## David Eugene Smith's Teaching Texts

David Eugene Smith wrote a large number of texts for pupils and for their teachers, some of which are major publications, while others are more minor works of 30 to 50 pages. Despite giving information on 37 of his books, there is no attempt to make the following list complete. We have omitted a large number of Smith's teaching books for we are only attempting to gain an idea of his remarkable publication record. Some of his books aimed at teaching school pupils about the history of mathematics are considered on another page.

- (with Wooster Woodrull Beman)
**New plane and solid geometry**(2nd edition) (1889).

1.1.**Review by: T J McC.**

*The Monist***10**(3) (1900), 473-474.

We are pleased to see this second, revised edition of Beman & Smith's 'Geometry'. It is an evidence that the efforts of our most advanced and enlightened educators are receiving their adequate appreciation at the hands of the pedagogic public. The best theoretical endeavours of Germany, France, England, and Italy are here combined with characteristically practical American points of view which lead us to believe that in matters of education we have in the last decade or two been doing work which in the end shall leave us in actual cultural results behind no other nation. ... The present work is a compromise between the traditional treatment of Euclid and Legendre, and the more natural and heuristic methods of the modern geometers. In the text, the authors have adhered to the ancient, the formal, and the logical method of exposition; in the definitions and the discussions they have made use of the more appropriate and the more realistic machinery of modern research; while in the exercises and examples they have supplemented in so practical a manner the matter of their text as to leave little to be desired from the point of view of a sound evolutionary instruction.

- (with Wooster Woodruff Beman)
**Academic algebra**(1902).

2.1.**From the preface.**

This work is intended to cover the subject of elementary algebra with sufficient thoroughness to prepare the student for college. It presupposes no knowledge of the subject, and it leaves for subsequent study many of the topics presented in the authors' "Elements of Algebra." At the same time it follows the latter work in the endeavour to modernise the subject and to pay relatively little attention to those portions which hold their place merely because of tradition. It is believed that teachers will welcome the logical, and at the same time simple, presentation of subjects like evolution, factoring, the theory of indices, and the treatment of the quadratic as set forth in this work. It is also felt that the time has arrived for the modern presentation of the imaginary as here given.

**The teaching of arithmetic**(1909).

3.1.**Review by: Anon.**

*The Journal of Education***78**(7) (1943) (1913), 189.

Dr David Eugene Smith has come to hold a rank in the mathematical textbook world such as a few men held in other generations, and he has come to this prominence because of a combination of talent and achievement rare even with the American masters. He knows the history and bibliography of mathematical teaching as none of the great textbook makers of other days knew them. He is also a great teacher of teachers of mathematics in a way that they were not. He is therefore great in theory and great in practice. This work considers the origin of arithmetic, the reasons for teaching the subject, the various noteworthy methods that have been suggested, and the work of the various school years.

- (with George Wentworth)
**Oral arithmetic**(1910).

4.1.**From the preface.**

The chief principles that have guided the selection and arrangement of material have been as follows: The oral arithmetic needed for practical life relates mainly to the fundamental operations. These operations should, therefore, be reviewed in each school year, the degree of difficulty increasing slightly as the pupils proceeds, but never becoming greater than that encountered in daily business life.

4.2.**Review by: Anon.**

*The Journal of Education***72**(3) (1789) (1910), 78.

This is a mental arithmetic with a new name. It has all the best of the old-time mental arithmetics with a complete modern spirit and setting. The great reforms are in the omission of large numbers, of complex and intricate conditions and tricky conundrums, and in setting all examples and problems in present-day conditions. For the first time, so far as we have observed, this is the first time that the school and every feature thereof is utilised in examples and problems. It also finds abundant and varied material in domestic, civic, social, industrial, agricultural, commercial, and transportation activities. There are nine thousand examples and problems in the book, and every one signifies something specific as to information, process, or power.

**The teaching of geometry**(1911).

5.1.**Review by: Anon.**

*The School Review***20**(1) (1912), 64-65.

The chapters of this volume which deal with the history, development, and methods of teaching geometry are very interesting and of great value to every teacher of the subject. In addition to a chapter giving a brief general history of geometry there are many historical notes upon the important propositions as they stand in the several books which constitute our texts. To call the attention of pupils to these historical facts is to add a human interest to the subject; and it is doubtful if there is any other book in the English language in which these facts are so easily accessible to high-school teachers. The chapter on the conduct of a class in geometry is followed by chapters each dealing with a book of geometry and its propositions. Here many practical applications and many excellent suggestions concerning the best way of introducing theorems are given. In regard to the remainder of the volume, however, it is rather disquieting to learn that the author has discovered a state of warfare which threatens the veritable citadel of geometry.

