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

2013 ◽  
Vol 60 (3) ◽  
pp. 197-205 ◽  
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.

Finger-based representation of mental arithmetic

2014 ◽  
Author(s):  
Michael Andres ◽  
Mauro Pesenti
Keyword(s):  
Mental Arithmetic ◽  
Adult Brain ◽  
Human Beings ◽  
Functional Magnetic Resonance ◽  
Imaging Studies ◽  
Simple Arithmetic ◽  
Number Representations ◽  
Fixed Order ◽  
Arithmetic Performance

Human beings are permanently required to process the world numerically and, consequently, to perform computations to adapt their behaviour and they have developed various calculation strategies, some of them based on specific manipulations of the fingers. In this chapter, we argue that the way we express physically numerical concepts by raising fingers while counting leads to embodied representations of numbers and calculation procedures in the adult brain. To illustrate this, we focus on number and finger interactions in the context of simple arithmetic operations. We show that the fixed order of fingers on the hand provides human beings with unique facilities to increment numerical changes or represent a cardinal value while solving arithmetic problems. In order to specify the influence of finger representation on mental arithmetic both at the cognitive and neural level, we review past and recent findings from behavioural, electrophysiological, and brain imaging studies. We start with anthropological and developmental data showing the role of fingers in the acquisition of arithmetic knowledge, then address the issue of whether number and finger interactions are also observed in adults solving arithmetic problems mentally. We suggest that arithmetic performance depends on the integrity of finger representations in children and adults. Finally, we overview the results of recent functional magnetic resonance imaging (fMRI) studies showing a common brain substrate for finger and number representations during and after the acquisition of arithmetic skills.

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

1993 ◽  
Vol 24 (4) ◽  
pp. 294-323 ◽  
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.

Does Solution of Mental Arithmetic Problems Such as 2 + 6 and 3 × 8 Rely on the Process of “Memory Updating”?

2006 ◽  
Vol 53 (3) ◽  
pp. 198-208 ◽  
Author(s):  
Maud Deschuyteneer ◽  
André Vandierendonck ◽  
Isabel Muyllaert
Keyword(s):  
Reaction Time ◽  
Choice Reaction Time ◽  
Mental Arithmetic ◽  
Response Selection ◽  
Reaction Time Task ◽  
Memory Updating ◽  
Delayed Choice ◽  
Selective Interference ◽  
The Difference

Two experiments are reported that used the selective interference paradigm to study whether, besides response selection, the process of memory updating is involved in simple mental arithmetic. Participants were asked to solve simple sums (e.g., 2 + 6, Experiment 1) or simple products (e.g., 3 × 8, Experiment 2) in a single-task control condition and in three dual-task conditions with a selective interference task, simple reactions, choice reactions, or delayed choice reactions. The role of memory updating was estimated on the basis of the difference in impairment due to the choice reaction time and the delayed choice reaction time task, whereas the difference in impairment between the simple reaction time and the choice reaction time task indicates the role of response selection. While replicating previous results concerning response selection ( Deschuyteneer & Vandierendonck, 2005 , in press ), the study showed that memory updating is strongly involved in solving simple mental arithmetic sums and products.

scholarly journals The Empty Number Line in Dutch Second Grades: Realistic Versus Gradual Program Design

1998 ◽  
Vol 29 (4) ◽  
pp. 443-464 ◽  
Author(s):  
Anton S. Klein ◽  
Meindert Beishuizen ◽  
Adri Treffers
Keyword(s):  
Instructional Design ◽  
Problem Solving ◽  
Mental Model ◽  
Program Design ◽  
Mental Arithmetic ◽  
Gradual Increase ◽  
Number Line ◽  
Mental Addition ◽  
Addition And Subtraction

In this study we compare 2 experimental programs for teaching mental addition and subtraction in the Dutch 2nd grade (N = 275). The goal of both programs is greater flexibility in mental arithmetic through use of the empty number line as a new mental model. The programs differ in instructional design to enable comparison of 2 contrasting instructional concepts. The Realistic Program Design (RPD) stimulates flexible use of solution procedures from the beginning by using realistic context problems. The Gradual Program Design (GPD) has as its purpose a gradual increase of knowledge through initial emphasis on procedural computation followed by flexible problem solving. We found that whereas RPD pupils showed a more varied use of solution procedures than the GPD pupils, this variation did not influence the procedural competence of the pupils. The empty number line appears to be a very powerful model for the learning of addition and subtraction up to 100.

Improving the questions we ask, with Psychology and Cognitive Conflict.

2018 ◽  
Author(s):  
Brett Buttliere
Keyword(s):  
Problem Solving ◽  
Scientific Method ◽  
Meaning Making ◽  
Cognitive Conflict ◽  
Empirical Literature ◽  
Present Evidence ◽  
Scientific Papers ◽  
Science In Society

Over the last decade, there have been many suggestions to improve how scientists answer their questions, but far fewer attempt to improve the questions scientists are asking in the first place. The goal of the paper is then to examine and summarize synthesize the evidence on how to ask the best questions possible. First is a brief review of the philosophical and empirical literature on how the best science is done, which implicitly but not explicitly mentions the role of psychology and especially cognitive conflict. Then we more closely focus on the psychology of the scientist, finding that they are humans, engaged in a meaning making process, and that cognitive conflict is a necessary input for any learning or change in the system. The scientific method is, of course, a specialized meaning making process. We present evidence for this central role of cognitive conflict in science by examining the most discussed scientific papers between 2013 and 2017, which are, in general, controversial and about big problems (e.g., whether vaccines cause autism, how often doctors kill us with their mistakes). Toward the end we discuss the role of science in society, suggesting science itself is an uncertainty reducing and problem solving enterprise. From this basis we encourage scientists to take riskier stances on bigger topics, for the good of themselves and society generally.

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