Instructional Strategies Used by Junior Primary Teachers in the Oshana Region of Namibia to Teach the Number Concept to Grade 1 Learners

Abstract

Teachers’ knowledge, beliefs, and attitudes contribute to the success of classroom instruction. Teaching approaches that are informed by teachers’ good content knowledge of mathematics they teach are regarded as more effective and produce high learning outcomes. It is critical that teachers possess both content and pedagogical content knowledge as these create confidence and a positive attitude toward the teaching of mathematics which in turn creates mathematically inclined learners. The problem identified in this paper is the low achievement in mathematics for learners at the junior primary level. The purpose of this paper is to identify the instructional strategies used by junior primary teachers when they teach the different aspects of the number concepts to Grade 1 learners. To achieve the goal of this study, an interpretative design was used to explore this phenomenon in detail and to help the researchers understand it in depth. The study found that junior primary teachers used a variety of methodological skills to teach the different aspects of early numeracy but lacked the appropriate pedagogical skills to effectively teach these aspects. The study recommends that junior primary teachers in the Oshana region of Namibia should be given continuous professional development workshops on pedagogy for them to acquire the skills and understanding necessary to effectively teach early numeracy skills.

Keywords

continuous assessment instructional strategies learning support early numeracy skills pedagogy

Introduction

After Namibia’s independence in 1990, the education system was revamped considering the international ideals on education at that time. Education reform in Namibia was based on the goals of equity, quality, access, and democracy which led to a change in pedagogy, shifting from teacher-centered education to learner-centered education (Ministry of Education [MoE], 2015b, 2015c; Ministry of Education and Culture [MoEC], 1993). According to the Namibian policy document: Towards Education for All (MoEC, 1993), the teacher-centered approach encourages passive learning because learners mostly listen and observe their teachers. Further, Towards Education for All explained that the teacher-centered approach regards learners as empty vessels who must be filled with knowledge contrary to the learner-centered approach which encourages active involvement in learning (Ministry of Education, Arts and Culture [MoEC], 1993). The learner-centered approach expects teachers to design teaching which allows learners to actively participate in the lessons by working in groups, discussing and debating ideas, evaluating situations, and representing concepts relevant to the learners’ contexts and needs (Grigg, 2010; Schoenfeld, 2019). The learner-centered approach is based on the constructivist theory of learning (MoEC, 1993), which is largely influenced by Jean Piaget and Lev Vygotsky. Piaget recommends that learners should be actively involved in their own learning if they are to create knowledge, while Vygotsky believes that learners need to be scaffolded by a knowledgeable other (N. Feza, 2014) if they are to learn. Both theorists highlighted the importance of the role of the teacher. This study is influenced by the social constructivism theory of learning (Schunk, 2012).

Acquisition of early numeracy skills and related understandings among young learners is a worldwide challenge that has been a focus of research and interventions for many years. Research that focused on upper primary and secondary phases in Namibia revealed that most teachers lack the competencies (pedagogical skills and subject content knowledge) to teach mathematics proficiently (Courtney-Clarke, 2012; Ilukena & Schäfer, 2013; Kapenda et al., 2015; Miranda & Adler, 2010; National Institute for Education Development, 2009), hence, the learners’ weak performance in mathematics. Even though Namibian junior primary learners have also been performing dismally in mathematics (MoE, n.d.) the researchers did not come across any Namibian research on the teaching of early numeracy skills in junior primary classes. The study was, therefore, motivated by a lack of research on early numeracy skills in Namibian junior primary education. It aimed to investigate the instructional strategies that junior primary teachers in the Oshana region of Namibia use to teach early numeracy skills to Grade 1 learners. This study is important because it enabled researchers to identify primary mathematics teachers’ areas of mathematics instructional and content needs that professional development programs and other government policy, and curriculum development support can hinge on (Luneta, 2012).

In the Namibian Grade 1 mathematics syllabus (MoE, 2015a), early numeracy skills comprise of subitizing, counting, odd and even numbers, number patterns, representing numbers, doubling and halving, place value, ordering and comparing, and number bonds. The component of early numeracy skills was chosen for this study because research (see Jacobi-Vessels et al., 2016) showed that it allows young learners the opportunity to acquire high mathematics competencies well beyond Grade 12 and also their ability to read.

The Instructional Strategies for Teaching Early Numeracy Skills

Jacobi-Vessel et al. (2016) argue that appropriate pedagogy is at the heart of effective teaching. They explained that the elements of effective pedagogy include structural elements such as physical space, routine, and materials as well as process elements such as identifying learners’ current knowledge, learning support, and continuous assessment, among others. Research (see Benner, 2010; Eaude, 2011; Jacobi-Vessel et al., 2016; Papadakis et al., 2017, 2018; Schoenfeld, 2014) has discussed endless instructional strategies for effective teaching of mathematics; however, Jacobi-Vessel et al. (2016) explain that although both structural and process elements are important for effective teaching and learning, process elements strongly relate to learners’ academic achievement. For this study, the following instructional strategies are discussed.

