Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

The aim of this study is to examine the error approach of middle school teachers and their noticing of their approaches. The study was designed as a case study, which is a qualitative research method, and conducted through four middle school mathematics teachers during the pandemic. The data regarding the study were gathered via in class video…

The differences in the development of students' thinking levels, especially in adolescence, impact the way they perceive problems. Contextual learning with ethnomathematics can provide opportunities for students to develop problem-solving abilities based on their level of thinking. This study examined the contextual learning with ethnomathematics…

Nowadays, mathematical reasoning and making proof have taken importance for all students from the grade level of elementary education to university. More specifically, mathematical induction (MI) is a kind of proof and reasoning strategy taking place nearly all grade levels. Moreover, teachers are important factors affecting student learning and…

This study analyzed cognitive representations of knowledge from the chemistry of matter unit in a ninth-grade science textbook--the only authorized textbook in Saudi Arabia. It examined textual and visual information from two lessons in order to identify the textbook's introduction of concepts, linguistic context, integration of concepts, and the…

The study of mathematics at the university level requires logical thinking and strong mathematical skills. Contemporary first-year students are not prepared for these demands and end up failing their courses. This study aims to present an instrument for enhancing mathematics teaching and promoting learning with understanding in higher education by…

Reading comprehension skill is seen as a predictor of word problem-solving performance, and the close relationship between reading comprehension and mathematical skills is accentuated. On the other hand, more research is needed as to determine how logical thinking and word problem solving are related to each other and to analyze the role of…

This article examines the performance of heritage speakers on a bimodal acceptability judgment task that targeted morphologically complex words. A major goal of the study was to compare participants' acceptance of conventional and creative words. Data were collected from 57 adult heritage speakers of Spanish who were subsequently divided into two…

Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

Online "Peer Instruction" has become prevalent in many "flipped classroom" settings, yet little work has been done to examine the content students generate in such a learning environment. This study characterizes a dataset generated by an open-source, web-based homework system that prompts students to first answer questions,…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

National student assessments from Uganda suggest low levels of proficiency for students in primary and secondary schools. This is confirmed by data for primary schools from the 2013 Service Delivery Indicators survey. The data are used in this article to conduct an assessment of factors affecting student performance. A unique feature of the data…

This study tests the role of verbal mediation during theory of mind processing in autism spectrum disorder (ASD). Adolescents with ASD or typical development completed a false belief task while simultaneously performing a verbal or nonverbal load task. There was no group difference in false belief "accuracy;" however, under verbal load,…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…

This "master volume" is a printed archive of all papers published in a peer reviewed online journal, "The Roundtable," which ceased to exist in 2013. The volume includes a total of 22 scholarly papers by 18 authors on the philosophical foundations of education published originally in the aforementioned online journal during…