Place-value understanding in number line estimation predicts future arithmetic performance

2016 ◽  
Vol 34 (4) ◽  
pp. 502-517 ◽  
Author(s):  
Julia F. Dietrich ◽  
Stefan Huber ◽  
Tanja Dackermann ◽  
Korbinian Moeller ◽  
Ursula Fischer
Keyword(s):  
Number Line ◽  
Place Value ◽  
Number Line Estimation ◽  
Arithmetic Performance

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.

Strategies in unbounded number line estimation? Evidence from eye-tracking

2015 ◽  
Vol 16 (S1) ◽  
pp. 359-363 ◽  
Author(s):  
Regina M. Reinert ◽  
Stefan Huber ◽  
Hans-Christoph Nuerk ◽  
Korbinian Moeller
Keyword(s):  
Eye Tracking ◽  
Number Line ◽  
Number Line Estimation

Figuring Out Children’s Number Representations

2014 ◽  
Author(s):  
John N. Towse ◽  
Kevin Muldoon ◽  
Victoria Simms
Keyword(s):  
Cultural Difference ◽  
Number Line ◽  
Developmental Differences ◽  
Cross Cultural ◽  
Place Value ◽  
Linguistic Differences ◽  
Number Representations ◽  
Mathematical Skill ◽  
Different Cultures

This chapter explores how numbers are represented amongst children in different cultures, and shows how this can enrich our understanding of mathematical cognition. It focuses on two specific, related topics: the representation of multi-digit numbers and the scaling of a mental number line. The authors consider whether linguistic differences in number structures directly influence children’s understanding of place value. They also consider whether cross-cultural and developmental differences in the quality of children’s mental representations of number are direct influences on mathematical skill. Together, these two topics allow us to consider evidence for the existence of cross-cultural difference in mathematics and investigate factors that might underlie them. The authors propose that whilst the interpretation of data needs to proceed cautiously, valuable insights can be gained from relevant research.

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