The Relationship Between a Sixth‐Grade Student's Ability to Predict Success in Solving Computational and Statement Problems and His Mathematics Achievement and Attitude¹

Abstract

A rather common teaching strategy used in an elementary school mathematics lesson is for the teacher to write a problem such as one hundred sixty-three added to two hundred twenty-eight on the chalk board and ask who in the class can work it, or to ask the class who can solve the fourth statement problem on page twenty-three in the textbook. Since the students are seldom, if ever, given sufficient time to actually solve the problem before being asked to respond, it would appear that the teacher is not asking "who can solve the problem" but rather "who thinks he can solve the problem?" In other words the teacher is asking the student to predict whether or not he is able to solve the problem correctly. Moreover, since only a few individuals are actually given the opportunity to make a response on a single question, the teacher many times relies on a show of hands to determine which student may or may not be able to solve the given problem. Thus, it would be logical to assume that the reliability of this procedure depends upon how well students are able to predict success in solving such problems. It may be further assumed that the students' ability to predict success in solving computational and statement problems is based on a number of complex cognitive and affective variables. However, before any study is made to identify such variables it would be of considerable value to the classroom teacher to seek answers to the following questions:1. How accurately can students predict success in solving computational and statement problems? 2. What relationship, if any, exists between a student's ability to predict success in solving computational and statement problems and his mathematics achievement? 3. What relationship, if any, exists between a student's ability to predict success in solving computational and statement problems and his mathematics attitude?In an attempt to seek some insight into these questions, the following pilot study was conducted. BACKGROUND The researcher was unable to locate any research which was directly re-

Towards Describing Student Learning of Abstract Algebra: Insights into Learners’ Cognitive Processes from an Acceptance Survey

“…However, simply because teachers draw great benefits from their field of work does not imply that these benefits also translate from teachers to students in the classroom. Indeed, it has been shown that there is no significant correlation between a teacher's knowledge in abstract algebra and students' achievement in school algebra [2][3][4][5][6][7][8][9]. This conflict raises the question of whether students themselves can benefit from learning abstract algebra if they are confronted with it instead of only their teachers.…”

“…The fact D 4 S 4 provides new problems to solve, i.e., discussions of why certain permutations do not describe isometries of the square. 3.…”