## Herbert Ellsworth Slaught on Mathematics and Teaching

Herbert Slaught wrote many articles on mathematics and teaching mathematics. Below we list a few of these articles and give brief extracts from them. Mainly we quote the introduction to give an idea of the problem being addressed and sometimes we also quote Slaught's conclusions. We urge the reader to look at the full paper for details of Slaught's arguments. We have listed them in chronological order.

**The interrelation of subjects in elementary mathematics, The Elementary School.**

*Teacher and Course of Study***3**(1) (1902), 30-32.

It is believed that the teaching of arithmetic should have as a rational basis a thorough knowledge of at least the elementary subjects of mathematics with which it is so closely connected. An appreciative familiarity with algebra, geometry, and trigonometry, and desirably the elements of analytic geometry and calculus, not only provides the teacher with a fund of illustrative material for use in the class-room, but also gives the breadth of view, keenness of insight, and clearness of thinking which enable the possessor to formulate and pursue a sound and inspiring method of teaching. This course is designed to set forth the close relationship among these subjects, and to discuss the bearing of this upon the teaching of arithmetic. The work will involve both theory and practice, and each will be considered from the standpoint of the pupil as well as that of the teacher in the upper grades.

**What Should Be Emphasized and What Omitted in the High-School Course in Algebra?**

*The School Review***16**(8) (1908), 503-516.

The wording of the topic implies that something is wrong at present in the high-school course in algebra. This assumption seems to find justification in the large number of papers on this subject which have been read in recent years before conferences and associations, in the reports which various committees have worked out and presented before representative bodies of teachers, and in the perennial agitation over the failure of the schools to make their pupils measure up to the college-entrance requirements. From the standpoint of the college and university the freshman far too frequently proves a disappointment and a sorrow in view of the time and pains which have been given him by the secondary teacher in his mathematical preparation; and from the standpoint of the usefulness and power which his knowledge of algebra should give the boy, whether he goes to college or not, there seems much to be desired. Opportunity to make any use of algebra within his environment is unknown and unlooked for by the pupil, and when, perchance, such an opportunity suddenly appears, say in the class in physics, he is taken completely by surprise and surrenders at once, especially if s and t are the unknowns instead of x and y. ... If, therefore, it is agreed that the highly complicated and abstract mechanical manipulations, as well as the purely theoretical and demonstrational portions, are to be postponed till the later course, then we have at once what may be used as the guiding principle in selecting topics for omission arid emphasis in the first year; namely, "Let the handling of the equation be the central theme and the solution of problems the main business of the course, and around these let the theory and practice of algebra be built."

**The Teaching of Mathematics in the Colleges.**

*Amer. Math. Monthly***16**(11) (1909), 173-177.

The first decade of the twentieth century is witnessing a wide spread wave of interest in the better teaching of secondary mathematics. This interest includes both the subject-matter and the form of presentation and arrangement in the curriculum and also the preparation of teachers for secondary schools. ... With respect to the preparation of teachers of secondary subjects, a great change has also taken place in recent years. Whereas, formerly there was no prevalent demand for college graduates as high school teachers, it is now true that it is very difficult for a teacher without a college degree to secure an appointment in any first-class high school. But further than this, specific training in the principles and practice of education is coming to be demanded. ... It would seem, therefore, with normal schools and certain schools of education devoting themselves to the training of teachers for the elementary schools, and with the colleges and universities awakening to their responsibility for the better preparation of teachers for the secondary schools, that education below the college grade is in a fair way to receive due attention, and with respect to mathematics that it will come in for its share of attention both as to subject-matter and as to the preparation of teachers.

**Incentives to Mathematical Activity.**

*Amer. Math. Monthly***20**(6) (1913), 169-173.

During the past ten years there has been a marked activity among teachers of mathematics in this country, looking toward improvement in methods and the reconsideration of subject matter, especially with reference to selection and emphasis. In this activity we are by no means alone. In fact, there has probably been still greater readjustment on the other side of the water. Doubtless the so-called Perry movement in England may be considered as one of the chief awakening influences underlying our own activity. But Professor Moore's presidential address before the American Mathematical Society in December, 1902, "On the Foundations of Mathematics," may have been the real source of inspiration in this country which led to the special period of activity beginning at about that time. ... While it is true that agitation does not necessarily mean progress, it is also true that there is seldom any progress without agitation. We confidently believe that the unprecedented activity among teachers of mathematics during the past decade has resulted, and will further result, in substantial progress. It should be a keen incentive to every teacher that he or she may have some active part in our nation-wide determination to reconsider the foundations of our teaching and to improve our methods wherever possible; and that in this effort we are allying ourselves with a world-wide movement toward the same end.

