**5. Research design**

*Metacognition in Learning*

**4. Nurturing self-efficacy of young children**

nurture self-driven learning. The strategies are as follows:

with the aim of extending them for further development.

**4.2 Scaffolding children's mathematics learning**

match others to start an intentional conversation [18].

**4.3 Developing mathematics from children's activity**

regulated behaviour in learning.

**4.1 Purposeful play for mathematics development**

but are ignored. This chapter advocates for nurturing of intellectual autonomy that is innate to young children to nurture self-efficacy, and independent learning.

Self-efficacy means independence and self-driven individual. Feza [15] synthesized a number of strategies to nurture mathematics stimulation of young children form the literature on early childhood mathematics. These strategies align in allowing children to use their intuitions to guide learning and instruction, hence they

Play on its own draws on young children's interests, curiosity and intuitions leading to full voluntary participation. The power of play resonates with peer interaction, development of vocabulary through interaction, development of social skills through behaviour and development of team work attributes [16, 17]. Hence, in mathematics block building nurtures spatial relationships and problem solving. It is during this play an educator can tap through observation into children's interests

Scaffolding is a concept that originates from Vygotsky's theory of social construction where scaffolding refers to the extension of the student's level of thinking [14]. Having observed the children playing or doing their own directed task the educator has to first identify the child's level of thinking through observations and engagement. Once the child's level is identified the educator can participate as a peer to assist the development of the next level of thinking. For example, a group of children were playing with pattern blocks sorting them. Their sorting rule was not clear whether it is by shape or colour since the same shapes share the same colour. The educator took a green block and asked the group to tell her where to place it. The group pointed her to the green triangles. That gave a hint to the educator of where the learners were. This also give the educator an opportunity to bring another block of a different colour and ask learners where to place it a colour that does not

Cognitively guided instruction (CGI) designed by [9, 19, 20] encourage educators to allow students use their intuitive strategies. This approach has proven to have significant gains on young students' mathematics performance. These studies proved that students' intuitions when allowed to be employed in problem solving, self-esteem and mathematics confidence of students increases [9]. This lead to self-

As indicated by [5] young children make more sense of the physical knowledge and therefore need physical manipulatives, and virtual manipulatives to explore and learn through the exploration. Jung [21] suggest that educators provide a variety of manipulatives and representations to extend and challenge

**4.4 Encourage and provide manipulatives for exploration and inquiry**

**86**

This chapter employs qualitative inquiry as it aims to provide insights on young leaners intuitions of mathematics in their free play. In order to achieve this aim interviews together with observations are used as exploring tools that will unravel these intuitions giving insights into learners mathematical thinking that exist before their formal schooling.

#### **5.1 Participants**

The chapter reports data from a three-year study that was funded by the National Research Foundation (NRF). The data reported was collected from 67 reception class students in five primary schools in the Eastern Cape. These schools are part of the funded project that provides professional development to educators of the 5–6 years old.

#### **5.2 Ethics approval**

Parental consent and learner ascent was negotiated and granted for all learners and educators participating in the project. However, for this study not all learners with consent from parents participated. In each school 15 students were selected across reception classes participating in the study. The selection was conducted by the students' educators prior beginning of the formal instruction in the beginning of the year. This chapter reports only on 67 students' data due to poor recording of the interviews and few learners who lost interest and left during interviews. In addition, an ethics approval for this study was also received from the authors' university. It is important to note that learners' comfort was important during data collection. Learners were allowed to leave the room when they needed to and also when they lose interest they were allowed to take a break and come back if they want to. Only few learners left before completing the interview in general less than 9.

#### **5.3 Instruments**

An interview protocol was developed on students' intuitions of mathematics. This protocol was accompanied by manipulatives to be used freely by students. The 20 minutes, interview protocol was piloted to six 5-year-old students in a primary school in Gauteng Province and revised after the analysis of the pilot data. The following **Figure 1** is a picture of manipulatives students were playing with during interviews.

It is important to note that the interview protocol allowed for questions guided by learners' play and activities. Students were left to play with the bottle tops for 3 minutes without interruption, then the interviewer asked to join in the game asking students to show her the correct way of playing. While playing, the interviewer probed about the interest of the student on the activity and if s/he will be willing to share it with others. After a while the interviewer does the pattern on **Figure 2** below and asks the student to play with her following her rules.

The interviewer gives the student a chance to develop his/her own pattern if possible. The same procedure continues with the shapes and pattern frames, except that for the shapes in **Figure 3** learners are asked to fill up the pattern frames.

**Figure 1.** *Counting manipulatives.*

**Figure 2.** *Pattern demonstration.*

**Figure 3.** *Shapes and pattern frames.*
