Primary Arithmetic Research Articles

On C. S. Peirce´s primary arithmetic

his paper presents the initial studies on Peirce´s Primary Arithmetic, a set of manuscripts, never published by the author, written at the end of the XIX century. The originals – organized and published by Carolyn Eisele in 1976 – was translated to Portuguese and some initial studies are being developed focusing on the possibility that some features of Peirce´s Philosophy could be pragmatically – but implicitly – present in such manuscripts. Our partial conclusions, now, show that Peirce´s life circumstances, more than his Philosophy, characterize the texts under examination. Keywords: Charles S. Peirce; Primary Arithmetic; Mathematics Education; History; Philosophy; Peirce´s Mathematical Writings.

Research on Primary Arithmetic Fact Mastery for Elementary School Children Education in China: a Computerized Programming Model of Problem Building

Young children often show uneven patterns of competencies in mathematics and some of them cannot even master basic arithmetic facts. This study concerns the primary arithmetic fact mastery for elementary school children education in China by developing an auto problem building model. To do this, a well-defined programming algorithm was first proposed to construct three-term arithmetic operation facts including addition, subtraction, multiplication and division, followed by construction of four-term hybrid combinations. The proposed algorithm was then implemented accordingly by Excel VBA to get a computerized system, which supports randomized operands, one-click building and customized settings. The results show that this model can be applied to the parents or experimenters to give their children routine education in a variety of exercise situations, which helps the school children become more expert at solving arithmetic calculations and perform better on standardized achievement tests.

Memórias de uma Escola Isolada Rural: estudo de um Livro de Visitas (1928-1948)

O artigo estuda o Livro de Visitas da antiga Escola Mista da Fazenda Ponte Alta/Bela Vista, vinculada ao Grupo Escolar da cidade de Bariri (SP). A partir dos registros de vinte anos de atividades (1928-1948), são consideradas as exigências dos inspetores de ensino e os modos como essas exigências eram (ou não) encaminhadas pelas professoras e pela comunidade campesina, com o que se esboça um cenário sócio-histórico sobre o ensino de primeiras letras na zona rural do interior paulista. Disso resulta a percepção de que o discurso que defendia a igualdade de oportunidades para as populações urbanas e rurais negligenciava, via de regra, a necessidade de promover a igualdade de condições para que a comunidade rural pudesse experienciar as oportunidades que lhes eram prometidas.

Discovering boundary algebra: A simple notation for Boolean algebra and the truth functors

Boundary algebra ( BA ) consists of Spencer Brown's [ Laws of Form , 1969 (Allen & Unwin, London)] primary arithmetic ( PA ) and primary algebra ( pa ), restated here in a more convenient notation. The PA consists of an ordered set B ={( ), “ =(( ))} of primitive values cum atomic formulae, formulae generated recursively by enclosure between '(' and ')' and juxtaposition, logical equivalence denoted by '=', and the axioms ( )( )=( )= “ ( )=( “ )=( ) “ , (( ))= “ = “ “ . Inserting variables with domain B into a PA formula yields a pa formula. The pa is a d B ,(·)·, B ¢ algebra of type d 2,0,0 ¢ , whose [ pa , calculus of truth values (CTV), dual CTV, Boolean] intended interpretations are: [( ), T , F ,1], [ “ , F , T ,0], [ ab , a b , a # b , a ? b ], [ ( a ),¬ a , ¬ a , a ' ], and [( a ) b , a M b ,¬( b M a ), a h b ]. The pa is thus a bracket-free notation for the Boolean algebra 2 and CTV, embodying the expressive adequacy of { / # ,¬} and { M ,¬/ F } . ( a ) a =( v ) a =( v ) and abc = bca form a basis. The pa simplifies duality, normal forms, natural deduction, Quine's truth value analysis and the decision procedure for monadic predicates. Syntactically, BA resembles Peirce's [Peirce, C.S. (1993) Collected Papers of Charles Sanders Peirce (Harvard University Press, Cambridge, MA), §§4.372-384] and Byrne's ["Two brief formulations of Boolean algebra", Bulletin of the American Mathematical Society , 52 , 269-272] Boolean notation; semantically, BA resembles Peirce's entitative graphs (Shin [ The Iconic Logic of Peirce's Graphs , 2002 (MIT Press, Cambridge, MA)]) and the system of Anderson and Belnap ["A simple treatment of truth functions", Journal of Symbolic Logic , 24 (1959), 301-302].

