When Does A Subtraction Algorithm Involve Borrowing?

1982 ◽  
Vol 75 (9) ◽  
pp. 771-775
Author(s):  
John R. Kolb
Keyword(s):  
Mathematics Teacher ◽  
Whole Numbers ◽  
Interesting Article

In the February 1982 issue of The Mathematics Teacher, Irvin Vance wrote an interesting article describing two algorithms for the subtraction of whole numbers. He describes an algorithm presented by Colton (1980) and concludes that it involves borrowing. Vance calls the second algorithm he discusses the residue method, and he claims that it does not involve borrowing. One of Vance's colleagues claims that both algorithms do involve borrowing. Vance ends the article by asking "What do you think—is borrowing involved?”

How to give your class the business (math)

1975 ◽  
Vol 22 (4) ◽  
pp. 313-319
Author(s):  
Joseph B. Shapiro
Keyword(s):  
Mathematics Teacher ◽  
Basic Number ◽  
Whole Numbers ◽  
Good Morning ◽  
Number Facts

Good morning, students. My name is Mr. Shapiro. I will be your mathematics teacher this year. During the course we will review the basic number facts of addition, subtraction, multiplication, and division of whole numbers. Then we will work on fractions, decimals, and percents. We will also try to ….”

Another Look at the Quadratic Formula

1982 ◽  
Vol 75 (2) ◽  
pp. 146-152
Author(s):  
Dean D. Obermeyer
Keyword(s):  
Standard Method ◽  
Mathematics Teacher ◽  
Quadratic Formula ◽  
Interesting Article

In a particularly interesting article from the Mathematics Teacher (May 1975), Larry Hoehn gave an alternate method of deriving the quadratic formula. Hoehn’s step-by-step comparison of the standard method and the alternate method is found in table I.

Teaching concepts incorrectly

1972 ◽  
Vol 19 (2) ◽  
pp. 137-140
Author(s):  
Bill Bompart
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Teacher ◽  
Whole Numbers

A very brief but provocative article by Julia Adkins appeared in the Mathematics Teacher several years ago (1964). It was entitled “Leave the Door Open!” and emphasized the importance of “providing an atmosphere conducive to the development of creativity,” (p. 486) by keeping questions open for later extensions. For instance, to tell students that it is impossible to subtract seven from three is to deny them the opportunity to think beyond the set of whole numbers. It is to be hoped that all mathematics teachers endorse this philosophy and try to “leave the door open” at every opportunity.

Letter to the Editor

1968 ◽  
Vol 61 (7) ◽  
pp. 701-712
Author(s):  
C. F. Hockett ◽  
Vida Augulis
Keyword(s):  
Mathematics Teacher ◽  
Hausdorff Space ◽  
Considerable Importance ◽  
Interesting Article ◽  
Letter To The Editor

In his interesting article in The Mathematics Teacher in the April 1968 issue, pages 304-95, Earl K McGeehee, Jr., fails to mention one nomenclatural point of considerable importance: A Hausdorff space that is also a door space is a house door space.

More about an Old Number Trick

1971 ◽  
Vol 64 (4) ◽  
pp. 348
Author(s):  
Allyn H. Nelson
Keyword(s):  
Mathematics Teacher ◽  
Algebraic Proof ◽  
Interesting Article

There is an interesting article by William F. Berry, entitled “Algebraic Proof of an Old Number Trick,” in the MATHEMATICS TEACHER for February 1966.

Pythagorean Triples from Harmonic Sequences

2001 ◽  
Vol 94 (3) ◽  
pp. 218-222
Author(s):  
Angelo S. DiDomenico ◽  
Randy J. Tanner
Keyword(s):  
Mathematics Teacher ◽  
Fibonacci Numbers ◽  
Whole Numbers ◽  
Multiplication Tables ◽  
Pythagorean Triples ◽  
Mathematical Experience ◽  
Ancient Times

Pythagorean triples have intrigued generations of mathematics explorers, including students, since ancient times. One of their most charming features is their connection with various other areas of mathematics. In the Mathematics Teacher, for example, authors have shown that Pythagorean triples can be generated from the Fibonacci numbers (Bertucci 1991), from geometric sequences (Carbeau 1993), and from both the addition and multiplication tables of whole numbers (DiDomenico 1993, 1995). These findings are indeed fascinating; when shared with students, they spark interest and curiosity and lead to a truly enriching mathematical experience. Students, in fact, independently found that Pythagorean triples could be generated from Fibonacci numbers and geometric sequences. This article reveals another surprising connection that shows how all primitive Pythagorean triples can be generated from harmonic sequences.

Using the research on intergroup conflict in nonhuman animals to help inform patterns of human intergroup conflict

2019 ◽  
Vol 42 ◽  
Author(s):  
Amanda R. Ridley ◽  
Melanie O. Mirville
Keyword(s):  
Large Body ◽  
Nonhuman Animal ◽  
Intergroup Conflict ◽  
Costs And Benefits ◽  
Animal Groups ◽  
Interesting Article ◽  
Nonhuman Animals

Abstract There is a large body of research on conflict in nonhuman animal groups that measures the costs and benefits of intergroup conflict, and we suggest that much of this evidence is missing from De Dreu and Gross's interesting article. It is a shame this work has been missed, because it provides evidence for interesting ideas put forward in the article.

MATHEMATICS TEACHER EDUCATION AND THE FLEXIBLE USE OF TECHNOLOGIES IN DIGITAL AGE

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Hans-Georg Weigand
Keyword(s):  
Teacher Education ◽  
Mathematics Teacher ◽  
Industrial Revolution ◽  
Empirical Studies ◽  
Mathematics Teacher Education ◽  
Digital Technologies ◽  
Digital Age ◽  
Competence Model ◽  
Advantages And Disadvantages ◽  
Concept Representations

Advantages and disadvantages of the use of digital technologies (DT) in mathematics lessons are worldwidedissussed controversially. Many empirical studies show the benefitof the use of DT in classrooms. However, despite of inspiringresults, classroom suggestions, lesson plans and research reports,the use of DT has not succeeded, as many had expected during thelast decades. One reason is or might be that we have not been ableto convince teachers and lecturers at universities of the benefit ofDT in the classrooms in a sufficient way. However, to show thisbenefit has to be a crucial goal in teacher education because it willbe a condition for preparing teachers for industrial revolution 4.0.In the following we suggest a competence model, which classifies– for a special content (like function, equation or derivative) –the relation between levels of understanding (of the concept),representations of DT and different kind of classroom activities.The flesxible use of digital technologies will be seen in relationto this competence model, results of empirical investigations willbe intergrated and examples of the use of technologies in the upcoming digital age will be given.

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