The purpose of this study was to examine the influences of various facets of middle school mathematics teachers' practical rationality on their instructional decision making as they plan to enact the Common Core State Standards for Mathematical Practice, CCSS-MP1 (perseverance in problem solving) and CCSS-MP3 (communicating and critiquing). The…

The use of multiuser virtual environments for educational purposes is in its infancy but offers potential for exploration of spatial contexts that could not otherwise be experienced. We report on pre-service teachers' experiences in designing learning activities as a result of immersion in the CAVE2™, a 320-degree, cylindrical 3D virtual…

Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

Mobile applications are popular among young children, yet there is a dearth of studies examining their impact on learning and development. A systematic review identified 19 studies reporting learning effects on children 2 to 5 years old. The number of children participating in experimental, quasi-experimental, or mixed-method studies was 862 and…

This article examines high school students' engagement in a set of trigonometry problems. Students completed this task independently in an online environment with access to Internet search engines, online textbooks, and YouTube videos. The findings imply that students have the resourcefulness to solve procedure-based mathematics problems in an…

Teachers' perceptions of students' capabilities are particularly important in efforts to support ambitious instructional reforms. In this paper, we explore one teacher's efforts to resolve conflicts and tensions as she engages with new practices associated with ambitious mathematics teaching. While many conflicts arose in the first year of the…

This study documents the inclusive, deliberate, and unintended educational practices in Japan for mathematically gifted students. It also aims to identify various schools' strengths and challenges in improving the mathematics education of these students. Case studies with multisite designs were undertaken in five middle schools selected using…

The new common core standards for mathematics demand that students (and teachers!) exhibit deeper conceptual understanding. That's music to the ears of education professor John Tapper, who says teachers have overemphasized teaching procedures--and getting right answers. In his new book, "Solving for Why," he makes a powerful case for moving beyond…

Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the…

This study critically examines a key justification used by educational stakeholders for placing mathematics in context--the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were…

In the health and life sciences and many other scientific disciplines, problem solving depends on mathematical skills. However, significant deficiencies are commonly found in this regard in undergraduate students. In an attempt to understand the underlying causes, and to improve students' performances, this article describes a ten-year survey…

Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated…

Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…

We investigate teachers' practices in a whole-class context when they scaffold students' learning in situations where students use technologies that facilitate group learning to solve mathematical problems in small groups. We describe teachers' practices in order to evaluate their contribution to "Whole-Class Scaffolding" in the context…

Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…