156 SCHOOL SCIENCE AND MATHEMATICS

over Waves." It concerned the various types of telephone service available andthe kind of wave used by each. He demonstrated and explained in a very strikingmanner the ordinary telephone, ship to shore phone, oversea phone, mobile tele-phones and the microwave transmission methods.Mr. Richardson then introduced the officers of the section and heard the report

of the nomination committee. The following officers were nominated and electedfor the coming year:

Chairman�Mrs. Delia Redman, High School, New Haven, Ind.Vice Chairman�Mr. S. Fred Calhoun, High School, Geneseo, 111.Secretary�Mr. Kenneth Vordenberg, Withrow High School, Cincinnati, Ohio

Mr. Glenn H. Updike told of the Physical Science course that had been de-veloped and introduced into the Elkhart Indiana High School. He told of theproblems involved and content of the course.

Mr. Robert Carleton, Esecutive Secretary of the National Science TeachersAssociation, spoke on the place of Physical Science in the High School curriculum.A period of general discussion then followed with many of those present joiningin.

S. FRED CALHOUN, Secretary

THE ELEMENTARY MATHEMATICS SECTION �

The Elementary Mathematics Section met in the Ball Room of the EdgewaterBeach Hotel on November 24th. The meeting was called to order at 2:40 P.M.by Chairman John R. Mayor of the University of Wisconsin. Dr. Mayor intro-duced the Secretary, Ella Marth. Mrs. Lucile Gates, Vice-Chairman, was notable to attend. About fifty member were present.The first speaker was Miss Alice Rose Carr of Ball State Teachers College,

Muncie, Indiana. Miss Carr spoke on the "Development of Concepts ThroughEmphasis on Generalizations in Arithmetic." The speaker emphasized thenecessity of every teacher being aware of the need for and the possibilities ofgeneralizations at all levels. She pointed out that a concept is built up by pre-senting the idea and then reinforcing it and extending it at each successive levelwith appropriate applications. To illustrate, the speaker indicated that in begin-ning number work the idea of adding like quantities is taught. This idea is ex-tended to computation with tens in the next grade. Later the same concept isused in adding fractions and again in computing with decimals. In algebra thepupils learn to manipulate further with like quantities in dealing with equations.

Miss Carr also stated how necessary it is for the teacher to clearly understandthe generalizations. She must have the total picture of the development of arith-metic concepts to achieve the desired continuity. Appropriate procedures arealso needed in this development.The second speaker, Mr. E. H. Hamilton of Iowa State Teachers College,

discussed how "Field Work Modifies Our Program in Arithmetic." Field work,which is done by the regular staff members of the teachers college under statecoordinators, consists of visiting schools, conferring with teachers and super-visors, and serving as resource people for county workshops. The major activityis demonstration teaching.

In his field work the speaker said he found too many instances in which thepupils are subjected to authoritarian teaching; that they are not stimulated toask questions; and that they are unaccustomed to handling materials in classes.Mr. Hamilton indicated that in the children’s minds a "great chasm" exists be-tween the symbol and physical reality which it represents. The reasons suggestedfor this condition are that teachers are teaching as they were taught and areafraid to allow pupils to ask questions. Furthermore teachers are not aware ofthe wide range of individual differences which exist in classes.To improve the teaching of arithmetic Mr. Hamilton made the following rec-

ommendations. The teacher training course should give emphasis on the "how

PROBLEM- DEPARTMENT 157

and why" of arithmetic processes. A collection of teaching aids should be made bystudent teachers for use in classes. The necessity of grouping children according toability and achievement should be clearly demonstrated. Student teachers shouldbe clearly demonstrated. Student teachers should also be made aware of therelation of behavior problems to non-achievement.The third speaker, Miss Mildred B. Cole of Bradwell School, Aurora, Illinois,

gave a discussion and demonstration on the "Use of Paper Folding in the UpperGrades." Miss Cole gave as her source the book, Geometric Exercises in PaperFolding by T. S. Row, published by the Open Court Publishing Company.The speaker provided her audience with squares of colored shelf paper and

gave directions for folding this into squares of various sizes, into triangles, andother plane figures including several other polygons. Miss Cole then demon-strated how various types of Christmas Tree ornaments might be made bysimple folding. The speaker had two very attractive arrangements of varied andinteresting patterns displayed on bulletin boards.Between the second and third talks the Chairman of the Nominating Commit-

tee, Dr. Glen Ayre of Western Illinois State College, presented the followingcandidates for offices for the coming year:

Chairman�Mrs. Lucile B. Gates, Chicago, 111.Vice-Chairman�Dr. Ella Marth, St. Louis, Mo.Secretary�Miss Glenadine Gibb, Cedar Falls, Iowa.

A unanimous ballot was cast for the candidates. The meeting was adjournedat 4:20 P.M.

ELLA MARTH, Secretary

PROBLEM DEPARTMENTCONDUCTED BY G. H. JAMISON

State Teachers College, Kirksville, Mo.

This department aims to provide problems of varying degrees of difficulty whichwill interest anyone engaged in the study of mathematics.

All readers are invited to propose problems and to solve problems here proposed.Drawings to illustrate the problems should be well done in India ink. Problems andsolutions will be credited to their authors. Each solution, or proposed problem, sentto the Editor should have the author’s name introducing the problem or solutionas on the following Rages.The editor of the department desires to serve its readers by making it interesting

and helpful to them. Address suggestions and problems to G. H. Jamison, StateTeachers College, Kirksville, Missouri.

SOLUTIONS AND PROBLEMSNote. Persons sending in solutions and submitting problems for solutions

should observe the following instructions.1. Drawings in India ink should be on a separate page from the solution.2. Give the solution to the problem which you propose if you have one

and also the source and any known references to it.3. In general when several solutions are correct, the ones submitted in

the best form will he used.

Late Solutions

2203. W. W. Funkenbifschj Michigan College of Mining and Tech.