scholarly journals A Field Guide to Whole Number Representations in Children’s Books

2021 ◽  
Vol 9 (4) ◽  
pp. 697-727
Author(s):  
Julie Nurnberger-Haag ◽  
Amy Scheurermann ◽  
Janis S. McTeer
Keyword(s):  
Mathematics Learning ◽  
Trade Books ◽  
Design Studies ◽  
Field Guide ◽  
Mathematical Ideas ◽  
Whole Numbers ◽  
Field Guides ◽  
Number Representations ◽  
Whole Number ◽  
Common Resource

Trade books are a common resource used to teach children mathematical ideas. Yet, detailed analyses of the mathematics content of such books to determine potential impacts on learning are needed. This study investigated how trade books represent whole numbers. A two-pronged approach was used a) one team documented every way 197 books represented numerical ideas and b) another team used standards to identify ideal representations. A third team validated the traits on 67 books. Greater variation than expected was documented (103 traits identified) and organized into a field guide for researchers to consult to design studies about how particular traits influence number learning. Studies could investigate how a particular trait supports learning or experimentally compare a selected combination of the 45 pictorial, 45 written symbol, 10 tactile, 2 kinesthetic, and 1 auditory trait. Implications for practice include recognizing what representations are present or missing from books used in classrooms. The study also serves as an example of how the field of mathematics education would benefit from adopting structures from disciplinary science, such as field guides, to inform how we organize phenomena of mathematics learning. 

Key Mathematical Competencies From Arithmetic to Algebra

2020 ◽  
Author(s):  
Kristie J. Newton ◽  
Christina A. Barbieri ◽  
Julie L. Booth
Keyword(s):  
Mathematics Learning ◽  
Numerical Magnitude ◽  
Major Area ◽  
Equal Sign ◽  
Negative Numbers ◽  
Mathematical Ideas ◽  
Whole Numbers ◽  
Mathematical Competencies ◽  
Number Lines ◽  
Over Time

Mathematics learning encompasses a broad range of processes and skills that change over time. Magnitude and equivalence are two fundamental mathematical ideas that students encounter early and often in their mathematics learning. Numerical magnitude knowledge is knowledge of the relative sizes of numbers, including whole numbers, fractions, and negative numbers, within a given scale. Understanding mathematical equivalence means understanding that two or more specific quantities with the same value can be represented in a variety of ways and remain equal and interchangeable. A major area of research on equivalence is knowledge of the equal sign. Both equal sign knowledge and magnitude knowledge are foundational in that they predict later learning in mathematics, including algebra. Implications for practice include the use of number lines and more variation in the way that arithmetic problems are formatted.

FOSTERING STUDENTS' INTEREST IN MATHEMATICS LEARNING WITH THE UTILIZATION OF ETHNOMATHEMATICS THROUGH MAKKUDENDENG TRADITIONAL GAME

MaPan ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Andi Aras ◽  
Fawziah Zahrawati
Keyword(s):  
Design Research ◽  
Mathematics Learning ◽  
Student Interest ◽  
Research Subjects ◽  
Whole Numbers ◽  
Learning Mathematics ◽  
Grade Ii ◽  
Learning Interest ◽  
Traditional Game ◽  
Is Design

Interest in learning is one important factor that determines student success in learning. Low student interest in learning is associated with their ability to master the concept of summing whole numbers. This study aims to foster students' interest in learning mathematics through makkudendeng traditional game. The research method is design research starting from the preliminary design, design experiment, and retrospective analysis. The research subjects were students in grade II primary school. The results of this study conclude that the makkudendeng traditional game, which is used as a learning resource in learning the addition of whole numbers, has relevance to the indicators of learning interest, which include: pleasure in learning, interest in learning, attention, and involvement in learning. It is because students learn while playing. So, the makkudendeng traditional game can be a solution to foster students' interest in learning mathematics.

VALIDITAS DAN KEPRAKTISAN PANDUAN LAPANGAN “KERAGAMAN BURUNG” DI KAWASAN PANTAI DESA SUNGAI BAKAU

Vidya Karya ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 193
Author(s):  
Maulana Khalid Riefani
Keyword(s):  
Direct Interaction ◽  
Learning Material ◽  
Learning Tools ◽  
Field Guide ◽  
Field Guides ◽  
Local Material ◽  
Vertebrate Zoology ◽  
Media Learning ◽  
Readability Test ◽  
Selection Of

