Expressed serious concerns regarding levels of numeracy

Published:

The Grade 3 Systemic Evaluation 2001 Mainstream Report (South Africa. Eastern Cape Department of Education [ECDoE], 2002) expressed serious concerns regarding levels of numeracy among Grade 3 learners. According to its findings (South Africa ECDoE, 2002), only 33% of Grade 3 learners were numerate in 2002. A second Grade 3 Systemic Evaluation was conducted during 2008, and although there was a slight increase to 35%, the findings again indicated that about two-thirds of Grade 3 learners were neither literate nor numerate (South Africa. Department of Basic Education [DoBE], 2008b).

In reaction to the disastrous results of the systemic evaluations, the government set targets

for improvement in learner achievement by 2014. The Minister has set a target of improving numeracy and literacy attainment levels of grades 3 and 6 from the current average attainment levels of between 27% and 38% to at least 50% by 2014. (South Africa. Department of Basic Education [DoBE], 2010c, p. 8)

The situation demands that three pertinent questions be asked: First, why are only a third of Grade 3 learners numerate? Secondly, can this low numeracy level be attributed, at least in part, to inadequate skills and knowledge development among Reception Year (Grade R) learners? The third question that needs to be asked is whether Grade R teachers have sufficient skills and knowledge to implement numeracy in Grade R classrooms? It is with the latter two questions that this research project is concerned.

Only a third of Grade 3 learners are numerate

Lady using a tablet
Lady using a tablet

Professional

Essay Writers

Lady Using Tablet

Get your grade
or your money back

using our Essay Writing Service!

Essay Writing Service

Why are only a third of Grade 3 learners numerate? The situation was revealed in the findings of the two Grade 3 Systemic Evaluation Reports (South Africa. Department of Education [DoE], 2003a, South Africa. DoBE, 2008a), which were conducted to determine the impact of implementing new curricula. The 2001 Grade 3 Systemic Evaluation was conducted after the introduction of the Statement of the National Curriculum for Grades R-9 (South Africa. Department of Education [DoE], 1997b) or Curriculum 2005, as it was commonly referred to. The second Grade 3 Systemic Evaluation focussed on the National Curriculum Statement or NCS (South Africa. Department of Education (DoE), 2002b), and required Grade 3 learners to demonstrate their abilities and competence whilst making use of a pencil and worksheet (South Africa. DoBE, 2008b).

It is important to bear in mind the history of Foundation Phase curriculum development in South Africa. Prior to the implementation of Curriculum 2005, Foundation Phase teachers implemented syllabi which were prescribed by the fragmented provincial and homeland Departments of Education in apartheid South Africa.

Then, during a period of only ten years, Foundation Phase teachers (including Grade R teachers) had to make significant curriculum paradigm shifts on two occasions. Teachers were expected, in 1998, to implement a new curriculum quite different from what they had been teaching. Four years later, another curriculum, namely the NCS, was introduced, and teachers had to adapt their classroom preparation and teaching methodologies once again to accommodate the curriculum requirements. All this change and adaptation led inter alia to teachers focussing on the administration of the curriculum rather than on teaching and learning. The Report of the Task Team for the Review of the Implementation of the National Curriculum Statement (South Africa, DoBE, 2009) makes it clear that teachers spent excessive time on planning and administration, which resulted in less time being devoted to teaching (pp. 26-27). In order to bring the focus back to teaching learners reading, writing and arithmetic, the Department of Education embarked on a Foundations for Learning Campaign during 2008: "The Foundations for Learning Campaign is a four year campaign to create a national focus to improve the reading, writing and numeracy abilities of all South African children" (South Africa. Department of Education, [DoE], 2008b, p. 4).

Chapter 2 of this study, which is divided into pre- and post-1995 sections, emphasizes the political and historical context of numeracy and describes the policies and documents that have been issued since 1995. The teacher cannot be divorced from the political and historical backgrounds of ECD: since 1995, numbers of curriculum policies, White Papers and other ECD documents have been issued by the government, and these have had a serious impact on how Foundation Phase teachers teach numeracy in their classrooms.

Chapter 3 deals intensively with the requirements of both Curriculum 2005 and the NCS, and how these have influenced Grade R teachers' planning and preparation for teaching and learning activities in their classrooms over the past twelve years.

