The difference in emphases between Standards-based and more traditional algebra curricula suggests a need for a detailed comparison of such curricula and the performance of students who study from them. It has been argued that detailed cognitive analyses of students’ responses, including solution strategies, justifications, and modes of representation, are important in understanding similarities and differences between groups in cross-national studies. We suggest that detailed analyses of students’ solutions are also important in understanding similarities and differences in achievement in comparative studies of mathematics curricula within a country. Specifically, the following questions are addressed in this brief report:
• What strategies do students studying algebra use to solve algebra problems?
• How are students’ strategies related to their achievement in solving these problems?
• How are students’ strategies related to the curriculum?
The success of any undertaking depends upon two vitally significant facts:?first, a well-organized plan of what you expect to accomplish, with the necessary materials and tools needed; and, second, cooperation between all concerned to bring about desired results. Pupils come up from the grades knowing little about the content of high school subjects or their significance. Their background is limited and most frequently they are prejudiced in favor of or against a subject. Certain subjects would be tabooed if students had their say in the matter. Algebra is one of these subjects and has been classed as “hard” because of the number of failures among beginners. These failures in algebra can be assigned to one or more of three causes psychological, physical or pedagogical. From the psychological point of view the student may be lacking in mathematical abilities a deficiency which may or may not be corrected, according to whether they are inherent or due to lack of training. But the student may have approached algebra from a wrong angle and this is an important point in the teaching of the subject and must be considered. From the physical point of view, apart from any personal physical handicaps, the atmosphere of the classroom, including the physical situation and the teacher’s attitude, has much to do with the advancement of a student in his progress in learning. An active spirit of cooperation between teacher and pupil is absolutely necessary to a student’s progress. From the pedagogical point of view, even with the advance that has been made in the teaching of mathematics, educators are confident that still more can be done to improve the pedagogy of the subject in order that greater interest may be aroused in the students and better results attained.
An “inspirational preview” or “a bird’s eye view” of the subject is one of the most valuable approaches to the study of algebra for awakening interest and putting before the class reasons for studying algebra and some of the things that are expected during the course. The important thing is to give the students an inviting introduction to it so that they will anticipate pleasure in the study of the subject. Then, it is the privilege of the instructor to see that this interest is kept up.