'Mathematical sophistication' behaviours are often exercised by mathematicians in their work. In this article, the importance of mathematical sophistication will be discussed and three mathematics problems that activate mathematical sophistication behaviours will be presented.

Students' effort and emotions are important contributors to math learning. In a recent study evaluating the efficacy of MathSpring, a scalable web-based intelligent tutoring system that provides students with personalized math problems and affective support, system usage data were collected for 804 U.S. 10-12-year-olds. To understand the patterns…

Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…

Compelling research evidence shows benefits for student learning from explaining one's ideas and engaging with the ideas of others. However, whether certain patterns of group interaction may engender this productive student participation is unknown. Using data from two third grade mathematics classrooms, and over the course of six days during a…

This study aimed to describe the creative thinking process of students with active learning styles in proposing and solving problems on geometry material. The research instruments were Honey and Mumford's Learning Style Questionnaire (LSQ), problem-solving and submission test sheets, and interview guidelines. The LSQ questionnaire was distributed…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…

Online educational games have been widely used to support students' mathematics learning. However, their effects largely depend on student-related factors, the most prominent being their behavioral characteristics as they play the games. In this study, we applied a set of learning analytics methods (k-means clustering, data visualization) to…

Online educational games have been widely used to support students' mathematics learning. However, their effects largely depend on student-related factors, the most prominent being their behavioral characteristics as they play the games. In this study, we applied a set of learning analytics methods ("k"-means clustering, data…

The ability to self-regulate learning (SRL) is a skill theorized to transfer across learning environments. Students with this ability can consider a learning task, identify a goal, develop a plan to achieve it, execute that plan, and monitor and adapt learning until the goal is met. This paper examines the educational implications of developing…

During the semester break, 36 second-grade students accessed a set of resources and completed a series of online math activities focused on the application of the model method for arithmetic in two contexts 1) addition/subtraction and 2) multiplication/division. The learning environment first modeled and then supported the use of a scripted series…

Seeking the right level of help at the right time can support learning. However, in the context of online problem-solving environments, it is still not entirely clear which help-seeking strategies are desired. We use fine-grained data from 38 high school students who worked with the Geometry Cognitive Tutor for 2 months to better understand the…

This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures…