Number Sense on the Number Line

2017 ◽  
Vol 53 (4) ◽  
pp. 229-236
Author(s):  
Dawn Marie Woods ◽  
Leanne Ketterlin Geller ◽  
Deni Basaraba
Keyword(s):  
Conceptual Understanding ◽  
Number Sense ◽  
Visual Representations ◽  
Number Line ◽  
Systematic Instruction ◽  
Future Success ◽  
Early Number ◽  
Explicit And Systematic Instruction ◽  
Mathematics Research ◽  
Support Students

A strong foundation in early number concepts is critical for students’ future success in mathematics. Research suggests that visual representations, like a number line, support students’ development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction to transition from concrete to visual to abstract representations of mathematics concepts supports students’ conceptual understanding. This column describes and illustrates how teachers can use number lines and features of explicit and systematic instruction to support students’ early development of number sense.

Building the Early Number Sense of Kindergarteners With Autism: A Replication Study

2019 ◽  
Vol 41 (6) ◽  
pp. 378-388 ◽  
Author(s):  
Jenny R. Root ◽  
Bonnie Henning ◽  
Bree Jimenez
Keyword(s):  
Number Sense ◽  
Classroom Teacher ◽  
Functional Relation ◽  
Kindergarten Students ◽  
Future Research ◽  
Early Numeracy ◽  
Systematic Instruction ◽  
Students With Autism ◽  
Early Number ◽  
Teacher's Perception

This study reports findings of a systematic replication and as such sought to evaluate effects of an early numeracy curriculum on early number sense attainment for Kindergarten students with autism. Through daily 15-min story-based math lessons with embedded systematic instruction delivered by their classroom teacher, participants learned to compare sets, identify and work with patterns, and use standard and nonstandard measurement, and calendar skills. Results indicate a functional relation between the intervention and early number sense, and students were able to generalize skills when systematic instruction was faded. Similar results were mirrored by pre–post standardized norm-referenced measures of early mathematics abilities. Implementation of the curriculum had positive results on the teacher’s perception of self-efficacy. The study’s contribution to research, recommendations for practice, and implications for future research are discussed.

Increasing the Number Sense Understanding of Preschool Students With ASD

2021 ◽  
pp. 027112142110061
Author(s):  
Bonnie L. Ingelin ◽  
Seyma Intepe-Tingir ◽  
Nanette C. Hammons
Keyword(s):  
Preschool Children ◽  
Number Sense ◽  
Functional Relation ◽  
Autism Spectrum ◽  
Future Research ◽  
Preschool Students ◽  
Children With Asd ◽  
Early Number ◽  
Mathematical Success ◽  
Number Talks

Teaching children with autism spectrum disorder (ASD) academic skills supports their future opportunities. For example, early number sense skills are predictive of future mathematical success for all children including children with ASD. Yet, research on foundational early childhood mathematics skills of children with ASD is limited. This study used an adapted version of Number Talks to increase the number sense skills of preschool children with ASD. Number Talks is a constructivist approach that was combined with systematic instruction (i.e., system of least prompts and modeling) in this study. A multiple probe across participants design established a functional relation between using an adapted version of Number Talks and the early number sense skills of preschool children with ASD. Findings suggest using an adapted version of Number Talks can increase the early number sense skills of preschool children with ASD. Implications for practice and future research are discussed.

A Proposed Instructional Theory for Integer Addition and Subtraction

2012 ◽  
Vol 43 (4) ◽  
pp. 428-464 ◽  
Author(s):  
Michelle Stephan ◽  
Didem Akyuz
Keyword(s):  
Number Line ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Realistic Mathematics Education ◽  
Instructional Theory ◽  
Education Theory ◽  
Addition And Subtraction ◽  
Support Students ◽  
Grade Classroom ◽  
Viable Model

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional sequence, which was based on a financial context, was designed using the Realistic Mathematics Education theory. Additionally, an empty, vertical number line (VNL) is posited as a potentially viable model to support students' organizing their addition and subtraction strategies. Particular emphasis is placed on the mathematical practices that were established in this setting. These practices indicate that students can successfully draw on their experiences with assets, debts, and net worths to create meaning for integer addition and subtraction.

Exploring teacher learning process in Chinese lesson study: a case of representing fractions on a number line

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xingfeng Huang ◽  
Rongjin Huang ◽  
Mun Yee Lai
Keyword(s):  
Germ Cell ◽  
Conceptual Understanding ◽  
Learning Process ◽  
Lesson Study ◽  
Number Line ◽  
Unique Contribution ◽  
Lesson Design ◽  
Content Type ◽  
Expansive Learning ◽  
Oriented Activity

PurposeThis paper presented the learning process of a group of primary mathematics teachers who participated in two iterations of lesson design, enactment and reflection in a Chinese Lesson Study.Design/methodology/approachAn expansive learning theory was employed to examine the teachers’ learning process in lesson study (LS) on representing fractions on a number line. The evolution of a germ cell was utilized to feature the transformation of the object of activity from abstract to concrete through resolving contradictions among LS members. The videos of lesson planning, research lessons (RLs) and debriefing meetings were collected and analyzed to reveal the expansive learning process.FindingsThe analysis showed that the teachers expanded their learning through transforming the object from diffuse to concrete and expanded through consciously articulating the germ cell. The outcomes of object-oriented activity include improving the enacted lesson which promoted students’ conceptual understanding.Originality/valueThis study made a unique contribution to understanding the learning process of teachers in Chinese LS from the perspective of expansive learning.

The Mental Number Line in Dyscalculia: Impaired Number Sense or Access From Symbolic Numbers?

2016 ◽  
Vol 50 (6) ◽  
pp. 672-683 ◽  
Author(s):  
Anne Lafay ◽  
Marie-Catherine St-Pierre ◽  
Joël Macoir
Keyword(s):  
Number Sense ◽  
Absolute Error ◽  
Number Line ◽  
Mental Number Line ◽  
Mathematics Difficulties ◽  
Quebec French ◽  
French Speaking ◽  
Per Se

Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks ( number-to-position and position-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.

scholarly journals Using Explicit and Systematic Instruction Across Academic Domains

2016 ◽  
Vol 48 (6) ◽  
pp. 273-274
Author(s):  
Jean Louise M. Smith ◽  
Christian T. Doabler ◽  
Edward J. Kame′enui
Keyword(s):  
Systematic Instruction ◽  
Explicit And Systematic Instruction

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).

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