This study examined seventh-grade students' emergent and progressive financial literacy in the context of risk and reward while working on two mathematical modelling tasks. The participants were six seventh-grade students identified as 'good at mathematics' by their teachers. The data sources comprised videotaped group discussions, group…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

Cognitively demanding tasks have been shown to support students' understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers…

Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means…

Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…

This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization…

Students encounter difficulties in solving areas of triangles and quadrilaterals due to a lack of conceptual understanding of the topic. The researchers have developed the following activities and the hypothetical learning trajectory (HLT) through the design research approach focusing on developing activities for students to learn the concepts…

This paper presents a qualitative study developed with a group of 16-year-old students who were asked to estimate large numbers of elements on a bounded surface. Taking the realistic mathematics education framework as a reference, we presented the students with an activity sequence comprised of four different tasks--each one with a different…

In this study, it was aimed to examine the argumentation structures of 5th-grade middle school students, while they were structuring geometric concepts in argumentation-based activities of geometric shapes. To this end, 7 fifth-grade students studying in a public middle school were included in the study. In the study, five geometry tasks involving…

Mathematical spaces extend far beyond the classroom and physical environments into virtual spaces. Today's students have more to consider than just their face-to-face experiences with mathematics inside or outside the classroom; they have the online perspectives of others to consider as well. To gain critical insight, we conducted this research…

Learning Transformation Geometry (TG) needs a more informal approach to concern situational problems. This study aims to develop actionable knowledge of TG in the form of design related to context and yet general enough to use digital manipulative activities in new situations. We propose such knowledge in the form of conjectured Local…

Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

This study addresses the need to better describe instructional strategies used by middle grades mathematics teachers. After coding 177 videos of grades 6-8 mathematics instruction for indications of effective instructional practices, we further analyzed 8 of the highly scored videos with specific attention to teachers' implementation of strategies…

In this report we show an investigation of how high-school students learn strategies to find intermediate numbers in an interval to understand the property of numerical density. Research has shown that some high-school students have difficulty in understanding this property. To mitigate this difficulty, we proposed a Hypothetical Learning…

This study investigated the effects of (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…