Insufficient exposure of young learners in Grade R to numeracy knowledge

Lady using a tablet
Lady using a tablet

Comprehensive

Writing Services

Lady Using Tablet

Plagiarism-free
Always on Time

Marked to Standard

Order Now

According to the Education White Paper 5 on Early Childhood Education (South Africa. Department of Education [DoE], 2001), not all young learners are exposed to early childhood education: it was found that only "1 million of an estimated 6 million children in the 0-6 years age are … enrolled in some type of ECD provision" (p. 18). The Systemic Evaluation Foundation Phase Mainstream National Report (South Africa. DoE, 2003a) emphasized the importance of young learners being exposed to developmental activities prior to Grade 1, in order for them to perform adequately in formal schooling (p. 18). The Education White Paper 5 (South Africa. DoE, 2001) points out that

The early years are also critical for the acquisition of the concepts, skills and attitudes that lay the foundation for lifelong learning. These include the acquisition of language, perception-motor skills required for learning to read and write, basic numeracy concepts and skills, problem-solving skills and a love of learning. With quality ECD provision in South Africa, educational efficiency would improve, as children would acquire the basic concepts, skills and attitudes required for successful learning and development prior to or shortly after entering the system, thus reducing their chances of failure. (pp. 11-12)

An important question arises: are Grade R learners sufficiently exposed to numeracy knowledge and skills development? The RNCS Grades R-9 Policy for Mathematics (South Africa. Department of Education (DoE) 2002a) stipulates that all Learning Outcomes must be achieved by the end of the Foundation Phase or Grade 3 (pp. 21-31). In order to achieve these Learning Outcomes, Assessment Standards for each grade are specified, which describe "the level at which learners should demonstrate their achievement of the various Learning Outcomes" (South Africa. DoE, 2003b, p. 9). Thus, the Mathematics Learning Area Statement (South Africa. DoE, 2002a) "stipulate[s] the concepts, skills and values to be achieved on a grade by grade basis" (p. 2). It has five Learning Outcomes and 25 Assessment Standards for Grade R, and forms the core of the Numeracy Learning Programme. But the Department of Education has also introduced numeracy milestones, within the Foundations for Learning Assessment Framework Foundation Phase (South Africa. DoE, 2008c), that learners need to reach in order to develop their literacy and numeracy skills (pp. 3-16). Numeracy milestones have also been introduced for Grade R learners (South Africa. DoBE, 2010a, pp. 12-14).

In Chapter 3, Curriculum 2005, the NCS and the newly proposed CAPS (South Africa. Department of Basic Education [DoBE], 2010e, South Africa. Department of Basic Education [DoBE], 2010f ) are teased out in detail in order to gain an understanding of the numeracy knowledge and skills that Foundation Phase learners, especially Grade R learners, need to be exposed to.

Grade R teachers lack the skills and knowledge to implement numeracy in Reception Year classrooms

The third question that needs to be asked is whether teachers, who are expected to lay the foundation in Grade R, are sufficiently equipped to implement numeracy in Grade R classrooms. The insistence in the White Paper 5 (South Africa. DoE, 2001) that all learners in Grade 1 should have attended a reception year class by 2010, makes it pivotal to look at the readiness, willingness, skills and knowledge of Grade R teachers to teach numeracy in their classes (p. 8).

Before a Grade R teacher can implement numeracy in her class, she needs to have an understanding of how a Grade R learner learns and acquires knowledge and skills. This thesis will analyse how four learning theories - namely, the neuro-science of learning, behaviourism, constructivism and multiple intelligences - can play a role in understanding and enhancing the implementation of numeracy in the Grade R classroom. Chapter 4 deals intensively with the different learning theories and their application to the curriculum and its implementation in the Grade R classroom.

Although the focus of this research study is not to investigate why Grade 3 learners are performing poorly in numeracy per se, it is necessary to ask these three questions in order to investigate possible reasons for the findings reported by the two systemic evaluations referred to above. This study aims to identify some of the root causes of the low numeracy levels of Grade 3 learners, and assess whether an appropriate foundation in numeracy is laid in Grade R.

