Promoting Discourse: Fractions on Number Lines

2021 ◽  
Vol 114 (4) ◽  
pp. 284-289
Author(s):  
Susan Ahrendt ◽  
Debra Monson ◽  
Kathleen Cramer
Keyword(s):  
Fourth Graders ◽  
Number Line ◽  
Number Lines ◽  
Mathematical Discussions ◽  
Five Practices

Examine fourth graders’ thinking about the unit, partitioning, order, and equivalence on the number line and consider ways to orchestrate mathematical discussions through the Five Practices.

scholarly journals Number line tasks and their relation to arithmetics in second to fourth graders

2021 ◽  
Vol 7 (1) ◽  
pp. 20-41
Author(s):  
Carrie Georges ◽  
Christine Schiltz
Keyword(s):  
Fourth Graders ◽  
Proportional Reasoning ◽  
Number Line ◽  
Numerical Magnitude ◽  
Cognitive Mechanisms ◽  
Bounded Number ◽  
Bias Model ◽  
Number Lines ◽  
Power Models ◽  
Log Linear

Considering the importance of mathematical knowledge for STEM careers, we aimed to better understand the cognitive mechanisms underlying the commonly observed relation between number line estimations (NLEs) and arithmetics. We used a within-subject design to model NLEs in an unbounded and bounded task and to assess their relations to arithmetics in second to fourth grades. Our results mostly agree with previous findings, indicating that unbounded and bounded NLEs likely index different cognitive constructs at this age. Bounded NLEs were best described by cyclic power models including the subtraction bias model, likely indicating proportional reasoning. Conversely, mixed log-linear and single scalloped power models provided better fits for unbounded NLEs, suggesting direct estimation. Moreover, only bounded but not unbounded NLEs related to addition and subtraction skills. This thus suggests that proportional reasoning probably accounts for the relation between NLEs and arithmetics, at least in second to fourth graders. This was further confirmed by moderation analysis, showing that relations between bounded NLEs and subtraction skills were only observed in children whose estimates were best described by the cyclic power models. Depending on the aim of future studies, our results suggest measuring estimations on unbounded number lines if one is interested in directly assessing numerical magnitude representations. Conversely, if one aims to predict arithmetic skills, one should assess bounded NLEs, probably indexing proportional reasoning, at least in second to fourth graders. The present outcomes also further highlight the potential usefulness of training the positioning of target numbers on bounded number lines for arithmetic development.

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.

scholarly journals Strategy use on bounded and unbounded number lines in typically developing adults and adults with dyscalculia: An eye-tracking study

2018 ◽  
Vol 4 (2) ◽  
pp. 337-359 ◽  
Author(s):  
Fae Aimée van der Weijden ◽  
Erica Kamphorst ◽  
Robin Hella Willemsen ◽  
Evelyn H. Kroesbergen ◽  
Anne H. van Hoogmoed
Keyword(s):  
Eye Tracking ◽  
Number Sense ◽  
Number Line ◽  
Strategy Use ◽  
Typically Developing ◽  
Target Number ◽  
Gaze Patterns ◽  
Pure Number ◽  
Number Lines ◽  
New Strategies

Recent research suggests that bounded number line tasks, often used to measure number sense, measure proportion estimation instead of pure number estimation. The latter is thought to be measured in recently developed unbounded number line tasks. Children with dyscalculia use less mature strategies on unbounded number lines than typically developing children. In this qualitative study, we explored strategy use in bounded and unbounded number lines in adults with (N = 8) and without dyscalculia (N = 8). Our aim was to gain more detailed insights into strategy use. Differences in accuracy and strategy use between individuals with and without dyscalculia on both number lines may enhance our understanding of the underlying deficits in individuals with dyscalculia. We combined eye-tracking and Cued Retrospective Reporting (CRR) to identify strategies on a detailed level. Strategy use and performance were highly similar in adults with and without dyscalculia on both number lines, which implies that adults with dyscalculia may have partly overcome their deficits in number sense. New strategies and additional steps and tools used to solve number lines were identified, such as the use of the previous target number. We provide gaze patterns and descriptions of strategies that give important first insights into new strategies. These newly defined strategies give a more in-depth view on how individuals approach a number lines task, and these should be taken into account when studying number estimations, especially when using the unbounded number line.

