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Natural Number Bias on Evaluations of the Effect of Multiplication and Division: The Role of the Type of Numbers
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Christou, Konstantinos P.; Vamvakoussi, Xenia – Mathematics Education Research Journal, 2023
Over the last years, there is a growing interest in studying students' difficulties with rational numbers from a cognitive/developmental perspective, focusing on the role of prior knowledge in students' understanding of rational numbers. The present study tests the effect of the "whole" or "natural number bias" (i.e., the…
Descriptors: Number Concepts, Bias, Multiplication, Division
Let's Be Rational: Worked Examples Supplemented Textbooks Improve Conceptual and Fraction Knowledge
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Barbieri, Christina Areizaga; Booth, Julie L.; Chawla, Kamal – Educational Psychology, 2023
The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…
Descriptors: Fractions, Mathematics Instruction, Teaching Methods, Algebra
Malleability of Whole-Number and Fraction Biases in Decimal Comparison
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Ren, Kexin; Gunderson, Elizabeth A. – Developmental Psychology, 2019
Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account…
Descriptors: Number Concepts, Fractions, Bias, Arithmetic
Type of Mathematical Proof: Personal Preference or Adaptive Teaching Behavior?
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Brunner, Esther; Reusser, Kurt – ZDM: The International Journal on Mathematics Education, 2019
In our study, 32 German and Swiss 8th/9th-grade classes of lower-secondary school worked with their teacher on the same proving problem. The sample belongs to the Swiss-German study "Quality of Instruction, Learning Behavior and Mathematical Understanding". Our data analyses relate to the teachers' approaches to generating a specific…
Descriptors: Foreign Countries, Mathematical Logic, Mathematics Education, Secondary School Mathematics
What Fills the Gap between Discrete and Dense? Greek and Flemish Students' Understanding of Density
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Vamvakoussi, Xenia; Christou, Konstantinos P.; Mertens, Lieve; Van Dooren, Wim – Learning and Instruction, 2011
It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number…
Descriptors: Foreign Countries, Mathematics Instruction, Comparative Education, Intervals
Abstracting the Density of Numbers on the Number Line--A Quasi-Experimental Study
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Merenluoto, Kaarina – International Group for the Psychology of Mathematics Education, 2003
The starting point for this study was the resistant nature of prior knowledge in conceptual change from natural numbers to rational numbers observed in our previous study. Thus, in this study the effects of deliberately teaching the abstraction of the density of numbers on the number line was tested in a quasi-experimental study at the beginning…
Descriptors: Control Groups, Numbers, Prior Learning, Number Concepts