Accessing Learners’ Prior Knowledge

According to Clements and Sarama (2009) and Jacobi-Vessels et al. (2016), teaching is not about replacing or side-lining what is already known but is about integrating new information, concepts, skills, and ideas with what learners already know from past experiences. The integration of what is already known with the new learning content enhances the quality of mathematics’ learning content because it makes the subject content comprehensible to learners (Schoenfeld, 2019). Falk (2009, p. 71) also agreed with integrating new learning content with learners’ current knowledge arguing that “in separation, all meaning evaporates.” However, integration of what is new with what is already known can only be possible when knowledgeable others are able to locate the learners’ zone of proximal development (ZPD) which is regarded as the heart of meaningful instruction.

Direct Teaching

Direct teaching is an instructional strategy whereby teachers talk directly to learners with the purpose to explain ideas and concepts and/or model skills. Direct teaching is not about filling learners with knowledge as if they are empty vessels but should be used to help them develop conceptual understanding of the necessary knowledge and skills. According to Schoenfeld (2019), teaching for conceptual understanding necessitates that learners acquire declarative knowledge, procedural knowledge, and conceptual and metacognitive (cognitive and meta-process) knowledge—all of which can be acquired partially or in totality through direct teaching. During direct teaching, learners should be meaningfully involved in the lessons by analyzing, illustrating, explaining, and demonstrating their understanding of the mathematics skills they are learning.

Engagement of All Learners in the Lessons

Schoenfeld (2019) argued that all learners should be meaningfully engaged in core mathematical skills to have equitable access to mathematical ideas. Similarly, Grigg (2010) also argued that when learners are exposed to learning activities which allow them to analyze, solve problems, evaluate, create, and reason, their understanding of what they are learning is enhanced compared to when they are rote learning.

Group Work

The use of groups such as small group and pair work also enhances learning. Cognitive theorists, especially socio-culturalists, believe that knowledge is not constructed by an isolated learner (Fisher, 2015; Schoenfeld, 2019) but is socially constructed with others as they negotiate meaning. Groups allow learners to independently engage with the learning content and analyze it, then apply and synthesize knowledge without the direct support from a teacher. When learners work independently, teachers can identify learners’ understandings, misconceptions and errors which can help teachers to easily identify/locate each learner’s actual and potential (ZPD) mathematical abilities.

Learning Support

Learning support is a strategy which is used to meet learners’ individual learning needs (Schoenfeld, 2019). It aims to ensure that all learners have equal access to the learning content. Learning support can be conducted individually or learners can be grouped for differentiated instruction.

Learning Through Play

Theorists such as Piaget, Vygotsky, Brunner, Smilansky, and Shefatifa have argued that play enhances learning in young children. N. Feza (2014) reveals that through play, learners acquire new vocabulary and learn social skills and how to control their behavior. Play allows learners to use multiple senses (eyes, ears, nose, and skin) and stimulates different thinking skills because it exposes learners to situations where they are expected to decide, reason, predict, record, and experiment. Play also engenders enjoyment and stimulates interest in the learning of mathematics.

Another instructional strategy for effective teaching of early numeracy skills is the enhancement of learner motivation. Eaude (2011) argues that when learners are highly motivated to learn, their curiosity and enthusiasm are awakened, and they are thus able to persist longer with challenging tasks. Learner motivation is linked to Maslow’s hierarchy of needs (Eaude, 2011); hence, motivation to learn can only be sustained when learners’ physiological, safety, and belonging needs are met.

Continuous Assessment

Jorgensen and Dole (2011) describe formative continuous assessment as “inexplicably bound to the teaching and learning process” (p. 84) in order to inform the teaching and learning process. While teaching, teachers assess learners to solicit their current mathematical thinking and understanding, as well as their potential, which should be used to craft productive learning environments (Schoenfeld, 2019).

Contextualization of Early Numeracy Skills

Paparadakis et al. (2017) and Clements and Sarama (2009) argue that early numeracy skills should be taught in context because young learners acquire mathematical knowledge best using experiences and problems that are realistic to them. They further argue that young learners bring to school a wealth of informal mathematical ideas and knowledge which teachers can use as a foundation for further mathematical knowledge. By carefully linking learners’ prior knowledge (informal knowledge) to the formal learning content in schools, their informal knowledge could be enhanced, and the subject content become more meaningful.

