Including Leap Year in the Canonical Birthday Problem

2004 ◽  
Vol 97 (2) ◽  
pp. 87-89
Author(s):  
M. J. Nandor
Keyword(s):  
High School ◽  
A Priori ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
High School Mathematics ◽  
Birthday Problem ◽  
The Subject

The solution to the canonical birthday problem is taught at all levels of high school mathematics from algebra to discrete mathematics. Although many excellent articles and applets have been written on the subject, I am surprised that the a priori assumption that only 365 days are in a year is ubiquitous; leap year is rarely—if ever—included in the calculation. In this article, I show how to include leap years, and I examine some of the consequences of doing so.

Interest of Pupils in High School Mathematics and Factors in Securing It

1927 ◽  
Vol 20 (1) ◽  
pp. 26-38
Author(s):  
Alfred Davis
Keyword(s):  
High School ◽  
Present Status ◽  
School Mathematics ◽  
High School Mathematics ◽  
Single Class ◽  
Class A ◽  
The Subject

A few years ago attention was attracted to the high percentage of failures among pupils taking high school mathematics. Sometimes as many as 50% or even more would fail in a single class. A little consideration would have convinced the teachers that such a situation must soon attract unfavorable criticism, and that this might be expected from those who were not most favorably disposed towards the subject. At a time when every subject was to be tried and judged, not according to its past achievements, nor according to its future possibilities, but according to present status alone, someone was certain to take a one-eyed view of high school mathematics and condemn it as an unsuitable subject to be required of all high school pupils.

Let’s Use Trigonometry

1975 ◽  
Vol 68 (2) ◽  
pp. 157-160
Author(s):  
John J. Rodgers
Keyword(s):  
High School ◽  
Subject Matter ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Order Of Presentation

All too often in the teaching of high school mathematics courses, we overlook the inherent flexibility and interdependence of the subject matter. It is easy to fall into the trap of presenting algebra, trigonometry, geometry, and so on, as separate areas of study. It is because they were taught this way traditionally. With relatively minor changes in the order of presentation, we can demonstrate to the student the vital interconnectiveness of mathematics. For example, many courses in high school geometry include a unit on trigonometry. The student learns three trigonometric ratios, namely, the sine, the cosine, and the tangent. He also learns to use the trigonometric tables to solve for an unknown side of a right triangle. Generally this material comes quite late in the year.

Finding Social Mathematics in School Activities

1936 ◽  
Vol 29 (7) ◽  
pp. 340-345
Author(s):  
Dorothy Noyes
Keyword(s):  
High School ◽  
School Organization ◽  
School Mathematics ◽  
High School Mathematics ◽  
School Activities ◽  
School Subjects ◽  
The Subject

Judging from a number of the recent articles on high school mathematics it would seem that there is much thinking and considerable experimenting being done on the subject of making mathematics more functional. Mathcmatics has its definite place in our school organization outside of the immediate classroom; a place proportionate to that of other school subjects but which perhaps has not been as evident.

Remedial work in High School Mathematics

1930 ◽  
Vol 23 (1) ◽  
pp. 36-51
Author(s):  
L. H. Whitcraft
Keyword(s):  
High School ◽  
Elementary Teachers ◽  
Secondary School ◽  
School Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
Secondary School Curriculum ◽  
The Subject ◽  
Method Of Instruction ◽  
Remedial Work

Teachers of high school mathematics are confronted with the fact that there are more failures in the mathematics of the secondary school than in any other subject in the secondary school curriculum. These failures may be traced to some one of the following factors; (1) the materials of mathematics, consisting of the textbook, practice exercises, and special devices; (2) the teacher's method of instruction and manner of presenting the subject matter to the pupils; or (3) the methods and processes of the pupils themselves. Now that the teachers of mathematics realize that there is a great amount of criticism due the department of mathematics what are they going to do about it? The answer should be the same as the elementary teachers have given to the criticisms which have come to them-give remedial work.

The Big Loser

1999 ◽  
Vol 92 (3) ◽  
pp. 208-213
Author(s):  
Daniel Marks
Keyword(s):  
High School ◽  
School Mathematics ◽  
High School Mathematics ◽  
Short And Long Term ◽  
The Subject ◽  
Mathematics Class

The identity of the team in greatest jeopardy of becoming the big loser is the subject of this article. This article explores several facts about the big loser, offering them in a hierarchy that may be appropriate for creating various short– and long–term projects for a high school mathematics class.

Comparison of Attitudes and Achievement Among Junior High School Mathematics Classes

1960 ◽  
Vol 7 (7) ◽  
pp. 351-356
Author(s):  
Lois Stephens
Keyword(s):  
High School ◽  
Junior High School ◽  
Junior High ◽  
School Mathematics ◽  
High School Mathematics ◽  
Know How ◽  
The Subject

ATTITUDES TOWARD ARITHMETIC have long been considered to be of great importance to the educator. It has been generally assumed that those students whose attitudes were more favorable toward the subject achieve at a higher level. It was found in a study of attitudes of junior high school students1 that most pupils (87%) enjoy problems when they know how to work them well.

Sound Off!: Beyond Topics: Benchmarks for Judging a High School Curriculum

2011 ◽  
Vol 104 (7) ◽  
pp. 486-488
Author(s):  
Al Cuoco ◽  
E. Paul Goldenberg
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Curriculum ◽  
The Subject

In a recent “Sound Off” in Mathematics Teacher, Robert Reys and Rustin Reys (2009) contrasted two curricular approaches, what they called “subjectbased” and “integrated.” They came down heavily in favor of the latter, arguing that many of the difficulties that students have with high school mathematics are consequences of the subject–based organization.

Mechanics

1923 ◽  
Vol 16 (2) ◽  
pp. 87-93
Author(s):  
Gordon R. Mirick
Keyword(s):  
High School ◽  
Angular Motion ◽  
School Mathematics ◽  
Engineering Science ◽  
High School Mathematics ◽  
Simple Machines ◽  
The Subject ◽  
Problem Material

The subject of mechanics and its application to engineering science opens up a possible source of problem material for high school mathematics. Such ideas as velocity, acceleration, angular motion, momentum, force and energy give rise to some problems that can be used in place of some that are already in our textbooks. A great many problems can be gotten together on statics and simple machines that are very elementary and worth while.

Using Special Interests to Stimulate the Study of Mathematics

1948 ◽  
Vol 41 (7) ◽  
pp. 309-310
Author(s):  
Ida Mae Heard
Keyword(s):  
High School ◽  
School Mathematics ◽  
College Preparatory ◽  
High School Mathematics ◽  
Special Interests ◽  
Traditional Course ◽  
The Subject ◽  
Course Of Study

The original traditional course in high school mathematics was college preparatory in nature. The teacher's time was largely spent in trying to pour facts into the youngsters rather than in drawing the youngsters out or in leading them toward the subject. If a student failed to pass the work, his failure was said to be caused by any of the following: a lack of application, stubborness, or laziness. This course of study made little provision for different interests, different abilities, or different needs.

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