scholarly journals MENINGKATKAN KEMAMPUAN ESTIMASI ROUNDING TERHADAP PENJUMLAHAN MELALUI PEMBELAJARAN BERBANTUAN KARTU DAN GARIS BILANGAN PADA SISWA KELAS VB SDN 2 TAMAN SARI LOBAR

2017 ◽  
Vol 2 (2) ◽  
pp. 81
Author(s):  
Yuni Maryati Yuni Maryati
Keyword(s):  
Elementary School ◽  
Action Research ◽  
Number Line ◽  
Teacher Observation ◽  
Research Subjects ◽  
Research Results ◽  
Student Activity ◽  
Number Lines ◽  
Field Notes ◽  
Student Test

The study was conducted to examine the improving ability of the estimation rounding of the students through assisted card learning and number line to describe the application of assisted learning and the number lines that improve the students rounding estimation’s ability of VB class of 2 Taman Sari State Elementary School, West Lombok.This study used classroom action research. In this case, the researcher had a role as a conduit of action, a key instrument, a reporter of the research results, and an interviewer on the research subjects. The data of this study are in the form of the review of the student test answers and the interviews. The data was collected by researcher by using the student activity observation sheets, field notes, teacher observation sheets, guidelines for scoring test questions, and interviewing guides. The Result of the study shows thatthe application ofassisted card learningandthe number line which canimprove the ability of rounding estimationconsistsof5stages namely:(1) observingthe card and number line, (2) writing down the reasons of estimation in the card,(3) displaying card whichcontainsthe estimation resultan,(4) comparing the estimationrounding,(5) presenting thereasonswiththe card. The criteria of  success which was specified by the researcher had been achieved in the second cycle. More detail the percentage of the students who did not make the mistake of the concepts, the calculations, and the procedures was as follows: (1) the percentage of the students who did not make the mistake of the concept was 76%, (2) the percentage of the students who did not make the mistake of the procedures was 70%, and (3) the percentage of the students who did not make the mistake of the calculation was 94% and (4) the percentage of the students who had reached the KKM was 87%.

Adults' Health-Related Problem Solving Is Facilitated by Number Lines, But Not Risk Ladders and Icon Arrays

2021 ◽  
Author(s):  
Marta Mielicki ◽  
Charles Fitzsimmons ◽  
Lauren Schiller ◽  
Dan Scheibe ◽  
Jennifer M Taber ◽  
...  
Keyword(s):  
Visual Display ◽  
Number Line ◽  
Math Skills ◽  
Number Lines ◽  
Health Related ◽  
Information Number ◽  
Math Problems ◽  
Line Condition ◽  
Better Than ◽  
Icon Arrays

Visual displays, such as icon arrays and risk ladders, are often used to communicate numerical health information. Number lines improve reasoning with rational numbers but are seldom used in health contexts. College students compared rates for information related to COVID-19 (e.g., number of deaths and number of cases) in one of four randomly-assigned conditions: icon arrays, risk ladders, number lines, or no accompanying visual display. As predicted, number lines facilitated performance on these problems – the number line condition outperformed the other visual display conditions, which did not perform any better than the no visual display condition. In addition, higher performance on the health-related math problems was associated with higher COVID-19 worry for oneself and others, higher perceptions of COVID-19 severity, and higher endorsement of intentions to engage in preventive health behaviors, even when controlling for baseline math skills. These findings have important implications for effectively presenting health statistics.

