Pedagogical Considerations

 

For approximately sixty years, there has been substantial emphasis on the learning theory of constructivism (see also Bruner 1961; Piaget 1967; Vygotsky 1978; Bauersfeld 1995; Wertsch 1997; Von Glasersfeld 1989). It is based on the assumption that our natural learning processes occur by drawing on individual prior experiences to construct new knowledge. Many pedagogical approaches have been developed based on this learning theory such as inquiry learning, discovery learning, play based learning; and in line with these assumptions provide a minimal guidance approach to let the student's cognitive intuition drive the learning (Kirschner, Sweller & Clark 2006). However, as Kirschner et.al (2006 p.76) explains, ‘minimally guided instruction proceeds with no reference to the characteristics of working memory, long term memory or the intricate relations between them’.

 

Explicit and direct instruction or schema based instruction (SBI), does provide students with both the experiences and explicit instruction to deeply construct mathematical concepts related to time, with the integration of learning strategies and resources that are compatible with human cognitive architecture - such as concrete models as described in the previous chapter.

 

Whilst minimal guidance pedagogies provide opportunities for students to spontaneously explore concepts and drive this exploration, Ginsburg, Lee & Boyd, (2008) says explicit instruction is the only way to ensure high quality mathematics education. Moreover, SBI allows learners to consolidate their mental schema and to understand and accommodate new concepts – an essential process in developing a robust (and importantly accurate) mathematical understanding. This is particularly relevant to the teaching of time, in that the ability to organise problems based on structural features (e.g. fractional / part-whole problems) as opposed to the surface understanding, (e.g. simply asking students to “tell” the time based on hand position) will support the structures necessary for effective problem solving of time (Jitendra, Star, Rodriguez, Lindell & Someki 2011).

 

In addition, Booker et.al (2010) explains that rather than relying on a formal sequence of lessons for students to construct this understanding, time should be immersed into daily conversations with students to practice these skills and concepts. For example, he suggests that a classroom should have two or more different clocks (analogue and digital) on display at all times for students to compare how the same point in time can be represented. 

 

Another important issue in the teaching of time is that the passing of time can be perceived through changes in natural phenomena, that is day/ night, seasonal changes in climate and nature, as well as the visual movements of clock hands or the changing of numerals on a digital clock (Booker et.al 2010). It cannot however, be perceived through sensory experiences in the way other measurement concepts can. It is therefore paramount that students either create or have access to a range of concrete materials to help make sense and represent each facet of time. 

 

With this in mind, the following teaching and learning resources have been developed as they support the pedagogical approach of Schema Based Instruction in the construction of time concepts.