**The Teaching of Mathematics.**

*Amer. Math. Monthly***22**(9) (1915), 289-292.

Owing to a wide divergence of opinion among college and university men as to the proper interpretation of the term pedagogy, and especially in view of the varying notions of that term in the minds of mathematicians, it seems desirable to formulate as definitely as possible what is conceived to be the relation of the 'Monthly' to the question of teaching in the field of collegiate mathematics. ... It is abundantly evident to the impartial observer that the teaching of college freshmen and sophomores is not so widely different from the teaching of high school juniors and seniors; and that, on the whole, there is as large a proportion of poor teaching done in the colleges as in the high schools; with the certainty that this proportion will rapidly increase unless remedial measures for the colleges are soon undertaken comparable with those now in operation for the high schools. The logical step forward is a graduate school of education and graduate departments of education which shall give serious and scientific attention to the betterment of college teaching.

**Subsidy Funds for Mathematical Projects.**

*Science, New Series***55**(1415) (1922), 146-148.

Heretofore little attention has been given to the question of subsidy funds for mathematical projects, quite unlike the case with some of the more spectacular sciences. The presumption is prevalent among non-mathematicians that mathematics is an organised and crystallised body of necessary conclusions drawn some decades or centuries ago from certain intuitional concepts of number an form, and that no special provision for equipment or funds is necessary for carrying on mathematical work. On the contrary, it is the purpose of this paper to show that mathematics, as a live and active subject, is in need of funds for its promulgation as much as any other science.

**Romance of Mathematics.**

*The Mathematics Teacher***20**(1927), 303-309.

We note that this article was reprinted in

*The Mathematics Teacher***59**(8) (1966), 744-748.

It may seem unwarranted to speak of romance in connection with a subject commonly supposed to be as dry and prosaic as mathematics. The dictionary de fines a romance as a "fictitious and wonderful tale." The tale which I am about to relate is indeed wonderful but it is not fictitious - it is true and it is the kind of truth that is stranger than fiction. It is the story of the birth and growth of the number concept in the human race - it is the story of the struggle of humanity to learn to count. We speak glibly of "thousands," and "millions," and "billions," but we should not forget that these concepts are the cumulative heritage of many centuries. Even today there are backward tribes in some parts of the world who have no number words beyond "one," "two," or "three" and who designate all larger groups under the single word "many."

**Greetings from Professor Slaught to Louisiana-Mississippi.**

*Mathematics News Letter***3**(3) (1928), 1-2.

I hope that the Council Branch will always hold one session in which the interests of secondary mathematics shall have primary consideration, that the Association Section will do like- wise for collegiate mathematics, and that one joint session will be held where each group may have the opportunity to see the other in action and where each may learn to appreciate fully the problems confronting the other - in general, yes, but in particular in Louisiana and Mississippi. You both have problems all your own as well as those which concern the country as a whole and I am sure you will be inspired by your cooperative activities to do all in your power for the betterment of mathematical teaching and for the promotion of mathematical appreciation in your own communities.

**Mathematics and Sunshine.**

*The Mathematics Teacher***21**(5) (1928), 245-252.

If the average man in the street were asked to name the benefits derived from sunshine, he would probably say "light and warmth" and there he would stop. But, if we analyse the matter a little more deeply, we will soon realize that sunshine is the one great source of all forms of life and activity on this old planet of ours. ... It is the purpose of this paper to support the proposition that mathematics underlies present-day civilization in much the same far-reaching manner as sunshine underlies all forms of life, and that we unconsciously share the benefits conferred by the mathematical achievements of the race just as we unconsciously enjoy the blessings of the sunshine.

**A Bit of Personal Experience.**

*Mathematics News Letter***3**(6) (1929), 8-10.