Teaching Early Numerical Skills Based on Research-Based Theories of Teaching Mathematics

Most theories of teaching mathematics to young learners recommend that early numeracy skills should be taught step by step (Aunio & Rȁsȁnen, 2015; Clements & Sarama, 2009; Papadakis et al., 2017) and in progression. The Realistic Mathematics Education theory of teaching early numeracy skills (Papadakis et al., 2017), has four stages. The theory explains that for learners to effectively acquire mathematical knowledge (skills and competencies), they should first acquire the skills and competencies of the first stage before proceeding to the next stage. Aunio and Rȁsȁnen (2015) designed a working model for teaching core numerical skills to learners aged 5 to 8 years that consists of four core groups. Jorgensen and Dole (2011), Witzel et al. (2013), and Wright et al. (2006) discussed the six stages of counting. In addition, Clements and Sarama (2009) developed the Learning Trajectories Theory which helps teachers understand two important issues regarding every learner in the class: the level of the learner’s understanding of the concept being taught and the knowledge of the developmental steps the learner needs to take in order to achieve the desired level of understanding. Teaching mathematics based on theories of teaching makes the teaching of mathematics purposeful and its assessment formative.

Use of Manipulatives in Mathematics Teaching

Miranda and Adler (2010) argue that the exploration of teaching and learning support materials (TLSM) arouses learning interest in young learners. N. Feza (2014) explains that when used purposefully and over time, manipulatives such as counters, number lines, and number cards help learners acquire powerful understanding of early numeracy skills. Digital technologies (e.g., computers and smart mobiles) can also enhance learners’ understanding of early numeracy skills provided they are used in developmentally appropriate ways and tasks. According to Papadakis et al. (2018), information and communication technologies (ICT) can benefit young learners significantly when they learn basic numeracy skills because they make mathematics content more practical and meaningful. Mobile ICT (e.g., iPad and tablets) has an advantage over other digital technology devices because of their size, portability, and being touch-screen operated (Papadakis et al., 2017). They argue that because such devices can be used at any time, learners can be engaged with the subject content both in independent and collaborative learning environments. Digital technologies support learning, however, they are still unrealistic for many countries and schools, especially in Africa. African countries should make this strategy viable, especially because of the lessons learned from the effects of the COVID-19 pandemic. The pandemic brought most educational systems to a halt because of a lack of viable ways to keep learners learning while out of school.

Previous Research

Findings from the Southern and Eastern Africa Consortium for Monitoring Education Quality III (SACMEQ III) assessment show that the general performance of Namibian learners has not yet reached the Education Training Sector Improvement Program national target of learners’ competence in Mathematics (MoE, n.d). The study also argues that 75% of Namibian teachers who participated in the study did not reach the highest level (level 8) of competence.

In South Africa, a study by Chikiwa et al. (2019) referred to research by Graven and Heyd-Metzuyanim, which found that many Grade 3 and Grade 4 learners had not yet developed the advanced skills expected at their grade levels for solving mathematics problems generated through the understanding of early numeracy skills. Another South African study claimed that teachers’ instruction of young learners (aged 5 and 6 years) did not develop conceptual understanding, nor did it extend mathematical ideas in learners because it (teaching) was dominated by teacher-directed activities. In addition, teachers failed to coordinate classroom discussions or activities that engaged learners’ understanding in productive ways.

In Namibia, the annual National Standardized Assessment Test that Namibian learners write in Grade 5 and Grade 7 showed low performance of learners in mathematics (MoEAC, 2016). A study by Van Graan and Leu (2006) on the use of learner-centered education strategies among Namibian primary teachers found that the teachers were unable to implement the most important elements of learner-centered education, except for group work. In her study, Courtney-Clarke (2012) argues that Namibian mathematics teachers lack the appropriate mathematical content and pedagogical knowledge base. Further, she argues that Namibian teachers emphasize procedural thinking and rote learning. Likewise, Kapenda et al. (2015) also argues that Namibian mathematics teachers chose to develop procedural mathematics skills compared to conceptual understanding. A study by Miranda and Adler (2010) found that Namibian teachers did not use manipulatives during lessons. They further argue that teachers also did not encourage learners to express their thoughts during lessons. A study by Ilukena and Schäfer (2013) reveals that Namibian mathematics teachers with a teaching qualification, “Basic Education Teachers’ Diploma” lacked both subject content and pedagogical knowledge of the mathematics they were required to teach. The study recommended a complementary course in mathematics for these teachers. Research (see N. Feza, 2014; Kapenda et al., 2015) has argued that teachers who lack appropriate pedagogical and subject content knowledge negatively affect the extent to which their learners can learn.