5.2.**Review by: Anon.**

*The Journal of Education***74**(8) (1843) (1911), 216-217.

Professor Smith is truly in love with his science, and his book cited above is a sort of pleasing summary of the present status of geometry and its probable development in the future. The book makes an excellent appearance, with its careful' cuts and clear print, and Professor Smith's style is excellent. Among the problems that he discusses are: Shall geometry continue to be taught as an application of logic, or shall it be treated solely with reference to its applications? Shall geometry be taught by itself, or shall it be mixed with algebra? Shall a textbook be used in which the basal propositions are proved in full, or shall one be employed in which the pupils are expected to invent the proofs for the basal propositions, as well as for the exercises? What form of terminology shall prevail? And shall geometry be made a strong elective subject to be taken only by those whose minds are capable of serious work?

5.3.**Review by: Anon.**

*The Mathematics Teacher***4**(2) (1911), 79-80.

An interesting book, giving Dr Smith's viewpoint on the methods and subject matter of geometry. The book first discusses the reasons for the study of geometry, and the discussion is sane and liberal. Following this is a brief history of the subject, touching only on points of some importance. The rest of the book is taken up with a discussion of methods, and a rather full discussion of the subject matter, definitions, axioms, and propositions.

- (with George Wentworth)
**Vocational algebra**(1911).

6.1.**Review by: James F Millis.**

*The School Review***20**(8) (1912), 572.

This book, as the title would suggest, is designed to meet the needs of so-called "vocational" classes. The elementary algebra used in the shop or in commercial work is but a small part of that usually taught in the secondary school. The book presents only those essentials of the subject required for preparation for the shop or commerce.

6.2.**Review by: Anon.**

*The Journal of Education***74**(10) (1845) (1911), 272.

It should be an aim of our commercial and vocational courses to send out boys who shall understand the language of their work in the shop or in the office. Among the pioneers in this new field is the "Vocational Algebra," by Wentworth and Smith, both men whose ability as makers of mathematical textbooks is proven. The book at hand is in a way a selection from Book Three of the authors' arithmetics to meet the needs of pupils in industrial and commercial classes.

- (with George Wentworth)
**Work and play with numbers**(1912).

7.1.**From the preface.**

It has been recognised ever since the days of Pestalozzi that children when they first enter school have a taste for number work and also a considerable knowledge of number forms. They use numbers in their game, they talk about them, they like to count, and they enjoy a little work and play with numbers within their mental grasp. On the other hand, children of this age are not ready for such a study of arithmetic as the formal textbook offers.

7.2.**Review by: Anon.**

*The Journal of Education***76**(15) (1900) (1912), 413.

When will wonders cease? "Work and Play With Numbers" is much more play than work. Here is a book that vies with the daintiest illuminated primers, a number book for the first two grades, with exquisite coloured pictures which will captivate a child as much as a costly holiday book, and it is for the school. ... Here is a book that leads the child into the domain of number with the same delight that he enters upon the study of reading, of nature, and of art, and that therefore fills a definite demand in modern education. The book furnishes a pleasing array of motives for work, presents the elementary facts of number in an interesting manner, and systematically arranges the number relations that every child is supposed to know upon leaving grade two.

- (with George Wentworth)
**Academic Algebra**(1913).

8.1.**Review by: Royal Russ Shumway.**

*Amer. Math. Monthly***20**(6) (1913), 193-194.

This book is the second of the Wentworth-Smith series. In it the authors have attempted to provide a high school course which shall cover the topics named in the various curricula suggested by educational associations. The topics considered valuable but not essential are placed in an appendix. More than this, the authors have sought, by means of the practical problems, to give proper preparation to those who are fitting themselves for a trade. The noteworthy features of the book are the early and simple introduction of graphs with a table of squares and cubes at the end of the book to facilitate computation, the large number of oral problems under each topic and the cumulative reviews at the end of the book. There is also a very brief history of Algebra.

8.2.**Review by: Anon.**

*The Mathematics Teacher***5**(4) (1913), 247.

This book is designed to cover all the topics demanded for entrance to college and all the work required for the boy or girl who is preparing directly for any trade or industry. It is in every sense a new work and is constructed on entirely modern lines. It begins in a way to arouse at once the interest of the pupil. It shows how algebra grows out of arithmetic; it makes clear at the outset many of the uses and applications of the subject; it correlates with algebra the arithmetic and mensuration that have already been studied.

- (with George Wentworth)
**School Algebra**(1913).

