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Learning and Instruction, ISSN 0959-4752, 06/2015, Volume 37, pp. 50 - 55
The development of rational number knowledge has been studied extensively by mathematics education researchers, cognitive-developmental psychologists and, more... 
Whole/natural number bias | Rational number knowledge | EDUCATION & EDUCATIONAL RESEARCH | FRACTION | WHOLE NUMBER | REACTION-TIME | BIAS | REPRESENTATION | MAGNITUDES | PSYCHOLOGY, EDUCATIONAL | Knowledge
Journal Article
Learning and Instruction, ISSN 0959-4752, 2004, Volume 14, Issue 5, pp. 453 - 467
In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular... 
Conceptual change | Density | Rational numbers | EDUCATION & EDUCATIONAL RESEARCH | rational numbers | conceptual change | density | PSYCHOLOGY, EDUCATIONAL | Numbers | Algebra | Mathematics Instruction | Secondary School Mathematics | Cognitive Structures | Grade 9 | Prior Learning | Teaching Methods | Number Concepts
Journal Article
Educational Studies in Mathematics, ISSN 0013-1954, 2/2013, Volume 82, Issue 2, pp. 323 - 330
This study tested the hypothesis that intuitions about the effect of operations, e.g., “addition makes bigger” and “division makes smaller”, are still present... 
Reaction time research | Education | Intuitions | Mathematics Education | Mathematics, general | Adults | Arithmetic operations | MATHEMATICS | EDUCATION & EDUCATIONAL RESEARCH | RULES | Accuracy | Mathematics Instruction | Mathematical Applications | Reaction Time | Mathematics | Intuition | Arithmetic
Journal Article
Cognition and Instruction, ISSN 0737-0008, 04/2010, Volume 28, Issue 2, pp. 181 - 209
We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The... 
Learning | Numbers | High school students | Symbolism | Natural numbers | Rational numbers | Questionnaires | Mathematics education | Decimals | Fractions | MATHEMATICS | PSYCHOLOGY, EXPERIMENTAL | PSYCHOLOGY, EDUCATIONAL | Intervals | Greece (Athens) | Theories | Mathematical Concepts | Mathematics | Foreign Countries | Secondary School Students | Arithmetic | Concept Formation
Journal Article
ZDM, ISSN 1863-9690, 8/2017, Volume 49, Issue 4, pp. 497 - 507
Journal Article
Journal of Mathematical Behavior, ISSN 0732-3123, 09/2012, Volume 31, Issue 3, pp. 344 - 355
► The natural number bias is examined from a dual process perspective. ► Fifty-eight educated adults took a rational number tasks test. ► Congruent items were... 
Natural number bias | Intuitive and analytic reasoning | Dual process perspective | Rational numbers | Reaction time methods | Numbers | Cognitive Processes | Thinking Skills | Reaction Time | Mathematics | Adults | Intuition | Error Patterns
Journal Article
2019, ISBN 9780128159521, Volume 5
Analogical reasoning is a fundamental aspect of human cognition: People, even young children, engage spontaneously in analogical reasoning to make sense of... 
Analogies | Bridging analogies | Number line | Analogical reasoning | Number concepts
Book Chapter
2007, ISBN 9780080449807, xxiii, 720 p., [8] p. of col. plates
Eye-movement recording has become the method of choice in a wide variety of disciplines investigating how the mind and brain work. This volume brings together... 
Eye | Pre-clinical Medicine: Basic Sciences | Movements | Congresses
Book
Journal of Numerical Cognition, ISSN 2363-8761, 06/2018, Volume 4, Issue 1, pp. 84 - 106
In this paper we focus on the development of rational number knowledge and present three research programs that illustrate the possibility of bridging research... 
educational implications | conceptual change | number cognition | natural number bias | rational number development
Journal Article
Frontline Learning Research, ISSN 2295-3159, 2015, Volume 3, Issue 1, p. 18
We present the results of an in-depth qualitative study that examined ninth graders' conceptual and procedural knowledge of fractions as well as their approach... 
Greece (Athens) | Mathematics Instruction | Task Analysis | Cognitive Style | Mathematical Concepts | Learning Processes | Foreign Countries | Individual Differences | Fractions | Accuracy | Knowledge Level | Profiles | Grade 9 | Qualitative Research | Statistical Analysis
Journal Article
Cognition and Instruction, ISSN 0737-0008, 04/2010, Volume 28, Issue 2, pp. 181 - 209
Journal Article
2018
We constructed and calibrated an instrument targeting conceptual and procedural fraction knowledge. We used this instrument in a quantitative study with 126... 
Knowledge Level | Grade 7 | Age Differences | Grade 9 | Mathematical Concepts | Foreign Countries | Adolescents | Individual Differences | Fractions | Mathematics Skills | Secondary School Students
Journal Article
Learning and Instruction, ISSN 0959-4752, 2011, Volume 21, Issue 5, pp. 676 - 685
It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places... 
Conceptual change | Density property | Rational numbers | EDUCATION & EDUCATIONAL RESEARCH | PSYCHOLOGY, EDUCATIONAL | Comparative Education | Intervals | Mathematics Instruction | Cognitive Structures | Foreign Countries | Prior Learning | Greece | Numbers | Comparative Analysis | Belgium | Grade 9 | Number Concepts | Concept Formation | Students | Study and teaching
Journal Article
2012, Volume 2, 4
Reference
Educational Studies in Mathematics, ISSN 0013-1954, 2/2013, Volume 82, Issue 2, pp. 323 - 330
This study tested the hypothesis that intuitions about the effect of operations, e.g., "addition makes bigger" and "division makes smaller", are still present... 
Addition | Reasoning | Adult education | Natural numbers | Rational numbers | Intuition | Mathematics education | Cognitive psychology | Reason | Empirical evidence
Journal Article
Mathematical Thinking and Learning, ISSN 1098-6065, 10/2012, Volume 14, Issue 4, pp. 265 - 284
In two experiments we explored the instructional value of a cross-domain mapping between "number" and "line" in secondary school students' understanding of... 
EDUCATION & EDUCATIONAL RESEARCH | CONCEPTUAL CHANGE | SCIENCE | RATIONAL NUMBERS | Intervention | Intervals | Greece | Numbers | Mathematics Instruction | Secondary School Mathematics | Geometric Concepts | Mathematical Concepts | Hypothesis Testing | Mathematical Logic | Foreign Countries | Secondary School Students
Journal Article
2018
In this paper we focus on the development of rational number knowledge and present three research programs that illustrate the possibility of bridging research... 
educational implications | number cognition | conceptual change | natural number bias | rational number development
Data Set
07/2010, ISBN 9780203847824
Book Chapter
Learning and Instruction, ISSN 0959-4752, 2004, Volume 14, pp. 443 - 467
In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular... 
Computer Science | Technology for Human Learning
Journal Article
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