Given the circumstances, this study aimed to investigate instructional strategies that Grade 1 teachers use to teach early numeracy skills. This understanding may provide some answers to why Namibian learners continue to perform poorly in mathematics. The study may also shed light on the professional development needs of junior primary teachers in this regard and how these needs can be addressed.

Research Objective

The objective of this study was to investigate the instructional strategies used by Grade 1 teachers in the Oshana region when they teach early numeracy skills.

Methodology

Research Procedures and Research Instruments

The study used an interpretative case study method because the researchers studied a real-life, contemporary bounded system over time. Miles and Huberman (1994) define a case study as a “unit of analysis,” a phenomenon which occurs in a bounded context. Likewise, Creswell (2013, p. 97) also refers to case study research as

a qualitative approach in which the investigator explores a real-life, contemporary bounded system (a case) or multiple bounded systems (cases) over time, through detailed, in-depth data collection involving multiple sources of information (observation, interviews, audio-visual material, and documents and reports) and reports a case description and case themes.

A qualitative case study method was deliberately chosen because the study sought to explore and understand in depth a “unit of analysis” (Miles & Huberman, 1994) (activities of a group of people) occurring in a bounded context. The activity (phenomenon) was the investigation of instructional strategies used by Grade 1 teachers in the Oshana region of Namibia to teach early numeracy skills. The contextual issues in which the study occurred are also of utmost importance to the understanding of this phenomenon because the boundaries between the phenomenon under study and the context of the study are not very clear (Yin, 2017). The research design was appropriate for the purpose of the study because it allowed the phenomenon to be studied in situ (Elshafie, 2013) so the researchers could understand the case in depth.

Before data for the study was collected, research instruments were piloted with a single teacher. The idea was to check for appropriateness of the content and language and the instruments’ ability to collect and when necessary, document the data they were intended for. After the piloting process, data collection instruments were improved based on the findings. The teacher who participated in the pilot study did not participate in the main study. It took over 3 months to collect data for this study, from January to April 2019 and during September 2019. The study used different data collection methods such as interviews (semi-structured), classroom observations, a short questionnaire, and document analysis. The interviews and classroom observation processes followed the Clinical Observation Model described by Gürsoy et al. (2013). The data collection instruments contained questions seeking information on the instructional strategies Grade 1 teachers normally use to teach early numeracy skills. Ethical clearance for this study was acquired from the University of Johannesburg while permission to do research in the Oshana region of Namibia was granted by the Regional Director of Education in the said region. The purpose, background, nature, and methods of the study as well as voluntary participation were clearly explained to the participants. Participants were also assured of anonymity and confidentiality of the information they shared. After approval and consent were sought from prospective participants, each participant was asked to sign a consent form.

To ensure the credibility of the study, the researchers discussed in detail (Baxter & Jack, 2008) the background of the study, its theoretical framework, the research design and the case itself. Data from different data collection instruments were triangulated (Baxter & Jack, 2008) and the researchers also stayed in the field for a prolonged time collecting and analyzing data.

Participants

The study took place in the Oshana region of Namibia which has a total of 170 Grade 1 teachers in government schools (MoEAC, 2020). The study purposefully selected 15 Grade 1 teachers teaching using Oshikwanyama as the medium of instruction. It was required that all study participants should hold a category C teaching qualification (3 years of teacher education) and should be teaching in government schools. All participants were also required to have 3 years or more of teaching experience. The researchers believed that teachers who met these criteria were reasonably qualified and experienced to understand the development of early numeracy skills in young learners. In Namibia, junior primary teachers are class teachers (teach all the subjects in the grades), hence, all participants were expected to comfortably understand the phenomenon at hand. The table below shows general information (school code, teacher code, years of teaching experience, highest qualification, age, gender, and the number of learners in the class) of the participants in the study (Table 1).

Table 1.

Participants’ General Information.

School	Teacher	Teaching experience JP (years)	Highest relevant qualification	Age (years)	Gender	Number of learners in class
A	T1	29	Basic Education Teachers’ Diploma	58	F	30
A	T2	9	Basic Education Teachers’ Diploma	30	F	30
B	T3	30	Basic Education Teachers’ Diploma	55	F	29
B	T4	5	Junior Primary Diploma	52	F	29
C	T5	27	Basic Education Teachers’ Diploma	51	F	29
C	T6	22	Basic Education Teachers’ Diploma	49	F	30
D	T7	34	Basic Education Teachers’ Diploma	59	F	36
D	T8	22	Basic Education Teachers’ Diploma	48	F	36
E	T9	10	Basic Education Teachers’ Diploma	37	F	42
E	T10	26	Basic Education Teachers’ Diploma	52	F	42
V	T11	20	Basic Education Teachers’ Diploma	49	F	40
W	T12	12	Basic Education Teachers’ Diploma	37	F	32
X	T13	7	Basic Education Teachers’ Diploma	44	F	31
Y	T14	29	Junior Primary Diploma	50	F	30
Z	T15	8	Basic Education Teachers’ Diploma	35	F	40

