Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

A. M. Teale; F. De Proft; P. Geerlings; D. J. Tozer

doi:10.1039/c3cp54528h

The Role of Representations in Fraction Addition and Subtraction

Mathematics Teaching in the Middle School ◽

10.5951/mtms.13.8.0490 ◽

2008 ◽

Vol 13 (8) ◽

pp. 490-496

Author(s):

Kathleen Cramer ◽

Terry Wyberg ◽

Seth Leavitt

Keyword(s):

National Science Foundation ◽

Sixth Graders ◽

Teaching Experiment ◽

School Students ◽

Urban District ◽

National Science ◽

Addition And Subtraction ◽

Do So ◽

Fraction Addition

Why do so many middle school students find fraction addition and subtraction difficult despite the fact that they have studied this topic since third or fourth grade? The Rational Number Project (RNP) (Cramer and Henry 2002; Cramer, Post, and delMas 2002) with support from the National Science Foundation is currently engaged in a teaching experiment with sixth graders from a large urban district in the Midwest to address this question.

Download Full-text

The Role of Self-Action in 2-Year-Old Children: An Illustration of the Arithmetical Inversion Principle before Formal Schooling

Child Development Research ◽

10.1155/2015/879258 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7

Author(s):

Amélie Lubin ◽

Sandrine Rossi ◽

Nicolas Poirel ◽

Céline Lanoë ◽

Arlette Pineau ◽

...

Keyword(s):

Cognitive Activity ◽

Inversion Problem ◽

Formal Schooling ◽

Early Mathematics ◽

Inversion Principle ◽

Addition And Subtraction ◽

Early Mathematics Education ◽

Improved Accuracy ◽

Mode A

The importance of self-action and its considerable links with cognitive activity in childhood are known. For instance, in arithmetical cognition, 2-year-olds detected an impossible arithmetical outcome more accurately when they performed the operation themselves (actor mode) than when the experimenter presented it (onlooker mode). A key component in this domain concerns the understanding of the inversion principle between addition and subtraction. Complex operations can be solved without calculation by using an inversion-based shortcut (3-term problems of the form a+b-b must equal a). Some studies have shown that, around the age of 4, children implicitly use the inversion principle. However, little is known before the age of 4. Here, we examined the role of self-action in the development of this principle by preschool children. In the first experiment, 2-year-olds were confronted with inversion (1+1-1=1 or 2) and standard (3-1-1=1 or 2) arithmetical problems either in actor or onlooker mode. The results revealed that actor mode improved accuracy for the inversion problem, suggesting that self-action helps children use the inversion-based shortcut. These results were strengthened with another inversion problem (1-1+1=1 or 2) in a second experiment. Our data provide new support for the importance of considering self-action in early mathematics education.

Download Full-text

Atomic Electron Affinities

IEEE Transactions on Nuclear Science ◽

10.1109/tns.1976.4328380 ◽

1976 ◽

Vol 23 (2) ◽

pp. 934-935 ◽

Cited By ~ 23

Author(s):

W. C. Lineberger

Keyword(s):

Atomic Electron ◽

Electron Affinities

Download Full-text

Selective Interference of Finger Movements on Basic Addition and Subtraction Problem Solving

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000188 ◽

2013 ◽

Vol 60 (3) ◽

pp. 197-205 ◽

Cited By ~ 31

Author(s):

Nicolas Michaux ◽

Nicolas Masson ◽

Mauro Pesenti ◽

Michael Andres

Keyword(s):

Problem Solving ◽

Mental Arithmetic ◽

Time Cost ◽

Finger Movements ◽

Subtraction Problem ◽

Imaging Studies ◽

Selective Interference ◽

Practical Tool ◽

Addition And Subtraction

Fingers offer a practical tool to represent and manipulate numbers during the acquisition of arithmetic knowledge, usually with a greater involvement in addition and subtraction than in multiplication. In adults, brain-imaging studies show that mental arithmetic increases activity in areas known for their contribution to finger movements. It is unclear, however, if this truly reflects functional interactions between the processes and/or representations controlling finger movements and those involved in mental arithmetic, or a mere anatomical proximity. In this study we assessed whether finger movements interfere with basic arithmetic problem solving, and whether this interference is specific for the operations that benefit the most from finger-based calculation strategies in childhood. In Experiment 1, we asked participants to solve addition, subtraction, and multiplication problems either with their hands at rest or while moving their right-hand fingers sequentially. The results showed that finger movements induced a selective time cost in solving addition and subtraction but not multiplication problems. In Experiment 2, we asked participants to solve the same problems while performing a sequence of foot movements. The results showed that foot movements produced a nonspecific interference with all three operations. Taken together, these findings demonstrate the specific role of finger-related processes in solving addition and subtraction problems, suggesting that finger movements and mental arithmetic are functionally related.

Download Full-text

Mental Strategies and Materials or Models for Addition and Subtraction up to 100 in Dutch Second Grades

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.24.4.0294 ◽

1993 ◽

Vol 24 (4) ◽

pp. 294-323 ◽

Cited By ~ 1

Author(s):

Meindert Beishuizen

Keyword(s):

Cognitive Psychology ◽

Field Study ◽

Procedural Knowledge ◽

Mental Arithmetic ◽

Declarative Knowledge ◽

Differential Effects ◽

Mental Addition ◽

Addition And Subtraction ◽

Support Conditions

Dutch mathematics programs emphasize mental addition and subtraction in the lower grades. For two-digit numbers up to 100, instruction focuses on “counting by tens from any number” (N10), a strategy that is difficult to learn. Therefore, many children prefer as an easier alternative “decomposition” in tens (1010) and units. Instead of the use of arithmetic blocks (BL), the hundredsquare (HU) was introduced in the 1980s because of a (supposed) better modeling function for teaching N10. In a field study with several schools, (a) we compared the strategies N10 and 1010 on procedural effectiveness and error types, and (b) we assessed the influence of the support conditions BL versus HU on the acquisition of mental strategies (we had also a control condition NO with no extra materials or models). Results confirmed the greater effectiveness of N10 but also the preference of many weaker children for 1010. Support for BL or HU had differential effects on mental strategies. Differences are discussed in terms of cognitive psychology: the role of declarative knowledge and the relation between conceptual and procedural knowledge. New Dutch proposals for the 1990s emphasize teaching both strategies N10 and 1010 to enhance the flexibility of students' mental arithmetic.

Download Full-text

The Unit Column vs. the Decimal Point: The Role of Place in Written Number

Mathematics Teacher ◽

10.5951/mt.40.1.0014 ◽

1947 ◽

Vol 40 (1) ◽

pp. 14-19

Author(s):

Hiram B. Loomis

Keyword(s):

Elementary Schools ◽

Decimal Point ◽

Addition And Subtraction

The importance of place in written number is evident when we realize that it is our Arabic system of writing number with zero to indicate the empty place or column that enables pupils in our elementary schools to perform arithmetical operations that would trouble good mathematicians confined to the Roman system. In addition and subtraction we have practically been forced to realize the desirability of keeping units digits under units digits and tens digits under tens digits; and in bookkeeping we have paper ruled for this purpose. The objective of this article is to present the desirability of training pupils to use similar columns for all written work in arithmetic; to put every units digit in the units column, every tens digit in the tens column, every tenths digit in the tenths column etc.: and to do this in multiplication and division as well as in addition and subtraction. This will eliminate the problem of “pointing off,” for the decimal point will necessarily be between the units column and the tenths column for every number on the paper.

Download Full-text