"Instant Insanity II" is a sliding mechanical puzzle whose solution requires the special alignment of 16 colored tiles. We count the number of solutions of the puzzle's classic challenge and show that the more difficult ultimate challenge has, up to row permutation, exactly two solutions, and further show that no…

"Mathematical modeling of the physical world should be the central theme of physics instruction" (Hestenes 1987). Science teachers know this, but because of standardized state testing, many math teachers and some science teachers feel the need to focus on memorizing facts that will be on a multiple-choice test (Volante 2004). As a…

Fractions are a well-researched area; yet, student learning of fractions remains problematic. We outline a novel path to initial fraction learning and document its promise. Building on Freudenthal's analysis of the fraction concept, we regard "comparing," rather than "fracturing," as the primary activity from which students are…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

There are various types of instructional media related to Valence Shell Electron Pair Repulsion (VSEPR) but there is a lack of diversity of resources devoted to assessment. This research presents an assessment and comparison of students' understanding of VSEPR theory before and after tuition involving the use of the foam molecule model (FMM) and…

The main objective of this research is to determine the feasibility of using a multi touch tabletop system for applied mathematics learning in primary education with students with special needs (SEN). The instructional content designed on the tabletop focuses on understanding and managing money, coins, and banknotes. The study also analyzes the…

Research into haptic picture perception has mostly concerned adult participants, and little is known about haptic picture perception in visually impaired and sighted children. In the present study, we compared 13 visually impaired children (early blind and low vision) aged 9-10 years and 13 agematched blindfolded sighted children on their ability…

A sizable body of literature exists studying various technologies and pedagogical practices for teaching secondary mathematics curriculum to students with a learning disability in mathematics. However, with the growing footprint of computer-based technologies in today's classrooms, some areas of study, such as the use of virtual manipulatives,…

This paper focuses on understanding the role that affordances played in children's learning performance and efficiency during clinical interviews of their interactions with mathematics apps on touch-screen devices. One hundred children, ages 3 to 8, each used six different virtual manipulative mathematics apps during 30-40-min interviews. The…

Recent research has explored the efficacy of the CRA-I (concrete-representational-abstract) strategy with students with disabilities (Strickland & Maccini, 2012, 2013). The CRA-I strategy is a promising practice that special educators have used to teach algebra to students with high-incidence disabilities. The CRA-I strategy is a modification…

The purpose of this project was to examine young children's mathematics learning using virtual manipulative touch-screen apps. We interviewed over 100 young children as they interacted with mathematics apps on iPads and examined how these interactions supported mathematics learning and contributed to changes in efficiency. Children interacted with…

What do you do when you want to get your Stage 3 students authentically and enthusiastically engaged in the active construction of their understanding and fluency with measurement, data collection, representation and interpretation? How do you enable them to make choices about their learning, to measure with purpose, to record and organise the…

Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students.…

With the adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), many concepts related to area are covered in third grade: (1) Recognizing area as an attribute of a plane figure; (2) Understanding that a square with a side length of one is a unit square; (3) Measuring area by tiling figures and counting the squares it…

More than 60 years have passed since the work of Rosalind Franklin, James Watson, and Francis Crick led to the discovery of the 3D-DNA double-helix structure. Nowadays, due to the simple and elegant architecture of its double helix, the structure of DNA is widely known. The biological role of the DNA molecule (e.g., genetic information), however,…