Numeracy

Typically, a child begins to count at about age three. This does not mean that he has a ready grasp of the concept of number. He must learn to distinguish three blocks from five and learn what it means to take away one or two blocks from his pile. The key in the early years is to work with blocks and other physical objects. Put down two blocks and ask how many. Then add one or two blocks and ask again, how many. Continue to add and subtract blocks, asking how many are left, how many did I take away, until the concept of number up to three blocks total is completely understood. Physical objects illustrate the idea of number in a way that makes learning concrete. It may seem that our first studies of mathematics in the Preparatory Lessons are rather juvenile and designed for children of six, rather than eight or ten. However, a great many of the problems students encounter later in mathematics are the direct result of not having a solid concept of number. Prior to beginning formal lessons, the child should learn number sense: the notion of how many and the ability to group like objects. This can be accomplished in any of a number of ways. One that was quite effective was developed by the German educator August Wilhelm Grubé in the late nineteenth century. His method used physical objects (simple blocks) to develop in the child the number sense upon which arithmetic is based. Others emphasized counting similar objects in the world of the child; yet others used dots in squares, cut-out squares, or sticks (counters) that can be bundled together in groups of ten. Be patient in teaching arithmetic and mathematics. Here is some good advice from Adelia Hornbrook: Do not take up a new combination of numbers until the child is able to give promptly those already taken. The learning of the addition combinations is a gradual process accomplished by many repeated perceptions on the part of the learner. Inexperienced teachers are cautioned not to be discouraged if the same pupil who has one day given the combinations correctly misses them at a later date. This merely shows that those paths in the undeveloped little brain need to be traversed again. Vary the work by having the child place and count squares, make and count dots, or count objects, real or imaginary. Primary Number Books Here I have collected the books that we recommend for under-8 Arithmetic and Number Studies. These are the very best books available. It is better to spend more time in each of these books than to seek out additional materials. Students who have completed the sequence will be ready for the course of Primary Arithmetic in the Academy. You can download the books by clicking on the links. Grubé's Method of Teaching Arithmetic by Levi Seeley Prior to beginning a Primary course or Arithmetic, the child should learn number sense: the notion of how many and the ability to group like objects. This can be accomplished in any of a number of ways. One that was quite effective was developed by the German educator August Wilhelm Grubé in the late nineteenth century. His method used physical objects (simple blocks) to help the child develop his number sense. Other educators emphasized counting similar objects in the world of the child; yet others used dots in squares, cut-out squares, or sticks (counters) that can be bundled together in groups of ten. Grubé also has an excellent section on fractions that should not be skipped. The First Steps in Number by G. A. Wentworth and E. M. Reed This text is designed to be used for the first formal experience with number. The authors begin with three, as most children enter school knowing the difference between one and two. The Introduction to Chapter 1 is invaluable in helping assess a child's readiness for number studies. The first ten chapters, which deal with numbers to ten, are designed to be presented orally. By the time he has finished these chapters, a typical child will have the manual dexterity required to write his numbers and can complete the text. First Days in Number. A Primer of Arithmetic by Della VanAmburgh This book begins with objects to count that are familiar to the child. It suggests nature lessons, where the child can learn to count whatever he encounters. Then, the numbers are introduced. The use of physical objects throughout is encouraged. Along with teaching the numbers two, three, four, five are the concepts of one-half, one-third, one-fourth, one-fifth, and so on through twenty and one-twentieth. The concepts of more and less than are illustrated. The book is intended as a supplement to the teacher's careful teaching. It is not a self-teaching text, but designed to be presented orally by the teacher. Two digit numbers are introduced. Solid shapes (cube, sphere, cylinder), Roman numerals, money, calendar, clock, liquid dry, and linear measures are presented. Students are asked to measure lines of different colors and to compare their lengths. Columns of numbers up to three digits are added. The concept of carrying over the next column in addition is not explained. It is expected that the teacher is available to show the student how to do the additions. Multiplication is introduced as repeated addition. The question mark as a place-holder in a simple equation is shown. The identity of multiplying by a fraction and division up to 5 is illustrated. Arithmetic Primer by Frank H. Hall This is another example of a book that starts at a very simple level and progresses through addition, subtraction, and multiplication of numbers to one-hundred, measurement, time, money, simple fractions. Return to the Academy home page Site and pages copyright by HighlandsAcademy.org