Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

Background/purpose: The application of learning models is expected to significantly promote the enhancement of students' problem-solving abilities through the development of interactive learning models. This study aims to (1) determine whether the Development of the Component Display Theory (CDT) Model is categorized as valid, practical, and…

The literature on proof by contradiction (PBC) is nearly unanimous in claiming that this proof technique is "more difficult" for students than direct proof, and offers multiple hypotheses as to why this might be the case. To examine this claim and to evaluate some of the hypotheses, we analyzed student work on proof construction problems…

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.…

Outside of education, many academic disciplines developed and promulgated checklists to evaluate the quality of qualitative studies. This article used an embedded mixed methods approach in three stages: development of a conceptual framework reviewing 62 guidelines; a content analysis of key areas of the guidelines; and review of dissertations to…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

This paper represents the third in a three-part series intended to challenge the social validity of the services provided by a university-based practicum for addressing the challenging behavior of individuals with disabilities. In this paper, we surveyed referring stakeholders (e.g., parents, teachers) of past service recipients to explore the…

In theory, the principles, processes, and concepts of applied behavior analysis are universally applicable. In practice, clinicians commit their lives to serving specific populations in specific settings for which specialization is needed. The purpose of this 6-year retrospective consecutive case series was to describe and evaluate the quality and…

This study aimed to analyze second-semester organic chemistry students' problem-solving strategies, specifically focusing on the resources activated while solving problems on E2, E1, and E1cB elimination reactions. Using the theoretical framework by Elby and Hammer, we defined a resource as a unit of information used in the problem-solving…

In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

In the current article, we describe the development and validation of the Social Comparison Rumination Scale. This measured was developed as a supplement to existing social comparison measures and to enable us to determine its potential relevance to perfectionism and other personality constructs. The Social Comparison Rumination Scale (SCRS) is a…

Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers' learning of these rules when being taught them explicitly. Our data come from academically motivated…

This study aims to determine the proof schemes used by primary education teacher candidates when solving a given problem and in their instructional explanations. Having a qualitative nature, the study utilized data collected from 277 third-year teacher candidates studying at the primary education department of the education faculty of a state…

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the…