Method or justification?

1972 ◽  
Vol 19 (8) ◽  
pp. 617-622
Author(s):  
W. G. Quast
Keyword(s):  
Elementary School ◽  
Whole Numbers ◽  
School Textbook ◽  
Textbook Series

Many of the recent elementary school textbook series and other programs utilize a variety of procedures in presenting the algorithms for work with whole numbers. The purpose of this multiprocedure approach is to seek to develop within the students some degree of understanding of computation rather than to rely on rote, mechanical, step-by-step directions. Unfortunately, the use of a variety of procedures raises some problems with regard to intent and implementation on the part of the teacher. In particular, teachers frequently become confused as to whether or not a given procedure is a method (an algorithm) or a justification for an a lgorithm.

A Comparison of Initially Teaching Division Employing the Distributive and Greenwood Algorithms with the Aid of a Manipulative Material

1973 ◽  
Vol 4 (4) ◽  
pp. 197-204
Author(s):  
Richard O. Kratzer ◽  
Stephen S. Willoughby
Keyword(s):  
Elementary School ◽  
Mental Functions ◽  
Elementary School Mathematics ◽  
Whole Numbers ◽  
Standard Algorithm ◽  
Textbook Series ◽  
Recording Process ◽  
Mathematics Program ◽  
The Common ◽  
Almost All

Division of whole numbers is traditionally accepted as a part of the elementary school mathematics program and is considered to be the most difficult of the four basic operations with whole numbers. The Greenwood algorithm is employed in most contemporary elementary tex tbooks to initially develop the recording process. The common usage of the Greenwood algorithm for division of whole numbers today is largely due to the study by Van Engen and Gibb, General Mental Functions Associated with Division (1956). Later, in almost all textbook series, the standard algorithm is used for the final recording process. Van Engen and Gibb, however, did not recommend converting to the standard algorithm after learning the Greenwood algorithm. This trans ition stage is the source of substantial difficulty for many pupils. lf the standard algorithm is to be the terminal algorithm, then perhaps an approach that initially employs the standard algorithm should be used.

scholarly journals Analysis of The Application of Learning Theory of J.B. Bruner in a Counseling Study Counting Operation to Add Whole Numbers

2021 ◽  
Vol 4 (1) ◽  
pp. 109
Author(s):  
Ejen Jenal Mutaqin ◽  
Neni Nadiroti Muslihah ◽  
Nizar Alam Hamdani ◽  
Sri Dewi Febriani Sasty
Keyword(s):  
Elementary School ◽  
Learning Theory ◽  
First Grade ◽  
Learning Ability ◽  
Learning Theories ◽  
Good Effect ◽  
Whole Numbers ◽  
Qualitative Descriptive ◽  
The Individual ◽  
Learning Concept

<p><em>This study was a qualitative descriptive study design which aims to find out the analysis results of the implementation of Jerome S. Bruner's learning theory in learning concept of addition count operations of whole numbers in the first grade of elementary school. Jerome S. Bruner's learning theory is one of the learning theories that emphasizes the learning process using mental, namely the individual who learns to experience what he is learning for himself, so that the process can be recorded in his mind by his own way. The stages of Bruner's learning theory are: (1) the enactive stage, (2) the iconic stage, and (3) the symbolic stage. Data collection techniques in this study used student worksheets, observation, interviews and documentation. Based on the results of the study, it can be concluded that the process of applying Jerome S. Bruner's learning theory can have a good effect and increase students' understanding and learning ability in learning addition count operations of whole numbers in the first grade of 1 Mekarsari Elementary School.</em></p>

The case for a more universal number-line model of subtraction

1973 ◽  
Vol 20 (1) ◽  
pp. 61-64
Author(s):  
Sister Marijane Werner
Keyword(s):  
Elementary School ◽  
Elementary School Teachers ◽  
Teaching Strategy ◽  
Number Line ◽  
School Teachers ◽  
Guided Discovery ◽  
Elementary School Mathematics ◽  
Whole Numbers ◽  
Single Exception ◽  
Mathematics Program

The use of a number line as a model for the four fundamental operations of mathematics has become a fairly common and effective teaching strategy. The number line has been the means to guided discovery for many pupils in the elementary school mathematics program. However, the model of subtraction of whole numbers on the number line that authors and editors of textbooks for teachers and pupils have commonly used has severe limitations. The single exception to this observation is the thirtieth yearbook of the NCTM, More Topics in Mathematics for Elementary School Teachers (1969), but the approach used there has not caught fire. Perhaps we need to rekindle the fire.