Conceptual background to the research

Confusion amongst Grade R teachers regarding how and when to implement numeracy in the Grade R daily programme

Lady using a tablet
Lady using a tablet

This Essay is

a Student's Work

Lady Using Tablet

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

Examples of our work

This research study focuses on the experiences of both professionally qualified teachers and Early Childhood Development (ECD) practitioners ("non-formally trained individuals providing an educational service in ECD") in implementing numeracy in Grade R (South Africa. DoE, 1996a, p. 3). The Interim Policy (South Africa. DoE, 1996a) defines ECD as "an umbrella term which applies to the processes by which children from birth to at least nine years grow and thrive, physically, mentally, emotionally, spiritually, morally and socially" (GLOSSARY, p. 1). In my capacity as a subject advisor for the Foundation Phase and ECD, I have noticed that professionally qualified teachers as well as ECD practitioners are experiencing confusion regarding what, how and when to implement numeracy in the daily programme of Grade R.

Prior to 1995, there was no fixed curriculum for pre-primary schools advocating a formal numeracy approach (Grobler, Calitz, Van Staden & Orr, 1992, De Waal, Behm, Daniel, Morris, Scholtz & Thompson, 1993). The focus was on discovering, exploring and experimenting with numeracy concepts such as measurement, shapes, patterns and counting, through play activities and concrete experiences (Faber & Van Staden, 1997, p. 105).

In 1996 the Interim Policy for ECD (South Africa. DoE, 1996a) was published by the Department of Education. This document recommended that:

A wide range of activities needs to be provided to assist the development of children's mathematical concepts, and their understanding and appreciation of relationships and pattern in number, time and space in their everyday lives. (South Africa. DoE, 1996a, APPENDIX 2, p. 9)

It stated that the teaching approach should be informal, and that

Programmes should focus more attention on "hands-on" experiences, the use of manipulative materials, questioning, justification of thinking and problem-solving approaches. Less time should be spent on rote practice and memorisation, one answer and one method, the use of worksheets and teaching by telling. (SA: 1996a, APPENDIX 2, p. 5)

During 1997 and 1998, Foundation Phase teachers were exposed to Curriculum 2005 in-service training, but no guidance regarding mathematical content or teaching approach was given to Grade R teachers.

Four years later the NCS (South Africa. DoE, 2002b) was introduced as an adapted curriculum. Again in 2004 Foundation Phase teachers, including Grade R teachers, received training in how to implement the NCS. Although the NCS clearly specifies the learning outcomes and assessment standards applicable to the Grade R learner, no particular content knowledge and skills or teaching methodology are recommended (p. 14). However, the NCS (South Africa. DoE, 2002b) prescribes an allocation of 35% of teaching time per day for numeracy activities in the Foundation Phase (p. 17).

During January 2010, the Minister of Basic Education launched the Foundations for Learning Assessment Framework for Grade R in order to assist teachers in planning for numeracy learning activities for each term (South Africa. DoBE, 2010a). This Framework, with its focus on numeracy milestones which need to be achieved by Grade R learners, "organises the Assessment Standards contained in the National Curriculum Statement into manageable 'sections'. This will help you with your planning and will structure your learners' learning" (South Africa. DoBE, 2010a, p. 1).

However, during September 2010, the Department of Basic Education (South Africa. DoBE, 2010e) circulated the draft Curriculum Assessment Policy Statement (CAPS) for inputs by the teaching fraternity. The Grade R draft CAPS document (South Africa. DoBE, 2010e) proposes a daily programme which integrates numeracy activities throughout the day. Targeted time slots for focussed or teacher-directed and planned numeracy activities for the whole class, for approximately 30 minutes per day, are also indicated. The numeracy activities are based on the five Mathematics Learning Outcomes of the NCS (South Africa, DoE, 2002a), namely Numbers and Number Operations, Space and Shape, Measurement, Patterns and Functions, and Data Handling (South Africa. DoBE, 2010e).

Prior to the launch of the Foundations for Learning Assessment Framework for Grade R (South Africa. DoBE, 2010e), only vague guidelines were provided by the government regarding how to implement numeracy in Grade R. This caused uncertainty among teachers, and many of them have consequently followed commercially bought learning and teaching support programmes, which advocate a more formal and worksheet approach toward enhancing numeracy skills. The Systemic Evaluation Foundation Phase Mainstream National Report (South Africa. DoE, 2003a) has also highlighted that some teachers do not feel sufficiently confident to implement the curriculum, despite undergoing training (p. 69). Faber and Van Staden (1997) argue that commercially bought learning materials often do not take cognisance of the young learner's prior experience of mathematical concepts, knowledge, skills and attitudes and "tend to reduce autonomy: teachers decide on the problems, how many are to be tackled and when, and whether the answers are right or wrong" (p. 109).

Sawyer (1995) adds that a high standard of planning and teaching depends upon "good quality resources for teachers and children, whether these be published schemes, resource books or apparatus" (p. 141). In order to counteract teachers' lack of confidence in teaching mathematics, Sawyer (1995) stresses the importance of rendering excellent in-service training and continuing support, "so that their knowledge and understanding base and their confidence in teaching mathematics can be improved" (p. 203). Sawyer (1995) points out that the feelings and concerns of teachers regarding "unfamiliar content, new teaching and assessment strategies, the amount of required paperwork and record keeping, and increasing pressures and resultant stress," cannot be ignored (p. vii). The over-reliance on workbooks in the teaching of mathematics is a reflection of teachers' insecurities regarding content (Sawyer, 1995, p. 141).

In contrast, other Grade R teachers opt to follow a laissez-faire approach - let the children learn through play - without the teacher being actively involved in constructing and channelling these play activities. Sheffield and Cruikshank (2000) make it very explicit that "…activities cannot by themselves teach. Augment them with reading, writing, discussion, examples, and thought" (p. 356).

Kirov and Bhargava (2002) argue that the informality of high-quality learning in the preschool years does not mean that there is no need to plan for mathematics. Instead of letting learners play without interference or guidance from their teachers, Kirov and Bhargava (2002) urge teachers to provide mathematics learning opportunities that will stimulate active learning and the use of rich mathematical language. Learners should give answers to "what?" "how?" and "why?" questions (Kirov & Bhargava, 2002, unpaginated).

According to Golbeck (2002) teachers should not experience confusion or frustration in implementing numeracy in their classrooms if they plan "developmentally appropriate practices" (unpaginated). This will provide the teacher with clarity both on the content that needs to be taught, and on her role in teaching this content.

During in-service training for the NCS (South Africa. DoE, 2002b), it was emphasized that the teacher needs to be an interpreter and designer of learning programmes and materials (p. 9). Outcomes-Based Education, as a principle of the NCS (South Africa. DoE, 2002b), emphasizes

participatory, learner-centred and activity-based education. They [learning outcomes and assessment standards] leave considerable room for creativity and innovation on the part of teachers in interpreting what and how to teach. (p. 12)

A Grade R teacher therefore has a big responsibility to develop and implement a Numeracy Learning Programme that is developmentally appropriate and states "beforehand what the learners are expected to achieve" (South Africa. DoE, 2002a, p. 94).

The rationale for implementing Numeracy in Grade R

In order to implement a good quality Numeracy Learning Programme, the Grade R teacher needs to understand the rationale for implementing numeracy in Grade R. The NCS (South Africa. DoE, 2002a) emphasizes that the purpose and/or rationale of mathematics is to enable a person "to contribute and participate with confidence in society" (p. 4). However, before a person can participate confidently in her social milieu, she needs to be taught and exposed to opportunities where she can practise this participation. The Numeracy Learning Programme, with its mathematical learning outcomes and assessment standards, provides a framework in which such participation can be experienced. The mathematical rationale in Grade R focuses on the development of number concept, patterns, space and shape, and data handling (South Africa. DoE, 2002a).

The draft CAPS for mathematics in the Foundation Phase (South Africa. DoBE, 2010f), is built on the above-mentioned NCS rationale. The CAPS (South Africa. DoBE, 2010f) promotes a curriculum that

gives expression to what is regarded to be knowledge, skills and values worth learning. It will ensure that learners acquire and apply knowledge and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes the idea of grounding knowledge in local contexts, while being sensitive to global imperatives. (p. 3)

According to the draft CAPS for mathematics in the Foundation Phase (South Africa. DoBE, 2010f), the aim of mathematics is to ensure that learners will be confident and competent in mathematical situations (p. 6). It aims further to equip learners with "deep conceptual understandings in order to make sense of Mathematics," as well as ensure that they are able to demonstrate the necessary mathematical competence, knowledge and skills (South Africa. DoBE, 2010f, p. 6). Grade R teachers therefore need to implement a content area consistent with the NCS Mathematical Learning Outcomes (South Africa, DoE, 2002a). The content area consists of:

Numbers, Operations and Relationships,

Patterns, Functions and Algebra,

Space and Shape (Geometry)

Measurement and

Data Handling Phase. (South Africa. DoBE, 2010f, p. 8)

The draft CAPS for Mathematics in the Foundation Phase (South Africa. DoBE, 2010f) emphasises that "Teaching in a Grade R set-up is INFORMAL but with a structured daily programme to create a set-up of 'play with a purpose'" (p. 6).

Only when the teacher is knowledgeable regarding the meaning of the relevant mathematical concepts, and knows which mathematical concepts and skills she wishes the young learner to understand and master, will she be able to provide learners with significant learning and teaching opportunities. It is important that the teacher takes into cognizance the developmental level of learners as well as their interests when she plans meaningful learning experiences (Kirov & Bhargava, 2002). According to Kirov and Bhargava (2002) it is important to allow

children time for free play that enables them to explore mathematical concepts. While children are engaged in an activity, the teacher can observe and then become active in guiding their learning. This interaction will help the children's progress from behavioral to representational understanding of mathematical concepts. (unpaginated)

Teachers' beliefs, experiences, knowledge and feelings regarding how young children learn mathematics

One reason why current pre-school programmes may not be capitalizing on the young learner's prior mathematical knowledge may be associated with teachers' beliefs, experiences, knowledge and feelings regarding how young children learn mathematics. According to Sheffield and Cruikshank (2000), there is a direct correlation between the teacher's beliefs about children and the children's performance. Two viewpoints are held: some maintain that young learners "must be left alone, to grow and develop with little interference from adults, and others believe that children must be closely watched and directed" (Sheffield & Cruikshank, 2000, p. 29). Sheffield and Cruikshank (2000) are of the opinion that the

overall degree of teaching success depends more on what teachers believe about children than on how they organize to teach them, because teachers interact with children in ways that reflect their beliefs about children. (p. 29)

Sheffield and Cruikshank (2000) urge educators to explore how reception year learners learn mathematics. They are of the opinion that once educators have an understanding of the aspects and stages of mathematical learning, young learners will "receive the kind of instruction most appropriate to their individual learning styles" (Sheffield & Cruikshank, 2000, p. 9). Sheffield and Cruikshank (2000) remark that an educator's job is to determine how children think about numbers. Therefore,

You are challenged to build on what children bring to the classroom and provide activities that help children further grow and develop their mathematical thinking and their understanding of the concepts of addition and subtraction. (Sheffield and Cruikshank, 2000, p. 154)

Campbell (1997) echoes this appeal for teachers to build on children's thinking, because this will make the learning meaningful to them and thus foster their mathematical understanding:

Instruction must build on children's existing ideas, so that the children will construct progressively more advanced understandings and simultaneously perceive mathematics as "making sense". It is important for each child to confidently think, reason, and explain mathematically. Eventually this understanding should be consistent with established standards for mathematics. Therefore, instructional practice cannot proceed without considering both mathematical content and children's current understandings. (Campbell, 1997, p. 24)

Chambers (2002) is also of the opinion that teachers need to build on learners' informal strategies. According to him, "young children solve mathematical problems by directly modelling the action or relationship described in the problem. They do not need to be taught how to use direct-modelling strategies, nor do they need such often-assumed prerequisite knowledge as number facts or computational algorithms" (Chambers, 2002, p. 12).

Campbell (1997) stresses the important factor that all young learners need to be actively engaged, participating in classroom discussions and investigations and being required to contribute and explain. There must be a shift from traditional mathematics teaching where the teacher merely demonstrates and explains to the learners, to a constructivist teaching approach, where the teacher asks what young learners think and "why … they think the way they do?" (Campbell, 1997, p. 24). If the teacher takes cognizance of how learners learn and think, she will be able to build on their understanding and construction of mathematical meanings.

Anghileri (1995) and Gurney (1997) stress that it is important for young learners to discuss mathematical concepts with their classmates, as they are not only constructing their knowledge when they talk about it but are also being exposed to various ways of thinking and learning about mathematics (Anghileri, 1997, p. xiv). Gurney (1997) points out that young learners will not be able to develop their conceptual understandings if they are not using appropriate mathematical language to do so (p. 6).

Loef, Carey, Thomas, Carpenter and Fennema (1988) highlight the importance of the teacher knowing the solution strategies that young learners use when addressing a problem in order "to design instruction that builds on children's knowledge" (p. 33). "Assessing children's thinking and knowing the processes that individual children use to solve problems are essential aspects of a program that focuses on problem solving. Once teachers know how pupils solve problems they can then use this information to determine the sequence of their instruction" (Loef, et al., 1988, p. 34).

Silver and Smith (1990) advocate a mathematics curriculum in which the learning of basic skills is integrated with thinking, problem solving and reasoning. High-level thinking among learners can be triggered off by the teacher asking them open-ended questions as well as creating opportunities for them to discuss multiple solution methods for mathematical problems (Silver & Smith, 1990, pp. 65-66).

However, Grouws and Good (1989) have found that problem-solving lessons are scarce. If they do occur, the problem solving is based on a section of the "textbook that deals with verbal problems" and requires only that the learner "select a computational operation" (Grouws & Good, 1989, p. 60). Grouws and Good (1989) maintain that enough time must be granted to learners to discuss problems with one another and to describe their own attempts at solving a problem (p. 62).

The Grade R teacher must be enthusiastic and excited about teaching mathematics. It is important for both young learners and their teachers to be intellectually and emotionally involved in the teaching and learning process (Schwartz & Riedesel, 1994, p. 2). The "attitude toward mathematics and the enthusiasm for teaching mathematics that the teacher brings to the class greatly affect children's confidence" (Schwartz & Riedesel, 1994, p. 12). The teacher's main role should be that of a motivator and facilitator, thus guiding learners to expand their mathematical knowledge through the discovery of different strategies for solving a problem. The teacher guides a learner who is not able to solve a problem with a question or comment designed to provide insight. Schwartz and Riedesel (1994) are strong believers in introducing new concepts with concrete material, and then working up to the stage of abstract thinking:

Paper and pencil mathematics should be reduced. Emphasis should be placed on orally presented problems, computations, and challenges. "Hands-on," interactive displays should be an integral part of the classroom as well as proper use of manipulatives such as Unifix cubes, Cuisenaire rods, geoboards etc. (Schwartz & Riedesel, 1994, p. 18)

Schwartz and Riedesel (1994) are also of the opinion that a young learner must be able to solve problems before he/she can calculate and work out a mathematical answer (p. 18). Therefore the teacher needs to adapt her teaching strategies in order to make provision for problem-solving activities.

In other words, straight drill and practice/rote memorization of formulas, without a clear understanding of the concepts, is absolutely unacceptable. Vocabulary/terminology (e.g. perimeter) should follow problem solving. Emphasis should be placed upon various techniques/ways of solving things so the student does not get discouraged if s/he cannot solve the problem or computation in a particular way. It is helpful if the student knows that there is more than one correct way to arrive at an answer, then; rather than hastily "giving up", the child will persevere. (Schwartz & Riedesel, 1994, p. 18)

In sum, teachers need to build on young children's informal knowledge when numeracy is being introduced in Grade R. They need to organize the Grade R classroom to support and encourage meaningful mathematics learning, and to integrate the learning of basic skills with thinking, problem solving and reasoning. Grade R teachers need to ask open-ended questions and create opportunities for learners to discuss multiple solution methods for mathematical problems. They should present mathematical activities according to the learner's pace of learning, and focus more on the process than on the product. A learner-centred approach should be implemented, in terms of which learners participate actively, contribute and explain in classroom discussions their investigations and how they solve problems. Chapter 4 provides an extensive literature review regarding learning theories and how these relate to the current curriculum. It also offers guidelines to assist teachers in the implementation of numeracy in Grade R.

Research Process

Chapter 5 deals with the research orientation, paradigm and modes of inquiry. It includes discussion of the research question and the aims of the study, as well as an in-depth look at its research design, data collection and analysis methods, before concluding with a critical evaluation of the research design.

1.3.1 Research Question

The literature review, as presented in Chapter 4, emphasizes the importance for teachers of understanding how young learners learn, and suggests guidelines for implementing learning theory in a Grade R classroom. But the question remains: are Grade R teachers really "buying into" these theoretical guidelines and implementing them appropriately in their classrooms? Or are they still feeling insecure and insufficiently knowledgeable to do so?

In order to have a clear picture of what is happening in Grade R classrooms, I ask the following research question:

What are the experiences of selected teachers in implementing numeracy in Grade R?

In unpacking the research question, two further sub-questions are asked, namely:

What are the challenges that face Grade R teachers when they implement numeracy? and

How do teachers' experiences regarding numeracy influence and affect their teaching strategies in numeracy?

