Abstracting in the context of Spontaneous Learning

Abstract

There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii's mental activities. Using video-stimulated interviews, the model was then used to analyse the behaviour of two Year 8 students who had demonstrated spontaneous abstracting. The analysis highlighted the crucial role of synthetic and evaluative analysis, two processes that seem unlikely to occur under guided construction.

Interdisciplinary Mathematics Education

“…This case study shows that the structure of the 'think big' aspect of the responses to each project gives opportunities to select and explore new mathematical ideas and the nature of the task is critical to the degree to which this is possible (Kieran et al, 2008;Williams, 2002). Students require opportunities to explore unfamiliar mathematical ideas by recognizing the relevance of known mathematics, building-with it in unfamiliar sequences and combinations, and synthesising these (constructing) to realise something mathematically profound (Dreyfus, Hershkowitz, & Schwarz, 2001;Williams, 2007Williams, , 2014. Key to achieving this is teacher awareness of the mathematics embedded within a STEM activity.…”

“…When students found that the hypotenuse could not be shorter than the height of the triangle, informal development of ideas about the relative lengths of sides of triangles was stimulated for some students. These students had thus discovered and decided to explore a mathematical complexity (Williams, 2007).…”

Lise Öğrencilerin Bilgiyi Oluşturma Süreçlerinde Öğretmen Etkisi

“…The questions enable the students to recognize the relationship between the preliminary and new knowledge and to ask questions are the hints to construct knowledge and facility the process. The results of Williams (2007) show that learners can construct knowledge spontaneously when the teacher reminded the class of the previous lesson before teaching. But it is a prerequisite that the preliminary information is sufficient for this and enough time is given.…”

Social C apital and Women’s Entrepreneurship

“…The concept of informal learning can be intertwined with several other understandings of leaning. For example, theorists have used different terms to refer to informal learning such as incidental learning (Marsick & Watkins, 2001), spontaneous learning (Williams, 2007), experiential learning (Dewey, 1938;Kolb, 1984), transformative learning (Mezirow, 1997), conversational learning (Baker, Jensen, & Kolb, 2002), tacit learning (Polanyi, 1967), situated cognition (Halpern & Wenger, 1991), and action learning (Foly, 1999). While these and other scholars address the concept of informal learning across different contexts and disciplines, they tend to agree that it can be defined as "any activity involving the pursuit of understanding, knowledge or skill which occurs outside the curricula of educational institutions, or the courses or workshops offered by educational or social agencies" (Livingstone, 1999, p. 51).…”