Different types of reasoning, such as intuitive, inductive, and deductive, are used in the generalization of figural patterns, as an important part of patterns in school mathematics. It is difficult to demarcate the constructive patterns where the regularity observed in the first few sentences is generalizable to the other sentences and each…

The present study aims to examine 8th grade students' proof writing and justification skills. The research was conducted using the document analysis method. The participants of the study consisted of 16 voluntary 8th grade students. The participants were determined according to the convenience sampling method. Data were collected with the…

Virtual reality (VR) is a promising avenue to enhance the independence and daily living skills of high school students with intellectual disability. This study investigated the efficacy of a non-immersive VR focused on teaching food preparation skills to secondary students with intellectual disability. Three high school students with intellectual…

Selecting and remembering the necessary information from rapidly increasing information requires summarization skills. Research on improving students' summarization skills has focused on deletion, generalization, and reconstruction strategies. However, direct teaching of these strategies does not yield successful results. For this reason,…

Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

Recent research seeks to develop more comprehensive learner models for adaptive learning software. For example, models of reading comprehension built using data from students' use of adaptive instructional software for mathematics have recently been developed. These models aim to deliver experiences that consider factors related to learning beyond…

The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective…

The purpose of this study is to investigate the quality of class talk during episodes corresponding to different levels of generalization. A total of 10 sessions in two classrooms in grade 7 were videotaped. A mixed approach was adopted to analyze the videotaped sessions. The findings show that triadic dialog was the dominant mode of interaction…

Given the importance of mathematics identity for students continued participation and engagement with mathematics, it is important for educators and researchers to be able to explore students' mathematics identity development. However, an instrument with validity evidence that can be used to explore mathematics identity efficiently and with groups…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

We investigate three 8th-grade students' mathematical meanings developed in the context of using linked representations to generate animations of figural models tuned in musical rhythm in "MaLT2," a programmable Turtle Geometry in 3D resource affording dynamic manipulation of variable values. We adopted a modified version of the UDGS…

Early algebraic thinking is the reasoning engaged in by 5- to 12-year-olds as they build meaning for the objects and ways of thinking to be encountered within the later study of secondary school algebra. Ever since the 1990s when interest in developing algebraic thinking in the earlier grades began to emerge, there has been a steady growth in the…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students' answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research, we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to…