Before discussing the place of junior high school mathematics in education, it will be well to decide what criteria to use in determining whether or not a subject or a method has educational value.
Kathleen Lynch and Jon R. Star
Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how 6 struggling students viewed the practice of learning multiple strategies at the end of a yearlong algebra course that emphasized this practice. Interviews with these students indicated that they preferred instruction with multiple strategies to their regular instruction, often noting that it reduced their confusion. We discuss directions for future research that emerged from this work.
O. H. Bigelow
We all know that due to external pressure the Mathematical Association of America appointed a committee called the National Committee on Mathematical Requirements and that this committee made recommendations for the reorganization of mathematics in secondary education. Through external pressure, I say, this was brought about; for either mathematicians were too near to be able to focus on the large defects that appeared to outsiders or were too busy amplifying and extending the knowledge brought down from the ancients to realize that times were changing and that if we were to give every child a high school education, we must use a different procedure from that of the old world where only a select class receive a broad education.
The difficulties facing the teacher of plane geometry grow constantly more baffling. Enforced attendance at school until the boy or girl is sixteen, with a group of pupils often unfitted mentally, by environment, or by ambition for a high school education, presents an immediate and ever-looming problem. An insufficient number of trade schools or excessive ambition on the part of generous parents, desirous of seeing their children in the professions rather than in the trades, fills the classes of such a subject as plane geometry. Moreover the subject is generally required for college entrance, and is regarded almost universally as cultural, broadening, and conducive to mental development characterized by clear expression and logical thinking. The position of the teacher of this subject fifteen or twenty years ago when a select few with real ability pursued the subject was not nearly so complex. Now every youth who has managed to pass to the tenth grade and takes up plane geometry all but assumes that a passing understanding of the subject is his birthright. Perhaps it would be conceded that plane geometry is the first great obstacle to the youth's securing a coveted diploma. Or possibly it might be stated thus: it is in his attack upon this subject in which the frailty of his mental make-up is most in evidence, most pitilessly laid bare, if there is such weakness; or, on the other hand, his power of intellect is here first appreciated by others, and, with great satisfaction, by himself. Hence the instructor of plane geometry to-day who would teach the subject in a forceful and effective manner, developing his pupils, convincing them of its influence, its use and keen intellectual enjoyment, must be forever on his toes inventing and contriving devices and stratagems to teach satisfactorily this large group, less clever, less ambitious, less able, than heretofore, taken in the cross-section. What a wonderful people the citizens of the United States would be intellectually several generations hence if all who attempt a high school education really had the ambition and ability to master it.
Joseph B. Orleans and Jacob S. Orleans
During the past two decades high school registration has increased many fold. The growth has been so rapid that in New York City, for example, the authorities have not been able to supply buildings fast enough to meet the new demands. Chief among the causes of this change is the Compulsory Education Law which complete many boys and girls to remain in school a year or two at least after their graduation from the elementary school. High school education has become the vogue and the high schools have therefore been forced to accept a large number of pupils who are not fitted for the various courses which are offered. The extent to which this condition holds is indicated by the number of failures each term. Commercial and vocational courses of various kinds have been introduced to take care of pupils whose needs are not met by the traditional subjects. The syllabi of the traditional subjects have been modified and simplified to meet the varying abilities and needs of the pupils. The effect of this tendency is seen in such courses as general science, general language and general mathematics.