Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

Although non-cognitive facets--such as interest, attitudes, commitment, self-concept and so on--of are prevalent in contemporary theoretical modeling of competence, they are often neglected in measurement approaches or measured only by global self-report questionnaires. Based on the well-established experience sampling method (ESM) and following…

Researchers promoting the inclusion of technology for teaching and learning have recently called for the integration of mathematical technologies into the preparation of future teachers. This report analyzes the dynamic geometry sketches produced by preservice secondary mathematics teachers when investigating trigonometric relationships. We…

This report presents dual analyses of an undergraduate student, Cassie, whose work provides nice contrasts between Grounded Theory (GT) analysis and Knowledge Analysis (KA). The analyses highlight particular methodological differences, such as grain size of findings, positioning of novices and more general implications about expert-novice studies.…

While explanations may help people learn by providing information about why an answer is correct, many problems on online platforms lack high-quality explanations. This paper presents AXIS (Adaptive eXplanation Improvement System), a system for obtaining explanations. AXIS asks learners to generate, revise, and evaluate explanations as they solve…

With traditional teaching methods pervasive in the U.S., it is crucial that mathematics teacher educators and professional development leaders understand what methods result in authentic changes in classroom instruction. Lesson study presents a promising approach to developing reform-oriented instruction, as it is situated within the classroom,…

What is the nature of art/science collaborations in museums? How do art objects and activities contribute to the successes of science centers? Based on the premise that art exhibitions and art-based activities engage museum visitors in different ways than do strictly factual, information-based displays, I address these questions in a case study…

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

Research suggests that inquiry-based strategies are the most effective modes of delivery in working with the gifted students. The characteristics of the gifted reveal a strong basis for understanding the power of question-asking as a part of differentiating curriculum. This article describes three different models of questioning--Guilford, Bloom,…

Background: Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem solving…

Previous research has pointed to the importance of transformational leadership in facilitating employees' creative outcomes. However, the mechanism by which transformational leadership cultivates employees' creative problem-solving capacity is not well understood. Drawing on theories of leadership, information processing and creativity,…

With the latest re-authorization of the Individuals with Disabilities Education Improvement Act (IDEA, 2004), states are allowed to use a Response to Intervention (RtI) framework to determine whether students qualify for special education services. Although RtI has promise and has been implemented well with documented results, further research is…

The much-lamented gap between theory and practice in education cannot be filled by practical knowledge alone or by explanatory knowledge alone. Principled practical knowledge (PPK) is a type of knowledge that has characteristics of both practical know-how and scientific theory. Like basic scientific theory, PPK meets standards of explanatory…