**3. Autonomy**

*Metacognition in Learning*

intuitions mediate self-regulated learning?

**2. Young children's mathematical intuition**

were made and a logico-mathematical knowledge is formed.

Furthermore, [6–8] affirm that children demonstrate spontaneous quantitative recognition at a young age. This spontaneity is a natural ability that is identified as intuitions by researchers [9]. For example, at 6 months old children are able to discriminate small numbers [6]. Clements [7] suggest that this skill demonstrated by the children at this infant stage is subitizing. Hyde and Spelke [10] extend this discovery by suggesting that babies under 9 months own two systems of nonverbal numerical cognition: one that is retorting to small quantities of individual objects and the other to approximately larger quantities. These systems contribute to the development of counting skills [11]. In addition, [12] brings forth the spatial intuitions of children's crawling which allows them to navigate and understand space. The above literature clearly indicates children's mathematical intuitions that need one to tap on in developing them further and deeper. For this chapter the big

This could be used for their benefit in developing their self-regulated skills towards learning. This chapter teases out these intuitions to inform instruction of young students that nurtures independent learning and self-regulation skills. This chapter aims to explore young children's mathematical intuitions before they enter formal schooling. This is achieved by conducting clinical interviews with 5–6 years old entering reception class for the first time. These intuitions are explored to inform research on possibilities of developing self-regulation of students while they are young and flexible to attain good habits, furthermore natural self-regulation can still be nurtured and sustained during the early years of education. This chapter responds to the following questions: (1) How do young children demonstrate their mathematical intuitions? (2) How are these intuitions aligned with curriculum specifically South African Curriculum for reception class? and (3) How do these

Jung [5] and Kammii and DeClark [6] describe young children's mathematical intuitions as internal abilities possessed by young children. In discussing the origins of such abilities [5] employs Piaget's three kinds of knowledge: "physical; logicomathematical and social" (p. 7) knowledge. The difference amongst these knowledge is derived from their sources and modes of structuring. Physical knowledge is knowledge of "objects in external reality." This knowledge can be observed, touched or felt using senses. This knowledge cannot develop without external influence or experience. On the other hand, logico-mathematical knowledge is formed internally through connections that are mentally made. For example, [5]'s story of a 6-yearold girl trying to understand the concept of Santa Claus. This girl started noticing some patterns about Santa Claus that made her ask some questions such as: "How come Santa Claus uses the same wrapping paper as we do?"; "How come Santa Claus has the same writing as Daddy?" (p. 45). Kammii's story of Santa Claus indicates that a young child believes all what her parents tells her. However, as she develops she begins to make connections in her brain. The girl in Kammii's story believe in Santa Claus/Father Christmas in South African language but one day he made some observations: (1) she observed that Santa Claus's writing on his presents is the same as her father, and (2) the way the presents are wrapped is the same as the way her mother wrap up presents at home. This pushed the girl to make connections that, she has never met Santa but Santa always knows what she wants. She therefore realized that there is no Santa as Santa is her father assisted by her mother in wrapping up the present. This indicates that the external or physical knowledge observed was then internalized by this child and became internal knowledge and connections

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The autonomy concept comes from Piaget's theory of construction of knowledge that originates from children's experiences of their world. The intuitions discussed above resonates well with the children's experiences. These experiences happen through senses physically. Kammii and DeClark [5] defines autonomy as being directed by yourself. In other words, being self-driven. In the case of mathematics learning the concept of autonomy will refer self-dependency and independent learning. There are two types of autonomy from the original theory: moral autonomy and intellectual autonomy.
