Analyzing the use of history in mathematics education: issues and challenges around Balacheff’s cKȼ model

Abstract

Part of the international reflection on the use of history in mathematics teaching consists in a quest of frameworks and models suitable for empirical studies. Following this demand, this paper explores the way Balacheff's cKȼ model, a model taken from the didactics of mathematics, can be used in the analysis of learning at student level. In the first part of this paper, Balacheff's cKȼ model (conceptions, Knowledge, ȼoncepts) is shortly presented, and in the second part, the relationship between the epistemological background of the model and the use of the history of mathematics is explored in order to show a possible suitableness. The third part addresses an example of a school activity (about ancient Indian geometry) in which the model is applied and the historical issues clarified. Questioning the role of problems both in the cKȼ model and in the use of history, the last part shows how a study at the students' conceptions level enlightens the way in which historical elements can interact with contemporary mathematical learning.

Assessing the added value of a history-based activity for students with low mathematics skills

“…However, it also presents several differences, such as its unique writing system, which can facilitate an epistemological shift. The utilization of a historical source compels students to reevaluate their mathematical knowledge, encouraging them to manipulate both their own conceptions and those derived from the past (De Vittori, 2018). This approach is intended to promote learning, as suggested by Jahnke (2014).…”

Through Their Eyes: Gifted Students’ Views on Integrating History of Mathematics Embedded Videos Into Mathematics Classrooms

“…It is equally important to use mathematics itself as a tool (Jankvist, 2009) for reading (modern) mathematics. Furthermore, de Vittori (2018) proposed Balacheff’s cKȼ model (conceptions, knowledge, and ȼoncepts) to analyze the use of history in mathematics education at the student level. The connections between the most abstract mathematics (concepts), what is taught (knowledge), and those used/understood by students (conceptions) are shown in that model (Balacheff, 2013).…”

“…It is important to note that this process is essentially a bottom-up process since the main input is the conception at the student level. The conception level is the main entry point of Balacheff’s model and focuses on what makes students’ tasks interesting (de Vittori, 2018). All of these into account, the theoretical framework proposed by Jahnke (2014) examines the interactions between students’ past and contemporary learning guided in this study.…”

Research and Planning Design of Traditional Village Tourism Pension Model—Taking Madiping Village in Longnan as an example

“…It is also the mainstream tourism pension mode at home and abroad and forms the corresponding industrial system. Vacation recuperation type is a tourism pension mode that combines hotel industry, tourism industry and recuperation industry [7]; It refers to the mode of interactive replacement of the residential right of the elderly in different cities [8]; The rural leisure type is a new rural tourism pension mode which combines tourism, leisure, sightseeing, rural life experience and pension community [9]; Based on the concept of health preservation, the three-dimensional health care model is a comprehensive pension model integrating sports, religion, tourism, medical and other health services [10]. The purpose of the evaluation of the pension problem is to establish a complete evaluation system and evaluate the pension scheme reasonably and effectively.…”