Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

While the coronavirus disease 2019 (COVID-19) is still considered as a pandemic in recent human history, evidence from World Health Organization (2021) so far has recorded a total of 116,521,281 confirmed cases of COVID-19 with 2,589,548 as a total of deaths from over 215 countries or territories worldwide. Recognizing that COVID-19 is not only…

This article describes a carefully structured exploration of formative assessment, conducted in the form of a classroom research experiment. The authors are an instructor and a student in a graduate course that assigned teachers to research formative assessment strategies, implement one or more strategies for several weeks, collect data from…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

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…

This is a study of my dramatized narrative based on a true story of what took place in a mathematics class in an international school setting. My narrative includes the exploration of a mathematical "mistake" and the discovery of newly emergent problems. The drama, commentary, and reflections provide a close examination of the conduct…

International surveys, such as TIMSS and PISA, frequently put Indonesia in the low ranks. It is an indication that the higher-order thinking skills (HOTS) of students in Indonesia are still low. This research aims to analyze students' difficulties in solving problems that measure HOTS. This is a case study research with a qualitative approach.…

In this article, we present the results of a research study that explores secondary students' capacity to perform translations of algebraic statements between the verbal and symbolic representation systems through the lens of errors. We classify and compare the errors made by 2 groups of students: 1 at the beginning of their studies in school…

The article aims to determine the academic performance and errors in the resolution of types of problems of application of the quadratic function, of high school students from the Los Lagos Region and Los Rios Region in Chile. The approach is qualitative and descriptive with case studies. A math test with open response problems and an opinion…

This study compares the effects of a concrete-representational-abstract (CRA) intervention against a modified CRA-Integrated (CRA-I) intervention using a pretest-posttest design with random assignment of matched pairs to intervention conditions. The researchers designed both interventions to improve participants' understanding of and ability to…

Teachers' pedagogical content knowledge (PCK) importantly contributes to instructional quality and student outcomes. We aimed to complement the limited insights into preservice preschool teachers' PCK, and its association with opportunities to learn (OTL), during teacher training. We offered 162 first-to-final-year preservice preschool teachers…

Problem-solving is one of the 21st-century skills. However, students still have difficulty solving sequences and series word problems. The purpose of this research is to analyze students' errors in solving sequences and series word problems based on problem-solving steps of Polya. The research method is descriptive qualitative. The research…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite, Pyke,…

This study reports errors and misconceptions about division operation in fractions made by eighth-grade students. To investigate these errors and misconceptions, the study examined students' understanding of division operation in fractions using a questionnaire and expectation table. Students' misconceptions were determined for each question and…