Using Metaphors to Unpack Student Beliefs About Mathematics

This paper reports on an exploratory study of the mathematical beliefs of a group of ninth and tenth grade students at a large, college preparatory, private school in the Southeastern United States. These beliefs were revealed using contemporary metaphor theory. A thematic analysis of the students' metaphors for mathematics indicated that students had well developed and complex views about mathematics including math as: an Interconnected Structure, a Hierarchical Structure, a Journey of Discovery, an Uncertain Journey, and a Tool. Another prevalent theme revealed by the metaphors was that students believe perseverance is needed for success in mathematics. The data also suggest an impact of gender and tracking on students beliefs about mathematics. Creating metaphors for mathematics provided a catalyst for student reflection, class discussion, and qualitative data, which could aid program evaluation. Several areas for future research were identified through this exploratory study.     

Preservice Teacher Beliefs About Proofs

This article describes a study of backgrounds, beliefs, and attitudes of teachers about proofs. Thirty preservice elementary teachers enrolled in a mathematics content course and 21 secondary mathematics teachers in an abstract algebra course were surveyed. The study explored four issues: preservice teachers' experiences/exposure to proof, their beliefs about what constitutes a proof and the role of proof in mathematics, and their beliefs about when proof should be introduced in grades K-12. Results of the survey are described as a means for discussing the backgrounds and beliefs future teachers hold with regard to teaching proofs in their own classrooms. Finally, a short collection of sample explorations and questions, which could be used to encourage the thinking and writing of proofs in grades K-12, is provided. One of these questions was posed to 215 secondary students; examples of their reasoning and a discussion of the various techniques employed by the students are included.     

Relationships Between Student,Teacher, and School Characteristics and Mathematics Achievement

A variety of factors contributes to student achievement in mathematics, including but not limited to student behaviors and student, teacher, and school characteristics. The purpose of this study was to explore which of these factors have an impact on student mathematics achievement. The target population for this study was North Carolina Algebra II students. Analyses of variance models were examined for group differences and a Three‐level Hierarchical Linear Modeling method was employed to examine individual predictors of student achievement in mathematics. Statistically, significant differences were found between students of different ethnicities, socioeconomic statuses (SES), and parental education levels. No gender effects were statistically significant. All teacher‐level variables investigated were found to be statistically significant, impacting student achievement in mathematics. School size and SES were not found to significantly contribute to student achievement. More research on the relationships between these factors shown to make statistically significant differences on mathematics achievement is needed to further explain several phenomena that this research reveals.     

Undergraduate Engineering Majors' Beliefs About Mathematics

This study examined the mathematics beliefs of college students in 10 undergraduate mathematics classes at a large engineering school in the Midwest. The beliefs of 254 engineering majors were measured by the Indiana Mathematics Belief Scales and compared to the beliefs of elementary education majors and remedial college mathematics students obtained from earlier studies using the same instrument. The results were interpreted in terms of the students' daily attitudes towards their mathematics classes and corresponding academic and demographic parameters. The study showed that in many respects, the beliefs of the engineering majors were not that different from the other populations. The correlations among beliefs for the engineering group tended to be higher although there were relatively few significant correlations between belief and background variables. Attitude data were collected across a full semester for the engineering majors. The relatively modest day-to-day variation in those attitudes suggests that they are based on deeply seated beliefs.     

The Impact of Problem Posing on Elementary Teachers' Beliefs About Mathematics and Mathematics Teaching

This study investigated the impact of incorporating problem posing in elementary classrooms on the beliefs held by elementary teachers about mathematics and mathematics teaching. Teachers participated in a year‐long staff development project aimed at facilitating the incorporation of problem posing into their classrooms. Beliefs were examined via pre‐ and postsurvey. Results indicated a positive impact on their beliefs about mathematics and mathematics instruction. Data from open‐ended written responses verified the impact of problem posing on the teachers and their classrooms. Based on these findings, it is recommended that problem posing be incorporated into all professional learning and undergraduate education programs.     

高校组织文化氛围视角下教师及学生满意度的关系研究

以高校组织文化氛围为视角,联系服务运作相关理论,建立了教师满意度与学生对教师满意度的模型.利用SPSS18.0和PLSGraph3.0软件对收集的数据和模型分别进行了信效度分析和模型检验,结果发现:教师满意度能提升学生对教师的满意度反之亦然.同时学生满意度低的教师其行为对学生的影响力度更大,另外还发现除了教师满意度会影响教师组织承诺以外,高校组织文化氛围和学生对教师的满意度也是影响的关键因素.     

A Comparison of Preservice Elementary Teachers' Beliefs About Mathematics and Teaching Mathematics: 1968 and 1998

The study replicates Collier's (1972) work. It focuses on the beliefs of a large sample of elementary education students at four stages of teacher preparation, about both the nature of and the teaching of mathematics. The instrument measures what Collier termed a “formal‐informal” dimension of belief. The data suggest that initially the 1998 students held significantly more informal (constructivist) beliefs than did their 1968 counterparts. In both years, students moved toward more informal beliefs during the course of their programs, with the most significant changes occurring in their beliefs about how mathematics should be taught. However, apparent contradictions in belief structures were observed both at the start and at the end of their programs. Thus, it appears that though many students acquired new, more informal beliefs during the course of their programs, they did not develop robust, consistent philosophies of mathematics education.     