1.3.2 Research Aim

The aim of the proposed research study is to understand and describe what is happening in Grade R classrooms when numeracy is implemented, as well as to identify barriers that Grade R teachers might possibly encounter in implementing numeracy. In order to understand the complexities of ECD in South Africa, a subsidiary aim of this thesis is to provide a comprehensive historical analysis of ECD. ECD is not a "new" concept in South Africa: it has a historical and political background that affects how numeracy is being implemented in Grade R classrooms.

1.3.3 Research Design

The Research Paradigm

This research study is underpinned by the naturalistic interpretive paradigm, as it focuses on trying to understand and interpret teachers' experiences of implementing numeracy in Grade R (Henning, et al., 2004, p.16). The naturalistic paradigm is anchored in qualitative research. This study intends to provide "thick description" of the perceptions, feelings, beliefs and values of Grade R teachers in implementing numeracy.

In this case study, I have adapted as a mode of interactive qualitative inquiry the Interactive Qualitative Analysis (IQA), a systems method for qualitative research, from Northcutt & McCoy (2004). The case study is descriptive and interpretative in nature.

The naturalistic interpretive paradigm

I chose to work within the interpretive paradigm as this paradigm enabled me to listen to, observe and describe the feelings, thoughts and actions of Grade R teachers (Henning, et al., 2004, p. 3). The case study lends itself to an interpretive approach, with its emphasis on the subjectivity and personal involvement of the researcher in a small-scale research study aiming to obtain an understanding of the actions of Grade R teachers in their classroom environments and their social interactions with their learners (Cohen, et al., 2000). Although I was subjectively involved in the research study, the data collection strategies of observation, unstructured open-ended focus groups and semi-structured individual interviews enabled me to listen to, capture and describe the research phenomena in a reasonably objective way. I use the words of the participants, verbatim, without interfering editorially and in this way manipulating events (Cohen, et al., 2000, p. 22).

Participant Selection

The sampling strategy that has been followed in this research study is non-probability convenience and purposeful, criterion case sampling (McMillan & Schumacher, 2001, Cohen, et al., 2000). Due to the fact that the research study is embedded in a naturalistic interpretive research design paradigm, it is not intended to be representative and generalizable to the wider Grade R population. Rather, the aim is to gain an in-depth understanding of what Grade R teachers' experiences are, when they implement numeracy, and as it occurs in the three different models of ECD provisioning.

I purposefully selected seventeen Grade R educators and Grade R practitioners to participate in this research study, in order to collect data that is rich and inclusive and provides a holistic and comprehensive picture of the experiences of teachers when they implement numeracy in Grade R.

1.3.4 Data Collection

Data was collected and analysed in three groups, entailing five stages.

Group One consisted of data obtained from a pilot research study, in which the Interactive Qualitative Analysis Systems Method Framework (IQA) of Northcutt & McCoy (2003) was tested and adapted. Group Two consisted of data that was collected and analysed from participants teaching in the Coastal Group A environment. In order to ensure that the data collection and analysis were comprehensive and rich, the research study was extended to include Group Three, which consisted of data from participants in Coastal Group B.

The first stage of the research flow referred to the process of articulating the main purpose of the research study, namely to explore, describe and understand teachers' experiences in implementing numeracy in Grade R.

The second stage entailed an unstructured open-ended focus group interview which was used to compile the interview framework for stage four.

The third stage entailed the audio-video taping of the daily programme activities in the classroom. The aim of the audio-video tape observations was to record how numeracy was implemented in the Grade R classroom.

The fourth stage of the research flow consisted of semi-structured open-ended interviews.

The fifth and final stage of the research process consisted of the reporting of findings.

1.4 Data Analysis & Findings

Before I could embark on the process of data analysis, I had to manage the data by transcribing the data collected from the three unstructured open-ended focus group interviews, nine semi-structured individual interviews and nine audio-video tapes of classroom activities. Once the data was transcribed and filed into electronic folders, I embarked on data analysis. By managing the data in a transcribed format, I was able to make use of narrative descriptions to tell how Grade R teachers implement numeracy and what these teachers experience, feel and believe when they are in their classrooms.

Data analysis consisted of two procedures, namely extracting coding themes and identifying patterns. In analysing the data, I used John Stuart Mill's Analytic Comparison as a technique to identify patterns amongst the themes (Neuman, 1997, p. 428). Mill's Analytic Comparison consists of the Method of Agreement and the Method of Difference (Neuman, 1997, p. 428). The Method of Agreement indicated that there were three categories, consisting of seventeen themes, present in all the descriptive narratives. I have labelled these categories Barriers, Classroom Activities and Teachers' Experiences.

