Developmental change in number line estimation: A strategy-based perspective.

2019 ◽  
Vol 73 (3) ◽  
pp. 144-156
Author(s):  
Koen Luwel ◽  
Dominique Peeters ◽  
Lieven Verschaffel
Keyword(s):  
Developmental Change ◽  
Number Line ◽  
Number Line Estimation

scholarly journals Intuitive proportion judgment in number-line estimation: Converging evidence from multiple tasks

2017 ◽  
Author(s):  
Emily Slusser ◽  
Hilary Barth
Keyword(s):  
Numerical Cognition ◽  
Developmental Change ◽  
Mental Representations ◽  
Number Line ◽  
Bounded Number ◽  
Proportion Estimation ◽  
Typical Performance ◽  
Number Line Estimation ◽  
Numerical Magnitudes ◽  
Fundamental Shift

How children’s understanding of numerical magnitudes changes over the course of development remains a key question in the study of numerical cognition. In an ongoing debate about the source of developmental change, some argue that children maintain and access different mental representations of number, with evidence coming largely from common number-line estimation tasks. In contrast, others argue that a theoretical framework based on psychophysical models of proportion estimation accounts for typical performance on these tasks. The present study explores children’s (n=71) and adults’ (n=27) performance on two number-line tasks, both the “number to position” or NP task and the inverse “position to number” or PN task. Estimates on both tasks are consistent with the predictions of the proportion estimation account and do not support the hypothesis that a fundamental shift in mental representations underlies developmental change in numerical estimation and, in turn, mathematical ability. Converging evidence across tasks also calls into question the utility of bounded number-line tasks as an evaluation of mental representations of number.

scholarly journals Intuitive proportion judgment in number-line estimation: Converging evidence from multiple tasks

2017 ◽  
Author(s):  
Emily Slusser ◽  
Hilary Barth
Keyword(s):  
Numerical Cognition ◽  
Developmental Change ◽  
Mental Representations ◽  
Number Line ◽  
Bounded Number ◽  
Proportion Estimation ◽  
Typical Performance ◽  
Number Line Estimation ◽  
Numerical Magnitudes ◽  
Fundamental Shift

How children’s understanding of numerical magnitudes changes over the course of development remains a key question in the study of numerical cognition. In an ongoing debate about the source of developmental change, some argue that children maintain and access different mental representations of number, with evidence coming largely from common number-line estimation tasks. In contrast, others argue that a theoretical framework based on psychophysical models of proportion estimation accounts for typical performance on these tasks. The present study explores children’s (n=71) and adults’ (n=27) performance on two number-line tasks, both the “number to position” or NP task and the inverse “position to number” or PN task. Estimates on both tasks are consistent with the predictions of the proportion estimation account and do not support the hypothesis that a fundamental shift in mental representations underlies developmental change in numerical estimation and, in turn, mathematical ability. Converging evidence across tasks also calls into question the utility of bounded number-line tasks as an evaluation of mental representations of number.

scholarly journals Digit identity influences numerical estimation in children and adults

2017 ◽  
Author(s):  
Maxine Lai ◽  
Alexandra Zax ◽  
Hilary Barth
Keyword(s):  
Developmental Change ◽  
Mental Representations ◽  
Number Line ◽  
Effect Sizes ◽  
Numerical Magnitude ◽  
Numerical Estimation ◽  
Target Values ◽  
Number Line Estimation ◽  
Digit Identity ◽  
Symbolic Number

Learning the meanings of Arabic numerals involves mapping the number symbols to mental representations of their corresponding, approximate numerical quantities. It is often assumed that performance on numerical tasks, such as number line estimation (NLE), is primarily driven by translating from a presented numeral to a mental representation of its overall magnitude. Part of this assumption is that it is the overall numerical magnitude of the presented numeral, not the specific digits that comprise it, that matter for task performance. Here we ask whether the magnitudes of the presented target numerals drive symbolic number line performance, or whether specific digits influence estimates. If the former is true, estimates of numerals with very similar magnitudes but different digits (such as 399 and 402) should be placed in similar locations. However, if the latter is true, these placements will differ significantly. In two studies (N = 262), children aged 7-11 and adults completed 0-1000 NLE tasks with target values drawn from a set of paired numerals that fell on either side of “Hundreds” boundaries (e.g. 698 and 701) and “Fifties” boundaries (e.g. 749 and 752). Study 1 used an atypical speeded NLE task, while Study 2 used a standard non-speeded NLE task. Under both speeded and non-speeded conditions, specific hundreds digits in the target numerals exerted a strong influence on estimates, with large effect sizes at all ages, showing that the magnitudes of target numerals are not the primary influence shaping children’s or adults’ placements. We discuss patterns of developmental change and individual difference revealed by planned and exploratory analyses.