9.1.**Review by: Royal Russ Shumway.**

*Amer. Math. Monthly***20**(7) (1913), 229.

This is the third of the Wentworth-Smith Series. The authors have prepared a two years course in algebra for high schools, to be issued in two volumes, of which this is the first. The plan of the work is similar to that of their Academic Algebra ...

9.2.**Review by: Anon.**

*The Mathematics Teacher***6**(1) (1913), 52-53.

The "School Algebra," which is a somewhat extended treatment of the material in the author's "Academic Algebra," is admirably adapted for those teachers who prefer a two-book arrangement, and offers ample material for a full two years' course. Book I covers algebra through an elementary treatment of quadratics, and provides a chapter on ratio and proportion that may be taken before geometry is begun. Book II contains a thorough review of Book I, with new and somewhat more difficult problems, gives a more extended treatment of quadratics, and carries the work through progressions, the Binomial Theorem, and complex numbers.

9.3.**Review by: Anon.**

*The Journal of Education***78**(12) (1948) (1913), 330.

Two of the most successful and eminent authors of textbooks in mathematics have made an heroic effort to provide a two-book course in algebra for the first two years in the standardized American high schools, books that shall be scholastically ideal, pedagogically correct, and produce adequate results without undue strain upon teacher or pupil, and they have succeeded. The authors have consulted the courses of study in general use in the leading cities of this country, have considered with care the syllabi and suggested curricula prepared by the various important associations of teachers of mathematics and have studied the papers recently set by the principal examination boards.

**The teaching of arithmetic**(2nd ed) (1913).

10.1.**Review by: Louis C Karpinski.**

*Amer. Math. Monthly***21**(3) (1914), 85-86.

Considerable attention should be paid to the teaching of arithmetic by all of those who have in charge the training of teachers and administrative officers of the public school system. Hence the universities as well as the normal and training schools should provide instruction along these lines. Both of these texts under discussion are well adapted for this purpose and it is to be hoped that they will enjoy wide use. Eleven years ago Professor Smith and Professor McMurry of Teachers College prepared for the Teachers College Record an able article on the teaching of arithmetic. This was well adapted for instruction purposes and was so used until the edition was exhausted. In 1909 Professor Smith prepared for the same journal a new article with the same title and used some of the same material. This was also published in book form by Teachers College. The latter has been somewhat revised and expanded for this work from the press of Ginn & Co.

10.2.**Review by: Anon.**

*The Mathematics Teacher***6**(1) (1913), 52-53.

This work on the teaching of arithmetic has been prepared to meet the needs of reading circles and of teachers in the elementary school. It considers the origin of arithmetic, the reasons for teaching the subject, the various noteworthy methods that have been suggested, and the work of the various school years. There is also a discussion of the subjects to be included, the nature of the problems, the arrangement of material, the place of oral arithmetic, the nature of written arithmetic, the analyses to be expected of children, the modern improvements in the technique of the subject, the question of interest and effort, the proper subjects for experiment, and the game element that plays such an important part in the primary grades.

- (with George Wentworth)
**Plane Trigonometry and Tables**(1914).

11.1.**Review by: Clide Firman Craig.**

*Amer. Math. Monthly***22**(4) (1915), 124-125.

This text is a revised version of the old and widely known book of similar content of the "Wentworth series." With a few exceptions it consists of a partial rearrangement of a portion of the material of the older book, and users of the older book will have no difficulty in recognizing the text and many of the problems of the newer book. Besides some new problems, there have been added a few notes of a historical character, a chapter on logarithms and a chapter on graphs.

11.2.**Review by: Anon.**

*The Mathematical Gazette***8**(117) (1915), 93-94.

This work is intended to replace the Wentworth Trigonometry which has been a standard text in America for the last generation. The principal characteristics are that the practical use of every new feature is clearly set forth before the abstract theory is developed, and that the scope is gradually enlarged as the growing ideas of the student develop greater capacity and a natural desire for further progress. By the inclusion of a full set of five-place tables the book is made complete in itself: a shorter set of four-place tables is also given. The whole work is excellent, in matter, style, type, and illustration; while the price is extremely moderate for the size. There is an abundance of problems and other applications, which cannot fail to inspire real interest in the subject, provided the student has sufficient time to do a good proportion of them.

11.3.**Review by: Anon.**

*The Mathematics Teacher***7**(2) (1914), 72.

In preparing this work the authors have carefully considered the demand for thoroughly teachable textbooks in trigonometry. The uses of the subject are clearly set forth in the opening pages, and a large number of practical problems are given as soon as the functions are defined.