By using The Method of Difference to compare the transcripts of the individual interviews with the transcriptions of the audio-video tapes, I found that a new pattern, namely "silent themes" came to the fore. A silent theme is a theme which was not identified during the focus group or individual interview analysis, but became prominent when I analysed the transcriptions of the audio-video tapes. Six "silent themes" were identified in the nine transcripts of the audio-video tapes of classroom activities.

Reflection on the six silent themes revealed that they tended to be negative. Neuman (1997) describes "things that are not in the data" as"Negative Evidence" (p. 435); but in the context of this study I disagree with his perspective. While the six silent themes may have revealed weaknesses in Grade R classrooms, to identify a weakness does not preclude improving or even rectifying matters. The term "silent theme" indicates that the teacher was unaware of the impact of this aspect of her behaviour and actions in the classroom. The silent themes point to the need for further training to address the lack of skills on the part of teachers in seven of the classrooms.

The findings of the data analysis provided answers to the research question and sub-research questions, which are discussed in Chapter 5. In summary, it was found that the Grade R participants in this study have a theoretical knowledge and understanding of what ECD and Grade R entail. However the challenges which Grade R teachers experience when they implement numeracy are:

teacher-centredness,

a lack of going beyond the minimum requirements of the assessment standards,

limited open-ended questions which made an appeal to learners' creative, thinking, reasoning and problem-solving skills,

absence of developmentally appropriate practices,

limited opportunities for learning through play and

a lack of organizing and managing the Grade R class to enhance numeracy skills.

These challenges indicated that seven teachers need to undergo further training regarding planning, organizing and managing classroom activities to enhance numeracy development by young learners.

The impact of Grade R teachers' experiences regarding numeracy on their teaching strategies revealed that teachers were frustrated by the prescribed method of planning, and, in one case, discipline problems. This frustration impacted negatively on the planning, preparation and provision of numeracy activities in classrooms. Most of the Grade R teachers in the case study focussed on the completion of worksheets. There was a general absence of the implementation of numeracy concepts and skills in a hands-on way. Only in two classrooms were creativity, thinking, reasoning and problem-solving skills encouraged. The teachers in these two classroom environments were the only teachers in this sample to have received formal training in ECD.

In addition, the research findings showed the importance of regular in-service support and mentoring visits.

1.5 A Brief Review of the Scheme of the Dissertation

Chapters 1, 2, 3 and 4 comprise the Literature Review. (Because of the diversity of the literature, I deemed it necessary to divide the Review into four chapters.)

Chapter 2 focuses on the historical and political context of implementing numeracy in ECD sites, as it not only forms part of Grade R teachers' experiences and background, but also has a definite impact on how numeracy is implemented in Grade R. For the purpose of this research study, I have divided the historical and political context of numeracy in ECD sites into two timeframes, namely pre-1995 and post-1995.

Chapter 3 gives an in-depth description of the curriculum road that Grade R teachers have had to travel in the past twelve years. It also provides an overview of the new curriculum direction they will have to take until 2014 (when the Curriculum and Assessment Policy Statements will be reviewed). One of the aims of this chapter is to provide the reader with an opportunity to experience the overwhelming curriculum demands which have been made of Grade R teachers and practitioners in the past twelve years. It is hoped that the reader will come to understand the feelings of curriculum overload that Grade R teachers and practitioners have experienced. In this chapter, there is discussion of the background of three curriculum policies, their principles and curriculum design features, as well as a comprehensive look at the numeracy and mathematical knowledge with which learners in the Grades R - 3 ECD Foundation Phase band are expected to be engaged.

Chapter 4 explains how learning by young learners takes place according to four learning theories. The relationships of each learning theory to Curriculum 2005 and NCS are discussed. Guidelines are provided regarding how a Grade R classroom should function when numeracy is implemented, in relation to each of the four learning theories.

Chapter 5 explains the research processes I used to collect rich and in-depth data reflecting the understanding and experiences of Grade R teachers when they implement numeracy in their classrooms.

Chapter 6 comprises the data analysis.

Chapter 7 makes suggestions on how the findings of the research can be used to ensure that Grade R teachers are knowledgeable and skilled when they implement numeracy in their classrooms, despite varying curriculum prescriptions. The strengths and limitations of the study are also discussed.