Primary Arithmetic: Children Inventing their Own Procedures

In an article that appeared in the Arithmetic Teacher, Madell (1985) described findings from a private school in New York City in which children were not taught any algorithms until the end of the third grade. Without algorithms, the children devised their own ways of solving computation problems. Madell's observation of the children's thinking led him to conclude that “children not only can but should create their own computational algorithms” (p. 20) and that “children can and should do their own thinking” (p. 22). The purpose of the present article is to reiterate Madell's call for reform, with supporting evidence from a public school near Birmingham, Alabama.

A Divided Attention Analysis of the Effects of Methylphenidate on the Arithmetic Performance of Children with Attention‐Deficit Hyperactivity Disorder

Thirteen boys with Attention-Deficit Hyperactivity Disorder (ADHD) completed 80 arithmetic problems presented on a computer screen by typing a two digit answer. On half the trials, a foot press was required to terminate a computer-generated tone presented 2 seconds before, 1 second before, 1 second after, and 2 seconds after arithmetic problem presentation. Compared to placebo, methylphenidate resulted in significantly faster reaction times (RTs) to tone probes and faster answers to arithmetic problems when the two tasks did not overlap in time, but not when simultaneous processing was required when the probe was presented 2 seconds after arithmetic problems. When dual processing taxed cognitive capacity, methylphenidate still improved accuracy on the primary arithmetic task relative to placebo, but at the expense of speed of performance on the secondary RT task. When ADHD children fail to allocate available resources to a primary cognitive task, treatment with methylphenidate may result in reallocation of existing cognitive capacity from a secondary task to the primary task.

Secret number sentence

Here is a game for primary arithmetic, providing stimulating drill on mathematical sentences and on addition, subtraction, multiplication, and division combinations.

A study of pupils' understanding of arithmetic in the primary grades

The Primary Arithmetic Understanding Test was used in this study.1 The test contains 114 multiple-choice items based on 59 arithmetic principles taught in the prima ry grades. The test consists of four parts: (1) number and numeration, (2) addition and subtraction, (3) multiplication and division, and (4) meaning of fractional numbers. The test items were designed so that written computation would not be necessary in selecting an answer. It was judged that without the aid of written computation, the pupil would need to make use of the underlying principle on which each test item was based in order to select a correct answer.

A Burden Turned Into Fun

Two suggestions for a change of pace in primary arithmetic

Book Vignettes

CLEMONS, ELIZABETH, Tide Pools & Beaches.BEISER, GERMAINE, The Story of the Earth's Magnetic Field.JEVONS, F. R., The Biochemical Approach to Life.SCHATZ, ESTHER E., AND WILSBERG, MARY E., Freeing the Learner in Primary Arithmetic.SUCKLING, E. E., The Living Battery.BARANOWSKI, RICHARD M., The Golden Bookshelf of Natural History—Insects.DARNOWSKI, VINCENT S., Computers—Theory and Uses.NSTA CURRICULUM COMMITTEE AND THE CONFERENCE ON SCIENCE CONCEPTS CALLED BY NSTA, Theory into Action…in Science Curriculum Development.RUBLOWSKY, JOHN, Life and Death of the Sun.WEST, JR., KARL H., Supplementary Geometry.DINKINES, FLORA, Elementary Concepts of Modern Mathematics.MOUSER, G. W., AND BROWN, ROBERT E., Techniques for Teaching Conservation Education.

Participation of young children in mathematics

Ever since primary arithmetic abandoned the paper-and-pencil standard, teachers have been concerned with problems of inattention and restless behavior during the mathematics period.

New vistas in primary arithmetic

My checking account is in a state of turmoil at this moment. Obviously, I'm not a mathematician! I would venture, nevertheless, to tell of an experience in teaching a primary grade in which the arithmetic classes sometimes turned into mathematics classes, and mathematics classes into a period of the most exciting discovery for all (including me).

The nongraded primary school and arithmetic

The results of certain traditional practices in the elementary school have been frustration and disappointment. The time-honored practice of classifying pupils as first graders, second graders, third graders, etc. according to their chronological age has created a rigid school organization and an inflexible curriculum supporting tmrealistic standards within which teachers labor diligently but hopelessly.

