Practice Material in the Estimation of the Quotient in Long Division Found in Current Arithmetic WORKBOOKS

Abstract

In a previous article1 the writer made an analysis of the examples in long division as found in nine current textbook series in arithmetic. It was found that there was little uniformity in the method suggested for estimating the quotient and in the number and types of examples given in each textbook. This study makes a similar analytical classifi cation of the estimations of the quotient for the different division ex amples found in current arithmetic workbooks. The selection of the workbooks to be included in this study was based on the manner in which they were issued. Each workbook to be selected had to be issued in a series of separate booklets for each grade for Grades III-VIII, inclusive. Since none of the booklets for the third grade con tained long division examples, the booklets scrutinized were for Grades IV-VIII, inclusive. An effort was made to include every series of prac tice booklets by different authors now extant which satisfied the cri terion of having a separate booklet for each grade above the third and extending through the eighth. If an author or a group of authors had written more than one series of workbooks, the edition having the latest copyright date was the only series considered for that author or group of authors. A separate booklet for each grade was essential to make the results obtained from the study comparable. The series had to cover the work for grades four to eight inclusive in order to make the results from this study comparable to those derived from the analysis of textbooks. In the latter case, the series of text books contained the subject matter of arithmetic for grades three to eight inclusive. Using the criterion of having all possible workbook series consist of a separate booklet for each grade from the third to the eighth inclusive, nine different series were selected. In the study of textbooks the method for estimating the quotient was classified under three headings. Two of these methods of estimation are used in this study. They are : First, the apparent method in which