We discuss a practical method for assessing mathematical proof online. We examine the use of faded worked examples and reading comprehension questions to understand proof. By breaking down a given proof, we formulate a checklist that can be used to generate comprehension questions which can be assessed automatically online. We then provide some…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

Secondary mathematics teachers' use of formative assessments have shown promise for developing models of their students' mathematical thinking and informing their instruction. While the complexities of secondary mathematics teachers' formative assessment practices are often captured in qualitative research, there is a critical need for synthesized…

Previous studies have tried to improve students' independence in online mathematics learning. However, the Flipped Learning model integrated with GeoGebra is scarce as none of the existing syntaxes accommodate the model. As the existing syntax is based on three phases: pre-class activity, in-class activity, and post-class activity. This research…

In this study we investigated pre-service teachers' (PSTs) proportional reasoning and how they interpret their calculations in proportional tasks. We administered a written questionnaire to 199 PSTs and used an inductive content analysis approach for data analysis. We found that one item, in which PSTs were asked to interpret the meaning of the…

This article presents activities focused on developing some essential Year 1-3 fraction understandings (i.e., joining/composing, decomposing/ partitioning) while aligning these activities to the Australian Curriculum content strands and content descriptions. Additionally, the authors describe the materials/resources needed, the key vocabulary…

Mathematical problem solving takes on many different forms and has long been established in school curricula with the terms, problems and problem solving taking on varied meanings. This article proposes a way of engaging students in mathematical open inquiry using a video clip as stimulus. It discusses findings from a recent study conducted in a…

Supporting students with difficulties in learning mathematics is a challenge for teachers and educational administrators. Formative assessment is considered to play a successful role in supporting at-risk students as well as students without difficulties in mathematics. There is a need for intervention programs, including formative assessment…

Posing questions is a direct way for teachers to push students to verbalize justifications and make connections among ideas--a crucial component of giving students with learning disabilities access to high levels of mathematical reasoning--but this skill is difficult to learn. We recruited four pre-service special education teachers to provide 1-1…

After some studies on students with Down syndrome (DS) who learned algebra and problem solving and few single case studies on analytic geometry, here the experience on analytic geometry was extended to 6 adolescents with DS, who attended mainstream schools. They were taught individually in the afternoon, one day per week, for 9 months by the same…

In this paper, we present parts of an online qualitative research project which lasted a whole semester about the understanding of real numbers by sixty first-year Greek mathematics undergraduate students during the COVID-19 pandemic. We focus on the distinction between rational and irrational numbers and their location on the number line using…

This research aims to explore students' learning obstacles in solving fraction problems in elementary school. This qualitative research used a case study method. The research subjects involved 30 third-grade elementary school students from two different schools in Bandung City, Indonesia. The instruments utilized were test and non-test. The test…

Early mathematics achievement is a significant predictor of future math learning. Current research shows that teachers lack knowledge in teaching methods for children with autism spectrum disorder (ASD). Specifically, research focusing on teaching mathematics in ASD is limited. A competency-based education (CBE) mathematics intervention was…

This study investigates the quality of tasks containing the use of dynamic geometry software (DGS) in the middle (5th-8th grade) and secondary school (9th-12th grade) mathematics textbooks in terms of mathematical and technological aspects. The DGS-related tasks in twenty-seven Turkish mathematics textbooks, approved by the Ministry of National…

This article is an advanced theoretical study as a result of a chapter from the first author's PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics…