In some math classrooms, students are taught to follow and memorize procedures to arrive at the correct solution to problems. In this article, author Mike Flynn suggests a way to move beyond answer-getting to true problem solving. He describes an instructional approach called three-act tasks in which students solve an engaging math problem in…

Digital games have demonstrated great potential for supporting students' learning across disciplines. But integrating games into instruction is challenging and requires teachers to shift instructional practices. One factor that contributes to the successful use of games in a classroom is teachers' experience implementing the technologies. But how…

We recently developed the "Framework of Achievement Bests" to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as "optimal achievement best," which stipulates the idea that individuals may, in general, strive to achieve personal…

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

This ethnographical study aims to interpret how an intelligent tutorial system, geogebraTUTOR, mediates to the student's argumentative processes. Data consisted of four geometrical problems proposed to a group of four students aged 16-17. Qualitative analysis of two selected cases led to the identification of the development of argumentative…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

In our contribution we focus on the possibility to use an educational tool called Concept Cartoons in future primary school teachers' education, as an instrument for observing how future primary school teachers reason about fractions. In the introduction section we present Concept Cartoons, and also the primary school level of the fractions topic.…

The research presented in chapters 2, 3, and 4 in this dissertation uses a sociocultural and sociohistorical lens, particularly around power, authority of knowledge and identity formation, to investigate the complexity of engaging in, supporting, and evaluating high-quality argumentation within a college biochemistry inquiry-oriented classroom.…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

The purpose of this study was to replicate and extend the study of the schema-based intervention (SBI) conducted by Jitendra et al. (2015) that demonstrated impact in proportional problem solving for a homogeneous sample of Upper Midwest students and teachers who were predominantly White and middle class. This study was replicated in two…

Within the context of complex cognitive processing and educational interventions, Woolfolk (2016) makes reference to problem solving acquisition, problem solving retention, and problem solving transfer. In each of the aforementioned types of problem solving activities, problem identification and problem representation (reflecting procedural…

Dynamic geometry environment allows us to investigate geometric relationships and problems more efficiently than the pencil-and-paper method. Continuous variation of geometric configurations shows the relationship from different points of view. This paper aims to provide some indications of how a dynamic geometry environment, especially GeoGebra…

In the 21st century when knowledge-based economy is emphasized, the cultivation of autonomous learning and problem-solving abilities presents the importance. With web-based collaborative problem-based learning (CPBL), learners could more conveniently cultivate their problem-solving abilities through autonomous learning. Nevertheless, learners are…

This study explored teachers' problem solving during technology-mediated professional development (PD) in the topic related to teaching English Learners (ELs, i.e. students whose home languages are not English). Open-ended PD provided authentic, situated contexts using videos of scenario to engage six elementary teachers to participate in small…

Students' grasp of the non-mathematical language in a mathematics story problem--such as vocabulary and syntax--may have an important effect on their problem-solving, and this may be particularly true for students with weaker language skills. However, little experimental research has examined which individual language features influence students'…