An APOS Analysis of students’ understanding of the concept of a limit of a function

Abstract

This article reports on a study which used the APOS (Action‐Process‐Object‐Schema) theory framework to investigate university students’ understanding of limits of functions. The relevant limit concepts were taught to undergraduate science students at a university in Kwazulu‐Natal in South Africa. This paper reports on the analysis of students’ responses to four types of questions on limits of functions. The findings of this study confirmed that the limit concept is one that students find difficult to understand, and suggests that this is possibly the result of many students not having appropriate mental structures at the process, object and schema levels.

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

“…It seems that several students perform poorly because they are unable to adequately handle information given in symbolic form which represents abstract entities, for example functions, or/and they lack adequate schema or frameworks, which helps to organize and link different objects (Maharaj, 2005). The implications of such findings are a variety of representations should be used, and that students should be encouraged to engage with a flexibility of mathematical conceptions of the derivative (Andresen, 2007;Maharaj, 2010Maharaj, , 2013. Hähkiöniemi (2004), as well as Roorda, Vos, and Goedhart (2009) noted that growth in understanding depends on a variety of connections, both between and within representations, and also between a physical application and mathematical representations.…”

An Investigation into the Preparedness of Teachers to Teach Grade 12 Mathematics: A Case Study

“…The theoretical framework for this study is APOS (action-process-object-schema) theory. APOS theory is based on the following assumptions (Dubinsky 2010;Maharaj 2010):…”

“…APOS theory postulates that a mathematical concept develops as one tries to transform existing physical or mental objects. The descriptions of action, process, object and schema given are based on those given by Weller et al (2009) and Maharaj (2010Maharaj ( , 2013Maharaj ( , 2014Maharaj ( , 2015.…”

Viewing basic math through the lens of history: Undergraduates’ reflective learning in a history-augmented mathematics classroom

“…APOS theory (Dubinsky & McDonald, 2001) proposes that an individual has to have appropriate mental structures to make sense of a mathematical given concept. The mental structures refer to the likely actions, processes, objects and schema required to learn the concept (Maharaj, 2010). The APOS theory begins with actions and moves through processes to encapsulated objects.…”