This study aimed to investigate the effect of experimenting with physical manipulatives (PM), virtual manipulatives (VM), and a blended combination of PM and VM on undergraduate students' understanding of concepts in the domain of "Light and Color." A pre-post comparison study design was used for the purposes of this study that involved 70…

An interview with a sixth-grade student illustrates how her number sense and understanding of variability relate to her ability and proclivity to apply a frequentist (statistical) approach to probability tasks. A general suggestion for teaching about mathematics of uncertainty through the gradual strengthening of estimation, as per the historical…

Thin-layer chromatography (TLC) is a widely used method of qualitative analysis in organic synthesis, as it uniquely combines low cost, rapidity, simplicity, versatility, small quantities of sample and low detection limits. The simplest and most economical method for the application of samples onto TLC plates is by hand, using glass capillaries.…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

An embodied approach to reading comprehension suggests that emerging readers must learn to map words and phrases onto their remembered experiences, but this is made difficult by the necessity of focusing attention on decoding. Having children manipulate toys to correspond to what they are reading overcomes this problem, but introduces its own…

The purpose of this study was to explore the impact of incorporating Magic Board in the instruction of concepts related to area. We adopted a non-equivalent quasi-experimental design and recruited participants from two classes of third-grade students in an elementary school in Taoyuan County, Taiwan. Magic Board was used as a teaching aid in the…

The need for improved mathematics education in many of America's schools that serve students from low income households has been extensively documented. This practical action research study, set in a suburban Title I school with a primarily Hispanic, non-native English speaking population, is designed to explore the effects of the progression…

In this article, the authors discuss their approach to column addition and subtraction algorithms. Adapting an original idea of Paul Cobb and Erna Yackel's from "A Contextual Investigation of Three-Digit Addition and Subtraction" related to packing and unpacking candy in a candy factory, the authors provided an analogous context by…

The purpose of this study was to explore pre-service and in-service mathematics teachers' analyses of student learning in a video case of mathematics instruction via an online learning forum. The study was conducted in the context of three different mathematics methods courses in a 4-year college in the Midwestern United States. Twenty-six…

This study investigated the effectiveness of two remedial mathematics courses that aimed to (a) present topics conceptually, (b) construct adequate schemata, and (c) introduce students to the culture of mathematics. The topics covered during the two courses were word problems, equivalence, variables and expressions, equations and inequalities, and…

Visualizing the structure and relationships in three dimensions (3D) of organs is a challenge for students of anatomy. To provide an alternative way of learning anatomy engaging multiple senses, we are developing a force-feedback (haptic) interface for manipulation of 3D virtual organs, using design research methodology, with iterations of system…

The author is a strong proponent of incorporating the Content and Process Standards (NCTM 2000) into the teaching of mathematics. For candidates in her methods course, she models research-based best practices anchored in the Standards. Her students use manipulatives, engage in problem-solving activities, listen to children's literature, and use…

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…

Biological energy flow has been notoriously difficult to teach. Our approach to this topic relies on abiotic and biotic examples of the energy released by moving electrons in thermodynamically spontaneous reactions. A series of analogical model-building experiences was supported with common language and representations including manipulatives.…

Students use manipulative models and small-scale simulations that promote learning of complex biological concepts. The authors have developed inexpensive wet-lab simulations and manipulative models for "Diagnosing Diabetes," "A Kidney Problem?" and "A Medical Mystery." (Contains 5 figures and 3 online resources.)