This research article is about "Introducing a Supportive Framework to Address Students' Misconceptions and Difficulties in Learning Mathematical proof techniques (MPT): A Case of Debark University". This study aims to develop, introduce, and implement a supportive framework to overcome students' misconceptions and difficulties in MPT.…

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

This position paper examines the phenomenon of the McNamara Fallacy to analyse flawed conceptions of "success" in mathematics learning, normalised assessment structures and their implications for mathematics education. The established presence of the McNamara Fallacy and the ramifications of this statistical fallacy provide a foundation…

The article presents one of the possible ways of overcoming the misconception that is one of the myths about mathematics, which says that teaching mathematics is based only on the transfer of mathematical knowledge in the finished form -- often in the form of certain algorithms. The newly proposed method of access to mathematics teaching is…

One pedagogical approach to challenge a persistent misconception is to get students to test a conjecture whereby they are confronted with the misconception. A common misconception about a 'direct linear relationship' between area and perimeter is well-documented. In this study, Year 4-6 students were presented with a conjecture that a rectangle…

A study of pre-service primary school teachers' content knowledge regarding real numbers related to infinity, i.e., division by zero and denseness of the real number line, was conducted at a Swedish university. Data were collected twice during the respondents' teacher education using questionnaires and interviews on both occasions. The data were…

Many pre-service mathematics teachers in South Africa are apprehensive about the content of Euclidean geometry, because they did not study Euclidean geometry in high school but will be expected to teach the content when they start their teaching career. This article reports on a study that explored the role of semiotic representations in…

While it is widely believed that Specialized Content Knowledge (SCK) is essential to effective and quality mathematics teaching, the specific constructs that compose SCK remain underspecified. This paper describes the development and use of a new framework that extends the notion of SCK. The framework was trialled with a cohort of 90 first year…

The purposes of this study are to investigate whether pre-service middle school mathematics teachers evaluate discussions in the cases regarding proof by contradiction correctly, to what extent they explain their correct evaluations by referring to proof by contradiction, and the reasons of their misinterpretations of discussions in the cases…

Developing students' geometric reasoning skills is dependent on the quality of task designs and the role of the teacher. The purpose of this study was to apply Sfard's (2008) interpretive framework to analyse changes in students' mathematical discourse. This paper reports on the results of an investigation into the ways one class of Year 7…

When teachers conduct a universal screening in mathematics, they identify students who are struggling with mathematical content and adjust their instruction. In this mixed-methods study in Kolkata, India, teachers piloted a screening tool at the beginning of the academic year in 5th grade to determine students' (n = 171) understanding of…

When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN ? QUAL) was used to examine students' reasoning processes when solving…

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

In this paper we explore first-year students' difficulties with the use and interpretation of definitions of mathematical objects as they attempt proof construction exercises in the area of elementary set theory. The participants are students at a historically disadvantaged university in South Africa. In this study the activities and utterances of…

Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that…