

Whole numbers, basic fractions, decimals (in the context of money)

Whole numbers, fractions, decimals (in context of money and measurement), percentages, ratios

Integers, fractions, decimals, percentages, ratios, exponents

As for SP, making extensive use of algebraic notations, including angles and ratios for

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FET Phase(Grades 10-12)trigonometric functions

Areas of particular difficulty in the mathematics for learners

Word problems (both additive relations and multiplicative reasoning), measurement contexts especially time.

Learners struggle with group counting and acting on groups (not on ones).

Recurrent problems with sense-making (evident in word problems).

Difficulties with division, fractions, ratio and rate contexts (all multiplicative reasoning)

Shift to Algebra in SP is a conceptual challenge, especially if early algebra work is not done in FP and SP.

Learners struggle with exponents and factorisation in particular.

Learners struggle with algebra, geometry and trigonometry.

Implications for interventions


Focus on number sense for solid foundation

Development of lexicon (specialized mathematical vocabulary) required to communicate meaningfully in mathematics.


Focus on quality of learning rather than number of passes.

Continue to build sound foundations relating to number sense.


Focus on quality of learning rather and number of learners opting for mathematics.


There are options to include number sense remediation and to target subject selection and subject combination interventions.

Focus on number, proportion (compared to mathematics literacy) and quality of passes in mathematics.In short term, quick fix interventions, focus on learners in B,C,D pass range and try to improve quality of pass.

Key transition years

Grade R is key transition year from home /preschool into primary school.

Grade 2 is key mathematics learning year as reading and language is more secure and shift into bigger numbers

Grade 4 is key transition year with shift into learning in English and more subjects.

Grade 7 is preparation for high school and introduction of formal algebra

Grade 8 is key transition year with shift into high-school and much more formal algebra.

Grade 10 is key transition year into FET and lays groundwork for Grade 12.

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(base-10 place value system) with group-wise actions necessary.

Grade 9 is key year for subject choice: mathematics/mathematics literacy

3.5.2 Neglected target groups

The experts were asked to rank the most neglected target audience for mathematics interventions in schools making use of 1 for the most neglected (and 2 and 3 for the next most neglected).

Table 1: Expert ranking of most neglected target groups

Target audience Rank 1 Rank 2 Rank 3 XTotal

pointsTeachers 12 13 8 15 122 In-service teachers of mathematics (> 4

years experience) 6 6 1 4 44

In-service newly qualified teachers of mathematics (< 4 years experience) 5 3 5 7 50

Pre-service/ initial classroom teachers of mathematics 2 4 2 4 28

Instructional leaders 10 10 9 5 96 School management and/or HoDs

expected to play instructional leadership role with regard to mathematics

7 6 4 4 58

District support (eg mathematics curriculum advisors) for mathematics instructional leadership

3 5 5 1 38

Other target groups 106Learners of mathematics 8 3 4 5 42Parents and community participating in mathematics learning 2 4 3 3 29

Learning support / remedial staff (tasked with specialist remediation and intervention for LSEN) in relation to mathematics

2 2 4 3 24

University lecturers 1 0 0 0 4Other – please explain 1 0 1 1 7

From this it is clear that teachers were considered the most neglected target audience, with in-service teachers (considering both newly qualified and experienced teachers) considered to be neglected more than the pre-service teachers. This was closely followed by concern about school management, heads of department and district support staff who are expected to play an instructional leadership role with regard to mathematics.

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3.5.3 Most neglected project inputs

The same process was adopted to calculate the total points weighting for the respondents ranking of neglected project inputs.

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Table 2: Expert ranking of most neglected project inputs

Most neglected project inputsRank 1 Rank 2 Rank 3

X (no ranking

provided) Total

Teacher training materials and remediation approaches for teachers 10 10 2 7 81Teacher training materials and course materials with a specific focus on mathematics 7 3 2 5 46Remediation/ learning support approaches and programmes for mathematics 3 7 0 2 35

Learning materials9 6 2 6 64

Learning materials/resources for after school independent study in mathematics 7 2 2 4 42Learning materials resources for during school study/activity in mathematics 2 4 0 2 22

Instructional leadership in mathematics (SMT and district levels)

7 5 4 5 56Professional development and tools for school management, instructional leadership in mathematics 5 0 3 3 29District capacity programmes in instructional leadership for mathematics 2 5 1 2 27Research (including monitoring and evaluation) 6 5 13 8 83Sharing of lessons and knowledge management across interventions 1 2 5 2 32Monitoring and evaluation of existing interventions 0 1 8 3 22

