scholarly journals Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge

PLoS ONE ◽  
2013 ◽  
Vol 8 (1) ◽  
pp. e54651 ◽  
Author(s):  
David C. Geary ◽  
Mary K. Hoard ◽  
Lara Nugent ◽  
Drew H. Bailey
Keyword(s):  
Number System ◽  
School Entry ◽  
System Knowledge ◽  
Entry Number

Early Conceptual Understanding of Cardinality Predicts Superior School-Entry Number-System Knowledge

2017 ◽  
Vol 29 (2) ◽  
pp. 191-205 ◽  
Author(s):  
David C. Geary ◽  
Kristy vanMarle ◽  
Felicia W. Chu ◽  
Jeffrey Rouder ◽  
Mary K. Hoard ◽  
...  
Keyword(s):  
Reading Achievement ◽  
School Readiness ◽  
Conceptual Understanding ◽  
Parental Education ◽  
First Grade ◽  
Number System ◽  
School Entry ◽  
Number Words ◽  
Education Levels ◽  
System Knowledge

We demonstrate a link between preschoolers’ quantitative competencies and their school-entry knowledge of the relations among numbers (number-system knowledge). The quantitative competencies of 141 children (69 boys) were assessed at the beginning of preschool and throughout the next 2 years of preschool, as was their mathematics and reading achievement at the end of kindergarten and their number-system knowledge at the beginning of first grade. A combination of Bayes analyses and standard regressions revealed that the age at which the children had the conceptual insight that number words represent specific quantities (cardinal value) was strongly related to their later number-system knowledge and was more consistently related to broader mathematics than to reading achievement, controlling for intelligence, executive function, and parental education levels. The key implication is that it is not simply knowledge of cardinal value but the age of acquisition of this principle that is central to later mathematical development and school readiness.

scholarly journals Enhancing Number System Knowledge to Promote Number Sense and Adaptive Expertise: A Case Study of a Second-Grade Mathematics Student

2018 ◽  
Vol 15 (3) ◽  
Author(s):  
Cami Player ◽  
Jessica Shumway
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Number Sense ◽  
Number System ◽  
Second Grade ◽  
Adaptive Expertise ◽  
Instructional Treatment ◽  
Mathematics Problems ◽  
System Knowledge

Instruction for developing students’ number sense is a critical area of research in mathematics education due to the role number sense plays in early mathematics learning. Specifically, number system knowledge—systematic relations among numerals and the use of number relations to solve arithmetic problems—has been identified as a key cognitive mechanism in number sense development. Number system knowledge is a component of number sense, and the researchers of this study hypothesize that it plays a critical role in second-grade students’ understanding of relationships among numbers and adaptive expertise with mathematics problems. The purpose of this exploratory case study was to investigate the variations of an eight-year-old student’s number system knowledge learning as she participated in an instructional treatment over nine weeks. The main research question of this study was: In what ways does a student struggling in mathematics develop number system knowledge during a nine-week period in her second-grade classroom as she engages in a number system knowledge instructional treatment? The case in this study was selected based on her low pretest score combined with her desire for making sense of mathematics. The data sources for this study were a number system knowledge assessment and student interviews. The analysis involved a multiple-cycle coding process that resulted in themes of adaptive expertise and the union of procedural and conceptual knowledge in mathematics instruction. The results suggest that this number system knowledge instructional treatment provided this case-study student to develop more pronounced adaptive expertise in solving mathematics problems. An in-depth analysis of how and why one struggling student develops number system knowledge during a nine-week instructional treatment within the context of her mathematics class provides exploratory evidence to help researchers and teachers develop and implement similar practices in elementary mathematics instruction. KEYWORDS: Number Sense; Number System Knowledge; Mathematics Education; Whole Numbers and Operations; Elementary Education; Teaching and Learning; Case Study Research

scholarly journals The Relationship of Reading Abilities With the Underlying Cognitive Skills of Math: A Dimensional Approach

2021 ◽  
Vol 12 ◽  
Author(s):  
Luca Bernabini ◽  
Paola Bonifacci ◽  
Peter F. de Jong
Keyword(s):  
Phonological Awareness ◽  
Cognitive Abilities ◽  
Cognitive Skills ◽  
Number Sense ◽  
Number System ◽  
Dimensional Approach ◽  
Reading And Math ◽  
Relationship Of ◽  
The Relationship ◽  
System Knowledge

Math and reading are related, and math problems are often accompanied by problems in reading. In the present study, we used a dimensional approach and we aimed to assess the relationship of reading and math with the cognitive skills assumed to underlie the development of math. The sample included 97 children from 4th and 5th grades of a primary school. Children were administered measures of reading and math, non-verbal IQ, and various underlying cognitive abilities of math (counting, number sense, and number system knowledge). We also included measures of phonological awareness and working memory (WM). Two approaches were undertaken to elucidate the relations of the cognitive skills with math and reading. In the first approach, we examined the unique contributions of math and reading ability, as well as their interaction, to each cognitive ability. In the second approach, the cognitive abilities were taken to predict math and reading. Results from the first set of analyses showed specific effects of math on number sense and number system knowledge, whereas counting was affected by both math and reading. No math-by-reading interactions were observed. In contrast, for phonological awareness, an interaction of math and reading was found. Lower performing children on both math and reading performed disproportionately lower. Results with respect to the second approach confirmed the specific relation of counting, number sense, and number system knowledge to math and the relation of counting to reading but added that each math-related marker contributed independently to math. Following this approach, no unique effects of phonological awareness on math and reading were found. In all, the results show that math is specifically related to counting, number sense, and number system knowledge. The results also highlight what each approach can contribute to an understanding of the relations of the various cognitive correlates with reading and math.

Visualizing Number: Instruction for Number System Knowledge in Second-Grade Classrooms

2020 ◽  
Vol 12 (2) ◽  
pp. 142-161
Author(s):  
Jessica F. Shumway ◽  
Kaitlin Bundock ◽  
Jessica King ◽  
Monika Burnside ◽  
Heather Gardner ◽  
...  
Keyword(s):  
Number System ◽  
Second Grade ◽  
System Knowledge

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

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