Nondecimal Slide Rules- and Their Use in Modular Arithmetic

1971 ◽  
Vol 64 (5) ◽  
pp. 467-472
Author(s):  
Katye Oliver Sowell ◽  
Jon Phillip Mcguffey
Keyword(s):  
The Other ◽  
Modular Arithmetic ◽  
Number Lines ◽  
Addition And Subtraction

Addition and subtraction are quickly done by means of two number lines placed one above the other.

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

The Relative Effectiveness of Two Different Instructional Sequences Designed to Teach the Addition and Subtraction Algorithms

1973 ◽  
Vol 4 (4) ◽  
pp. 251-262
Author(s):  
Clyde A. Wiles ◽  
Thomas A. Romberg ◽  
James M. Moser
Keyword(s):  
Relative Effectiveness ◽  
The Other ◽  
Second Grade ◽  
Whole Numbers ◽  
Instructional Activities ◽  
Instructional Sequences ◽  
Addition And Subtraction

The purpose of this study was to compare the relative effectiveness of two instructional sequences designed to teach the addition and subtraction algorithms for two-digit whole numbers. One of these sequences is the traditional sequence of addition followed by subtraction. The other sequence is an integrated p resentation of the two tasks. Each sequence was embodied in a set of instructional activities that were used with a randomly selected group of second-grade children.

Quick Reads: Another Good Idea: Integers Made Easy: Just Walk It Off

2007 ◽  
Vol 13 (2) ◽  
pp. 118-121
Author(s):  
Julie Nurnberger-Haag
Keyword(s):  
Number Line ◽  
Similar Process ◽  
Learning Modalities ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Brain Based Learning

Walk It Off is a multisensory method that I developed to teach students how to multiply and divide as well as add and subtract integers. In my experience, this method makes these processes much more effective, efficient, and entertaining than other approaches. Students have the opportunity to use the Process Standards while exploring a topic that is often taught strictly as algorithms without understanding. In addition to having visual, oral, and aural characteristics, Walk It Off is kinesthetic, because students literally walk off problems on number lines. The multiple learning modalities that this method uses are compatible with brain-based learning. Students become actively involved in doing calculations as they physically act out problems using the underlying concepts of integers. Although many books and lessons already use number lines to demonstrate addition and subtraction in various ways, the Walk It Off method makes it possible to use a number line for multiplication and division of integers as well. Using integers becomes easy, because students learn only two slightly different processes for the two basic groups of operations: one process for addition and subtraction and a similar process for multiplication and division.

Integer Target: Using a Game to Model Integer Addition and Subtraction

2007 ◽  
Vol 12 (7) ◽  
pp. 388-392
Author(s):  
Jerry Burkhart
Keyword(s):  
Small Groups ◽  
Number Line ◽  
Target Number ◽  
Number Lines ◽  
Addition And Subtraction

Imagine a classroom where students are gathered in small groups, working with number lines and cards marked with integers. The students have chosen a “target number” on the number line and are deep in discussion, trying to find ways to make the sum of the integers on their cards match this number. There is a deck from which they draw, discard, or exchange cards. They also give, take, or trade cards with one another.

scholarly journals IX.—On the Establishment of the Elementary Principles of Quaternions on an Analytical Basis

1874 ◽  
Vol 27 (2) ◽  
pp. 175-202
Author(s):  
Gustav Plarr
Keyword(s):  
The Other ◽  
Analytical Basis ◽  
Polynomial Expression ◽  
Addition And Subtraction

The extension which is required to be given to the meaning of algebraic addition and subtraction, for the purpose of representing a vector by a polynomial expression (by the algebraic sum, namely, of components differing in direction from one another), renders it necessary to investigate into the question of what the geometrical signification of the result of the other elementary operations of algebra will become when these operations are performed on those polynomial expressions?

