This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in…

Integers present a global challenge for students due to their abstract nature and complex operations. To delve into the challenge students encountered, error analysis served as an alternative method to investigate errors diagnostically. This study aimed to explore error patterns related to integer addition and subtraction among seventh-grade…

In numerous studies, intelligent tutoring systems (ITSs) have proven effective in helping students learn mathematics. Prior work posits that their effectiveness derives from efficiently providing eventually-correct practice opportunities. Yet, there is little empirical evidence on how learning processes with ITSs compare to other forms of…

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

This study seeks to ascertain the degree to which context-based items are offered in Turkish mathematics textbooks as well as the quality of the items in terms of item writing guidelines, whether or not they are given as traditional or context-based. A qualitative research approach is used in this study. The eighth-grade mathematics textbook used…

Students' contributions that are not yet mathematically complete, precise, or correct are crucial for learning through classroom discussions. We aim to support teacher candidates (TCs) to see students' ideas as evidence of sensemaking and to respond in ways that keep student thinking central to the discussion. Although approximations of practice…

Errors are a major component of the pedagogical content knowledge (PCK) needed for teaching mathematics. In this study, 25 prospective teachers (PTs) in high schools were invited to solve a trigonometric task that had been assigned to high-school students and, subsequently, to relate to an authentic solution containing mathematical errors, which…

Errors in mathematics are common hurdles for teachers and students; therefore, it is important to learn what errors students make and how students treat them. This study initially identified the types of errors students made while working with algebraic expressions and documented and analyzed the process of students completing an error analysis…

The purpose of this research was to describe the positions and causes of students' errors in algebraic thinking based on the cognitive style. This study was qualitative research with subject consisting of twelve students. The results showed that (1) students with Field Independent type tended to make errors at the stage of comprehension,…

Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

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…

Media play an important role in young people's lives as an agent of socialization, both generally and with regard to mathematics. To understand the mathematics-related messages disseminated to young people via popular media, we analyzed portrayals of mathematics and mathematicians in over 40 media examples (television shows, movies, websites,…

The results of educational research studies are only as accurate as the data used to produce them. Drawing on experiences conducting large-scale efficacy studies of classroom-based algebra interventions for community college and middle school students, I am developing practice-based data cleaning procedures to support scholars in conducting…

This study applies the Mathematics Acquisition Framework (MAF) (Bossé, Ringler, Bayaga, Fountain, & Young, 2018) to investigate fifth- through seventh-grade students' comprehension of fractions and decimals and examines how students build understanding of mathematical principles and concepts regarding fractions and decimals. Based on case…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…