This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

This research aims to describe students' level of algebraic reasoning based on the adversity quotient types of climber, camper, and quitter in solving PISA model mathematics problems. This research is descriptive research with a qualitative approach. The research began by administering a questionnaire to determine the student's adversity quotient…

In Victoria, Australia, senior secondary mathematics students are expected to use technology and thus need to make decisions about using pen-and-paper (P&P) or technology when solving mathematics problems. The predominant technology is a Computer Algebra System (CAS). This study investigated the beliefs about CAS held by twelve Year 11…

We present a model for roleplaying (RP) for university students that is aimed at fostering the interactions of each learner with the teacher and coursemates, self- and peer-assessment, as well as an awareness and meaningful learning of mathematics. Specific features of our model are its focus on metacognition and individualized learning, based on…

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…

The aim of this study is to examine the argumentation-based problem solving processes of 10th grade students in the context of quadratic equations. The study was carried out in a public high school in Istanbul. The study group consists of three male students selected by the method of "homogeneous sampling". In the research, special case…

This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The…

This study describes students' learning obstacles in solving early algebra problems requiring functional thinking ability. To reach this aim, qualitative research was conducted in this study. Participants of this study were 39 ninth graders and a mathematics teacher at one of the lower secondary schools in Bandung, Indonesia. The data were…

Realistic mathematics education (RME) has proven to be an effective model for mathematics elsewhere. However, students and teachers still grapple to confront the circle equation to learn and teachers to teach. This study explored students' didactical phenomenological discourses in the circle equation as an alternative. The mixed methods research…

Proportional reasoning and knowledge of fractions are critical skills for completing algebra successfully, yet many students with mathematics learning disabilities (MLD) enter algebra classes without adequate prior knowledge of these skills. This study used a single-subject/case research, combined multiple-baseline and alternating-treatment design…

This study aimed to examine the effect of cooperative problem-solving method on grade nine secondary school students' motivation towards learning algebra. In this study, pretest-posttest non-equivalent group quasi-experimental design was employed. The data were collected from 142 grade ninth students using mathematics motivation questionnaire and…

Quantitative reasoning is defined as reasoning about relationships between items, measurements of objects, and quantities rather than numbers. Both in the transition from arithmetic to algebra and in the problem-solving process, quantitative reasoning is seen as a critical instrument for the development of students' mathematical skills. In the…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

Perseverance is vital for the process of learning mathematics with understanding. To do so, students must wrestle with obstacles and amend their problem-solving plan when necessary. I collected qualitative data to investigate the nature of perseverance for 11 ninth-grade algebra students working on a challenging task for which they affirmed…

As proof and proving are the key elements of mathematics, several frameworks evaluating this process have been presented. Proof image, being one of them, was introduced by Kidron and Dreyfus (2014) through analyses of two mathematicians' activities. Authors clarified it in the context of components, and emphasized its relation with formal proof.…