Modelling ability is one of the essential elements of the latest educational reforms, and Trends in International Mathematics and Science Study (TIMSS) is a curriculum-based assessment which allows educational systems worldwide to inspect the curricular influences. The aims of this study were to examine the role of modelling ability in the…

The purpose of this study is to explore elementary educators' perceptions regarding what it means to conceptually understand mathematics, the emphasis teachers place on utilizing evidence-based teaching processes, as identified as effective by National Council of Teachers of Mathematics (NCTM), and how these perceptions influence their…

The worked example effect indicates that examples providing full guidance on how to solve a problem result in better test performance than a problem-solving condition with no guidance. The generation effect occurs when learners generating responses demonstrate better test performance than learners in a presentation condition that provides an…

Making the connection between science and technology might be important for students to learn to identify and solve problems and to acquire scientific knowledge and skills. The research reported in this article concerned the development of a design situation in a science classroom and the study of students performing in this situation. More…

Response to intervention (RtI) is an influential system of service delivery in contemporary schools, but the specific role of school consultation in RtI implementation is not clearly defined. Instructional consultation provides a potential meeting point between consultation and RtI practices. Through a mixed-methods approach, this study explored…

Many approaches to instruction focus on helping people learn to recognize "the old in the new"--to turn what would otherwise be novel problems into familiar patterns that can be solved efficiently through the reuse of prior learning. Instruction that leads to efficient transfer is important, but it can also promote what we call "overzealous"…

This article presents 10 research-based principles of instruction, along with suggestions for classroom practice. The principles come from (a) research in cognitive science, (b) research on master teachers, and (c) research on cognitive supports. The instructional principles are: (1) Begin a lesson with a short review of previous learning to…

With the aim to promote students' mathematics learning, we extended the Cognitive Tutor Algebra (CTA), a computer-based tutoring system for high school mathematics, to a collaborative setting. Furthermore we developed a collaboration script to support students' interactions. In an experimental classroom study, we compared three conditions:…

Too often, teachers scratch their heads and ask, "What were my students thinking?" then answer, "I don't want to know." But teachers should want to know, and students should question their own thinking, as well. Critical thinking involves not just problem solving, creativity, analysis, and synthesis but also self-awareness of learning and learning…

The purpose of this study was to investigate the effects of type of question prompt and level of prior knowledge on non-routine mathematical problem solving. A computer game was blended within the pattern reasoning tasks, along with question prompts, in order to demonstrate and enhance the connections between viable problem-solving strategies and…

Society's failure to educate proportionate numbers of African American students in mathematics is an ongoing problem. The roots of this problem lie in systemic racism and segregated schools. The overwhelming majority of economically disadvantaged African American high school students at segregated schools receive substandard mathematics education.…

This study was designed as a confirmatory study of work on "productive failure" (Kapur, "Cognition and Instruction," 26(3), 379-424, 2008). N = 177, 11th-grade science students were randomly assigned to solve either well- or ill-structured problems in a computer-supported collaborative learning (CSCL) environment without the provision of any…

Two developments have contributed to the convergence of views about the benefits of real-life and inquiry-based pedagogies in mathematics learning. First, the mathematics teaching community is increasingly focused on the learning of mathematics that involves the transfer of prior knowledge to novel problem-solving situations, a key element in…

Research is only beginning to show the benefits of the effective use of manipulatives with students who have disabilities. This article highlights how teachers can incorporate three manipulative instructional strategies to help students with high-incidence disabilities.

The paper describes the rationale and 10-day implementation in a 5th-grade classroom (n=19) of an experimental ratio-and-proportion instructional design. In this constructivist-phenomenological design, coming from our theoretical perspective, design research, and domain analysis, students: (1) link "real-world" and "mathematical" objects…