Research in mathematics teaching3 1 0 2 17

Research in mathematics learning2 1 0 1 12

Other inputs

Mechanisms for parental/community involvement in improving mathematics learning 1 2 3 2 18Assessment practices in mathematics 2 1 2 2 17Other – please explain 2 1 1 0 13

Here the highest neglect was indicated for teacher training materials and course materials with a specific focus on mathematics. The lack of remediation or learning support approaches for teachers could be linked to this concern. Learner resources for both during school and after

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school independent study were also identified as inputs that are largely neglected. Materials and programmes for instructional leadership (at both district and school management team levels) were also identified as neglected. Finally, various aspects of research – including sharing lessons across initiatives, evaluation of existing initiatives and research into mathematics learning and teaching were also mentioned. Those who felt research was neglected called for evidence-based interventions in mathematics education.

3.5.4 Priority investments

The experts were asked what they would invest in if they were planning a new large scale mathematics intervention for South Africa. We considered the primary project inputs that respondents were describing (resources; teacher development and/or support; learner-focused inputs and parent and community inputs) to classify the suggested investments. Most respondents selected teacher training as the priority investment. There were clear overlaps between project inputs. For example, while teacher training emerged as the most common suggested intervention, investment in common programme design (including common teacher materials and use of ICT resources using blended learning environments) were mentioned as possible mechanisms for supporting collaboration on and delivery of teacher training and professional development support.

4. Emerging recommendations

In this section we offer our recommendations to Zenex Foundation for their new mathematics programme. In so doing we offer different (at times complementary) recommendations that we think emerge as clear potential priority investments.

Our review of government strategy documents and related interventions in terms of mathematics reveals an emerging coherence in terms of both the acknowledgement of what is at issue; related targets to improvement of mathematics attainment at all phases of the schooling system and some emerging alignment between the targets set and mechanisms for intervention which are clustered in terms of:

● Teacher development (with consideration given for 4 + 1 and investments in teacher centres for in-service provision);

● Feedback on attainment in the system (through ANAs, NSC, SAQMEC and TIMMS processes); and

● Teaching and learning support materials (with particular investments in printed workbooks and technology-based resources).

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The fact that initial teacher education is within the remit of the Department of Higher Education and Training (DHET) creates somewhat of a disjuncture in the transition from initial teacher education to continuing professional development while in schools. We nevertheless note that the Department of Basic Education is willing and interested to collaborate on a new mathematics intervention.

While the 4 + 1 training provides a policy framework for significant long term professional development with mathematics teachers, it seems that currently this landmark agreement is being implemented to differing degrees (with varying levels of success) at the provincial level. It would seem that an intervention that targeted one or more of the under researched and supported PDE’s (i.e neither Western Cape nor Gauteng) to support the effective and researched implantation of the 4 + 1 model (as requested by the DBE expert) would be a strategic and worthwhile investment.

Recommendation 1: Target one or two PDEs to support, research and implement their 4 + 1 in-service training model for mathematics teachers in collaboration of the Department of Basic Education

There seems to be near unanimous agreement on the ‘central’ or ‘pivotal’ role of teachers in the schooling system. At the same time, teachers cannot be supported in isolation and the involvement and support of provincial, district and school structured are considered important components of any teacher-focused intervention. There are vast requirements in terms of teacher development and training. Several of the experts allude to the need to support initial teacher training offerings; while others refer to potentials of ongoing professional support for teachers through professional learning communities and making use of school-based support and mentoring. Recommendation 1, which responds to a government request for collaboration pertains to ongoing professional development. In embarking on this recommendation there are numerous lessons relating to how best to engage in-service teachers on their knowledge for mathematics teaching. Lessons pertaining to professional learning communities; supporting teachers to better make use of available materials and resources (through scripted lessons as for GPLMS, and/or through better use of the available learner workbooks, or engagement with assessment data and using learner error analysis approaches as for DPIP project) are all possible approaches which could be trialled within the 4 + 1 framework. A key element of this recommendation is the need for structuring this intervention as a research activity which allows for iterative design and reflection cycles which build the capacity of the PDE to implement the national framework.

Building on the scope of this landscape review, it seems that investing in further consolidation of the lessons, and impact pertaining to knowledge for mathematics teaching (and related impact

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on learner attainment in mathematics) is required. Such analysis could then feed into the design of an appropriate programme (or contrasting programmes) which form the heart of a PDE strategy to implement the 4 + 1 framework which is squarely within the in-service continuing professional development sphere.

