This article describes how a crystal ball known as "The Flash Mind Reader" is played. "The Flash Mind Reader" is a mathematics game in which the player is invited to select any-two digit number and then subtract the sum of these two digits from the original number. A chart is provided in which the (adjusted) number they…

In this second of a series of four articles, the author deconstructs the primary national strategy's (PNS) approach to written subtraction. The approach to subtraction is divided into three stages: using the empty number line; partitioning; and expanded layout leading to column methods (called "standard methods" in the consultation document). The…

This study investigates how well 381 prospective elementary, early childhood, and special education majors solved four arithmetic problems that required using the order of operations. Self-reported data show these students to be relatively able mathematically and confident in their ability, with no substantial dislike of mathematics. The…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

At the heart of the debate about the place of standard arithmetic algorithms is the practice of teaching subtraction through decomposition. One welcome feature of the national numeracy strategy in both its initial and current incarnations has been the introduction of a focus upon a variety of mental strategies supported by jottings. In this…

There is evidence for both semantic and asemantic routes for naming Arabic digits, but neuropsychological dissociations suggest that number-fact retrieval (2x3=6) can inhibit the semantic route for digit naming. Here, we tested the hypothesis that such inhibition should slow digit naming, based on the principle that reduced access to multiple…

In this study, children were encouraged to abstract mathematical principles by making connections between procedures. Children from 2 sixth-grade classes (N = 58) were asked to solve and explain subtraction examples in 3 different number domains (whole numbers, fractions, and decimals), solve subtraction word problems, compare the procedures, and…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

In the author's second grade maths class, the students were excited and energised after discovering, understanding and learning an advanced mathematical concept. In the class, the second-graders spent a great deal of time discussing how they used the number grid to work out 96 - 7. In this article, the author presents a portion of the class…

A paucity of research has directly compared empirically supported interventions to examine their effectiveness among students with different mathematics fluency skills. The purpose of this study was to compare the effects of two empirically supported interventions and a control condition on the mathematics fluency of 98 second and third grade…

The juxtaposition of articles by Ian Thompson and Ian Sugarman in "MT202" on addition and subtraction respectively engendered some bemused thoughts in this author, who for some years has been sheltered from controversy by retirement. In this article, Fielker shares some thoughts on addition and subtraction raised by Thompson and Sugarman in their…

The present research involved gauging preschoolers' learning potential for a key arithmetic concept, the addition-subtraction inverse principle (e.g., 2+1-1=2). Sixty 4- and 5-year-old Taiwanese children from two public preschools serving low- and middle-income families participated in the training experiment. Half were randomly assigned to an…

This book contains a compilation of papers presented at the International Psychological Applications Conference and Trends (InPACT) 2018, organized by the World Institute for Advanced Research and Science (W.I.A.R.S.). Modern psychology offers a large range of scientific fields where it can be applied. The goal of understanding individuals and…

The principle of inversion--that a + b - b must equal a--requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the…