11.4.**Review by: Anon.**

*The Mathematics Teacher***8**(3) (1916), 163.

This book differs from its predecessors in the series principally in the order of topics. Application of right triangle methods to problems that involve only small numbers is immediately followed by the introduction of logarithms and by the solution of oblique triangles. Identities, trigonometric equations, graphs, etc., are left until the end of plane trigonometry. ... The lists of problems are excellent and the text seems to be interesting and clear. The tables are unusually readable, as great care has been taken to make the pages less crowded.

- (with George St Lawrence Carson)
**Plane geometry Part I**(1914).

12.1.**Review by: Anon.**

*The Mathematical Gazette***8**(117) (1915), 96-97.

The first 90 pages of this book introduce in a practical manner correct notions of position, shape and size, symmetry, similarity and the forms of plane figures and the simpler solids. Before reading this section of this book, I was thoroughly convinced by my own experience for the last fifteen years that this "playing about with ruler and compass" was sheer waste of time. I still think the same, but am not quite so certain. ... I cannot say that I care for the style in which the proofs are written out, with reasons and explanations interpolated in small italics, as well as side references; but this must not be considered a drawback, since any teacher using the book can insist on his own method of "writing out."

- (with George Wentworth and William S Schlaich)
**Commercial algebra Book I**(1917).

13.1.**Review by: Anon.**

*The Mathematics Teacher***10**(3) (1918), 163-164.

This book in intended for the first course in algebra for commercial high schools. It retains the usual topics only in so far as they have commercial bearing. The authors believe, however, that such a general foundation has been laid that another half year's work will prepare a student for college.

- (with George Wentworth and William S Schlaich)
**Commercial algebra Book II**(1917).

14.1.**Review by: Anon.**

*The Mathematics Teacher***11**(2) (1918), 98.

The first book of this set was reviewed in a former number. The second book, which is intended for advanced classes in commercial high schools, goes much more deeply into the subject. It also derives its problems more largely from actual business experiences. The subject matter includes logarithms and the slide rule, compound interest and its application, equation of payments, life insurance, and several other topics. This should prove a very valuable book for classes studying such topics.

- (with George Wentworth)
**City arithmetics**(1917).

15.1.**Review by: Anon.**

*The Journal of Education***87**(24) (2184) (1918), 668.

There is a spirit of newness in the air and nothing can escape the necessity of doing even the oldest things in the newest ways. Arithmetic makers have been vying with one another as to how to be new without ceasing to be old. There is something heroic in the persistent demand that elementary arithmetic remain very much as it has always been, a great drill subject. Teachers do enjoy the opportunity to know just how well children have mastered a subject. ... The wonder of the series really is the combination of authorship. The basis of the series is the historic Wentworth series, than which no series has had a greater sale in the last quarter of a century. This has been thinned out in spots and thickened in other spots by David Eugene Smith of Teachers College, Columbia University, who is the master genius of theorists and demonstrators in the scholastic use of all in the science and art. of elementary mathematics.

- (with George Albert Wentworth)
**School arithmetics Books I, II and III**(1920).

16.1.**From the preface.**

The safe mean proceeds on the supposition that the pupil should be led to his arithmetic through paths which are interesting; that he should see that he is studying a subject which is usable in school, in his play, in his home, and in all other phrases of his daily life; and that, so far as possible, the applications should be real to the pupil, particularly in those grades in which his tastes are being formed and in which his outlook on life is very limited. It is possible to accomplish all this by arranging the work by arithmetic topics, showing the pupil the reason for studying each topic and the uses to which it can be applied.

16.2.**Review by: Anon.**

*The Journal of Education***94**(4) (2340) (1921), 105.

There is something quite stimulating in seeing a series of arithmetics that is the latest evolution of a series that has been largely in use for many years. It is easy to tie to a book, because it is familiar, and equally easy to welcome a book that is captivating because it is "so different," but neither represents the same educational attitude as the reception given a book because it is the latest and the oldest at the same time.

- (with George Wentworth and Lewis Parker Siceloff)
**Analytic geometry**(1922).

17.1.**Review by: Anon.**

*The Mathematical Gazette***11**(163) (1923), 282.

The book is intended for a year's work at college (presumably this includes schools), for beginners. "It is not so elaborate in its details as to be unfitted for practical classroom use; neither has it been prepared for the purpose of exploiting any special theory of presentation; it aims solely to set forth the leading facts of the subject clearly, succinctly." We agree that this is borne out by the book itself, and with a few slight reservations can heartily recommend it for general use.

- (with George Wentworth and Herbert Druery Harper)
**Fundamentals of practical mathematics**(1922).