However, given that the source of the problem relates to inadequate knowledge for teaching mathematics we think that the priority investment should be in initial teacher development and consider this to be recommendation 2. Support for teacher education providers (in this case universities) necessarily involves interaction with teachers in schools when pre-service teachers engage in their teaching practice component of their work. In our view this is a critical intervention area, which would have the long-term effect of requiring less sustained and intensive professional development needs in the in-service environment. We think that it is significant that the project input of most neglect related to ‘teacher training materials and course materials with a specific focus on mathematics’ which suggests that some research and development of common standards materials and approaches in this regard would be a worthwhile investment. For this reason, we place strategic priority on improving the quality of initial teacher education for mathematics teaching.

Recommendation 2: Invest in initial teacher education relating to knowledge for mathematics teaching is a strategic investment with the potential for significant long term impact. There should be a particular focus on common standards, and teacher training materials.

It should be noted that investment in recommendation 2, may produce tools and course materials which would be of value to in-service teacher education provision. It may therefore be possible to develop a dual approach: focusing on one province relating to the 4 + 1 offering, and working with universities to improve the quality of the knowledge for mathematics teaching. For such a dual approach to be effective however we recommend that the mathematics which is in focus is limited to a particular content strand and particular phase level

Both recommendations 1 and 2 require a strategic choice of phase or level in which to intervene in terms of mathematics. Considering the expert opinions, the only phase which is thought not to be neglected is the FET phase. Foundation, Intermediate and Senior Phase are thought to require intervention. While we concur with the NECT (2015) finding that each phase has particular characteristics and all require intervention, we do think that there are particularly strong arguments and research supporting early intervention.

The projects included in this landscape review suggest that there a more interventions directed at secondary schools than at primary schools. In addition, there are strong economic and

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evidence-based arguments relating to higher impact of earlier intervention in the schooling system. Finally, where there are requests for support at Senior Phase level, several of these pertain to creation of tools and materials for the remediation of number sense (which learners are not demonstrating at high school level). Therefore, an intervention at targeting the development and remediation of number sense at the primary level, would be of value at high school level.

Recommendation 3: Focus on primary schools, with explicit attention to number sense (which can also be used for remediation of ‘absent/lack of number sense’ in the Senior Phase).

The inclusion of ‘number sense’ as the content focus is not incidental. Many of the experts made reference to this with regard to strand 1: conceptual understanding in terms of the mathematical proficiency for both teachers and learners. The need to shift from reliance on procedures and rules, to deep and flexible understanding of number is a topic that cuts across the primary and secondary school sector. There is also research evidence suggesting that learner attainment in number sense related tasks are better predictors of future attainment in mathematics in high levels (in comparison to other content areas such as measurement; data handling and geometry).

Support for an intervention focused on primary school mathematics is provided in the recommendations emerging from the NEEDU 2014 evaluation report where Recommendation 6 pertains to ‘Identifying and rolling out a primary numeracy and mathematics programme'. It is important to realize that although the NEEDU 2014 report focused on the quality of high school education in South Africa, it is recommended that a primary school numeracy and mathematics programme be conceptualised (to support the number sense required for successfully meeting the learning outcomes at the Senior Phase level in high school). A focus on number sense would support this simplification of developmental progression with regard to mathematics – where the grade level expectations can then be seen as possible benchmarks for attainment. We think that the draft NEEDU framework provides a starting point for such work, but that research findings from both mathematics education realms (cognitive development as well as approaches to mathematics pedagogy for early number development) ought to be used to inform such a refined developmental trajectory for early grade number sense.

There are a few other possible investments which we think are worth considering – although most of these are of less strategic importance than the above. We briefly list those options which have surfaced through this landscape review process, many of which could be combined as supporting focus areas for the three recommendations made above.

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Recommendation 4: Considering research and development relating to remediation of mathematics learning with regard to differentiated assessments and learning materials. This related to developmental trajectories for mathematics which are independent of the CAPS grade level expectations. Such learning support or remediation would be relevant at all levels of the school system; but we notice particular need being expressed at Intermediate and Senior Phases. Again a focus on number sense as a starting point in this regard, would be appropriate. Such research and development would necessarily involve engagement with both teachers and learners in South African schools as it anticipated that the assessment tools; and related remediation interventions would be led by teachers with the support of instructional leaders (in the SMT) and learning support staff (in provinces where such appointments exist).

