In this third of a series of four articles, the author deconstructs the primary national strategy's approach to written multiplication. The approach to multiplication, as set out on pages 12 to 15 of the primary national strategy's "Guidance paper" "Calculation" (DfES, 2007), is divided into six stages: (1) mental…

In Singapore, 6-12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13-17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is…

The formation constant of iron(III) complex with glycine (Gly) ligand in aqueous acidic medium (0.2 M HNO[subscript 3], I = 0.2 M at 28 plus or minus 1 degree C) was determined spectrophotometrically in which a competing color reaction between Fe(III) and SCN[superscript -] was used as an indicator reaction. Under the specified conditions Fe(III)…

This research examines students' ability to integrate algebraic variables with arithmetic operations and symbols as a result of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from arithmetic to algebraic reasoning. It presents data from pre- and post-instruction clinical…

Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…

Two commercial self-heating food products have been used to apply chemical concepts such as stoichiometry, enthalpies of reactions and solutions, and heat transfer in a classroom activity. These products are the self-heating beverages sold in Europe and the Meals, Ready to Eat or MREs used primarily by the military in the United States. The main…

The relationship between pH and the aqueous solubility of heavy metals is explored by considering the environmental impact of acidic mine drainage. Acid mine drainage is an important environmental concern in many areas of the United States. Associated with coal mining in the East and hard rock mining in the West, the acidity originates primarily…

During a roller coaster ride, the body experiences acceleration in three dimensions. An accelerometer can measure and provide a graph of the forces on the body during different parts of a ride. To couple the experience of the body to pictures of the ride and an analysis of data can contribute to a deeper understanding of Newton's laws. This…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

This is a powerful critique of two decades of educational reform in New Zealand, from an educator who was deeply involved. It is also a provocative call for action. Bali Haque has been both a secondary school principal required to implement reform and a senior public servant in the New Zealand Qualifications Authority (NZQA) tasked with pushing…

Looking away from an interlocutor's face during demanding cognitive activity can help adults and children answer challenging mental arithmetic and verbal-reasoning questions (Glenberg, Schroeder, & Robertson, 1998; Phelps, Doherty-Sneddon, & Warnock, 2006). While such "gaze aversion" (GA) is used far less by 5-year-old school children, its use…

Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3+4+6=3+__) and completed a…

Approximately 93 percent of Americans indicate that they experience some level of math anxiety. Math anxiety is defined as negative emotions that interfere with the solving of mathematical problems. Studies have found that some students who perform poorly on math assessments actually have a full understanding of the concepts being tested; however,…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

This case study stresses the need to broadly consider an entire system, including all of the energy inputs and outputs involved, to determine the real efficiency of that system. It also asks its student audience to consider the role that scientific input plays in policy decision-making processes. It emphasizes that, despite the importance of this…