18.1.**Review by: Ernest Rudolph Breslich.**

*The School Review***30**(10) (1922), 792.

Teachers engaged in vocational or pre-vocational training will be interested in a book in which it is attempted to present the general basic principles which the pupil must know whatever special vocation he may prepare for. The material is grouped into four divisions: arithmetic, mensurational geometry, trigonometry, and practical applications.

18.2.**Review by: Anon.**

*The Mathematics Teacher***15**(5) (1922), 315.

In reading this book, the reviewer is impressed with (1) the fact that the book teaches. It is more than a collection of practical problems, for it develops those basic principles which the student must know, whatever vocation he is to follow; (2) the thirty-six full page blue prints, which give a sense of reality to the exercise; and (3) its mechanical and literary excellence.

- (with George Wentworth and Herbert Druery Harper)
**Machine shop mathematics**(1922).

19.1.**Review by: Ernest Rudolph Breslich.**

*The School Review***31**(4) (1923), 316-317.

It has been claimed by some educators that pupils preparing for vocations do not have the time to study the mathematics usually offered in high schools and that they do not need the training derived from that study. Furthermore, it has been said that intensive training in mathematics should be left to the particular group which the pupil has entered and that the amount of mathematics taught should be determined by the needs of each vocational group. It is the opinion of the authors of 'Machine Shop Mathematics' ... that they have succeeded in finding a type of work from the study of which "certain classes in high schools will receive greater benefit than from the abstract mathematics commonly offered." 'Machine Shop Mathematics' is prepared to meet the mathematical needs of students who expect to become machinists.

**Essentials of Plane and Solid Geometry**(1923).

20.1.**Review by: H A W.**

*Peabody Journal of Education***1**(5) (1924), 290.

Dr Smith, the author, is well known as a historian of mathematics; hence, his publishers can claim with propriety, no doubt, that from the clay tablets of ancient Babylon, from the papyrus of Egypt, from the palm-leaf books of the Hindus, from Euclid's first drawings, and from all that has followed, the best in method and matter has been selected. Certainly some of the worst in geometry has been eliminated, for the language is informal and the illustrations clear. Many difficulties of the beginner are recognized, and the way smoothed. A good textbook.

20.2.**Review by: Anon.**

*The Mathematics Teacher***16**(7) (1923), 447-448.

There are two types of text books that are particularly difficult to review, - the type that contains little or nothing that might be considered a contribution to the teaching of the subject, and the type about which little, or nothing but commendation can be said. Smith's 'Essentials of Plane Geometry' is an excellent illustration of the second type.

- (with Lewis Parker Siceloff)
**College algebra**(1924).

21.1.**Review by: Herbert W Turnbull.**

*The Mathematical Gazette***12**(173) (1924), 261.

This book is written for first year students at colleges and technical schools in America, and is in many respects parallel with the recent book on Analytical Geometry by the same authors. The book opens with a rapid sketch of elementary algebra. The later chapters are devoted to "College Algebra" - e.g. mathematical induction, permutations, probability, determinants, theory of equations - followed by "Optional Special Topics" - partial fractions, interest and annuities, infinite series, and so on. Considering the elementary nature of the work this variety of material is good. As may be expected, the treatment by these authors is lucid and, with one exception, satisfactory. ... The exception is the treatment of infinite series.

- (with William David Reeve)
**Essentials of algebra Book I**(1924).

22.1.**Review by: Anon.**

*The Mathematics Teacher***17**(5) (1924), 317.

Most authors of recent texts in algebra have shown a decided tendency to reduce very markedly the emphasis that has been given to special products, factoring, fractions and operations with long polynomials. The formula and the graph, along with the notion of dependence, have been more fully treated. Numerical trigonometry has been given a place in first-year texts. Timed practice tests (with definite norms) have replaced the in discriminate and unmotivated practice of the older books. The value of the subject is made more apparent to the pupil. In each of these respects, 'Essentials of Algebra' is conspicuously modern.

22.2.**Review by: Anon.**

*The Journal of Education***100**(16) (2502) (1924), 443.

The finding of David Eugene Smith and holding the scholastic and educational prestige of Professor Wentworth's mathematical texts by putting behind them a larger historical background for mathematics while demonstrating the most successful adventuresome vision in modern methods was an achievement like that of making horseless carriages into Pierce-Arrows. To have seen such transformation is one of the joys of having seen the great past transfigured into the greater present.

- (with William David Reeve)
**Essentials of algebra Book II**(1925).