Recommendation 5: Research and develop standardised assessment instruments for gauging Knowledge for Mathematics Teaching (KfMT) of teachers which would be relevant for different phases of the South African school system. It seems that there are several initiatives aimed at improving KfMT, but there is a lack of standardised data which can be used to identify gaps, prioritise interventions and measurement improvements (or regressions). The work conducted by the Mathematics chairs in this regard may be an important staring point. Together with the diagnostic assessment tools developed by Pearson and the DBE, more robust approaches to measuring and tracking teacher knowledge for mathematics may be developed.

Recommendation 6: Focus on tools, courses and professional learning communities targeting school management and leadership (including Subject Advisors at district level and HoDs at school level) tasked with instructional leadership for mathematics. We see this recommendation emerging from the recognition that teacher development cannot take place in the absence of these support structures. We think that there is potential to combine the focus on standardised assessments with this recommendation as assessments could be used as basis for define work-place skills plans and professional development pathways open to both teachers and instructional leaders or mathematics.

Recommendation 7: There seems to be some potential in supporting parents and community involvement in mathematics learning. However – like the focus on instructional leadership – we don’t think that this can happen without also focuses on teacher development. It may therefore be appropriate to consider including an element which focuses on parents and community engagement alongside the recommendation to invest in the research and development of a long-term in-service teacher development programme.

Recommendation 8: Support a programme of professional development for the subject advisors of mathematics at district level in identified province(s). This relates to the need

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for expert or lead teachers or mentors to offer school-based support relating to mathematics at school level. Currently the subject advisors are not considered to have the deep mathematical knowledge for teaching which is required to play a meaningful instructional leadership role in terms of mathematics. There are some existing training programmes (a few of which directly target facilitators or instructional leaders) which may be a basis for such an intervention. This may be worthwhile investment to consider alongside the 4+ 1 training suggestion (see recommendation 1).

Recommendation 9: Support research in mathematics education interventions which seeks to consolidate lessons, design tests and develop interventions that work and which are then scaled up as randomised control trials. We include this recommendation as a strategic option considering different scales of investment possible in the mathematics education landscape. While research was not identified as particular area of priority, it is clear from this landscape review exercise that there is progress relating to emerging lessons and approaches to interventions focused on improving mathematics attainment. However, these initiatives are frequently conducted on a small scale (qualitative work is necessary to understand the context and develop robust designs) however these are lessons are seldom then taken to large-scale programme intervention design level, where the impact of small scale findings can be tested on a wider scale. There were two (in our view complementary rather than oppositional) approached to mathematics education research which surfaced through our engagement with the expert network. The first related to the rigour of design experiment methods (educational design research) where small scale implementation of intervention is trialled with repeated cohorts of learners, or repeated at different schools in order for a robust design intervention to be developed. This takes into account the fact that the ‘best way’ to intervene is not known, but rather a process of trialling approaches which are then refined based on feedback from the system into which the design is implemented. The second related to a call for more randomised control trials. This was considered necessary to be able to measure impact of particular intervention against control schools (and or classes) within the same context. We argue that these two approaches can be related as it more cost effective to trial an experimental design on a small scale in several schools, attending to refinements in intervention design and to then follow this with a large scale RCT to test the efficacy of the rigorously researched design.

5. Concluding remarks

We trust that this landscape review makes a contribution towards the planning of a new Zenex Foundation mathematics intervention in South African schools. In particular, we recognise the significant progress that is being made from various sectors in the South African landscape – including government strategy and related government-lead interventions which result in large-scale implementation; and the smaller scale innovation; research and development work which

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is undertaken by universities; various not-for-profit organisations through the support of private sector funding. We are excited that the South African trade unions have agreed to an extensive long-term investment in the ongoing professional development of South African teachers and school’s leaders; and notice the work conducted by unions in supporting this process.

We believe that there are many lessons which have emerged from these collective efforts and are pleased to be able to collate these into this landscape review. Within this rich context of innovation; research; and reflection we see little point in embarking on a completely new intervention and recommend that initiatives that are showing demonstrated improvements in teacher knowledge and related improvements in learners’ attainment; be supported. Such support may be in the form of expanding their reach (in terms of schools and or provinces); and or in the form of expanding their sphere of influence (in the form of documented lessons, research outputs; and collaborative opportunities which encourage replication and further reflection and design).

We thank the expert network who willing engaged in this process, providing both their time and expertise to shape this landscape review. We look forward to further engagement with them and the Zenex Foundation to further refine the emerging recommendations and the resultant new mathematics programme.

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Documents

zenexfoundation.org.zazenexfoundation.org.za/images/stories/Zenex_Foundation... · Web view2016-07-13 · There is a plethora of mathematics related interventions in South Africa