Abstract
Background: One of the problems in mathematics education is students’ little understanding of mathematics both at the basic and higher educational levels, which is why we consider essential the design of adequate instruments and methods that can measure understanding about specific concepts. Objective: To assess the understanding of university students of the concept of a real function. Design: The research is qualitative as the attributes of a cognitive construct were analysed and interpreted. Setting and participants: There were 36 students of a degree in mathematics (18-20 years old) whose productions were analysed. All the students had taken the Calculus I course. Data collection and analysis: A test of six items related to tasks that involved the concept of function was applied, the data analysis was carried out from the evaluation categories proposed by Albert and Kim, who consider three categories to assess understanding, those being: the ability to justify, to understand why a particular mathematical statement is true, and to understand where a mathematical rule comes from. Results: The evaluation of the understanding of the concept of function has shown that, in order to achieve a high understanding, not only skills must be developed for the recognition of aspects of the function such as its definition, its discrimination or its application, but the ability to be able to justify such aspects must be considered too. Conclusion: The categories of understanding considered help to strengthen conceptual and procedural understanding, indicating comprehensive understanding.
Highlights
The understanding of a mathematical concept is a topic that has gained wide participation in the research carried out in mathematics education
Compared to what is mentioned by the Common Core State Standards for Mathematics (2010), we can say that university students do not understand efficiently, for they could not use properties established in the concept of function to generate solid arguments in relation to the development of their mathematical processes, neither could they to criticise the reasoning of their other colleagues
In relation to what is mentioned by the Common Core State Standards for Mathematics (2010), we can affirm that few university students made conjectures about their process to explore their veracity, conducting inductive reasoning according to the context of the information provided by the problem situation
Summary
The understanding of a mathematical concept is a topic that has gained wide participation in the research carried out in mathematics education To this end, different theoretical frameworks that address this line of research have been implemented (e.g., Skemp, 1980; Sierpinska, 1990; Pirie & Kieren, 1994; Kastberg, 2002; Arnon et al, 2014; Albert & Kim, 2015), which show the characterisation of understanding from each of their perspectives, their similarities and their differences, but all with a common objective, to measure or assess the mathematical understanding of students. Data collection and analysis: A test of six items related to tasks that involved the concept of function was applied, the data analysis was carried out from the evaluation categories proposed by Albert and Kim, who consider three categories to assess understanding, those being: the ability to justify, to understand why a particular mathematical statement is true, and to understand where a mathematical rule comes from. Conclusion: The categories of understanding considered help to strengthen conceptual and procedural understanding, indicating comprehensive understanding
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