23.1.**Review by: Sophia R Refior.**

*The Mathematics Teacher***18**(7) (1925), 442-443.

This text is designed for a third semester in algebra in either the tenth or eleventh grade. It embodies the latest developments in education not only in the selection and arrangement of material, but also in its presentation.

- (with William David Reeve)
**Essentials of algebra. Complete course**(1925).

24.1.**Review by: Anon.**

*The Journal of Education***102**(22) (2558) (1925), 602.

Algebra is no longer a mere mathematical science to be studied for disciplinary effect and is no longer taught by boring drill method. It is now a very live subject, is taught in a very live way and has developed very live textbooks as the Smith-Reeve "Complete Algebra" demonstrates. Every fairly well educated person today needs to be familiar with modern algebra, for without it one can not read even daily papers intelligently. Every important magazine such as well informed persons read uses graphs, formulas, and simple equations. Dr David Eugene Smith has had the widest experience in teaching algebra and writing its texts, and he is looking forward, as he has always done. Nothing progressive in mathematics ever catches him unaware, and he has an ideal running mate in William David Reeve.

- (John Albert Farbeg and William David Reeve)
**General High School Mathematics**(1925).

25.1.**Review by: W O H.**

*The High School Journal***8**(8) (1925), 106-107.

The aim of the authors in preparing this volume, as stated in the preface, was "to give a course that shall open the door to mathematics and give the student that appreciation of the meaning of mathematics as a science which is an essential today for every educated man or woman." This aim was supplemented by four fundamentally sound principles as a guide to the authors in selecting the material to go into the book. The first two principles, namely, "... that the work should proceed from the simple to the complex" and that "... the student should proceed gradually from the familiar to the new by means of easy steps which bring out the relation of what he already knows to the new field upon which he is entering," have characterised the first six chapters of the book. While these two principles have been of most use in the preparation of the chapters which serve as a transition from the elementary to the high school mathematics, they have been regarded throughout the preparation of the entire book. The selection and arrangement of the topics in this volume was done on the principle that "a student is more successful if he studies one thing at a time, and for a sufficient length of time to acquire at least some feeling of mastery." The selection of the exercises and problems for the student rests on the principle that "a student has the right to see the genuine practical applications of the work upon which he is engaged, and conversely that he has an equal right not to have thrust upon him a mass of applications which he will realize are merely made up for the occasion in order to lend an appearance of reality to the work."

- (with William David Reeve and Edward Longworth Morss)
**Exercises and Tests in Algebra Through Quadratics**(1926).

26.1.**Review by: Vera Sanford.**

*The Mathematics Teacher***22**(1) (1929), 62-63.

This booklet of 224 sets of exercises provides material which may be used either to develop algebraic technique, or to test the mastery of this technique. It is evident that the purpose of the authors was not to provide drill solely for its own sake, but first to facilitate the acquisition of important skills by the student to the end that he may have more time to devote to other parts of mathematics, and secondly to provide the teacher with carefully graded material that may be used for diagnosis, drill, and testing whether by a class or by individuals and which will be economical of time both in administering and in scoring.

26.2.**Review by: Anon.**

*The Journal of Education***104**(15) (1926), 387.

The Smith-Reeve-Morss mathematical tests fit all modern courses. It would not be easy to get together three men who would mean more in the mathematical world than do these authors of "Exercises and Tests in Algebra," and no one has prepared a more wholesome series of tests or measurements. The plan is wholly new and meets the new conditions.

- (with William David Reeve and John S Foberg)
**General High School Mathematics, Books I and II**(1927).

27.1.**Review by: Anon.**

*The Mathematics Teacher***20**(4) (1927), 239-240.

"Why teach all this factoring and purposeless algebraic manipulation during the first semester when it is so fatal?" Mathematics teachers often ask themselves this question, and should therefore welcome with joy the appearance of a new textbook which has the courage to incorporate a more vital organization of material for the senior high school. General High School Mathematics, Books I and II, are designed for use in the first two years of a four-year high school course. Book one is essentially a vitalized algebra, and book two a vitalized, modernized geometry.

- (with George Walker Mullins)
**Freshman mathematics**(1927).

28.1.**Review by: Martin Noordgaard.**

*The Mathematics Teacher***20**(8) (1927), 473-477.

[The book] is not a unified course in the strict sense of the word ; for the different fields of mathematics, though closely correlated, are in the main treated separately. ... This text is admirably adapted for classes having had only two semesters of algebra. ... Of special merit is the chapter on trigonometry. ... The classification and organization of the material in this book is a work of art. The goal of the authors is so clear, the progress towards it so undeviating, the style of presentation so smooth, that one seems to be reading a poem. One is seized by a strong desire to try out the book before the living forms in a class room.

