Problem Posing: A Neglected Component in Mathematics Courses for Prospective Elementary and Middle School Teachers

The purpose of this article is to describe a scheme which is designed to guide the prospective teacher beyond the point of proficiency as a student solving given problems. By experiencing several stages of inquiry, the scheme provides a mechanism where by the prospective teacher advances toward assuming the role of a teacher posing his or her own problems. Although the scheme has been developed within the context of a standard mathematics course for preservice teachers, the ideas set forth are equally appropriate for incorporation within a science course for prospective teachers.     

Motivation and Attitude of Preservice Elementary Teachers toward Mathematics

This study investigated preservice elementary teachers' achievement goal orientations for learning mathematics and the relationship of those goals to their attitudes toward mathematics. Self‐report instruments were administered to assess three achievement goals—mastery, performance‐approach, and performance‐avoid, and three constructs of attitude—confidence in learning mathematics, usefulness of mathematics, and mathematics as a male domain. The preservice teachers were higher in mastery goals than in performance goals, and performance‐avoid goals were higher than performance‐approach goals. Mastery goals correlated positively to all three constructs of attitude. Since mathematics classes are traditionally performance‐oriented, these results suggest a mismatch between personal and classroom goals that could result in negative attitudes and the adoption of maladaptive performance‐avoid goals. These findings suggest that mathematics content courses for preservice elementary teachers should be taught in a classroom climate that supports and encourages mastery goals.     

Preservice Elementary Teachers' Mathematics Content Knowledge and Teacher Efficacy

The purpose of this study was to examine the relationship between mathematics content knowledge and teacher efficacy during an elementary mathematics methods course. A positive moderate relationship between content knowledge and personal teaching efficacy was found, and this relationship was stable during the course. No relationship was found between content knowledge and outcome expectancy. Written artifacts were used to understand and elaborate on these findings. Those data suggest that prior learning experiences may help explain this relationship. Additionally, they suggest that preservice teachers with different levels of content knowledge may attend to different sources of information when making efficacy judgments about teaching.     

Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

Research suggests the importance of mathematics knowledge for teaching (MKT) for enabling elementary school teachers to effectively teach mathematics. MKT involves both mathematical content knowledge (M‐CK) and mathematical pedagogical content knowledge (M‐PCK). However, there is no consensus on how best to prepare elementary preservice teachers (PSTs) to achieve M‐CK and M‐PCK. This study builds on research related to MKT by investigating influences of mathematics content courses designed specifically for elementary PSTs (IMPACT courses—Impact of Mathematics Pedagogy and Content on Teaching) on their attitudes (i.e., confidence and motivation) toward M‐CK and M‐PCK. Results suggest that the PSTs who participated in these IMPACT courses not only acquired high levels of confidence and motivation toward M‐CK, but also showed significant and greater gains in attitudes toward M‐PCK, after taking the required mathematics methods course, than their counterparts. Further, the findings suggest that these IMPACT courses provided a mathematical foundation that allowed the PSTs to engage in mathematics teaching methods better than those PSTs who did not have such a foundation. These results suggest potential course experiences that may enhance M‐CK and M‐PCK for elementary PSTs.     

Effectiveness of a Mathematics Methods Course in Reducing Math Anxiety of Preservice Elementary Teachers

In an attempt to find ways of reducing the mathematical anxiety of preservice elementary teachers, three cases were investigated. The first was a section of mathematics for elementary teachers taught in a very traditional manner, and the second was the same course taught in a manner consistent with the recent recommendations of the National Council of Teachers of Mathematics. The third case included two sections of a methods course which covered the same mathematical content, as well as addressing how it should be taught to children. The Mathematics Anxiety Rating Scale for Adults was administered before and after the courses. No significant reduction of anxiety was measured in either mathematics section, but both sections of the methods course showed a significant reduction.     

Relationship Between Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

The purpose of this study was to investigate the change in teacher efficacy beliefs about mathematics and science teaching during participation in methods courses and student teaching, as well as the relationship between mathematics and science teaching efficacy. Data revealed that, as science and mathematics teacher education in a methods course progressed, science and mathematics teaching efficacy significantly increased. This effect appeared to decrease slightly by the end of student teaching. Analysis of data indicated a significant difference in both the personal mathematics and personal science teaching efficacy scores, as well as mathematics outcome expectancy. Additionally, preservice teachers' personal mathematics and science teaching efficacies were directly related, as were their mathematics and science teaching outcome expectancies.     

Integrating Science and Mathematics: Perceptions of Preservice and Practicing Elementary Teachers

One hundred and sixty-one undergraduate elementary education majors and sixty elementary teachers completed an eight-item questionnaire designed to assess their perceptions toward integrating science and mathematics in the elementary grades. The two groups of subjects differed significantly on their responses to five of the eight items. Chi square analyses suggest that practicing elementary teachers felt they had more background in mathematics and science, were more aware of curriculum materials in this area, did not think that integration was currently a common practice, and were more likely to indicate that there was not sufficient time in the school day to integrate the subjects. Preservice teachers were more likely to indicate that integrating the disciplines was preferred to teaching them separately. In addition to the analyses of data, a list of recommendations are provided for teachers, curriculum developers, and policy makers interested in advancing the concept of integrating science and mathematics in instruction.     

Preparing Middle Level Preservice Teachers to Integrate Mathematics and Science: Problems and Possibilities

Many members of the mathematics and science education community believe that the integration of mathematics and science enhances students' understanding of both subjects. Despite this belief, attempts to integrate these subjects have frequently been unsuccessful. This study examines the development and implementation of a team‐taught integrated middle level mathematics and science methods course. The data presented in this study were collected from three groups of preservice teachers who were enrolled in a grades 5–8 middle level teacher certification program in Connecticut from 1998–2000. The data analysis indicates that preservice teachers appreciated the emphasis on integration used in the course, but at the same time when concepts did not integrate easily they were frustrated. Despite this frustration, the preservice teachers' understanding of integration was enhanced as a result of the course.     

Mathematics Anxiety and Preservice Elementary Teachers' Confidence to Teach Mathematics and Science

Sixty‐five preservice elementary teachers' math anxiety levels and confidence levels to teach elementary mathematics and science were measured. The confidence scores of subjects in different math anxiety groups were compared and the relationships between their math anxiety levels and confidence levels to teach mathematics and science were investigated. The results suggest that low math anxious preservice teachers are more confident to teach elementary mathematics and science than are their peers having higher levels of math anxiety. Negative correlations were found between preservice teachers' math anxiety and their confidence scores to teach elementary mathematics (r = ?.638) and between preservice teachers' math anxiety and their confidence scores to teach elementary science (r = ‐.417). Also, personal math and science teaching self‐efficacy scores of participants were found to be correlated at .01 level (r =.549).