The Relationships Between Parental Influence and Student Achievement in Seventh Grade Mathematics

Parental influence has been identified as an important factor affecting student achievement, but the variables addressed by various parent-school partnership programs vary, and lack literature support. This deficiency was ameliorated in this study through an analysis of a national data base from the Longitudinal Study of American Youth (LSAY). AH parental variables investigated in LSAY were considered in this study, and significant variables of students' achievement in seventh grade mathematics were selected through the Backward Elimination Procedure in the Statistical Analysis System (SAS). The results show that those variables significant at α= .05 have accounted for around 22% variability of the student achievement. A further analysis of the empirical results seems to indicate that parent education and encouragement are strongly related to improved student achievement. However, parents should attempt to understand students' feeling, and expect students to take the full responsibility for their successes in the school.     

Student and Teacher Perspectives Across Mathematics and Science Classrooms: The Importance of Engaging Contexts

Substantial recent focus has been placed upon the competitiveness of American students in increasingly global economies and entrepreneurial enterprises. As concerns center on students’ educational preparedness and their efforts at continued learning, researchers acknowledge the importance of student engagement with school. In order to foster engaged learners, teachers must be able to determine and monitor their students’ levels of engagement. The current study examined the alignment of perceptions of engagement by students, teachers, and outside observers across middle and high school mathematics and science classrooms. Results indicated significant teacher‐student differences in perceptions of student cognitive engagement across mathematics and science classrooms with teachers consistently perceiving higher levels than students. Moreover, most effect sizes were moderate to large. A subsequent multi‐level analysis indicated that while teacher perceptions of student cognitive engagement were somewhat predictive of student reported cognitive engagement, academic engagement ratings by outside observers were not.     

Reforming Elementary Science Teacher Preparation: What About Extant Teaching Beliefs?

A common maxim in the educational profession is that one teaches the way one is taught. Indications are that preservice teachers' beliefs, attitudes, and practices may be linked to previous experiences. Calderhead & Robson (1991) underscored this concern by asserting that teachers use good teachers as models for developing their own images as teachers. Others have argued that the images held by teachers are used as frames of reference for their own teaching practices. In this article, preservice teachers' perceptions of themselves as science teachers are examined. The assertion is made that a long history of stereotypical science learning experiences — in elementary school, high school, and college — powerfully impacts the way in which elementary preservice teachers understand the nature of science and come to believe science should be taught. In the current study, the images and perceptions preservice teachers bring to science methods courses (as evidenced in drawings of themselves as science teachers at work) are identified and ways these images and perceptions may have been formed and how they can be reinforced or modified during a science methods course are discussed.     

Teacher Learning and Mathematics Manipulatives: A Collective Case Study About Teacher Use of Manipulatives in Elementary and Middle School Mathematics Lessons

This collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K‐8) involved in lesson study as part of a professional development program. The study found that in three of four lessons studied manipulative use was turned into an end in and of itself, rather than a tool, and that in the fourth lesson manipulative use hindered rather than helped student learning. These problems with manipulative use by teachers in the lessons provide helpful guidance for planning of future professional development for math teaching. Our conclusion contains recommendations for successful implementation of manipulatives for both teachers and professional developers. Most importantly, we stress the need to emphasize the link between pedagogy and content, not the specific use of manipulatives.     

Preservice Teachers' Beliefs and Attitude About Teaching and Learning Mathematics Through Music: An Intervention Study

This article presents exploratory research investigating the integration of music and a mathematics lesson as an intervention to promote preservice teachers' attitude and confidence and to extend their beliefs toward teaching mathematics integrated with music. Thirty students were randomly selected from 64 preservice teachers in a southern university. A 90‐minute mathematics lesson integrated with a music composition activity was taught by the first author. Pre‐ and postquestionnaires were provided to evaluate the change in preservice teachers' attitude and beliefs toward mathematics. The results demonstrated that the mathematics lesson integrated with music had a positive effect on preservice teachers' attitude and beliefs toward mathematics teaching and learning.     

Development and Validation of the Mathematics Teachers' Beliefs About English Language Learners Survey (MTBELL)

Given the increasing number of English Language Learners (ELLs) in secondary mathematics classrooms, it is imperative that mathematics teacher educators develop measures for determining how and why secondary mathematics teachers (SMTs) understand and respond instructionally to these students. This paper reports on the initial development and validation of the Mathematics Teachers' Beliefs about English Language Learners survey, an instrument that measures SMTs beliefs, attitudes, knowledge base, and instructional practices in relation to meeting the academic and language needs of ELLs. Through piloting processes, the instrument was refined for a research study through which reliability and validity were established. The five constructs identified from exploratory factor analysis illustrate perceived opportunities and barriers in meeting ELLs' academic and language needs among SMTs. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.