Counteracting Destructive Student Misconceptions of Mathematics

Abstract

Abstract:In this article, we ask the question of what it takes for targeted efforts to be reasonably successful in altering students' misconceptions and unproductive beliefs and ensuing myths about mathematics as a discipline and a school subject and about themselves in relation to mathematics, so as to pave the way for satisfactory learning. We attempt to answer this question through the analysis of three cases of upper secondary school students, who all struggled with mathematics-related difficulties due to myths resulting from misguided beliefs, erroneous proof schemes, or mistaken interpretations of the didactical contract, the three theoretical constructs we employ in the study. We describe how specially educated teachers, so-called "mathematics counsellors", taking part in a professional development program conducted by the authors, were able, firstly, to identity these students, then to diagnose more precisely the nature of their difficulties, and finally to design targeted interventions in order to assist the students in actually overcoming (parts of) their difficulties and eventually dispelling some of the myths they were influenced by. We further offer an analysis of the elements responsible for the success of these interventions. More precisely, we identify five such elements. Finally, we zoom in on the role and intricate connectedness of the three theoretical constructs mentioned above.

A Review of Students’ Common Misconceptions in Science and Their Diagnostic Assessment Tools

“…Among several methods in diagnosing misconceptions, interviews have a significant role because researchers may get detailed information about students' cognitive knowledge structures. Interviewing is one of the best and most widely used techniques to find out the knowledge and possible misconceptions a student has (Fuchs & Czarnocha, 2016;Jankvist & Niss, 2018;Wandersee et al, 1994). Interviews can be used to translate student responses or answers to be analyzed and classified based on appropriate scientific conceptions (Shin et al, 2016).…”

Enhancing Student Motivation in Secondary School Mathematics Courses: A Methodological Approach

“…On the other hand, the habit of doing homework-which is essential in mathematics for assimilating and understanding the content correctly [11]-tends to be crucial for achieving good academic results [12]. In spite of that, in general terms, it can be assessed that many students do not feel motivated to do math homework [11] and, in many cases, they wonder about the real usefulness of this subject [13][14][15]. Although this demotivation may be due to the direct influence of the subject teacher [16], who may be demotivated him/herself [17,18], most math teachers are worried about improving the teaching-learning process and, hence, they try to find solutions and to use innovative methodologies that enhance the students' active participation during the classes and that reinforce the acquired knowledge in order achieve better academic results [19].…”

Tracing proof schemes: some patterns and new perspectives

“…However, Harel and Sowder stated that they do not believe that external proof schemes are necessary for the development of analytical proof schemes but that external authoritarian schemes and empirical schemes should fill only the roles of confirmation and assumption at some stages for mathematics students. In the study of Jankvist and Niss (2018), a student who uses the authoritarian sub-scheme of external conviction exemplifies this situation by constantly asking both the teacher and classmates for approval in everything she did in mathematics. In their study, an attempt was made to move this student from at least this scheme to a more empirical one, thus showing her why and how it is appropriate to some extent to "experiment" as part of executing mathematical processes.…”