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.

Sharing Teaching Ideas: A Squeeze Play on Quadratic Equations

1982 ◽  
Vol 75 (2) ◽  
pp. 132-136
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
Quadratic Equation ◽  
Senior Year ◽  
Quadratic Formula ◽  
Mathematics Courses ◽  
Quadratic Equations ◽  
Teaching Ideas

As a mathematics teacher whose present assignment is to teach science, I was somewhat dismayed when my physics class wa unable to solve a nontrivial quadratic equation. These students are all enrolled in senior-year mathematics and had taken all lower level mathematics courses available in our small Western Kansas high school. They charged this inability to having forgotten the quadratic formula. To the e students the quadratic formula is a magic passkey to solving “unfactorable” quadratic equations. On further di scussion, l discovered that they vaguely remembered having heard of the method of completing the square, but they saw no connection between the quadratic formula and that method of solving a quadratic equation. They could solve simple quadratics by hit-and-miss factoring, but that was their only tool with which to attack this problem.

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.

Another Way to Divide a Line Segment into n Equal Parts

2005 ◽  
Vol 98 (6) ◽  
pp. 428-433
Author(s):  
Nathan Besteman ◽  
John Ferdinands
Keyword(s):  
High School ◽  
New York ◽  
High School Students ◽  
Standard Method ◽  
Mathematics Teacher ◽  
Line Segment ◽  
New York Times ◽  
Popular Media ◽  
School Students ◽  
Wall Street

In summer 1995, two high school students, David Goldenheim and Dan Litchfield, discovered a way to divide a line segment into any number of equal parts. Their method differed from the standard method of Euclid. Together with their teacher Charles Dietrich, they wrote an article on their method, which appeared in the January 1997 issue of the Mathematics Teacher (Litchfield, Goldenheim, and Dietrich 1997). The discovery received considerable publicity in the popular media and was written up in the Wall Street Journal and the New York Times. The authors gave talks at several professional conferences and were invited to meet the secretary of education.

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?”

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.

Percentage of Inadequate Phlebograms and Observer Agreement in Thromboprophylactic Multicenter Trials Using Standardized Methodology and Central Assessment

1996 ◽  
Vol 76 (06) ◽  
pp. 0893-0896 ◽  
Author(s):  
P Kälebo ◽  
S Ekman ◽  
S Lindbratt ◽  
B I Eriksson ◽  
U Pauli ◽  
...  
Keyword(s):  
Standard Method ◽  
Observer Agreement ◽  
Observer Variability ◽  
Intraobserver Agreement ◽  
Multicenter Trials ◽  
Kappa Value

SummaryThis study examines inadequacy rates for phlebography in two multicenter trials for the prevention of post-operative DVT and determines inter- and intra-observer variability in evaluating phlebograms. A total of 991 (I) and 385 (II) patients underwent bilateral phlebography in two studies of thromboprophylaxis. Phlebography was performed using a standard method designed to visualize and assess all deep veins. Each vein was scored as normal, DVT or inadequate by both local and central assessment. The study showed low inadequacy rates for phlebograms of 12.2% (121/991) and 6.5% (25/385). Inter-observer agreement (local vs. central assessment) was moderate in both studies (1:74.8%, Kappa-value 0.41; II: 82.6%, Kappa-value 0.51). Good intraobserver agreement (within the central assessment group) was observed (I: 88.8%, Kappa-value 0.75). This study demonstrates low inadequacy rates for phlebograms using a standardized methodology and superior intra-observer agreement compared to inter-observer agreement and supports the importance of central assessment of phlebograms in thromboprophylactic multicenter trials to reduce observer variability.

A Modified Thromboplastin Screening Test

1961 ◽  
Vol 06 (03) ◽  
pp. 492-497 ◽  
Author(s):  
Janet C. Macpherson ◽  
R. M Hardisty
Keyword(s):  
Standard Method ◽  
Comparative Studies ◽  
Screening Test ◽  
Incubation Mixture ◽  
Surface Contact ◽  
Modified Test ◽  
Effect Of Surface

SummaryA modification of the thromboplastin screening test of Hicks and Pitney is described, in which the effect of surface contact on the test plasma is controlled by the addition of a suspension of kaolin to the incubation mixture before recalcification.Comparative studies show the modified test to give more reproducible results than the standard method.

Beyond the Apnoea–Hypopnoea Index – Prognostic Value of Other Elements of Polysomnography to Describe Sleep-disordered Breathing in Heart Failure

2009 ◽  
Vol 5 (2) ◽  
pp. 53
Author(s):  
Philip B Adamson ◽  
Keyword(s):  
Heart Failure ◽  
Standard Method ◽  
Patient Population ◽  
Prognostic Value ◽  
Sleep Disordered Breathing ◽  
Treatment Success ◽  
Multiple Components ◽  
Severity Of The Disease ◽  
Disordered Breathing

There is increasing appreciation of the prevalence of sleep-disordered breathing (SDP) in heart failure. As we examine this patient population, the difficulties of determining success in the treatment of SDB are becoming evident. The apnoea–hypopnoea index (AHI) is the standard method of measuring both the severity of the disease and treatment success, but in itself is a composite of multiple components. This article examines both current and developing measurements in the treatment of SDB.

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