A relative extrema optimization problem is one in which the domain of the objective function (i.e. the function whose maximum or minimum value is to be found) is an open interval. An absolute extrema optimization problem is one in which the domain of the objective function is a closed interval. Analysis of task-based interviews conducted with 12…

In this study we investigated the development of 245 kindergarteners' mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects…

This study has aimed to determine 8th grade middle school students' skills and knowledge on irrational numbers. A total of ten 8th grade students from a public school in Polatli District of Ankara were participated. In the study, a basic qualitative research design was used, and data were collected by means of clinical interviews. Interview…

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…

Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was…

Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in student thinking, we engaged a pair of undergraduate students in a ten-session teaching experiment. The students successfully reinvented four basic counting…

This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…

This study investigates error sources and the effects of each error source to determine optimal weights of the composite score of teacher recommendation letters and self-introduction letters using multivariate generalizability theory. Data were collected from the science education institute for the gifted attached to the university located within…

The aim of this study was to examine the mistakes made by freshman students of science teaching during the process of proving and the reasons for these mistakes. To this aim, the study, which was conducted via the case study method, was performed with 52 freshman students who were studying at the department of science teaching in a state…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children's mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise…

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six-week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

Although teachers' professional knowledge and instructional beliefs are known to have a variety of subcomponents, research on the structure and interrelations of these subcomponents is relatively scarce. This article presents some findings of a preliminary, quantitative empirical study examining the relationships between mathematics teachers'…

Statements conveying a degree of certainty or doubt, in the form of hedging, have been linked with logical inference in students' talk (Rowland, 2000). Considering the current emphasis on increasing student autonomy for effective mathematical discourse, I posit a relationship between hedging and student autonomy. In the current study, high school…