Observations

In qualitative research, the techniques that are normally employed are observation, individual interviews and document analysis. Since this research follows the qualitative approach, the researcher used all three techniques. The process of data collection was followed in three phases.

Creswell (2010:83) explains observation as a systematic process of recording the behavioural patterns of participants, objects and occurrence without necessarily

communicating with them. Observation is an everyday activity whereby we use our senses (seeing, hearing, touching, smelling, tasting) but also our intuition to gather bits of data. McMillan and Schumacher (2010:208) allege that observation is used to describe the data that are collected, regardless of the technique employed in the study.

Observational research methods also refer, however, to a more specific method of collecting information that is very different from interviews or questionnaires. The observational method relies on a researcher’s seeing and hearing things and recording these observations, rather than relying on subjects’ self report responses to questions or statements. De Vos (2002:278) describes observation as a typical approach to data, which implies that data cannot really be reduced to figures. In the observation of participation the emphasis is thus both on one’s own and on the participation of others. Denzin and Lincoln (2000:673) add that researchers observe both human activities and physical setting in which such activities take place.

Observation is used to describe the data that are collected, regardless of the technique used in the study. Classroom observations were the most important tools of the said qualitative research as the researcher witnessed all the processes of teaching in a natural setting (McMillan and Schumacher 2010:208).

According to Creswell (2010:83), there are four kinds of observation that are used in qualitative research.

The first is complete observer. This researcher is a non participant observer who looks at a situation from a distance. It is the least obtrusive type of observation. The second is an observer as a participant. This observer gets involved in the situation. The observer does not get involved or influence the dynamics of the setting. The third type is the participant as observer. This is characteristic of action research projects in which the observer becomes part of research process.

complete participant. The observer is totally immersed in the situation such that those involved do not even notice that they are being observed. This may sometimes raise grave ethical concerns when those being observed were not asked for consent.

In this study the researcher acted as a non – participant observer during data collection. The researcher assumed the role of non - participant observer when investigating different schools and held informal one- to- one observation with individual teachers. The researcher sat at the back of the classroom taking field notes describing the classroom activities using an observation guide (Appendix: B). The researcher wanted to explore the approaches teachers use during the teaching of mathematics computation. The researcher observed the following:

• Classroom organization

Mercer (2006:507) charges that children construct solutions for mathematics through talk. Therefore it is important to organize children in groups in order to encourage child participation (2.4.2). Alexander (2000) also concurs with Mercer by arguing that dialogic teaching encourages children’s active participation (section 2.4.2).

• Classroom Resources

Carruthers and Worthington (2006:74) and Willis (1998) allege that children would understand learning content better if they use objects derived from their own environment in their learning (2.4.3). Crawford and Witte (1993:34) claim that the use of resources encourages active learning by children. This makes the children active participants in their own learning (2.6.5). Fagnant (2005:355) also supports these assertions by claiming that using counters develops children’s skills of addition and subtraction (2.6.5).

• Teacher Activity

According to Even and Tirosh (1995:164) if a teacher and her children understand concepts, she will have a better control and direction of classroom activities (2.5.1). De Corte (2004:280) supports Even and Tirosh’s allegation and adds that children should learn by understanding and not by rote. Therefore the children’s understanding of concepts will help to facilitate learning (2.6.5).

• Teacher child interaction

Van de Walle (2007:30) states that teacher - child interaction in which children are actively engaged in the process of constructing numerical knowledge and understanding is effective in the learning situation. The children learn by doing and thus help to find the solutions to problems themselves (2.2.1). Schunk (2004:412) also argues that children construct mathematical knowledge as advised by teachers. Teachers therefore do not give children solutions to problems but guide the children to find these solutions. Success gained this way would lead to more interest to participate in learning.

• Child to child interaction

Van de Walle (2006) argues that child interaction enhances social interaction as children can share how they arrived at the answers (section 2.2.1). Vithal et.al. (1992) suggest that dialogue between children and teachers is good for the learning process. This helps the introvert to open up and participate in the learning process too (2.2.2).

Lewins and Silver (2007:10-11) outlined the advantages of observation. The advantages include the fact that the observer is actively engaged in activities at the research site, where there is first hand involvement and immersion in a

The researcher gains insight into the views of the participants more readily, develops a relationship with them, and hears, sees and begins to experience reality as the participants do. The researcher does not stand aside as an outsider.

Observations give comprehensive perspective on the problem under investigation. The researcher also learns from her own experience and reflections, which form part of the emerging analysis. Data are gathered directly and are never of a retrospective nature. Informal observation data was supported by semi structured interviews during her experience within the context and by the verification of factual data through the interrogation of documents where necessary.

4.4.1.1 Observation guide

1. The classroom environment was observed to determine if it contributed to mathematics teaching problems. The following were observed:

• Classroom resources • Classroom organisation

2. Teaching activities are important variables that influence successful teaching and learning. These will include:

• Teacher - child interaction • Child participation

• Child - to - child interaction

3. Methods used to teach mathematics computations are regarded as the major determinants of successful learning. The methods used were observed for their effectiveness on children’s successful learning.