Conceptual knowledge, procedural knowledge, and metacognition in routine and nonroutine problem solving
DW Braithwaite, L Sprague - Cognitive Science, 2021 - Wiley Online Library
When, how, and why students use conceptual knowledge during math problem solving is
not well understood. We propose that when solving routine problems, students are more …
not well understood. We propose that when solving routine problems, students are more …
Predicting middle school profiles of algebra performance using fraction knowledge
CA Barbieri, LK Young, KJ Newton… - Child Development, 2021 - Wiley Online Library
Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for
advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the …
advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the …
Integrated knowledge of rational number notations predicts children's math achievement and understanding of numerical magnitudes
LK Schiller, RS Siegler - Cognitive Development, 2023 - Elsevier
We propose that integrated number sense, the ability to fluidly translate and compare
magnitudes within and across notations, is central to understanding of rational numbers …
magnitudes within and across notations, is central to understanding of rational numbers …
Fraction arithmetic development: An examination of students' patterns of growth and errors across the intermediate grades.
KA Gesuelli, NC Jordan - Journal of Educational Psychology, 2024 - psycnet.apa.org
Fraction arithmetic facility is fundamental to learning more advanced math topics. However,
attaining the ability to add and subtract fractions is hard for many students. The present …
attaining the ability to add and subtract fractions is hard for many students. The present …
Cross-notation knowledge of fractions and decimals
Understanding fractions and decimals requires not only understanding each notation
separately, or within-notation knowledge, but also understanding relations between …
separately, or within-notation knowledge, but also understanding relations between …
Distributions of textbook problems predict student learning: Data from decimal arithmetic.
This study investigated relations between the distribution of practice problems in textbooks
and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of …
and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of …
Perceptions of ease and difficulty, but not growth mindset, relate to specific math attitudes
Background People report negative attitudes towards fractions and percentages relative to
whole numbers (WNs, Sidney, Thompson, Fitzsimmons, & Taber, 2021), and these attitudes …
whole numbers (WNs, Sidney, Thompson, Fitzsimmons, & Taber, 2021), and these attitudes …
Building integrated number sense in adults and children: Comparing fractions-only training with cross-notation number line training
Mounting evidence points to the predictive power of cross-notation rational number
understanding (eg, 2/5 vs. 0.25) relative to within-notation understanding (eg, 2/5 vs. 1/4) in …
understanding (eg, 2/5 vs. 0.25) relative to within-notation understanding (eg, 2/5 vs. 1/4) in …
Parental support for mathematical problem solving: Proximal and distal influences within the religious practice of tithing
This study examined the relation of mathematical learning and problem-solving to influences
close to the child (proximal) and social structures more removed (distal). A socio-ecological …
close to the child (proximal) and social structures more removed (distal). A socio-ecological …
Toward a unified theory of rational number arithmetic.
DW Braithwaite, L Sprague… - Journal of Experimental …, 2022 - psycnet.apa.org
To explain children's difficulties learning fraction arithmetic, Braithwaite et al.(2017)
proposed FARRA, a theory of fraction arithmetic implemented as a computational model …
proposed FARRA, a theory of fraction arithmetic implemented as a computational model …