Error analysis is an instructional strategy that can assist teachers to identify learners' areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman's Error Analysis Model. A research study explored the…

Quadratic equations are a notorious topic for the challenge it provides to students in secondary mathematics. Despite this, there is limited research, particularly in the Australian context, that explains why such challenges persist. This article details the causes of Year 11 students' difficulties in solving quadratic equations. Observing…

Descriptive correlational research was conducted to discover misconceptions on Rate of Reaction (RR) that impact on Chemical Equilibrium (CE) misconceptions. This research was conducted to 245 eleventh-grade students of High School in Gowa, South Sulawesi, Indonesia, that having been studied the RR and CE topics. Misconceptions data were collected…

If using different instruments obtained a different analogical reasoning component. With use people-piece analogies, verbal analogies, and geometric analogies, have analogical reasoning component consists of encoding, inferring, mapping, and application. Meanwhile, with use analogical problems (algebra, source problem and target problem is equal),…

The phenomenon of emerging water jets from the holes of containers has been extensively studied; nevertheless, it continues to inspire researchers and teachers. The main aspects of the recent studies concern: the range of the jets trajectories; the extension of Bernoulli's equation, of which Torricelli's expression represents an ideal situation,…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for…

Flexibility is an important element in learning mathematics. The purpose of this study was to investigate whether flexibility in linear equation solving predicts future academic achievement in mathematics and other subjects. Participants were 149 Finnish high-school students. Results show that flexibility was related to grades in both tracks of…

The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

This article emerged from an analysis of learners' responses to a task presented to learners studying Mathematics and Mathematical Literacy (ML) in Gauteng, South Africa. Officially, Mathematics and ML are two separate learning areas. Learners from Grade 10 onwards are supposed to take either one or the other, but not both. This means that by…

This article reports on a study of six Grade 11 learners' levels of understanding of concepts related to the function definition and representation. Task-based clinical interviews were used to elicit the learners' interpretations and reasoning when working with these function-related concepts. Indicators for Action-Process-Object-Schema (APOS)…

We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…

In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…

Teachers of mathematics recognize the difficulty of reaching every student when the range of student abilities puts a considerable strain on the classroom discussion and time. In a response to the problem, students are grouped so that those with greater mathematical aptitude help those who have difficulties. While this approach is to be…