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.

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

Indigenous Language Speaking Students Learning Mathematics in English: Expectations of and for Teachers

2015 ◽  
Vol 44 (1) ◽  
pp. 48-58 ◽  
Author(s):  
Cris Edmonds-Wathen
Keyword(s):  
School Readiness ◽  
Mathematics Curriculum ◽  
Ethnographic Study ◽  
Indigenous Language ◽  
Prior Learning ◽  
Teacher Interviews ◽  
Teaching Context ◽  
Learning Mathematics ◽  
Age Appropriate ◽  
Australian English

Effective mathematics teaching for Indigenous language speaking students needs to be based on fair expectations of both students and teachers. Concepts of ‘age-appropriate learning’ and ‘school readiness’ structure assessment expectations that entire cohorts of Indigenous language speaking students are unable to meet. This institutionalises both student and teacher failure, as both are exhorted to meet unachievable expectations. The voices of teachers teaching in a very remote school provide insight into teachers’ responses to the mismatch between the system expectations and the teaching context. Teacher interviews in a small Northern Territory school, conducted within an ethnographic study, showed that teachers’ decisions regarding the level of mathematics curriculum taught were informed by students’ prior learning and by the language dynamic in their classrooms. The need and pressure to teach Standard Australian English also affected how mathematics was taught. This leads to a reformulation of the concept of school readiness to ask how schools can be more ready for their Indigenous language speaking students in terms of preparing and supporting teachers.

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.

ONE POINT OF VIEW: Sense and Nonsense about Fractions and Decimals

1980 ◽  
Vol 27 (5) ◽  
pp. 5-7
Author(s):  
Joseph N. Payne
Keyword(s):  
Elementary School ◽  
Mathematics Curriculum ◽  
Point Of View ◽  
School Mathematics ◽  
Slow Movement ◽  
Elementary School Mathematics ◽  
Fraction Concepts ◽  
School Mathematics Curriculum

With our certain, albeit slow, movement to the metric system and with the widespread use of calculators, there is general agreement that decimals wiU be introduced earlier in our elementary school mathematics curriculum. Decimals for tenths, for example, have been taught successfully in grade three. Nevertheless, there are major questions, substantial disagreements, and some sheer nonsensical statements being made about fraction concepts, fraction computation, and decimal computation.

Developing Number Sense on the Number Line

2001 ◽  
Vol 6 (8) ◽  
pp. 448-451
Author(s):  
Jennifer M. Bay
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Young Children ◽  
Conceptual Understanding ◽  
Rational Numbers ◽  
Number Line ◽  
School Students ◽  
Large Numbers ◽  
Learning Mathematics ◽  
And Algebra

One of the most important lessons that I have learned as a teacher is that seemingly boring problems on paper can come alive if I can find a way to lift them off the page. This transformation took place when the number line in my classroom became a brightly colored rope that stretched the length of the room, held by a student at each end. I first saw this idea as an approach to help young children order numbers from 1 to 10, then adapted it for middle school students. The scope of the activity eventually expanded to include explorations of large numbers, rational numbers, and algebra. As I saw improvement in students' conceptual understanding and their enjoyment of the life-sized number line, I used it more often in my classroom. I also found that the activities with the number line involved communication, reasoning, and justification— important processes in learning mathematics (NCTM 1989, 2000).

scholarly journals Special Issue on Digital Games for Learning Mathematics

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Alessandro De Gloria
Keyword(s):  
Conceptual Understanding ◽  
Mathematical Thinking ◽  
Leading Edge ◽  
Digital Games ◽  
Online Games ◽  
Special Issue ◽  
Learning Mathematics ◽  
Games For Learning ◽  
Thinking Processes

Given the huge relevance of mathematics, for both reasoning and applications, it is important to develop more engaging and effective methods that can be used to enhance children’s conceptual understanding of mathematics, develop mathematical thinking processes and improve arithmetical skills. Digital games provide interesting possibilities to support these goals and one can easily find great deal of online games and apps targeted for learning mathematics. This spoecial issue is devoted to present leading-edge research and perspectives in the field.

scholarly journals ANALYSIS OF SKILL CRITICAL THINKING STUDENTS ON LEARNING MATHEMATICS CURRICULUM 2013 CLASS V SDN 59 PEKANBARU

2020 ◽  
Vol 4 (5) ◽  
pp. 965
Author(s):  
Cindy Rahmadani Putri
Keyword(s):  
Critical Thinking ◽  
Mathematics Curriculum ◽  
Mathematics Learning ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Male Students ◽  
Research Subjects ◽  
Class V ◽  
Learning Mathematics ◽  
Alternative Solutions

Critical thinking skills are very important owned, because having critical thinking skills can help us think logically in overcoming the problems we face and looking for and developing alternative solutions to those problems.This study aims to identify and describe student’s critical thinking skills in mathematics learning curriculum 2013 class V SDN 59 Pekanbaru. This research was conducted on January 22, 2020. Research subjects totaled 35 students consisting of 19 male students and 16 female students. This type of research is qualitative research. Data collection instruments in the form of test questions consisting of 5 essay questions and interview guidelines conducted on several students. The results showed 60% in the very low category, 27.5% in the low category, 8.5% in the medium category, and 2.8 in the high and very high categories. Based on the result of data analysis, it can be concluded that the critical thinking skills of studnts in learning mathematics in curriculum 2013 class V SDN 59 Pekanbaru are in the very low category.

Editorial for Special Issue on Writing and Editing in the Mathematics Curriculum: Part I

PRIMUS ◽  
2014 ◽  
Vol 24 (6) ◽  
pp. 443-446 ◽  
Author(s):  
Martin Montgomery ◽  
Ryan Stuffelbeam
Keyword(s):  
Mathematics Curriculum ◽  
Special Issue

Activities for Students: Algebra on the Number Line

2010 ◽  
Vol 104 (5) ◽  
pp. 379-386
Author(s):  
Terence McCabe ◽  
M. Alejandra Sorto ◽  
Alexander White
Keyword(s):  
High School ◽  
Middle School ◽  
Number Line ◽  
Instructional Tool ◽  
Mathematical Concepts ◽  
Absolute Value ◽  
Algebraic Concepts ◽  
Numerical Operations

The number line is a powerful instructional tool for teaching the meaning of many mathematical concepts taught in middle school, including numerical operations. The number line can also be used as a tool for thinking about algebraic concepts taught in high school, such as an abstract or algebraic understanding of distance, absolute value, and inequalities.

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