Data Analysis Method

Initially, all interviews were audio-recorded and some lessons were video-recorded. All the data from interviews, observations, document analysis, and the questionnaires were transcribed verbatim. After transcribing the data, the researchers read through all the transcripts to familiarize themselves with the data. The data which was relevant to the objective of the study was coded manually. Keeping the objective of the study in mind, thematic analysis was used to analyze the data. O’Leary (2017) argues that thematic analysis is a flexible way of analyzing data which is compatible with the constructionist paradigm. Data was analyzed inductively because the researchers wanted the data to tell the story of this study. According to Atieno (2009) and Braun and Clarke (2006) bottom-up (inductive) analysis is data-driven and allows the story to reflect the understanding of research participants. In addition, inductive analysis also helps to provide a rich, comprehensive, and complex account of data (O’Leary, 2017). Because there were no pre-set codes for the study, open coding was used in all the transcripts to code each segment of data which was important and relevant. Codes were carefully examined and eventually grouped into themes which were used during the presentation and discussion of results. For example, data segments such as, “knowing what learners already know to determine the level of understanding of a particular concept” and “ensuring that learners are not disturbing each other during the lesson process” were grouped under the theme “creating a positive learning environment.” As in many qualitative studies, data analysis was done concurrently with the data collection process and findings from different data sources were triangulated to validate the data (Kumar, 2019).

To enhance the dependability of the results of the study, the researchers opted to integrate the member-checking process and debriefing sessions (Creswell, 2013). Member checking and debriefing sessions provided opportunities for the researchers to share their analysis and interpretations of the data with the participants and solicit feedback from them. The researchers were unable to use an “independent coder” (Henning et al., 2004) because of financial constraints.

Results

The objective of this study was to investigate the instructional strategies used by Grade 1 teachers when they teach early numeracy skills. The analysis of data culminated in the following themes (instructional strategies) which were used to describe the findings of this investigation: developing a positive learning environment, direct/explicit teaching, group work, learning support, continuous assessment, and use of TLSM. It is important to share here that during the pre-observation conference, most Grade 1 teachers indicated that they were comfortable with the content of the Grade 1 mathematics syllabus. Only two teachers were not comfortable with teaching place values and subitizing.

Developing a Positive Learning Environment

To develop a positive learning environment, Grade 1 teachers used one or more warm-up strategies such as counting, singing, and/or managing learners’ behavior. The teachers who used songs to introduce their lessons explained that singing aroused the young children’s interest and curiosity and so could be equated to teaching through play. Grade 1 teachers also engaged learners in conversations regarding behavior during lessons and also referred to classroom rules which were displayed on almost all the classroom walls. Teachers who engaged learners in these conversations before the beginning of lessons believed that such talks directed learners’ behavior during the lessons. T5, for example, engaged learners in the following conversation at the beginning of her lesson.

Teacher:

“There are things that we should not do in the class, do you still remember them?”

Learners:

“Yes.”

Teacher:

“Tell me, what are they?”

Learners:

“We should not make noise; we should not touch things which are on top of our desks; we should always look at the teacher and we should listen to her.”

Teacher:

Yes, so that tomorrow you know what happened in the lesson.”

Besides managing learners’ behavior at the beginning of a lesson, some teachers continued to do so throughout the lesson, telling learners to listen, and/or to keep quiet.

To create a positive learning environment, Grade 1 teachers also checked the learners’ current knowledge of the different aspects of early numeracy skills they were teaching. Ten teachers checked their learners’ current knowledge before they started with the lessons, however, they did that for different reasons. For some, it was checked to inform the lessons which were in progress, while for others, it was checked to ascertain whether learners could still remember what was learned during the previous day’s lesson, even when what was taught did not relate to the current lesson. T1, whose lesson was on doubling and halving, accessed her learners’ prior knowledge of what they learned during the previous mathematics lesson and the conversation went like this.

Teacher:

“What did we learn yesterday?”

Learners:

“We did addition.”

Teacher:

“What is addition?”

Learners:

“Is when you add things together and you get more.”

Teacher:

“Yes that is what we learned yesterday. Today we are going to learn about doubling and halving. Do you know what doubling is?”

Contrary to what T1 did, T6 asked some questions on the topic of the day (numbers).

Teacher:

“We have been learning numbers, which number are we learning this week?”

Learners:

“Number four.”

Teacher:

“Who will come and write symbol four on the chalkboard?” (One learner went to write.)

Teacher:

“Is that correct?”

Learners:

“Yes.”