lnstagrams, or instant histograms

1967 ◽  
Vol 14 (3) ◽  
pp. 222-224
Author(s):  
Charlotte Lowrey
Keyword(s):  
Elementary School ◽  
School Teacher ◽  
Elementary School Teacher ◽  
Important Task ◽  
Whole Numbers ◽  
Reasonable Degree ◽  
Computational Skill ◽  
Speed And Accuracy

Even in this age of computers an important task of the elementary school teacher is to teach boys and girls to perform arithmetic computations with a reasonable degree of speed and accuracy. Intelligent development of computational skill implies the use of checking procedures that are fast, readily used, and easily called to mind. For work with whole numbers, checking computations by casting out nines is easy and rapidly done. However, some youngsters refuse to use it voluntarily, possibly because they do not understand the rationale behind the check. They view it as an interesting trick and then forget it.

scholarly journals School textbook as an object of pedagogical research

2021 ◽  
Vol 104 ◽  
pp. 02009
Author(s):  
Yaroslava Kodliuk ◽  
Nadiya Bibik ◽  
Ihor Kodliuk ◽  
Liubov Kodliuk ◽  
Olha Radchenko
Keyword(s):  
Elementary School ◽  
Analysis And Evaluation ◽  
School Textbook ◽  
Teaching Aids ◽  
Methods Of Analysis ◽  
Ex Post ◽  
Ex Post Facto ◽  
Main Components ◽  
Definition Of ◽  
Pedagogical Research

The article deals with investigations of scientists in the field of school textbook theory. The material has been structured taking into account the main components of this field of knowledge: purpose (the dual essence of this type of educational literature has been revealed – it is a carrier of educational content and teaching aids; position of the textbook as a model of integral learning process has been substantiated (systematization, consolidation and control, self-education, integrating, coordinating, developmental-educational), structure (general didactic structure of the school textbook covers the text and non-text components – the apparatus of mastering, illustrative material, orientation apparatus), methods of analysis and evaluation (distinguish traditional and theoretical) – analytical and formalized methods; the structural-functional approach to the textbook analysis has been proved). The peculiarities of textbooks for elementary school have been analyzed: the most complete definition of this phenomenon has been formulated; the leading functions of the textbook addressed to junior students have been defined – informational, developmental, educational, motivational; the features of structural components (taking into account the age of students) have been specified; methods of analysis and evaluation of the textbook have been classified: methods of analysis of the manuscript, methods of evaluation of the textbook itself, diagnostic evaluation ex post facto; a comprehensive approach to the analysis of textbooks for elementary school has been proposed; methods of analysis of certain aspects of the textbook (motivational component, developmental orientation, etc.) have been offered.

scholarly journals MATHEMATICAL CONNECTION ABILITY INSTRUMENT FOR PRIMARY SCHOOL STUDENTS

2021 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Hafiziani Eka Putri ◽  
Cahya Karisma Pertiwi ◽  
Aisyah Herlina Arrum ◽  
Rifa Nurhanifa ◽  
Aan Yuliyanto
Keyword(s):  
Elementary School ◽  
Research And Development ◽  
Primary School ◽  
Elementary School Students ◽  
Primary School Students ◽  
School Students ◽  
Discrimination Power ◽  
Purposive Sampling ◽  
Whole Numbers ◽  
Mathematical Connection