The relationship between number line estimation and arithmetic competencies depends on age, operation and skill

2013 ◽  
Author(s):  
Julia Bahnmueller ◽  
Stefan Huber ◽  
Korbinian Moeller ◽  
Hans-Christoph Nuerk
Keyword(s):  
Number Line ◽  
Number Line Estimation ◽  
The Relationship

Improving Struggling Fifth-Grade Students’ Understanding of Fractions: A Randomized Controlled Trial of an Intervention That Stresses Both Concepts and Procedures

2021 ◽  
pp. 001440292110088
Author(s):  
Madhavi Jayanthi ◽  
Russell Gersten ◽  
Robin F. Schumacher ◽  
Joseph Dimino ◽  
Keith Smolkowski ◽  
...  
Keyword(s):  
Randomized Controlled Trial ◽  
Explicit Instruction ◽  
Controlled Trial ◽  
Number Line ◽  
Randomized Controlled ◽  
Fifth Grade Students ◽  
Linear Representations ◽  
Mathematical Explanations ◽  
Grade 5 ◽  
Number Line Estimation

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study ( n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and relied on linear representations (e.g., Cuisenaire Rods and number lines) to demonstrate key fractions concepts. Enhancing students’ mathematical explanations was also a focus. Results indicated that intervention students significantly outperformed students from the comparison condition on measures of fractions proficiency and understanding ( g = 0.66–0.78), number line estimation ( g = 0.80–1.08), fractions procedures ( g = 1.07), and explanation tasks ( g = 0.68–1.23). Findings suggest that interventions designed to include explicit instruction, along with consistent use of the number line and opportunities to explain reasoning, can promote students’ proficiency and understanding of fractions.

Associations of Number Line Estimation With Mathematical Competence: A Meta-analysis

2018 ◽  
Vol 89 (5) ◽  
pp. 1467-1484 ◽  
Author(s):  
Michael Schneider ◽  
Simon Merz ◽  
Johannes Stricker ◽  
Bert De Smedt ◽  
Joke Torbeyns ◽  
...  
Keyword(s):  
Meta Analysis ◽  
Number Line ◽  
Mathematical Competence ◽  
Number Line Estimation

Children can accurately monitor and control their number-line estimation performance.

2016 ◽  
Vol 52 (10) ◽  
pp. 1493-1502 ◽  
Author(s):  
Jenna L. Wall ◽  
Clarissa A. Thompson ◽  
John Dunlosky ◽  
William E. Merriman
Keyword(s):  
Number Line ◽  
Estimation Performance ◽  
Number Line Estimation ◽  
And Control ◽  
Monitor And Control

Fixated in unfamiliar territory: Mapping estimates across typical and atypical number lines

2019 ◽  
Vol 73 (2) ◽  
pp. 279-294
Author(s):  
Sabrina Michelle Di Lonardo ◽  
Matthew G Huebner ◽  
Katherine Newman ◽  
Jo-Anne LeFevre
Keyword(s):  
Numerical Range ◽  
Number Line ◽  
Strategy Use ◽  
Reverse Direction ◽  
Tracking Data ◽  
Spatial Processes ◽  
Number Lines ◽  
Number Line Estimation ◽  
The Right ◽  
Typical Range

Adults ( N = 72) estimated the location of target numbers on number lines that varied in numerical range (i.e., typical range 0–10,000 or atypical range 0–7,000) and spatial orientation (i.e., the 0 endpoint on the left [traditional] or on the right [reversed]). Eye-tracking data were used to assess strategy use. Participants made meaningful first fixations on the line, with fixations occurring around the origin for low target numbers and around the midpoint and endpoint for high target numbers. On traditional direction number lines, participants used left-to-right scanning and showed a leftward bias; these effects were reduced for the reverse direction number lines. Participants made fixations around the midpoint for both ranges but were less accurate when estimating target numbers around the midpoint on the 7,000-range number line. Thus, participants are using the internal benchmark (i.e., midpoint) to guide estimates on atypical range number lines, but they have difficulty calculating the midpoint, leading to less accurate estimates. In summary, both range and direction influenced strategy use and accuracy, suggesting that both numerical and spatial processes influence number line estimation.

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