- (with William David Reeve)
**The teaching of junior high school mathematics**(1927).

29.1.**Review by: Raleigh Schorling.**

*The Journal of Educational Research***18**(1) (1928), 89-90.

The development of the junior high school has been accompanied by a marked reorganization of the mathematics for Grades VII, VIII, and IX, and a consequent improvement of teaching to present changed courses and to meet newly defined objectives. The recent book dealing with this task contains a discussion of these objectives, outlines the content and organization of the courses, and offers guidance in the teaching of the materials. The units advocated may be described as arithmetic, intuitive geometry, algebra, numerical trigonometry, and demonstrative geometry. Several model lessons are given in detail, and treatments of supervision and instruction, tests, homemade instruments, clubs and contests, and recreations are given.

29.2.**Review by: J P Everett.**

*The Mathematics Teacher***21**(1) (1928), 55-56.

This book is to a considerable extent a pioneer in the field of the teaching of junior high school mathematics, but with none of the evidences of dogmatism or untried theory that frequently accompany a new work of this kind. The wide experience of the authors both as teachers and writers is reflected throughout. The trend of the book is distinctly favourable to general mathematics, but not in a manner that is likely to offend more conservative teachers. ... The book is written in a style that is distinctly readable. The topics, in their arrangement and general treatment, are psycho logically sound. Even more commendable is the extent to which the point of view of the classroom teacher is represented. The practical attitude of the text and the ease with which it can be followed are calculated to strongly encourage the reading of the book by teachers already in service, while at the same time such qualities are just what are needed in a work that is to be used in classes studying the profession of teaching in schools of education.

29.3.**Review by: Anon.**

*The Journal of Education***106**(12) (1927), 312.

So far as we know "The Teaching of Junior High School Mathematics" is the first successful venture in "stepping-down" senior high school teaching of nine-ten-eleven-twelve grade high school teaching to seven-eight-nine grade junior high school students. We regard this as one of the notable textbook creations of the times.

- (with William David Reeve and Edward Longworth Morss)
**Exercises and Tests in Plane Geometry**(1928).

30.1.**Review by: Vera Sanford.**

*The Mathematics Teacher***22**(3) (1929), 181.

The booklet is proving exceedingly useful for its introduction to geometry and it effectively solves the question of quiz material for the early part of the work. Furthermore, whether assigned as home work, class work, or examinations, the student is brought to the writing of a formal proof in a way that guards against the forming of bad habits of presentation and that facilitates pendant work. The student is asked to select relevant data, to supply reasons for statements, to determine necessary and sufficient conditions for a proof, and the like.

- (with Eva May Luse and Edward Longworth Morss)
**Walks and talks in Numberland**(1929).

31.1.**Review by: Anon.**

*The Journal of Education***109**(17) (1929), 488.

It is not easy to think of a number book for the second grade that could need three such authors as have combined their talent and experience in the creation of "Walks and Talks in Numberland."' We went with great care over each of the 182 pages and then looked over the first 100 pages again. It is easy to see that "Walks and Talks in Numberland" is a work of art as different from a book evolved by a clever teacher as a portrait is from a snapshot. There is nothing that could have been different without marring the perfection of the arrangement. We came to enjoy it with a professional thrill.

- (with Eva May Luse and Edward Longworth Morss)
**The problem and practice arithmetics**(1929).

32.1.**Review by: Anon.**

*The Journal of Education***111**(16) (1930), 460.

It is a real joy to see how easy it is for makers of arithmetics in other days to create an arithmetic that is fascinatingly enlightening in all the thinking that is required in practice for skill, and may have a real social value. [The] Third Book gives an immense amount of information about the daily life of the family, of the significance of earning money, spending money, using money in earning.

32.2.**Review by: Anon.**

*The Journal of Education***111**(1) (1930), 24.

Apparently there are some people who do not expect eighty-five per cent, of the arithmetic to be eliminated immediately, for here is. one of the most elaborate and most beautiful first arithmetics ever published. It will be impossible for any child to escape the fascination of the illustrations and there is no picture that is not used in some way, to create problems and produce practice opportunities. Every suggestion of pedagogical science is in the background for the teacher, while only an almost infinite variety of attractive devices with the latest facts and phrases, that appeal to children of the second and third grades are utilised.

- (with Aaron Bakst)
**The play of imagination in geometry**(1930).

33.1.**Review by: Samuel Eugene Rasor.**

*Educational Research Bulletin***10**(11) (1931), 308.

