Sampling

Creswell (2010:79) explains sampling as the process used to select a portion of the population for a study. Sampling implies selecting a section of a population for investigation in which we are interested. A sample is studied in an effort to understand the population from which it was drawn. As such, we are interested in describing the sample not primarily as an end in itself, but rather as a means of helping us to explain some facet of the population (de Vos 2000:199 and Bryman (2012:416). McMillan and Schumacher (2010:129) describe sampling as the group of participants from whom the data are collected is referred to as the sample.

The sample can be selected from a larger group of persons, identified as the population from whom data are collected even though the subjects are not selected from the population.

Sampling decisions are made for the purpose of obtaining the richest possible source of information in order to answer the research questions. Qualitative research usually involves smaller sample sizes than those required for quantitative research studies. Sampling in qualitative research is flexible and often continues until new themes no longer emerge from the data collection process – termed data saturation (Creswell (2010:82).

4.3.1 Types of sampling

There are two types of sampling namely a probability sample and non - probability sample. Probability sample is a sample selected by using a random selection whereby every member of the population has a chance of being selected. Probability sample can be divided into: simple random sample, systematic sample, stratified random sample, and multi stage cluster sample.

The first is the most basic form of probability sample with everyone in the population standing an equal probability of being included in the sample. The second type implies selecting participants (units) directly from the sampling frame without using a table of random numbers. The third type is where you want your sample to be representative of all various elements, inclusive type implies dividing the population into clusters and then using probability sampling method to select a sample from among those selected in the clusters (Bryman 2012:416).

Qualitative research can also be based on non-probability. A non – probability sample implies a selection of a sample not using a random method of selection and some members of the population are more likely to be selected than others. A non – probability sample covers all other kinds of sampling not conducted according to probability sampling. It includes convenience sampling, snowball sampling, qouta sampling and purposive sampling. Convenience sampling is simply available to the researcher by virtue of its accessibility. Snowball sampling may be experienced when the researcher meets or makes contact with a group of people relative to the topic under

research and then uses them to make contact with others. (For example make initial contact with Mamelodi Sundowns players and then through them make contact with Orlando Pirates’ players). Qouta sampling is used mostly in commercial research and very rare in academic social research. Qouta sampling aims to produce a sample that reflects a population in terms of proportions of people different categories for example gender, age – groups or ethnicity, Bryman (2012:416).

Purposive sampling was chosen for this study, because it would be the most representative way of looking at the targeted population. For the researcher, this was appropriate because it would allow for the selection of specific schools. The researcher also considered certain specific characteristics when selecting this sample. Among others, children who are in Grade 3, whose ages are between nine and ten, and Grade 3 teachers in disadvantaged areas. The rationale for the choice of this sampling procedure is elaborated below.

4.3.2 Purposeful sampling

Purposive sampling means that participants are selected because of some defining characteristics that make them the holders of the data needed for the study. Sampling decisions are made for the purpose of obtaining the richest possible source of information in order to answer the research questions. Purposive sampling decisions are not only restricted to the selection of participants but also involve settings, incidents, events and activities to be included for the data collection.

According to White (2005:120 and, McMillan and Schumacher (2010:138), in purposeful sampling, the researcher identifies “information–rich” participants as they are possibly knowledgeable about the phenomenon under investigation. Purposive sampling also defines a type of sampling that allows one to choose a case because it illustrates certain features in which one is interested.

Purposive sampling is based entirely on the judgment of the researcher in that a sample is composed of elements that contain the most characteristics that are representative or typical attributes of the population (de Vos, 2004:207). For the purpose of this study, the targeted population was Grade 3 children and teachers in primary schools in Mamelodi.

The sample comprised five schools purposely selected in Mamelodi Township in the Tshwane South district of the Gauteng Department of Education. These were schools known to experience problems in the teaching of mathematics. One teacher was selected per school since all the schools had one Grade 3 class. The focus was on the Grade 3 teachers’ teaching activities and children responses to the teaching. The teachers were studied not only for what they taught but also whether they offered learning support to children experiencing problems.