tion and translation; (3) the equation (limited to positive numbers). The work in intuitive geometry offers opportunity for the use of compasses and ruler in simple constructions, drawing to scale, similarity, and field work. The work of the eighth grade.-In the first half there is an extension of the algebra begun in the seventh grade. The work still centers about (1) the formula, its derivation and graphic representation; (2) simultaneous equations, solved graphically and algebraically; (3) the number system extended to include negative numbers; (4) fundamental operations with simple algebraic expressions. The second half takes up the problems in percentage relations, which are widely used in the business world and which seem to be beyond the pupils' experience while in the seventh grade. The usual social-economic13 topics of interest, insurance, taxes, discount, and the like, are used as applications. The spirit of junior high school mathematics.-The spirit of the junior high school work is shown in the constant effort to avoid types of problems that go to make a perfect technique and to replace these by work rich in human interest and opportunity for problem. solving. The entire object of the junior high school course is naturally not to perfect technique but to enable the pupil to read with some degree of intelligence the more or less scientific articles which he is apt to run across in his general reading. Plane geometry in the ninth year. The heart of the course in the ninth year is plane geometry, finally demonstrative in its nature. The transition from intuitive geometry is made most gradual. There is an effort to make a close connection with art, applied science, and algebra. The course in outline is as folows: (1) Introductory work in (a) the history of geometry, (b) observation of some of the uses of geometry, (c) application of the simplest constructions to making designs, pupil experimentation leading to the desire for a proof; (2) algebraic fractions, ratio, and proportion; (3) areas; (4) similarity; (5) trigonometric functions and simple applications; (6) logarithms; (7) locus problems; and (8) the circle (measurement of angles and mensuration of the circle). 13 In the year 1921-1922 this social-economic arithmetic was removed from the eighth grade. It will probably be offered as an elective, parallel with solid geometry and trigonometry in the twelfth year,-surely a significant change. The aim is to make this course truly practical but it explores not only the applications of geometry but also the power and dignity of its logic. The pupil who has taken it knows whether he is fitted and desires to delve more deeply into the realms of demonstrative geometry. The later years. In the tenth and eleventh school years the student may elect a rigorous course in plane geometry. In this course the emphasis is constantly on the technique of thinking employed in plane geometry, as is also the case in the last half of the twelfth school year in which the pupil may elect solid geometry. The need for adequate preparation for plane geometry.From the foregoing it will be seen that the Ethical Culture School has realized the difficulties of a plane geometry course and has set about developing with great care a course that is a gradual transition from the ninth year. Whether the reorganization effected for the seventh and eighth school years which shifts some of the intuitive geometry to these grades, will decrease the amount of intuitive geometry to be taught in the ninth school year, remains to be seen. The important fact is that it is the opinion of the mathematics teachers in the Ethical Culture School that plane geometry is scarcely worth doing unless it is done well, and that it cannot be done even in mediocre fashion by plunging children of the tenth or eleventh school year into it without adequate preparation during the junior high school years. Of those Mathematical library.-The library consists of about 300 volumes of which more than one third are reference books. most helpful to the pupils might 'be mentioned: Cox: Manual of the Slide Rule. Heath's Monographs on Famous Problems. Klein: Famous Problems of Elementary Geometry. White: Scrap Book of Elementary Mathematics. Ball: Mathematical Recreations. Abbott: Flatland. Henrici: Congruent Figures. Clifford: Common Sense of the Exact Sciences. Becker: Geometrisches Zeichnen. Smith: Euclid, his Life and System. Conant: Number Concept. Fine: Number System of Algebra. Manning: Non-Euclidean Geometry. Cavendish Recreations With Magic Squares. Dudeney: Canterbury Puzzles. Hill: Geometry and Faith. Schubert: Mathematical Recreations. Abrens: Mathematische Unterhaltungen und Spiele. Allman: Greek Geometry from Thales to Euclid. Gow: A History of Greek Mathematics. Equipment. The equipment that has meant most to pupils and teachers alike has not been the purchased apparatus so much as that which has been made by the pupils. The home-made list includes quadrants, diagonal scales, pantograph, slide rule, astrolabes, plumb levels, theodolite, proportional dividers, parallel rules, and models for use in solid geometry. The helpful purchased list includes large black globe on pulleys, coördinate boards, pantograph, proportional dividers, transit, sextant, set of mechano, plane table, knitting needles and five wire needles of different lengths for building figures for use in the study of solid geometry, lantern slides, and solid geometry models. Rejected experiments.