Diverse Science

Turner, Ethel M. | Teaching Aids for Elementary Mathematics

  • First edition, first printing of this book of cutting edge teaching aids by the African American mathematics professor Ethel M. Turner.

    Turner earned both her MA and doctoral degree in education at Columbia University, then became chairman of the Department of Mathematics at Cheyney State College, now Cheyney University of Pennsylvania, the first of the Historically Black Universities in the United States (Sammons, Blacks in Science and Medicine, p. 235). She published several books on mathematical education, with this one geared toward early learning.

    As she writes in the preface, “This book is offered as a sourcebook of teaching aids and ideas for the elementary teacher... In the face of the current revolution in mathematics education, educators have been forced to examine the school curriculum. This examination has brought new topics and ideas into the content of courses. Also, subject matter that had for years been reserved for the high school curriculum, has found its way into the elementary school... The traditional content is now in a new framework. Its philosophy has been centered on teaching through the ‘discovery’ approach, which emphasizes learning mathematics through the study of patterns and structure. Consequently, those teachers who have considered arithmetic only as ‘number work’ must restructure their thinking on the meaning and significance of mathematics education. They must teach more than computation. Other aspects to be stressed are conceptual learnings, seeing relationships and developing reasoning, Also, mathematics should be shown as a way of thinking, an art or form of beauty, and as human enrichment.”

    The lessons offered here cover a variety of elementary mathematical concepts in original and engaging ways, often as simple games and puzzles. Among them are “Climbing the Steps to the Fairy Castle” to review fundamental operations and learn to carry the ten; “Mathematical Cookie Cutters” to “increase interest in mathematical activities, to review knowledge of symbols, and to relate mathematics to the world of industrial arts”; the Sieve of Eratosthenes to find prime numbers; a lesson on applying the Fibonacci sequence to botanical life; constructing “Jesse’s Rods” (based on Napier’s bones); lessons on ancient numeration systems, including Egyptian, Greek, Hebrew and “a Roman boy’s arithmetic” and medieval algorithms for addition and multiplication, all of which could be incorporated into history lessons; magic squares; mathematical “crisscross puzzles” similar to crosswords; using points on graphs to create pictures; and even instructions for creating a Moebius Strip.

    Of particular interest are the lessons dealing with computing: deciphering binary code on punched paper tape; using algorithms for cryptanalysis; and a lesson on “some uses of computers”: “counting and tabulating, such as votes, census figures... (UNIVAC)”, “handling telephone calls (AUDREY)”, “bookkeeping for bank accounts (ERMA)”, “detecting planes and missiles (SAGE)” and, in what may be the greatest understatement in all of mathematical education, “working out details for constructing new weapons (ENIAC)”.

  • New York: Holt, Rinehart and Winston, 1966.

    Octavo. Original white wrappers printed with a design of numbers and geometric shapes in colour. Colour illustrations and diagrams throughout. Inked-out signature and pencil erasures to the front free endpaper. Wrappers a little rubbed and toned, with some small spots and a crease to the upper wrapper, which is also a little curled from use. Contents clean and fresh. A very good copy.