I have never tried to act as a judge to decide on technical and theoretical grounds which group of the psychologists have the balance of evidence in their favor with respect to the "transfer of training" in the domain of mathematics. We shall probably never see that question finally closed. It very likely may be a question wherein faith intervenes when sight fails, and if so then, like all other matters of faith, it must rest upon individual experience. ... When I was a student in an academy devoted entirely to preparation for college, I met my first mathematical thrill in beginning the study of algebra under a teacher who was not a mere lesson hearer but who put due emphasis upon the reasons for every step in a solution and insisted upon our seeing the logic involved in every process. That was my first introduction to precise thinking and I was deeply impressed with its significance and importance as compared with the flood of loose thinking and random guesses with which one is surrounded in the ordinary associations of every day life. But this thrill from the study of algebra was as nothing compared to that which I was to receive when we began geometry. To set up a hypothesis, and to draw an inescapable conclusion there from this was indeed a new game and it was full of thrills. I well remember how I went from one conquest to another not only with the theorems in the text but also with the "originals" which I laid low with especial glee.

**The Lag in Mathematics Behind Literature and Art in the Early Centuries.**

*Amer. Math. Monthly***41**(3) (1934), 167-174.

Among the various characteristics which distinguish man from the lower animals, there are two which stand out in bold relief; namely, the language concept and the number concept. These will be made the basis of study and contrast in the present discussion. It will be found that these two concepts did not develop in the human mind with equal ease or with equal speed, and it will be of more than passing interest to examine some of the reasons for such great disparity and possibly to suggest and support an explanation which has not been dwelt upon by the historians. In a word we shall try to find out some of the reasons why mathematics lagged so far behind literature and art in the early centuries. ... it seems clear that the number concept and its development in algebraic science have caused the human race far greater trouble than the language concept and its development in literature; and that the lag of mathematics behind literature was an inevitable consequence of the relative difficulties involved in these two concepts.

**A Message from Honorary President H E Slaught.**

*The Mathematics Teacher***29**(4) (1936), 184-185.

A number of Dr Slaught's friends have wondered how he came to be so much interested in the secondary situation, when he had so many alluring attractions to occupy his attention in the collegiate and graduate fields while holding his professorship (1892-1932) at the University of Chicago. We have induced him to give us a few facts bearing on the answer to this question. We have outlined these below: 1. His first teaching (1883-1892) was in a secondary school where he completely reorganized the mathematical department. 2. From his early experiences at the University of Chicago which included supervision of entrance examinations and official visiting of secondary schools, he obtained ample evidence of the need of more effective training in high school mathematics. 3. For a long term of years, the University held an annual conference with cooperating high schools and Dr Slaught had full responsibility for the conduct of the mathematics section, which brought him in close contact with the schools. 4. A year of graduate study in Germany (1902-1903) gave him fine opportunity, on the side, for observing the thorough methods in use in the schools there. 5. Upon his return in 1903, the Central Association of Science and Mathematics Teachers was just getting under way and he at once allied himself with that organization and became one of its most active supporters. (He is now one of three or four honorary life members.) 6. When the Mathematical Association of America was organized (1916) primarily for operation in the Collegiate field, Dr Slaught was one of the first to insist on Cooperation with the secondary schools through the joint National Committee and this led to the organization of the National Council of Teachers of Mathematics, as explained in his message above. 7. It will thus be seen that Dr Slaught has practised what he preached. He believes that the interests of mathematics can best be served not by putting up a wall of partition between the secondary school and the college, but by cooperation wherever possible among the representatives of the respective organizations. 8. Dr Slaught's recent election as honorary president of the National Council of Teachers of Mathematics is an honour which he has well earned by his devotion to our cause.

**Greetings to My Friends of the National Council.**

*The Mathematics Teacher***30**(4) (1937), 186-187.

The National Council occupies a unique position in the field of mathematical pedagogy and every member has the opportunity to contribute toward the betterment of teaching in whatever phase of elementary or secondary mathematics he may be most interested. For example, the teaching of arithmetic is a fertile field in which there is ample room for improvement, and the topics of senior high school and junior college are always open for expert pedagogical attention. The Mathematics Teacher affords a medium for the promulgation of ideas in the realm of elementary and secondary mathematics that no teacher in this realm can afford to be without. Moreover, such possession is a mark of professional standing. The Yearbooks sponsored by the Council bring to the teacher the very latest and best considerations in the line of our mathematical interests. There are now eleven such volumes. If all these things are good for our four or five thousand members, they are also good for twice that number. So here's to our slogan: "Ten thousand members by 1940."