Prospective Elementary Teachers' Understanding of Order of Operations

Peter L. Glidden

This study investigates how well 381 prospective elementary, early childhood, and special education majors solved four arithmetic problems that required using the order of operations. Self-reported data show these students to be relatively able mathematically and confident in their ability, with no substantial dislike of mathematics. The percentage of answers that were incorrect that is attributable to order of operations ranged from 21.7% to 78.5%. Overall, fewer than half the subjects answered more than two questions correctly. Of those subjects who performed multiplication before addition, which indicates some knowledge of order of operations, 30.9% performed addition before subtraction and 38.0% performed multiplication before division rather than from left to right, which suggests that instead of using the correct order of operations, these students used the common mnemonic PEMDAS or “Please excuse my dear Aunt Sally” literally, performing multiplication before division and performing addition before subtraction, rather than from left-to-right. Furthermore, 78.5% of subjects used the incorrect order of operations to compute -32.

Science and Mathematics Instruction in a Reform-based Teacher Preparation Program

Douglas Huffman, Kelli Thomas, & Frances Lawrenz

This study examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP). The focus of this study was on examining the extent to which science and mathematics teachers used more reform-oriented instructional practices in their classes when they entered the teaching profession. Data were gathered from twelve different CETP projects across the United States. A quasi-experimental design was used where science and mathematics teachers who were initially prepared by the CETP program were followed into the field and compared to teachers who were not prepared by the CETP program. The results indicate that the teachers prepared by the CETP program used slightly more reform-oriented instructional practices than teachers who were not prepared by the CETP program, although both mathematics and science teachers reported low levels of reform-oriented instruction. Implications of results for large-scale reform of science and mathematics teacher preparation are discussed.

Perceptions of Mathematics and Gender

Peter Kloosterman, Janet (Hagemeyer) Tassel, Ann G. Ponniah, & N. Kathryn Esses

This study examined students' perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre-service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz (Leder, 2001). The data indicate that, similar to findings from the 1970s, students believe that mathematics is gender neutral, although females hold this belief more strongly than males. Female secondary school students hold beliefs in gender neutrality more strongly than female pre-service teachers. Data for secondary school students indicate that both males and females see differences in the way boys and girls act and are treated in mathematics classes (e.g., boys cause more distractions while girls care more about doing well). The data also show that secondary school males who believe they are good mathematics students tend to have more gender-neutral perceptions than those who believe they are average or below average. No such pattern appears for secondary school females.