It is widely recognized that students encounter difficulties with proof across all grades and beyond, yet standardized instruments related specifically to students' perceived self-efficacy for mathematical proof have not been readily available. The purpose of this study was to develop and investigate preliminary validity evidence for a new…

Mathematical thinking beliefs are a significant element in supporting teachers' practices of learning and teaching school mathematics. Most prior researches on mathematics beliefs have focused on teachers' beliefs about learning and teaching mathematics in general. This research aimed to validate a Mathematical Thinking Belief instruments (MTB).…

While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

This study presents the development of a mathematical creativity test and exploration of its psychometric properties. The study was conducted in six public schools and a high ability center between 2015 and 2018. The sample of the study included 1129 middle school students. The Mathematical Creativity Test (MCT) consists of problem posing, making…

The aim of this study is to develop a rubric to assess mathematical reasoning competence. Since the aim is to assess a competency, the frameworks of the PISA exams in the literature, which give an important place to competencies, have been examined. Due to its focus and in-depth analysis of mathematical reasoning, each of the actions expected from…

We discuss a practical method for assessing mathematical proof online. We examine the use of faded worked examples and reading comprehension questions to understand proof. By breaking down a given proof, we formulate a checklist that can be used to generate comprehension questions which can be assessed automatically online. We then provide some…

Not enough effort has been invested in developing reliable and valid assessment instruments to measure students' development of reasoning competences in mathematics. Previously developed tests rely mostly on standardized multiple-choice assessments, which primarily focus on procedural knowledge and rote learning and not on how students argue for…

Developing a new assessment requires the expertise of both content experts and assessment specialists. Using the example of an assessment developed for Ontario's Colleges Mathematics Assessment Program (CMAP), this article (1) describes the decisions that must be made in developing a new assessment, (2) explores the complementary contributions of…

The following report describes an assessment instrument called the Mathematics Performance and Cognition (MPAC) interview. The MPAC interview was designed to measure two outcomes of interest. It was designed to measure first and second graders' mathematics achievement in number, operations, and equality, and it was also designed to gather…

This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

Multiple reports highlight the increasingly quantitative nature of biological research and the need to innovate means to ensure that students acquire quantitative skills. We present a tool to support such innovation. The Biological Science Quantitative Reasoning Exam (BioSQuaRE) is an assessment instrument designed to measure the quantitative…

In this article, we highlight the need for a precisely defined construct in score-based validation and discuss the contribution of cognitive theories to accurately and comprehensively defining the construct. We propose a framework for integrating cognitively based theoretical and empirical evidence to specify and evaluate the construct. We apply…

Students who complete kindergarten with an inadequate knowledge of basic mathematics concepts and skills will continue to experience difficulties with mathematics throughout their elementary and secondary years and may be at increased risk for math disabilities. There is a critical need to identify students experiencing difficulties in mathematics…

These proceedings contain the papers of the 16th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2019), held during November 7-9, 2019, which has been organized by the International Association for Development of the Information Society (IADIS) and co-organised by University Degli Studi di Cagliari, Italy.…

The initial steps necessary for constructing an analogies test are described. Basic mathematics being the context, the aim of the test is to predict student performance in research statistics courses characteristic of graduate education and social science programs. Items involving analogies in a quantitative context were built, sorted into two…