Physical artefacts, for example, can have both intrinsic and extrinsic value for a learner. The intrinsic value is derived from the learner's personal interests in the use of that artefact, and his or her self-directed competence to actively construct meaning through the process of using it. Intrinsic value is also derived from the learner's personal interests in the physical properties and characteristics of the artefact. For example, an octopus will not cease to be an octopus because it is stored in a freezer. If the freezer breaks, the octopus grows old and dies.
Creating a learner-centred approach for mathematics learning must be underpinned by an understanding of what good teaching is. A good teacher is someone who brings the subject to life, who connects with their students in a way that engenders excitement and confidence. A good teacher must be a skilled communicator and empowers the learners' intelligence to reach its own solution. Therefore, it is important to also include a description of how this understanding is realised through lesson planning. We begin by explaining a range of lesson plans (from Flint and Magill 2000) which support the development of the understanding of mathematical concepts. We describe the principles of contemporary mathematics education in these plans enabling you to personalize the process of planning your own lessons.
The learner-centred approach has its ontological foundations in the humanistic perspective of development. Humanists embrace the importance of holistic development, self-directed learning, and self-actualization through learning. Furthermore, humanists place high value on the role of the affective domain (including self-concept, self-esteem, motivation, and emotional satisfaction) in learning (Marquardt and Waddill 2004; Qi 2012; Rogers 1961). Both affective and cognitive needs are very important in humanistic teaching, and the goal is to develop self-actualized learners in a cooperative and supportive environment. Empathy, unconditional positive regard, genuineness, non-directivity, and the encouragement of critical thinking is regarded as crucial components of the learning process (Cornelius-White 2007). d2c66b5586