Quick Reads: Another Good Idea: Integers Made Easy: Just Walk It Off

2007 ◽  
Vol 13 (2) ◽  
pp. 118-121
Author(s):  
Julie Nurnberger-Haag
Keyword(s):  
Number Line ◽  
Similar Process ◽  
Learning Modalities ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Brain Based Learning

Walk It Off is a multisensory method that I developed to teach students how to multiply and divide as well as add and subtract integers. In my experience, this method makes these processes much more effective, efficient, and entertaining than other approaches. Students have the opportunity to use the Process Standards while exploring a topic that is often taught strictly as algorithms without understanding. In addition to having visual, oral, and aural characteristics, Walk It Off is kinesthetic, because students literally walk off problems on number lines. The multiple learning modalities that this method uses are compatible with brain-based learning. Students become actively involved in doing calculations as they physically act out problems using the underlying concepts of integers. Although many books and lessons already use number lines to demonstrate addition and subtraction in various ways, the Walk It Off method makes it possible to use a number line for multiplication and division of integers as well. Using integers becomes easy, because students learn only two slightly different processes for the two basic groups of operations: one process for addition and subtraction and a similar process for multiplication and division.

Integer Target: Using a Game to Model Integer Addition and Subtraction

2007 ◽  
Vol 12 (7) ◽  
pp. 388-392
Author(s):  
Jerry Burkhart
Keyword(s):  
Small Groups ◽  
Number Line ◽  
Target Number ◽  
Number Lines ◽  
Addition And Subtraction

Imagine a classroom where students are gathered in small groups, working with number lines and cards marked with integers. The students have chosen a “target number” on the number line and are deep in discussion, trying to find ways to make the sum of the integers on their cards match this number. There is a deck from which they draw, discard, or exchange cards. They also give, take, or trade cards with one another.

Reconstructing the unit on the number line: Tasks to extend fourth graders’ fraction understandings

2018 ◽  
Vol 11 (3) ◽  
pp. 180-194 ◽  
Author(s):  
Kathleen Cramer ◽  
Debra Monson ◽  
Susan Ahrendt ◽  
Terry Wyberg ◽  
Christy Pettis ◽  
...  
Keyword(s):  
Fourth Graders ◽  
Number Line

Fixated in more familiar territory: Providing an explicit midpoint for typical and atypical number lines

2020 ◽  
pp. 174702182096761
Author(s):  
Sabrina Di Lonardo Burr ◽  
Jo-Anne LeFevre
Keyword(s):  
Eye Tracking ◽  
Number Line ◽  
Estimation Accuracy ◽  
Tracking Data ◽  
Number Lines ◽  
Number Line Estimation

Does providing an explicit midpoint affect adults’ performance differently for typical and atypical number line tasks? Participants ( N = 29) estimated the location of target numbers on typical (i.e., 0–10,000) and atypical (i.e., 0–7,000) number lines with either an explicitly labelled midpoint or no midpoint. For the typical number line, estimation accuracy did not differ for the explicit- and implicit-midpoint conditions. For the atypical number line, participants in the explicit-midpoint condition were more accurate than those in the implicit-midpoint condition and their pattern of error was similar to that seen for typical number lines (i.e., M-shaped). In contrast, for participants in the implicit-midpoint condition, the pattern of error on the atypical line was tent-shaped, with less accurate estimates around the midpoint and quartiles than the endpoints. Eye-tracking data showed that, for all number lines, participants used the middle of the line to guide their estimates, but participants in the explicit-midpoint condition were more likely to make their first fixation around the true midpoint than those in the implicit–midpoint condition. We conclude that adults have difficulty in estimating on atypical number lines because they incorrectly calculate the numerical value of the midpoint.

Life on the Number Line: Routes to Understanding Fraction Magnitude for Students With Difficulties Learning Mathematics

2016 ◽  
Vol 50 (6) ◽  
pp. 655-657 ◽  
Author(s):  
Russell Gersten ◽  
Robin F. Schumacher ◽  
Nancy C. Jordan
Keyword(s):  
Mathematics Curriculum ◽  
Deep Understanding ◽  
Number Line ◽  
Advanced Mathematics ◽  
Instructional Tool ◽  
Special Issue ◽  
Learning Mathematics ◽  
Fraction Concepts ◽  
Number Lines ◽  
General Part

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part–whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.

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