As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…

Exploratory learning is recognized as a developmentally appropriate practice in early childhood education. During exploration, exposure to new things guides children in the acquisition of knowledge, while interactions with a range of familiar and unfamiliar artifacts can support developmental integration. Exploratory activity may occur…

It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics…

The authors, in a nonexperimental randomized study, used national data from the Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) to examine present instructional practices for Grade 5 mathematics classrooms and its impact on achievement for White non-Hispanic non-English language learners (ELLs), Hispanic non-ELLs, and Hispanic…

Learning materials and teaching methods used in early childhood classrooms have fluctuated greatly over the past century. However, one learning tool has stood the test of time: Wood building blocks, often called unit blocks, continue to be a source of pleasure and learning for young children at play. Wood blocks have the unique capacity to engage…

This article describes a hands-on approach to learning proofs by induction. Students create patterns of dominos so that when the first domino is pushed, the entire design collapses, one domino at a time. Students then build designs that do not work. By constructing a list of conditions that ensure a given pattern will collapse, students discover…

If students are in an advanced mathematics class, then at some point they enjoyed mathematics and looked forward to learning and practicing it. There is no reason that this passion and enjoyment should ever be lost because the subject becomes more difficult or rigorous. This author, who teaches advanced precalculus to high school juniors,…

What students and teachers often ask is, how are nano-sized materials made when they are so small? One answer is through the process of self-assembly in which molecules, polymers, and nanoparticles connect to form larger objects of a defined structure and shape. Two hands-on experiments are presented in which students prepare capsules in real time…

Researchers are increasingly aware of the role of spatial skills in preparing children for future mathematics achievement (National Mathematics Advisory Panel, 2008). In addition, sex differences have been consistently documented showing boys score higher than girls in assessments of spatial ability, particularly mental rotation (Linn &…

Solubility is challenging for many general chemistry students, and the interactions of aqueous species are difficult to conceptualize. Derived from the pedagogies of Johnstone, Bloom, and Piaget, our primary research questions probe whether students' conceptual understandings of solubility could be enhanced by participation in a concept-building,…

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…

Using data from 503 inservice elementary teachers, this study investigated the relationship between teachers' background characteristics, teachers' beliefs about manipulatives, and the frequency with which teachers use manipulatives as part of their mathematics instruction. Findings from the study show that teachers' grade level and beliefs about…

With the increased use of computer manipulatives in teaching there is need for theoretical discussions on the role of manipulatives. This paper reviews theoretical rationales for using manipulatives and illustrates how earlier distinctions of manipulative materials are broadened to include new forms of materials such as virtual manipulatives.…

How do concrete objects that cue real-world knowledge affect students' performance on mathematics word problems? In Experiment 1, fourth- and sixth-grade students (N = 229) solved word problems involving money. Students in the experimental condition were given bills and coins to help them solve the problems, and students in the control condition…

The purpose of this study was to examine young children's views about shadows. Young children hear references to or are involved in many scientific experiences in their everyday lives, and shadows are a part of children's everyday experiences. Young children may have constructed their knowledge about shadows through their daily experiences.…