This is a teacher's handbook for use with the educational talking picture entitled "The Play of Imagination in Geometry." The book gives the three following aims and purposes of this talking picture: geometry may be taught for general information, for a natural exercise in rigid, logical thinking, and for the pleasure of its acquisition. ... This little pamphlet should be in the hands of teachers of mathematics.

- (with William David Reeve and Edward Longworth Morss)
**Text and Tests in Plane Geometry**(1933).

34.1.**Review by: Vera Sanford.**

*The Mathematics Teacher***26**(2) (1933), 119-121.

This work is so far removed from the usual text book in geometry that it merits a longer description than is offered in the usual book notes, but while the consideration of its features makes one enthusiastic about it, the real "proof of the pudding" will come when it meets the test of class-room use. ... At first sight, the reader suspects that this text is best fitted for the slower pupil, but closer study will convince him that there are many more originals than he at first supposed, and that they are so arranged as to develop power on the part of the more able students.

**The poetry of mathematics and other essays**(1934).

35.1.**Review by: Eric Temple Bell.**

*Amer. Math. Monthly***42**(9, 1) (1935), 558-562.

This compact collection of charming essays by Professor Smith is the first volume of a series announced by 'Scripta Mathematica' "designed to furnish, at a nominal price, material which will interest not only teachers of mathematics but all who recall their contact with the subject in their school or college days." ... the publication of a volume of essays like Professor Smith's acquainting laymen with something of the potential worth of mathematics in any modern civilization is an event of social importance. These essays are at least a step in the right direction, and a long one, but, after all, only a step. However, as it is the first step which counts the most, our successors in America will probably look back on Professor Smith as the pioneers in a vigorous movement to preserve American mathematics in the middle 30's from the savage assaults of a mob of influential haters of mathematics who, although high in our councils of education, have not the remotest conception of what even elementary mathematics accomplishes for a civilised society.

35.2.**Review by: William David Reeve.**

*The Mathematics Teacher***28**(4) (1935), 250-251.

In these days when we hear so much about correlating the work of the various fields, the first article of this little book emphasizes the relation ship between fine arts to mathematics through the vehicle of poetry in a fascinating way. The second article on the Call of Mathematics ought to help many to at least hear the call of mathematics on the lower levels at least. The third article on Religio Mathematica while not intended to develop mathematicians or to clarify religious dogma should lead thoughtful students to some serious thinking along interesting paths. The fourth and fifth articles show the statesman Jefferson as deeply interested in mathematics, and the mathematician Monge as deeply interested in the affairs of state. Teachers and friends of mathematics will find this volume a fine inspiration for developing in youth an abiding love of mathematics.

**Challenging Problems in American Schools of Education**(1935).

36.1.**Review by: Ralph Beatley.**

*Amer. Math. Monthly***43**(10) (1936), 633-635.

In these two lectures, delivered at Teachers College, Columbia, in February 1935 ... Dr Smith arraigns the teachers colleges in no uncertain terms for foisting upon the schools of this country a vast mass of beings labelled "teacher" whose training in pedagogy has been uncoordinated and often ridiculous, whose knowledge of the subjects they expect to teach is quite inadequate, and whose general cultural background is woefully meagre. Dr Smith recalls recent efforts in certain quarters to make the training of educational administrators and of college teachers of education more substantial. He would make at least equal provision for prospective teachers in secondary schools. Though he holds up to ridicule a certain teachers college which offers twenty-two courses in the teaching of mathematics alone, he does not decry all training in Education. Though he praises the scholarly and professional spirit of the Ecole Normale Supérieure at Paris, with its great emphasis on command of subject and its slight attention to Education, he would not have our teachers colleges neglect either subject matter or Education, but emphasise both, offering substantial and dignified instruction in each, and adding a third feature, the broad cultural formation of the prospective teacher.

- (with William David Reeve and Edward Longworth Morss)
**Text and Tests in Elementary Algebra**(1941).

37.1.**Review by: John P Everett.**

*The Mathematics Teacher***34**(8) (1941), 374.

The first thing that an observer may note is the dignified title of the book, "Text and Tests in Elementary Algebra." The straight forward unaffectedness of this designation seems to be symbolic of the manner in which the authors have presented the subject. One finds a good many evidences that the authors have taken into account the contributions which experience has made to the teaching of algebra. The order of topics is designed to give the student acquaintance with, and understanding of, algebraic symbolism well ahead of ex tended operations with algebraic numbers. In this particular especially the book seems to lessen the danger always present of promoting manipulation without comprehension. ... The book reflects very positively the experience and scholar ship of its authors.

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