Logarithms for ten-year-olds

1968 ◽  
Vol 15 (3) ◽  
pp. 273-275
Author(s):  
Emma C. Carroll
Keyword(s):  
Elementary School ◽  
Fifth Graders ◽  
History Of Mathematics ◽  
The Other ◽  
Geometric Progression ◽  
Real Place ◽  
Moving Points ◽  
History Of ◽  
Addition And Subtraction

Great inventions from the history of mathematics are finding a real place in mathematics for the elementary school. One such idea—Napier's conception of logarithms as a comparison between two moving points, one generating an arithmetical and the other a geometric progression—developed into a challenging activity for my fourth- and fifth-graders. When they witnessed the simplicity and beauty of reducing difficult multiplication and division into easy addition and subtraction through a simple “log” table, eager experimenters took over, tried the “logs,” checked results with the more cumbersome multiplication and division, and raced home with “log” table copies to share the magic with parents.

Piaget's Concept of Number Development: Its Relevance to Mathematics Learning

1981 ◽  
Vol 12 (3) ◽  
pp. 179-196
Author(s):  
Gisèle Lemoyne ◽  
Mireille Favreau
Keyword(s):  
Information Processing ◽  
Mathematics Learning ◽  
The Other ◽  
External Memory ◽  
Natural Numbers ◽  
Processing Methods ◽  
Addition And Subtraction ◽  
End Of Grade ◽  
Operational Group ◽  
Number Development

By the end of Grade 1, many children cannot solve problems such as addition and subtraction with a term missing. In order to explain these failures, the children's information-processing methods were analyzed. Children who had successfully completed Grade 1 (admitted into Grade 2) were separated into preoperational and operational groups. The main strategies of operational children were based on knowledge of addition and subtraction tables and of the properties of the sequence of natural numbers. Half the preoperational children used similar strategies, whereas the other children could not devise effective ones. An analysis of the strategies showed that operational children, who were at Stage 3 in logic tests, constructed numerical strategies, thus displaying an excellent comprehension of the ordinal and cardinal character of numbers, the additive composition of numbers, and the reversibility of operations. The numerical strategies devised by almost half the preoperational children also indicated this degree of comprehension. Last, in their use of some numerical strategies, the preoperational children resorted to external memory more frequently than did the operational group.

Stromatoporoids from the Famennian (Devonian) Wabamun Formation, Normandville oilfield, north–central Alberta, Canada

1988 ◽  
Vol 62 (03) ◽  
pp. 411-419 ◽  
Author(s):  
Colin W. Stearn
Keyword(s):  
Patch Reef ◽  
Abundant Species ◽  
The Other ◽  
North Central ◽  
Biotic Crisis

Stromatoporoids are the principal framebuilding organisms in the patch reef that is part of the reservoir of the Normandville field. The reef is 10 m thick and 1.5 km2in area and demonstrates that stromatoporoids retained their ability to build reefal edifices into Famennian time despite the biotic crisis at the close of Frasnian time. The fauna is dominated by labechiids but includes three non-labechiid species. The most abundant species isStylostroma sinense(Dong) butLabechia palliseriStearn is also common. Both these species are highly variable and are described in terms of multiple phases that occur in a single skeleton. The other species described areClathrostromacf.C. jukkenseYavorsky,Gerronostromasp. (a columnar species), andStromatoporasp. The fauna belongs in Famennian/Strunian assemblage 2 as defined by Stearn et al. (1988).

D. The Line Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 207-244
Author(s):  
R. P. Kraft
Keyword(s):  
Variable Stars ◽  
The Other ◽  
Line Spectrum ◽  
Afternoon Session ◽  
Empirical Information ◽  
Pulsating Variable Stars ◽  
Almost Continuous ◽  
Informal Approach

(Ed. note:Encouraged by the success of the more informal approach in Christy's presentation, we tried an even more extreme experiment in this session, I-D. In essence, Kraft held the floor continuously all morning, and for the hour and a half afternoon session, serving as a combined Summary-Introductory speaker and a marathon-moderator of a running discussion on the line spectrum of cepheids. There was almost continuous interruption of his presentation; and most points raised from the floor were followed through in detail, no matter how digressive to the main presentation. This approach turned out to be much too extreme. It is wearing on the speaker, and the other members of the symposium feel more like an audience and less like participants in a dissective discussion. Because Kraft presented a compendious collection of empirical information, and, based on it, an exceedingly novel series of suggestions on the cepheid problem, these defects were probably aggravated by the first and alleviated by the second. I am much indebted to Kraft for working with me on a preliminary editing, to try to delete the side-excursions and to retain coherence about the main points. As usual, however, all responsibility for defects in final editing is wholly my own.)

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

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