AbstractThis study was motivated by the importance of mathematical connection ability for elementary school students. It was necessary to develop an instrument that suitable the indicators of mathematical connection ability to understand the students' mathematical connection ability. The goal of this research was to develop an appropriate mathematical connection ability instrument for primary school students. This study was applied using Research and Development. The participants were 34 third-grade students at an elementary school in Purwakarta, SDN Nagrikaler, chosen through purposive sampling. The instrument was an essay test consisting of six open questions about whole numbers. The indicators developed in composing questions were related to the mathematical connection ability, namely connections inter topics in mathematics, other subjects, and everyday life. The questions were made beforehand in the expert judgment, then tested to see the validity, reliability, difficulty index, and discrimination power index. The validity test analysis indicated that six items on the instrument were valid, the reliability of the test instruments was very high. Meanwhile, the difficulty level was classified as difficult and moderate, and the discrimination power was also categorized as good and very good criteria. Thus, those six developed questions could be applied to measure mathematical connections in the topic of operations of whole numbers for second-grade elementary school students and were suitable for further research instruments on similar subjects and variables even at different times and places.AbstrakPenelitian ini dilatarbelakangi oleh pentingnya kemampuan koneksi matematis bagi siswa sekolah dasar. Penelitian ini bermaksud mengembangkan instrumen yang sesuai dengan indikator kemampuan koneksi matematis untuk memahami kemampuan koneksi matematis siswa. Penelitian ini bertujuan untuk mengembangkan instrumen kemampuan koneksi matematis yang sesuai untuk siswa sekolah dasar. Penelitian ini menggunakan metode Research and Development. Partisipan adalah 34 siswa kelas III SD di Purwakarta, SDN Nagrikaler, yang dipilih secara purposive sampling. Instrumen yang digunakan adalah tes esai yang terdiri dari enam pertanyaan terbuka tentang bilangan cacah. Indikator yang dikembangkan dalam menyusun soal berkaitan dengan kemampuan koneksi matematis, yaitu koneksi antar topik dalam matematika, mata pelajaran lain, dan kehidupan sehari-hari. Soal-soal tersebut dibuat terlebih dahulu sesuai saran expert, kemudian diuji untuk melihat validitas, reliabilitas, indeks kesukaran, dan indeks daya diskriminasi. Analisis uji validitas menunjukkan bahwa enam item pada instrumen tersebut valid dan reliabilitas instrumen tes sangat tinggi. Sedangkan tingkat kesukaran tergolong sukar dan sedang, dan daya pembedanya juga termasuk kriteria baik dan sangat baik. Dengan demikian, 6 item soal yang dikembangkan tersebut dapat diterapkan sebagai instrumen untuk mengukur koneksi matematis dalam pembelajaran matematika pada topik operasi hitung bilangan cacah terhadap siswa kelas dua SD dan layak digunakan untuk instrumen penelitian selanjutnya pada subjek dan variable sejenis meskipun pada waktu dan tempat berbeda.

Teaching one of the differences between rational numbers and whole numbers

1971 ◽  
Vol 18 (5) ◽  
pp. 317-320
Author(s):  
Robert W. Prielipp
Keyword(s):  
Elementary School ◽  
School Children ◽  
Rational Number ◽  
Elementary School Children ◽  
Rational Numbers ◽  
Whole Numbers

What are some ways in which rational number (fractions) differ from whole numbers? How can we make these differences evident to elementary school children? We begin by looking at two ways in which rational numbers and whole numbers differ, and then we consider in depth a procedure that can be followed to teach one of these differences.

Multiplication is repeated addition

1965 ◽  
Vol 12 (7) ◽  
pp. 550-551
Author(s):  
David Rappaport
Keyword(s):  
Elementary School ◽  
School Mathematics ◽  
Concerted Effort ◽  
Elementary School Mathematics ◽  
Whole Numbers ◽  
Multiplication Of Fractions

In the new elementary school mathematics programs there appears to be a concerted effort to avoid teaching multiplication as repeated addition. This is done for two reasons. First, it is generally believed that multiplication should be considered as an operation that is independent of addition. Second, there is wide pread belief that, although multiplication of whole numbers can be shown as repeated addition, it is not possible to show multiplication of fractions as repeated addition. It is the purpose of this article to show that multiplication of fractions, as well as multiplication of whole numbers, can be taught as repeated addition. Furthermore, it is this writer's belief that the effort to avoid multiplication as addition is psychologicaUy unsound and pedagogically ineffective.

Thou Shalt Not Divide by Zero

1990 ◽  
Vol 37 (7) ◽  
pp. 50-51
Author(s):  
Viji K. Sundar
Keyword(s):  
Elementary School ◽  
School Teacher ◽  
Elementary School Teacher ◽  
Whole Numbers ◽  
Basic Concepts ◽  
Clear Statement

Many textbooks that deal with the basic concepts of division of whole numbers make a very clear statement that “division by zero is not permitted.” Henry (1969) states that “instead of completely avoiding the issue by merely telling the student that he must never ask about 6 ÷ 0, guide him to discover for himself that this operation is without meaning.” I agree. This article includes an approach to help elementary school teacher understand the difficulties involved in division by zero and some teaching suggestions to help teachers guide students as well.

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