The concept of multiple representations of functions and the ability to make translations among representations are important topics in secondary school mathematics curricula (Moschkovich, Schoenfeld, & Arcavi, 1993; NCTM, 2000). Research related to students in this domain is fruitful, while research related to teachers is underdeveloped. This…

Gain a new perspective on the sharing of erroneous solutions in classroom discussions. Based on their research in grades four and six, the authors reveal how student-to-student correction of errors promotes mathematical reasoning and understanding. Tips for teachers include strategies for using students' errors to encourage reasoning during…

Education in the twenty-first century must prepare students to meet the challenges of a dynamic and interconnected world. However, assessment of students' skills tends to focus primarily on static tasks. Therefore, it is not known whether knowledge about successful strategies displayed on static tasks can be transferred to interactive and dynamic…

Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

In order to self-regulate, students need to honestly reflect on their learning and to take appropriate corrective action. A simple procedure to cultivate student skills in self-regulated learning, known as the Task Evaluation and Reflection Instrument for Student Self-Assessment (TERISSA) is discussed in this paper. TERISSA guides students through…

The purpose of this study is to investigate, via a model, the explanatory and predictive relationships among the following variables: Mathematical Problem Solving and Reasoning Skills, Sources of Mathematics Self-Efficacy, Spatial Ability, and Mathematics Achievements of Secondary School 8th Grade Students. The sample group of the study, itself…

Resilience has often been defined as the ability to bounce back in times of adversity and to develop in a positive way when faced with setbacks. Children routinely show high amounts of resilience mostly because of temperament and a built-in sense of autonomy.Children are able to overcome adversity to bounce back before social and emotional harm is…

Case studies hold great potential for engaging students in disciplinary content. However, little is known about the extent to which students actually cover the problem space afforded by a particular case study. In this research, we compared the problem space afforded by an instructional design case study with the actual content covered by 16…

This study investigated the effect of different methods of guidance with anchored instruction on students' mathematical problem-solving performance. The purpose of this research was to iteratively design a learning environment to find the optimal level of guidance. Two iterations of the software were compared. The first iteration used explicit…

Twenty-first century teaching and learning focus on the fundamental skills of critical thinking and problem solving, creativity and innovation, and collaboration and communication. Metacognition is a crucial aspect of both problem solving and critical thinking, but it is often difficult to get students to engage in authentic metacognitive…

Based on the needs for viable melodic dictation strategies and thoughtful approaches to teaching prerequisite skills, the central research question guiding this qualitative study was as follows: What strategies do dictation takers describe having used on successfully completing a standard melodic dictation? Six sophomore music majors, recommended…

This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or minimum…

Research experience has been proven to be effective in enhancing the overall educational experience for undergraduate students. In this article, two engineering research projects with undergraduate students involvement are discussed. The projects provided the undergraduate student researchers with motivation for independent research work and…