This paper explores the impact of the course "Teaching and Learning of Mathematics (Grades 7 and 8)" for the preparation of pre-service secondary mathematics teachers. It examines how pre-service teachers perceived mathematical problem solving and communicating mathematical knowledge before and after the course. The main objective of the…

When teaching algebra concepts to middle school students, the author often hears questions that echo her own past confusion as a young student learning to write linear equations using data tables that show only input and output values. Students, expected to synthesize the relationship between these values in symbolic representation, grow…

The aim of this study is to determine analogies that are used in Turkish secondary school mathematics textbooks. According to this aim, 7 textbooks are analysed: 3 of them are published by the commission of Ministry of Education and 4 of them are published by private publishing companies. The document analysis method is used in the study.…

In this study, we investigated students' thinking about the use of letters in algebra. Responses from over 1,400 Australian secondary school students to a set of three algebra items were analysed to determine the prevalence of the "letter as object" misconception. We estimate that 50% to 80% of Year 7 students bring this misconception to…

Based on Confucius' saying "A word may change your mind, an emotion may change your life and a person may change you", our emotions affect our learning if we take life as a process of learning. Some of our learning on which we are successful and unsuccessful are student characteristics. Effective properties are one of the characteristics…

We study the usage of a self-guided online tutoring platform called Algebra Nation, which is widely by middle school and high school students who take the End-of-Course Algebra I exam at the end of the school year. This article aims to study how the platform contributes to increasing students' exam scores by examining users' logs over a three year…

An argument is presented for including exponentiation as a "basic" of school mathematics. Key elements of the argument include the topic's increasing relevance in a rapidly changing world and its utility for supporting understandings of role of analogy in mathematical thought. The discussion is illustrated with an account of a…

It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics…

The study aimed at improving students' algebraic thinking ability in the eighth-grade junior high school student through multiple representation strategies using realistic approach. The multiple representation strategies consist of orientation, exploration, internalization, and evaluation. This is a quasi-experimental study with nonrandomized…

Reflective practice in mathematical teaching improves teaching skills and confidence. This paper investigates affect-based critical moments as a reflective practice for pre-service teaching. An embedded case study is presented by one regional university as a discovery into the "reflective" phase of the Enhancement-Learning-Reflection…

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

The purpose of this study was to investigate gender differences in students' mathematics achievement and in their attitudes toward mathematics. Another purpose was to examine mathematics teachers' beliefs and their perceptions of their male and female students' ability. The sample consisted of 692 students (353 girls, 339 boys) between the ages of…

Middle school serves as a key milestone for pre-algebra mastery, enabling students to be successful in high school algebra. Yet, at the point when students should be transitioning from learning arithmetic to learning mathematics, many are unprepared in fundamental mathematics concepts that strongly predict algebra achievement. Because mastering…

Using data from a large urban district, this study investigated whether racial inequality in access to eighth-grade algebra is a reproduction of differences in prior opportunities to learn (as evidenced by grades, test scores, and level of prior mathematics course) or whether patterns reflect an increase in inequality such that racial differences…

Recognising teachers' knowledge as one of the main factors influencing their practices and student learning, we aim to contribute to obtaining a better and deeper understanding of the specificities of teachers' mathematical knowledge. A case study involving one 8th-grade Chilean mathematics teacher is presented in the context of rational numbers.…