Factors in the Formation of Attitudes Toward Mathematics

Abstract

IN THE LAST few years, much attention has | been given to the growing shortage of graduates in the physical sciences. Since an u n de r standing of mathematics is basic to the physical sciences and since there is also a shortage of mathematicians, there has been increasing concern about the much publicized dislike and fear of mathematics among high school students. A number of studies have made contributions to our understanding of factors related to mathemati cal ability and interest. Both are related to one's ability to make abstractions and thus correlate with intelligence (Cattell, 1945;Hamza, 1952;Krathwohl, 1946; Revesz, 1940). However, when intelligence is held as a constant, why does one student like mathematics while another student dislikes the sub ject? A study by Cattell (1945) indicates that per sonality factors are not s i g n i f icantly correlated with mathematical ability when the effects of intel ligence is parceled out. On the other hand, Hamza (1952) feels that in a study of 12 and 14-year-old boys he demonstrated the relation of motivational and attitudinal factors to the problem. It is to this latter relationship that we wish to direct our atten tion. With our present knowledge ofidentificat ion theory and childhood conditioning, we would logic ally assume that the basic attitudes toward mathe ? matics would tend to develop within the confines of | the nuclear family and that the school would build upon what had already begun. With this approach j in mind, a pilot study (Poff en berger and Norton, | 1956) was conducted in the summer of 19 5 5, con sisting of an intensive interview of the 16 students enrolled in two mathematics courses being offered during that summer. A questionnaire was construc ted on the basis of the preliminary study and given to all entering freshmen at the University of Cali fornia at Davis in the fall of 1955. The question naire consisted of 140 questions, some of which were multiple-choice check questions while others ? were of the writein type. The validity of the ans wers are open to the well-known hazards of a ques tionnaire which depends upon the ability of the stu dent to recall and his willingness to report accur ately his conscious attitudes. * The group studied consisted of 390 students, 52% males and 48% females. Over two-thirds (68%) at tended high schools of over 500 s tudents. Nearly half of both the fathers and mothers had attended one or more years of college although 29% of the fathers and 19% of the mothers did not graduate from high school. As has been pointed out, ability i n such a study is an important factor to control since one's own attitude as well as parental expectations will depend to a large extent upon whether one is mentally able to handle abstract symbols with sufficient ease. The fact the students were admitted to the University was an indication of ability since studies indicate that entering freshmen at the University come from the top 12% of high school graduates. The American Council on Education Psychologi cal Examination was given at the s a m e time the questionnaire was administered and to be sure that students of poorer ability were not inc ludedinthe sample, the lower 14% of the total (T) score were omitted. The T score was used rather than the quantitative Q score since the value of Q in indicating mathematical ability is not yet clear. 2 After removing the bottom 55 of the total group, only 3% of the remaining 335 students received less than a B average in high school. It w a s assumed that the remaining sample had the initial ability to handle basic mathematical concepts and that other factors could be studied with ability partially con trolled. 3