Adapting the Curriculum in Primary Arithmetic to the Abilities of Children

That the abilities of children vary is a generally accepted fact. It follows then, that children will not all learn the same things at the same rate, neither will the quality of the work done be the same for all of them. In planning the curriculum in any subject, provision should be made not only for differences in the learning rates of children, but also for differences in the standards of achievement expected of them.

Book Review: Primary Arithmetic Pad

Book Review: Primary Arithmetic Pad

Book Review: Lippincott's Practical Primary Arithmetic, First Book and Second Book

Book Review: Lippincott's Practical Primary Arithmetic, First Book and Second Book

Analysis of Colburn's Arithmetics. V

Previous articleNext article FreeAnalysis of Colburn's Arithmetics. VWalter S. MonroeWalter S. Monroe Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 13, Number 6Feb., 1913 Article DOIhttps://doi.org/10.1086/454223 Views: 16Total views on this site Citations: 1Citations are reported from Crossref Journal History This article was published in The Elementary School Teacher (1902-1914), which is continued by The Elementary School Journal (1914-present). PDF download Crossref reports the following articles citing this article:Viktor Freiman, Alexei Volkov In a Search for Innovative Approaches to Teaching Primary Arithmetic: David Eugene Smith (1860–1944) and His Early Works on Mathematics Education, (Jun 2022): 65–89.https://doi.org/10.1007/978-3-030-95235-8_4

Analysis of Colburn's Arithmetics. IV

Previous articleNext article FreeAnalysis of Colburn's Arithmetics. IVWalter S. MonroeWalter S. Monroe Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 13, Number 5Jan., 1913 Article DOIhttps://doi.org/10.1086/454214 Views: 97Total views on this site Citations: 1Citations are reported from Crossref Journal History This article was published in The Elementary School Teacher (1902-1914), which is continued by The Elementary School Journal (1914-present). PDF download Crossref reports the following articles citing this article:Viktor Freiman, Alexei Volkov In a Search for Innovative Approaches to Teaching Primary Arithmetic: David Eugene Smith (1860–1944) and His Early Works on Mathematics Education, (Jun 2022): 65–89.https://doi.org/10.1007/978-3-030-95235-8_4

Book Review: The Teaching of Primary Arithmetic.

Book Review: The Teaching of Primary Arithmetic.

Warren Colburn on the Teaching of Arithmetic Together with an Analysis of His Arithmetic Texts [Continued

Previous articleNext article FreeWarren Colburn on the Teaching of Arithmetic Together with an Analysis of His Arithmetic Texts [Continued]Walter S. Monroe and Warren ColburnWalter S. Monroe Search for more articles by this author and Warren Colburn Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 12, Number 10Jun., 1912 Article DOIhttps://doi.org/10.1086/454166 Views: 134Total views on this site Citations: 4Citations are reported from Crossref Journal History This article was published in The Elementary School Teacher (1902-1914), which is continued by The Elementary School Journal (1914-present). PDF download Crossref reports the following articles citing this article:Viktor Freiman, Alexei Volkov In a Search for Innovative Approaches to Teaching Primary Arithmetic: David Eugene Smith (1860–1944) and His Early Works on Mathematics Education, (Jun 2022): 65–89.https://doi.org/10.1007/978-3-030-95235-8_4Ryan Ziols, Kathryn L. Kirchgasler Health and pathology: a brief history of the biopolitics of US mathematics education, Educational Studies in Mathematics 108, no.1-21-2 (Oct 2021): 123–142.https://doi.org/10.1007/s10649-021-10110-8Margareta Engvall, Joakim Samuelsson, Rickard Östergren THE EFFECT ON STUDENTS’ ARITHMETIC SKILLS OF TEACHING TWO DIFFERENTLY STRUCTURED CALCULATION METHODS, Problems of Education in the 21st Century 78, no.22 (Apr 2020): 167–195.https://doi.org/10.33225/pec/20.78.167Ernest C. Mcdougle A Contribution to the Pedagogy of Arithmetic, The Pedagogical Seminary 21, no.22 (Jun 1914): 161–218.https://doi.org/10.1080/08919402.1914.10532675