On Some Necessary Conditions of Learning

Abstract

The purpose of this article is to identify some necessary conditions of learning. To learn something, the learner must discern what is to be learned (the object of learning). Discerning the object of learning amounts to discerning its critical aspects. To discern an aspect, the learner must experience potential alternatives, that is, variation in a dimension corresponding to that aspect, against the background of invariance in other aspects of the same object of learning. (One could not discern the color of things, for instance, if there was only one color.) The study results illustrate that what students learn in a sequence of lessons is indeed a function of the pattern of variation and invariance constituted in that sequence. All teachers make use of variation and invariance in their teaching, but this study shows that teachers informed by a systematic framework do it more systematically, with striking effects on their students' learning.

What is made possible to learn when using the variation theory of learning in teaching mathematics?

“…The point of departure of variation theory concerns the means with which we can help learners to handle novel situations in powerful ways (Marton and Pang 2006). Originating from the phenomenography tradition, variation theory posits that learning implies seeing or experiencing critical aspects of an object of learning (Marton and Booth 1997;Marton 2015).…”

“…The variation theory of learning (Marton 2015;Marton and Booth 1997) points to variation as a necessary component in teaching in order for students to notice what is to be learned. Studies on how variation can be used to enhance students' learning have been reported (e.g., Bartolini Bussi et al 2013;Huang and Yeping 2017;Marton 2015;Marton and Pang 2013;Sun 2011;Watson and Mason 2006).…”

“…Studies on how variation can be used to enhance students' learning have been reported (e.g., Bartolini Bussi et al 2013;Huang and Yeping 2017;Marton 2015;Marton and Pang 2013;Sun 2011;Watson and Mason 2006). A conclusion drawn from these studies is that how the content is handled and what aspects are made possible to discern in a lesson affects what is made possible to learn.…”

Non-affirmative Theory of Education as a Foundation for Curriculum Studies, Didaktik and Educational Leadership

“…Rather than focusing the learner's learning strategies, learners' ways of understanding the contents described. The phenomenographic approach developed by Marton and numerous colleagues (Marton 2014) has been influential since. Phenomenology and hermeneutics have most often been applied as epistemic positions (Claesson et al 2011) but also as ontologically oriented theory of human experience and Bildung (Gustavsson 1996;Bengtsson 2003;Kristensson-Uggla 1999.…”

“…kokemus, Ge. Erfahrung), or to the actual loss of a previous way of understanding the world requiring a possible reorientation (Uljens 1992;Benner and English 2004;Marton 2014). Second, all of the above regarding Bildung as an interpretative process is equally valid for the leader and teacher.…”