Researchers who study student acceptance of evolution rely on surveys that are designed to measure evolution acceptance. It is important for these surveys to measure evolution acceptance accurately and in isolation from other constructs, so that researchers can accurately determine what leads to low acceptance. The Inventory of Student Evolution…

In this paper, we explore the role of mathematical proof summaries as a tool for capturing students' reading comprehension of a given proof. We present an interview study based on mathematicians' pairwise evaluations of student-produced summaries of a proof demonstrating the uncountability of the open unit interval. We present a thematic analysis,…

In this dissertation, I report results from a study that investigated the impact of students' engagement in a series of tasks in an introductory proof course that was designed to stimulate their learning of reading strategies to support their comprehension of mathematics proofs. Specifically, I investigated the impact of the design of five…

Much recent research and theorizing in the field of reasoning has been concerned with intuitive sensitivity to logical validity, such as the logic-brightness effect, in which logically valid arguments are judged to have a "brighter" typeface than invalid arguments. We propose and test a novel signal competition account of this…

Proof is central to mathematics and has drawn substantial attention from the mathematics education community. Yet, valid and reliable measures of proof comprehension remain rare. In this article, we present a study investigating proof comprehension via students' summaries of a given proof. These summaries were evaluated by expert judges making…

The present study investigates the incremental validity of the traditional books-at-home measure and selected extensions (i.e., number of children's books and number of ebooks) for explaining students' academic achievement as measured by their academic language comprehension. Using multiple linear regressions, we additionally explore the role of…

In this digital ITEMS module, Dr. Jacqueline Leighton and Dr. Blair Lehman review differences between think-aloud interviews to measure problem-solving processes and cognitive labs to measure comprehension processes. Learners are introduced to historical, theoretical, and procedural differences between these methods and how to use and analyze…

Arguably the largest obstacle freshmen face in their mathematics courses is their unfamiliarity with the language of mathematics. Addressing this problem right at the start seems like a sensible strategy, as comprehension of mathematical communication helps students in all mathematics courses they will take. In this paper we discuss general…

Proof generally has a bad reputation among students, especially at the high school level. In fact, when the first author initially mentioned to her students that she would like to interview them about proof, many reacted with fear. Further, classroom experiences and existing research (Stylianou, Blanton, and Rotou 2015) suggest that undergraduate…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

In this paper I explore eleven undergraduate students' comprehension of a proof taken from an undergraduate abstract algebra course. My interpretation of what it means to understand a proof is based on a proof comprehension model developed by Mejia-Ramos, et al. (2012). This study in particular examines the extent to which undergraduate students…

This study is a part of a large scale project in which an action research design is used to teach proof to 11th grade students. This part of the project aims to identify students' comprehension level through five proof comprehension tests developed by the researchers based on the National Geometry Curriculum. Data were analyzed by considering the…

Habermas and Arendt defend two contrasting accounts of discussion. While both accounts acknowledge the importance of knowledge as basis of discussion, Habermas emphasizes the aim of reasoned agreement and Arendt focuses on plural interpretative perspectives. I will explore the tension between the two accounts in order to clarify the phenomenon of…

This paper is an exploration of the relevance of Habermas's social theory for understanding meaning making in the context of shared online interaction. It describes some of the key ideas within Habermas's work, noting the central importance it gives to the idea of communicative action - a special kind of discourse in which there is "no other…

A significant body of research literature in mathematics education attends to mathematical proofs. However, scant research attends to proof comprehension, which is the focus of this study. We examine perspective secondary teachers' conceptions of what constitutes comprehension of a given proof and their ideas of how students' comprehension can be…