Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

The present study investigates the understanding of the equals sign among middle school students. The study data were gathered from a total of 433 middle school students (111 in the fifth grade, 106 in the sixth grade, 95 in the seventh grade and 121 in the eighth grade) using a ten-item equals sign test developed by the researcher. The study…

The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial…

We study the automatic identification of educational items worthy of content authors' attention. Based on the results of such analysis, content authors can revise and improve the content of learning environments. We provide an overview of item properties relevant to this task, including difficulty and complexity measures, item discrimination, and…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 third-grade students on a measure…

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 3rd-grade students on a measure of…

The present study examined the ability of content domain (algebra, geometry, rational number, probability) to classify mathematics misconceptions. The study was conducted with 1,133 students in 53 algebra and geometry classes taught by 17 teachers from three high schools and one middle school across three school districts in a Midwestern state.…

The purpose of this study was to apply a random item mixture nominal item response model (RIM-MixNRM) for investigating instruction effects. The host study design was a pre-test-and-post-test, school-based cluster randomized trial. A RIM-MixNRM was used to identify students' error patterns in mathematics at the pre-test and the post-test.…

In online educational systems we can easily collect and analyze extensive data about student learning. Current practice, however, focuses only on some aspects of these data, particularly on correctness of students answers. When a student answers incorrectly, the submitted wrong answer can give us valuable information. We provide an overview of…

Researchers interested in exploring substantive group differences are increasingly attending to bundles of items (or testlets): the aim is to understand how gender differences, for instance, are explained by differential performances on different types or bundles of items, hence differential bundle functioning (DBF). Some previous work has…

The aim of the study is to examine prospective mathematics teachers' pedagogical content knowledge in terms of knowledge of understanding students and knowledge of instructional strategies which are the subcomponents of pedagogical content knowledge. The participants of this research consist of 98 prospective teachers who are studying in two…

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when…

The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers' perceptions of students' ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From…

A content-oriented analysis of written solutions to test items in Israeli high school graduation examinations in mathematics yielded six error categories: misused data; misinterpreted language; logically invalid inference; distorted theorem or definition; unverified solution; and technical error. (Authors/MNS)