Even though reflective symmetry is heavily embedded in the everyday, learners continue to experience challenges when they mathematize concepts from this informal/everyday context. In this article we argue that symmetry exists in nature, it can also be symbolized algebraically and it can be abstracted into the world of axioms and theorems. We…

This paper presents a comprehensive synthesis of physics education research at the undergraduate level. It is based on work originally commissioned by the National Academies. Six topical areas are covered: (1) conceptual understanding, (2) problem solving, (3) curriculum and instruction, (4) assessment, (5) cognitive psychology, and (6) attitudes…

The recent push for more problem solving in elementary school mathematics classrooms intimidates many teachers. Anyone can look at the arguments--that problem solving deepens knowledge, provides real-world context, allows for multiple entry points, and so on--and see their logic and potential (Lester and Charles 2003). But teachers tend to think…

This paper examines the use of contextual problems to support mathematical learning based on current classroom practice. The use of contextual problems offers some potentials to engage and motivate students in learning mathematics but it also presents some challenges for students in classrooms. Examples of the use of contextual problems from…

The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…

Organic chemistry education is one of the youngest research areas among all chemistry related research efforts, and its published scholarly work has become vibrant and diverse over the last 15 years. Research on problem-solving behavior, students' use of the arrow-pushing formalism, the investigation of students' conceptual knowledge and…

An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

This study attempts to design a survey to assess students' perceptions of twenty-first-century learning practices in their classrooms and the resulting knowledge creation self-efficacy among the students. In addition, it also explores the relationships among the various dimensions of twenty-first-century learning practices. Four hundred and…

In the current educational climate, teachers are required to find methods to give all students, including students with mild intellectual disability, access to the general education curriculum. The purpose of this study was to investigate the combined effects of the concrete-semiconcrete-abstract instructional sequence and model-based problem…

There were two purposes in the study. One was to explore the cognitive activities during spatial problem solving and the other to probe the relationship between spatial ability and science concept learning. Twenty university students participated in the study. The Purdue Visualization of Rotations Test (PVRT) was used to assess the spatial…

Decision making during instruction that is responsive to children's mathematical thinking is examined reflexively by the researcher in the context of teaching second graders. Focus is on exploring how the research base on learning informs teaching decisions that are oriented to building on children's sound conceptions. The development of four…

In this article, we report on two lessons aimed at introducing junior high school students to the idea of shearing in a touchscreen dynamic geometry environment. By using shearing, we hoped to shift students' attention away from a formula-driven, computational conception of area toward a more geometric one. We found that the students were able to…

The present study describes the usage of strategies of symbolic representation during teaching introduction of decimal system in primary school in Mexico. Our research is based on Activity Theory conception of teaching-learning process and of gradual introduction of scientific concepts in school age. The method includes symbolic external…

Although a large part the Physics Education Research (PER) literature investigates students' conceptual understanding in physics, these investigations focus on qualitative, conceptual reasoning. Even in modeling expert problem solving, attention to conceptual understanding means a focus on initial qualitative analysis of the problem; the equations…

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…