Abstract. The control of the learning material needs to be supported by the availability of learning resources, media, learning tools, and selection of strategy accuracy. Direct interaction in the field can provide real experiences, motivate and enhance students' knowledge. Learning the concept of aves in the Vertebrate Zoology course still contains a small local material of wetland. The aim is to describe the validity of the field guide and activities of students for using the field guide. The field guide was developed based on the results of the study and validated by experts. The level of readability is tested, while practicality is seen from their activity. The validity of the field guide is very valid, while the readability test is very good. Products of field guides have been made interestingly, easily, and be able to be used by students. Keywords: validity, practicality, field guide, bird, vertebrate zoology Abstrak. Penguasaan materi perlu didukung ketersediaan sumber belajar, media, perangkat pembelajaran, dan pemilihan ketepatan strategi. Interaksi langsung di lapangan dapat memberikan pengalaman baru dan nyata, memotivasi dan meningkatkan pengetahuan peserta didik. Pembelajaran konsep aves pada matakuliah Zoologi Vertebrata yang dilakukan selama ini masih sedikit memuat materi lokal berbasis lahan basah. Tujuan penelitian untuk mendeskripsikan validitas panduan lapangan hasil pengembangan dan aktivitas peserta didik dalam menggunakannya. Panduan lapangan dikembangkan berdasarkan hasil penelitian dan divalidasi ahli. Tingkat keterbacaan diuji oleh peserta didik, sedangkan kepraktisan dilihat dari aktivitas dalam penggunaan. Validitas panduan lapangan termasuk sangat valid, sedangkan uji keterbacaan sangat baik. Produk pengembangan telah dibuat menarik, mudah dipahami dan digunakan peserta didik. Kata kunci: validitas, kepraktisan, panduan lapangan, burung, zoologi vertebrata

scholarly journals Discussion on the structure of atomic nuclei

1929 ◽  
Vol 123 (792) ◽  
pp. 373-390 ◽  
Keyword(s):  
Accurate Determination ◽  
Essential Point ◽  
Whole Numbers ◽  
Atomic Nuclei ◽  
Whole Number ◽  
Nuclear Atom ◽  
The Individual ◽  
The Masses ◽  
Made In

Sir Ernest Rutherford: It was on March 19, 1914, that the Royal Society held its last discussion on the constitution of the atom—just fifteen years ago. I had the honour to open the discussion on that occasion, and the other speakers were Mr. Moseley, Profs. Soddy, Nicholson, Hicks, Stanley Allen, S. P. Thomp­son. In my opening remarks I put forward the theory of the nuclear atom and the evidence in support of it, while Mr. Moseley gave an account of his X-ray investigations, which defined the atomic numbers of the elements, and showed how many gaps were present between hydrogen number 1 and uranium number 92. Prof. Soddy drew attention to the existence of isotopes in the radioactive series, and also to a remarkable observation by Sir Joseph Thomson and Dr. Aston, who had obtained two parabolas in the positive ray spectrograph of neon, and he suggested that possibly the ordinary elements might also consist of mixture of isotopes. I think you will find that the remarks and suggestions made in this discussion fifteen years ago have a certain pertinence to-day. In particular Hicks and Stanley Allen drew attention to the importance of taking into account the magnetic fields in the nucleus, although at that time we had very little evidence on that point, and even to-day our information is very scanty. What has been accomplished in the intervening period ? On looking back we see that three new methods of attack on this problem have been developed. The first, and in some respects the most important, has been the proof of the isotopic constitution of the ordinary elements, and the accurate determination of the masses or weights of the individual isotopes, mainly due to the work of Dr. Aston. This has led in a sense to an extension of the original ideas of Moseley. The experiments of the latter fixed the number of possible nuclear charges, while Aston has shown that there are a large number of species of atoms each defined by its nuclear charge, although their masses and their nuclear constitution may be different. The essential point brought out in the earlier work of Dr. Aston was that the masses of the elements are approxi­mately expressed by whole numbers, where oxygen is taken as 16—with the exception of hydrogen itself. But the real interest, as we now see it, is not the whole number rule itself, but rather the departures from it.

New Challenges to the Research Community: Reflections of the Research Advisory Committee

1998 ◽  
Vol 29 (5) ◽  
pp. 499-502
Keyword(s):  
Teaching Practice ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Research Community ◽  
National Council ◽  
Mathematical Ideas ◽  
Education Community ◽  
Research Findings ◽  
New Challenges ◽  
Children’S Thinking

Drawing on several decades of research findings, the National Council of Teachers of Mathematics (NCTM) produced, between 1989 and 1995, three volumes of Standards in which members of the mathematics education community formulated new visions of mathematics learning, teaching, and assessment. These new visions comprise an ambitious agenda for the mathematics classroom—one that includes, but surpasses, mastery of facts and procedures, the mainstay of extant practice—designed to engage students in the exploration of mathematical ideas and their interrelationships. Students would now be invited to articulate their ideas, and teachers to identify and mobilize those elements in children's thinking upon which stronger conceptions can be built. Paralleling this ambitious departure in teaching practice, new means of assessment were proposed to capture progress toward these far-reaching goals.

scholarly journals Students' Mathematical Communication Ability through the Brain-Based Learning Approach using Autograph

2019 ◽  
Vol 4 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Mailis Triana ◽  
Cut Morina Zubainur ◽  
Bahrun Bahrun
Keyword(s):  
Communication Skills ◽  
Mathematics Learning ◽  
Descriptive Analysis ◽  
Learning Approach ◽  
Observation Data ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Communication Ability ◽  
Brain Based Learning ◽  
The Brain

