The number of complaints university lecturers make about a lack of knowledge, especially first-year students' procedural knowledge, has increased recently. Due to missing adequate empirical evidence, a survey of procedural knowledge among students of Austrian high schools in their final year was conducted. For this purpose, test items for…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

The present study aimed to examine children's and adults' performance and strategies in volume estimations. Three tasks were designed and presented to 40 adults and 40 6th grade children who were asked to estimate: (a) the number of unit measures (bricks/rice spoons) that may be put in a container, (b) the quantity of bricks/rice, between two…

Conjecturing has been considered to inspire the need for proof, enhance the understanding of proofs, and construct a valid proof. This study describes students' processes of formulating a Euclidean geometry conjecture in the form of a conditional statement through constructing a geometric figure and using measuring and dragging modalities of a…

Storytelling is a valuable form of human expression that allows audience members to connect their own experiences with the narrative. As a pedagogical tool, storytelling has been explored mainly in primary school education but rarely in higher education. However, its potential for assisting students in learning mathematics and the societal…

This study aims to examine the strategies developed by 7th grade students while shading different percentages of geometric shapes. The study was carried out with 113 7th graders studying at a state middle school in a province of Turkey. The data were gathered using the Shading Percentage Test, which consisted of seven tasks. Data analysis employed…

This article reports on results from a design research project that implements a formative assessment practice with support from a classroom response system (CRS). Cumulatively building on earlier research and drawing on iteratively generated data from secondary schools in Sweden, the article elaborates on design principles and task types for…

This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

From an APOS (Action-Process-Object-Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the…

This study investigates sixth-grade students' explorations of tessellations with Scratch through the mathematical aesthetics. For this purpose, the study analyzed the students' explorations by considering the roles of mathematical aesthetics identified by Sinclair (2004): generative, evaluative, and motivational role. Six middle-school students…

This study is a case study within a three-year-long design research study. The purposes of this study are twofold. The first purpose includes investigating whether there is a significant difference in seventh-grade students' proportional reasoning skills before and after a teaching experiment conducted in line with the perspectives of Hypothetical…

The article focuses on study visits from the perspective of mathematical project work. Project work means a systematic organizing method of teaching that is based around a project. The research questions are the kinds of study visits students made, the meaning(s) of those visits, the mathematical content in the visits and how such study visits…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

The purpose of the study was to explore students' consistency in their notions encountering different methods in solving the same task of comparing values of certain infinite series. The participants were 93 male students aged 16-17. Applying cognitive conflict approach and the data were collected through a questionnaire administrated in two…

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded…