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"Understanding is a measure of the quality and amount of links that a new thought has with existing thoughts. The larger the amount of links to a community of ideas, the better the understanding (Van de Walle, 2007, p.27)." My philosophy of a constructivist mathematics education At exactly what stage does a pupil, in most intents and purposes, encounter some thing mathematical? Does it symbolise a student that may remember a formula, write down symbols, or see a design or solve a problem? I believe in enhancing and enabling a pupil's mathematical expertise that fundamentally stems from a Piagetian hereditary epistemological constructivist model. This permits the pupil to scaffold their learning through cognitive processes that are facilitated by teaching in a resource rich and collaborative environment (Thompson, 1994, p.69). Constructivist learning Constructivist learning in mathematics must endeavour to encourage students to "construct their own mathematical knowledge through social interaction and purposeful activities (Andrew, 2007, p.157)." I want students to come up with their own conceptual frameworks, experiences, environment and prior knowledge. With learning being a societal process, students can talk in small groups their alternative strategies rather than quietly working at their desks (Clements et al., 1990, p.2). Constructivist teaching I believe the use of this constructivist teacher to enable to guide and facilitate a student's thought processes and support the creation of workable mathematical notions. A skilled teacher will even construct an appropriate classroom environment where students openly talk, reflect on and create sense of activities put before them (Clements et al, 1990). During peda...