-For a time the attempt was made to teach some of the eighth grade material through the use of the project method in an extensive study of such matters as the city water supply system. The teachers feel that such projects are artificial in this year and that they begin and end in names and confusion. The department has also discontinued the course in mathematics specially designed to meet the needs of non-mathematical students of fine arts. The facts seem to indicate, that students failing in the exploratory course of the ninth school year could not study fine arts with profit nor could a geometry course be designed for them which they could pursue in a satisfactory manner. The Horace Mann School for Girls, New York City A COURSE FOR GIRLS IN THE ELEVENTH SCHOOL YEAR The Horace Mann School was established in 1897 as a department of Teachers College. For a time this school was used as a practice school for students in education. The chief function of the school now is to serve as a demonstration school for Teachers College. Up to 1914 the school was co-educational in all grades. The growth of the school and of Teachers College made it desirable at that time to transfer the boys of the six upper grades to a new building at Fieldston. In this report, the secondary department which is housed in the Teachers College group of buildings, will be referred to as the Horace Mann School for Girls. The high school is organized in. two sections, grades seven, eight and nine constitute the junior high school, whereas the last three years make up the senior high school. The teachers.-The mathematics of the six high school grades is taught by four teachers. These teachers are well trained, both in mathematics and in education courses., In fact, each teacher has had training somewhat beyond the masters' degree. Their experience ranges from five to twenty years in various secondary schools throughout the country. The department is particularly fortunate in having as advisors Professors David Eugene Smith and Clifford B. Upton, Provost, of Teachers College. The equipment and the library.-The school has still another unique advantage in that it has access to the mathematical equipment of Teachers College, and to many of the valuable books and instruments belonging to Professor Smith. The teachers assert that this mathematical equipment is used by high school pupils for the following purposes: (a) To provide opportunity for the pupils to make generalizations, definitions, and to discover laws for themselves. (Models of geometric solids, metric weights and measures, Fahrenheit and Centigrade thermometers, spiral springs, pulleys, and other appliances illustrative of the law of the lever.) (b) To show how the world has applied the principles of mathematics to solve some of its problems. (The abacus, quadrant, sextant, astrolabe, transit and rod, and slide rule.) (c) To encourage pupils to solve their own problems. (The pantograph, squared black board, yard and meter stick, fifty-foot tape, and large protractor. Other equipment necessary for this purpose the pupils make for themselves, applying the principles they have learned, just as the world has done. As for the library, it is extensive but many books are used only once or twice during a year. A few are in nearly constant use. Chief among the latter are: Number Stories of Long Ago. David Eugene Smith. Ginn & Company. A Brief History of Mathematics. Fink. Translated by Beman and Smith. Open Court Publishing Company. Story of Arithmetic. Susan Connington. Swan, Sonnenschein & Co., London. Easy Mathematics. Sir Oliver Lodge. Macmillan Company. A Source Book of Problems for Geometry. Mabel Sykes. Allyn & Bacon. Famous Geometrical Theorems and Problems. N. C. Rupert. D. C. Heath & Co. For history and biography the encyclopedias are used quite as much as histories or mathematics. Four important problems.-The mathematics teachers are given much freedom in their demonstration work. They not only strive to employ the best practice but venture from time to time to undertake distinct innovations. During the last ten years materials and methods have been created which center around the following four problems. (1) to construct mathematics courses for the junior high school grades; (2) to place a unit of demonstrative geometry in the minimum requirement (the mathematics for citizenship); (3) to improve the results of teaching plane geometry; and (4) to teach a more meaningful course to the girls in the senior high school. Each of these will now be discussed briefly. A junior high school course.-The junior high school curriculum tries not to lose sight of the fact that there are two classes of pupils to be provided for: those who drop out sometime during the junior high school period, and those who continue through to the end. An effort has been made to open the door of mathematics to all in order that they may be able to decide intelligently whether or not to elect further work in this field. In consequence, no year is devoted exclusively to arithmetic or entirely to algebra. The first half year of the 7th grade is devoted to arithmetic,1 the last half year to geometry. In the 8th grade, the work of the first half year is devoted to algebra, and the second half to arithmetic. In the 9th grade the first semester consists of algebra and the second semester of geometry. A special feature of the junior high school course is the intuitive geometry, taught in the last half of the seventh school year. The seventh grade geometry unit aims to familiarize the pupils with the 14 The school follows the work as outlined in Wentworth-Smith-Brown, Junior High School Series, Books I, II and III. |