AStudents’ skills in expressing mathematical ideas in various ways have not met the expectation. Teachers need to apply the learning providing students’ opportunities to present their mathematical ideas. Utilizing the Brain-Based Learning (BBL) approach with Autograph can help students develop their mathematical communication skills. The purpose of this study was to analyze the development of students’ mathematical communication skills. Twenty-eight 10th grade students in one of the high schools in Banda Aceh participated in the study. The instruments used were a mathematical communication skills test and the activity observation. Data were analyzed using descriptive analysis. The study showed that mathematics learning applying BBL approach with Autograph contribute to developing students’ mathematical communication skills.

scholarly journals Ethnomathematics Exploration of The Masjid Raya Bandung Ornaments in Transformation Geometry Materials

2021 ◽  
Vol 5 (2) ◽  
pp. 235
Author(s):  
Tia Purniati ◽  
Turmudi Turmudi ◽  
Dadang Juandi ◽  
Didi Suhaedi
Keyword(s):  
Qualitative Research ◽  
Literature Review ◽  
Mathematics Learning ◽  
Research Data ◽  
Geometric Transformation ◽  
Data Display ◽  
Islamic Culture ◽  
Alternative Source ◽  
Mathematical Ideas ◽  
Transformation Geometry

The mosque is the result of acculturation between Islamic culture and local culture. Many mosque ornaments use geometric motifs.  This research is an ethnomathematics study that aims to explore the ethnomathematics aspects of mosque ornament, especially the material of geometric transformation Ethnomathematics research is part of qualitative research, so this research uses qualitative research. The purpose of ethnomathematics research is to study the mathematical ideas contained in a culture, so the method used is ethnographic. The research location is Masjid Raya Bandung which was selected by purposive sampling. The researcher acts as an instrument that collects data through observation, documentation, and literature review. The research data were analyzed through data condensation, data display, and concluding. The results showed that there are ethnomathematics aspects of Masjid Raya Bandung ornaments in the material of transformation geometry, namely translation, reflection, rotation, and dilation. The mosque ornaments can be used as an alternative source of learning in mathematics learning, especially transformation geometry material. Keywords: ethnomathematics, transformation geometry, mosque ornament.

Divisibility and the base-ten numeration system

1964 ◽  
Vol 11 (8) ◽  
pp. 563-568
Author(s):  
George Spooner
Keyword(s):  
The Other ◽  
Numeration System ◽  
Whole Numbers ◽  
Whole Number ◽  
The One

There exists in the arithmetic of whole numbers several tests of divisibility which permit us to determine whether or not a given whole number is divisible by another given whole number without our having to divide the one given number by the other. The purpose of this paper is to examine the mathematical rationale or justification behind some of these tests. In our discussion we shall say that one whole number is divisible by another if and only if the remainder is zero.

By Way of Introduction: Show Me the Mathematics!

2006 ◽  
Vol 13 (1) ◽  
pp. 4-5
Author(s):  
P. Mark Taylor
Keyword(s):  
Professional Development ◽  
Mission Statement ◽  
Mathematics Learning ◽  
Pedagogical Strategies ◽  
Mathematical Ideas ◽  
Link Type

The Editorial Panel of Teaching Children Mathematics (TCM) welcomes you to volume 13! We are committed to the goals and ideals summarized in TCM's mission statement, which can be found at the bottom of the masthead page of each issue. The mission statement embraces the NCTM ideal of more and better mathematics for all students through the exchange of mathematical ideas, activities, and pedagogical strategies and through sharing and interpreting research. In view of NCTM's professional development focus of the year—“Show Me the Mathematics: Learning through Representation” (www.nctm.org/focus/)—we would like to highlight the specific mathematics represented in this volume of Teaching Children Mathematics.

Rapid Communication: Understanding the Real Value of Fractions and Decimals

2011 ◽  
Vol 64 (11) ◽  
pp. 2088-2098 ◽  
Author(s):  
Teresa Iuculano ◽  
Brian Butterworth
Keyword(s):  
Linear Representation ◽  
Number Line ◽  
Target Number ◽  
The Real ◽  
Rapid Communication ◽  
Whole Numbers ◽  
Whole Number ◽  
Adults And Children ◽  
Real Value

Understanding fractions and decimals is difficult because whole numbers are the most frequently and earliest experienced type of number, and learners must avoid conceptualizing fractions and decimals in terms of their whole-number components (the “whole-number bias”). We explored the understanding of fractions, decimals, two-digit integers, and money in adults and 10-year-olds using two number line tasks: marking the line to indicate the target number, and estimating the numerical value of a mark on the line. Results were very similar for decimals, integers, and money in both tasks for both groups, demonstrating that the linear representation previously shown for integers is also evident for decimals already by the age of 10. Fractions seem to be “task dependent” so that when asked to place a fractional value on a line, both adults and children displayed a linear representation, while this pattern did not occur in the reverse task.

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