The conversation continued with all the numbers which were taught before number 4 (1, 2, 3). Another way they developed a positive learning environment was by ensuring that all learners were comfortable during the lessons. Grade 1 teachers continuously asked learners not to laugh at each other when, for example, a learner made a mistake.

One strategy which Grade 1 teachers used to teach early numeracy skills was talking to learners; for example, to emphasize positive behavior during lessons, to check learners’ prior knowledge, and so on in order to develop a positive learning environment for all the learners.

Direct/ Explicit Teaching

Direct teaching was a popular instructional strategy in this study which was mainly done in whole class groups. During direct teaching, only four teachers gave their learners opportunities to contribute to the lessons, the rest (N = 11) did not do so or only gave one or two opportunities. During T8’s lesson on numbers, the teacher named, counted, and displayed numbers while the learners passively listened and watched. Part of her lesson went like this: “Now let me see whether you know how many objects are represented by each number symbol. If I ask you to go outside and get six counters for me, will you be able to bring exactly six? Now let us start with one, when we are talking about one we are talking about one object/ item/ child. Now, look at me.” The teacher went on to display a number card with symbol one (1) and a picture of one object on a chalkboard while the learners watched. She continued in the same fashion teaching up to number five.

T1 also taught by telling. She asked her learners: “Do you know what doubling is?” and without waiting for a reply, she started to explain that “doubling is when you have for example two things and you add two more, or maybe you have three and you add three more. To double is to add the same amount/ number.” Another strategy used by Grade 1 teachers to teach early numeracy skills was “pouring subject content” into learners.

Group Work

Group work was observed in three lessons (T3, T14, T13) but it seemed as if in all three lessons it happened incidentally. In the case of T3, she grouped her learners in three big groups each with over nine learners. The learners were not given individual responsibilities to contribute to the given task. One teacher also did not prepare enough materials for all three groups which she only realized after she had already started teaching. She told the learners that “in your groups I want you to order these number cards from the smallest to the biggest.” While distributing the number cards she realized that there were not enough for all the groups. She then said: “Oooh, I do not have enough for all the groups. Wait … this group will use bottles” and gave the third group three empty bottles of different lengths. “The group with the bottles, order the bottles from the shortest to the tallest.”

Pair Work

Although pair work is regarded as the most preferred type of groupings for young learners (McGrath, 2010), it was only observed in two lessons (T5 & T10). It was, however, observed in T10’s lesson that learners were struggling to work as partners because each learner was doing their own work instead of collaborating.

Individual Work

Individual work was a popular strategy because it was used in all the lessons. During end-of-lesson activities, learners always received individual activities, mainly written activities.

Another strategy used by Grade 1 teachers was groupings, be it small groups or pairs. However, some groups were too big, materials used were not always prepared on time and learners were not assigned individual responsibilities toward the successful completion of the group task. Concerning pair work, learners were not co-operating but each was doing his/ her own work. They seemed not to know that they were expected to work together.

Learning Support

From the interviews, all teachers (N = 15) seemed to believe that there would always be some learners who would need learning support in order to understand a subject content. However, learning support was only observed in two lessons (T1 and T14). In both cases, learning support was not part of the lesson plans.

T1 was observed trying to support a boy who was struggling counting some objects. The learner was not observing the one-to-one correspondence between objects and number words. Instead of explaining the one-to-one correspondence principle to the learner, the teacher told him to drag counters as he was counting. The learner started to drag the counters but still did not observe the said principle. Feeling helpless and frustrated, the teacher told the learner: “I told you to learn the numbers and how to count” and left his desk.

In T14’s lesson, she tried to support learning but grouped seven learners in a “one size fits all” type of group without clearly understanding each learner’s problem.

Peer Teaching

Peer teaching was observed in a single lesson (T1). Three learners were observed helping fellow learners with a task on halving and doubling. The peer tutors, however, did not show any understanding of how to help others effectively. One peer tutor (PT1) tried to explain the subject content to another learner but was saying the number words in English, not in Oshikwanyama, which was the medium of instruction. PT2 was heard telling a learner she was helping “put four here, yes, write four here.” She (PT2) gave the correct answers. PT3 wrote the correct answers for the learners she was assisting. It was revealed in the post-observation conference that the peer tutors were not trained on how to support fellow learners.

During the post-observation conferences, some Grade 1 teachers were asked why they did not give any type of learning support even when it seemed necessary. Referring to Lotte, a girl in her class, T12 explained that

Lotte is just like that. She is not a person you could really spend time on. She will not learn even a simple thing. So yes, I only give her attention when I have time when I know that some other children do not need my help.

T13 indicated that she only gives learning support in mathematics on Wednesdays after classes not during lessons “because of time. I always run out of time during teaching time and that is why I help them after lessons, but only on Wednesdays.”

Another instructional strategy used by Grade 1 teachers was learning support although only a few teachers used it. In general, teachers were able to identify learners who were struggling with subject content matter, but did not always try to understand individual challenges which learners may be experiencing. As a result, some of the support rendered to learners was not useful as it did not bring about the changes envisaged. Learning support was rendered by teachers and other learners who seemed to understand the subject content. Peer tutors were not adequately equipped to tutor other learners.

Continuous Assessment

The Namibian curriculum reform of 1992 adopted learner-centered education (MoEC, 1993) to facilitate better learning for all learners. In the lessons observed, the assessment was done through observations, written activities, and oral questioning. It was observed that questions were asked for different purposes. For example:

assessing learners’ prior knowledge (T1: “What is addition?”)

confirming (T10: “Is that correct?”)

checking on learners’ speed (T11: “Are you done?”)

calling for learners’ attention and/or arousing curiosity (T11: “I drew two houses here, can you see them?”)

checking whether learners are following (T5: “What did I say estimation is?”)

revise lessons (T9: “What did we learn today?”)

To assess the learners, Grade 1 teachers observed and questioned the learners orally and gave them written activities. However, most questions asked were closed questions.

Use of TLSM

Grade 1 teachers used counters such as stones and bottle tops during their lessons. Other manipulatives such as abacuses, number lines, or number cards were used sparingly. T13 and T14 asked learners to identify numbers represented by pictures in the textbooks when both taught place value. The learners were, however, not familiar with the base 10 blocks (flats, rods, and units) represented in pictures.

Another strategy used by Grade 1 teachers to teach early numeracy skills was using teaching and learning support materials such as counters, number lines, number cards, and pictures in the books (base 10 blocks). However, learning support materials from textbooks such as pictures of base 10 blocks were not familiar to learners.

Discussion

The purpose of this study was to investigate the instructional strategies used by Grade 1 teachers when they teach early numeracy skills. In general, the Grade 1 teachers were aware of the different instructional strategies they could use to teach early numeracy skills but had challenges implementing them effectively. Considering how they felt about their abilities to teach Grade 1 mathematics it is clear that Grade 1 teachers were not aware of their own challenges in this regard.

Grade 1 teachers understood that for learners to learn effectively, they should be taught in positive learning environments where they are comfortable and are not afraid of intimidation or judgement. Hence, the teachers tried to instill positive behavior among learners and checked the learners’ prior knowledge, among others. Research (see Eaude, 2011; Munn, 2008; Schoenfeld, 1992) has argued that a positive learning environment allows all learners to have a sense of belonging, to feel safe and accepted and to not be afraid to make mistakes. Further, accessing learners’ prior learning helps teachers design learning activities which are within the learners’ ZPD and therefore is meaningful to them (Jorgensen & Dole, 2011; Kilpatrick et al., 2001; Schoenfeld, 2019; Schunk, 2012).

All Grade 1 teachers in the study directly taught their learners but only a few interacted with them during teaching. Fuson et al. (2015) argued that the types of classroom talk whereby a teacher teaches by pouring the subject content into the heads of learners without encouraging them to actively participate in the lesson do not challenge learners cognitively. They further argued that active participation of learners in their learning is important for the development of early numeracy skills. Schoenfeld (2019) and Papadakis et al. (2017) also advocated a two-way type of teaching, where teachers purposefully interact with their learners to ensure quality learning.

Grade 1 teachers (n = 3) used groups during their teaching. However, the groups were very big and learners were not given specific roles to fulfil in the group. Benner (2010) and Frei (2010) explained that young learners learn better in smaller groups and when they are given specific roles to contribute to the successful completion of group tasks. The group activities given were also not well planned because in one case, TLSMs were not enough. It has been found that group work strategy is only powerful when it is well planned because it is only then that it can promote learner participation, social interaction, and peaceful cooperation (Eaude, 2011).

In terms of learning support, the Grade 1 teachers seemed to believe that some learners will always need extra support in order to learn something. However, only a few of them rendered learning support while a single teacher indicated that she only supports learners who she believes would benefit from her support. This finding is consistent with what Schoenfeld (2019) argued that teachers’ beliefs of whether learners are able to learn something or not, affect how they communicate with them and eventually the extent to which learners can learn. Peer tutoring was also used in a single lesson; unfortunately, the peer tutors were not trained to understand the dynamics of their task and as a result, their support was not effective. This finding is consistent with Benner’s (2010) argument that peer tutoring can only be effective when peer tutors are well prepared. One Grade 1 teacher failed to render the necessary support that a particular learner needed for him to count objects correctly. The teacher’s inability to explain the necessary counting principle to the boy showed the lack of pedagogical and subject content knowledge on her side. Shulman (1986) noted that teachers who do not have the appropriate pedagogical and subject content knowledge of the level of the mathematics they are teaching negatively affect the understanding of their learners.

Another instructional strategy used by Grade 1 teachers was using the TLSM to enhance learners’ understanding of early numeracy skills. The teachers used some manipulatives such as counters and some pictures in the textbooks. However, learners did not understand the pictures in the textbooks. In their study, Fuson et al. (2015) explained that although pictures in textbooks can increase learning and understanding of numbers, it is only possible when learners understand what is represented in pictures with real-world objects.

Implications

The purpose of this paper was to investigate the instructional strategies used by junior primary teachers in the Oshana region when they teach early numeracy skills to Grade 1 learners. The findings revealed that Grade 1 teachers used a variety of instructional strategies to teach early numeracy skills such as explicit teaching, groupings, individual activities, encouraging positive behavior during lessons, accessing learners’ prior knowledge, learning support, assessing continuously, and using TLSMs. The study also revealed that many of the instructional strategies were not effectively used and therefore, hardly enhanced quality learning of early numeracy skills. This showed a lack of pedagogical knowledge among Grade 1 teachers and to some extent, a lack of subject content knowledge.

Many teachers used teacher-centered strategies instead of learner-centered strategies. They talked for prolonged periods without giving learners opportunities to discuss, share, explain, argue, speculate, and justify their understanding. According to Schoenfeld (2014), these types of talks are unlikely to develop mathematical authority, agency, identity, and accountability and eventually self-efficacy of early numeracy skills among learners. Learning support was minimally provided, thus it is reasonable to argue that there was no equitable access to mathematics content for all learners. The study also revealed that assessment was not used for formative purposes. Most of the questions used were closed and were unlikely to encourage learners to open up and clearly show their understandings and misunderstandings when they responded. Written assessment activities were monotonous and were not based on each learner’s levels of understanding. Written assessment activities were also given at the end of the lessons when most Grade 1 teachers did not have enough time to mark and help learners on a one-on-one basis.

As far as subject content knowledge, the study revealed that some Grade 1 teachers failed to explain important concepts to learners such as the one-to-one correspondence principle. They also failed to identify the developmental stages of counting (oral counting, cardinality, and subitizing) individual learners were operating at. All these challenges need to be corrected if junior primary teachers in the Oshana region are to teach early numeracy skills proficiently. As indicated earlier, knowledge of early numeracy skills enhances learners’ mathematics skills as far as grade 12 and beyond.

Based on the findings, we established that many teachers in the sample lacked pedagogical and subject content knowledge, hence, the researchers developed an intervention manual that can be used by trainers of junior primary teachers to support their participants to understand and teach early numerical skills effectively. We also envisage that the teachers’ participation in the study strengthened their knowledge of mathematics instruction that could cascade to their colleagues through interaction. We therefore recommend that junior primary teachers in the Oshana region be provided with continuous professional development (CPD) workshops that expose them not only to research-based instructional strategies but also to how the strategies can be used to effectively enhance learners’ understanding of early numeracy skills. Secondly, junior primary teachers in the Oshana region also need to be equipped with the necessary early numeracy knowledge that enable them to design quality assessment activities for all learners in their classes. We recommend that the intervention manual developed in this study should be published and used in professional development initiatives as well as disseminated to schools for junior primary school teachers to use some of the activities and assessment tasks that were developed by the researchers and the teachers. Chikiwa et al. (2019) argued that although some teachers might have teaching qualifications, they might not be adequately equipped during their initial teacher education to meet the demands of teaching. Continuous professional development activities can correct the practices of junior primary teachers which do not support quality learning of early numeracy skills and harmonize them with best practices.

Limitations and Future Research

This study collected data from 15 Grade 1 teachers who were teaching through Oshikwanyama as the medium of instruction in the Oshana region of Namibia. The generalizations of the findings of this study are therefore only limited to those particular Grade 1 teachers and not to Grade 1 teachers who use other languages as a medium of instruction or who are teaching elsewhere in the country. This study also only investigated early numeracy skills as stipulated in the Namibian Grade 1 syllabus and did not cover other components of mathematics such as geometry, data handling, problem solving, and computation.

Since this study found that Grade 1 teachers lacked accurate mathematics’ pedagogical and subject content knowledge, it is recommended that a large-scale study on Namibian junior primary teachers’ mathematics pedagogical and subject content knowledge be undertaken. The study also found that Grade 1 teachers did not offer quality learning support to learners, hence, it is recommended that a study be conducted on the implementation of learning support in the junior primary phase in the Oshana region of Namibia.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Paulina Hamukonda

Kakoma Luneta

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