Middle‐School Mathematics Teachers' Beliefs in NCTM's Vision

This study examined the extent to which seventh‐ and eighth‐grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in these documents. Quantitative data were collected through the Mathematics Standards Belief Survey (MSBS), a survey specifically designed to measure teachers' overall belief in NCTM's vision as well as in certain philosophical tenets of NCTM. Of the 82 seventh‐ and eighth‐grade mathematics teachers in the identified school district of Nevada, 73 (89.0%) participated in this study. The data revealed that, among seventh‐ and eighth‐grade mathematics teachers, secondary‐certified teachers had significantly higher MSBS scores than elementary‐certified teachers. A number of other findings were made, including significant differences among mean belief scores in the philosophical tenets of NCTM.     

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.     

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 Influences of Three Interventions on Prospective Elementary Teachers' Beliefs About the Knowledge Base Needed for Teaching Mathematics

To meet the challenge to reform mathematics education, effective opportunities to learn are needed to promote prospective elementary school teachers' development of the knowledge base that supports teaching for mathematical proficiency. This article describes three professional development interventions and their influence on prospective teachers' beliefs about mathematics, how children learn mathematics, and mathematics teaching. The three interventions consisted of problem‐solving journals, structured interviews, and peer teaching that were integrated in a PreK‐6 mathematics methods course. Results of precourse and postcourse survey data are included that measured 24 prospective teachers' beliefs about the knowledge base needed to teach elementary school mathematics. Data indicated that using these interventions and other course experiences facilitated change in the prospective teachers' beliefs, with a shift toward reform‐oriented mathematics education perspectives.     

Non‐Traditional Preservice Teachers and Their Mathematics Efficacy Beliefs

In Florida, recent legislative changes have granted community colleges the ability to offer baccalaureate degrees in education, frequently to non‐traditional students. Based on information obtained from the literature covering preservice teachers' math knowledge, teachers' efficacy beliefs about math, and high‐stakes mathematics testing, a study examined a population of preservice teachers in a new Florida teacher preparation program. The research investigated relationships surrounding non‐traditional preservice teachers' characteristics such as: ages, high‐stakes math failures, lower division mathematics history, and math methods course performance, in relation to their efficacy beliefs about mathematics. Results revealed that preservice teachers' ages, lower division mathematics history, and math methods course performance, did have a significant relationship with their math efficacy beliefs, as measured by the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI); the variable of high‐stakes math failures did not. Additionally, a multiple regression model including the aforementioned variables did predict preservice teachers' MTEBI scores, but did not generalize to the greater population. The findings from this study can assist new teacher preparation programs in isolating variables that identify preservice teachers who are at risk for poor mathematical attitudes; can posit avenues for fostering positive math beliefs in preservice teachers; and can recommend further research in this area.     

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.     

A Longitudinal Study of Elementary Pre‐service Teachers' Mathematics Beliefs and Content Knowledge

This study investigated the mathematics beliefs and content knowledge of 103 elementary pre‐service teachers in a developmental teacher preparation program that included a two course mathematics methods sequence. Pre‐service teachers' pedagogical beliefs became more cognitively‐oriented during the teacher preparation program with these changes occurring during the two methods courses. Pedagogical beliefs remained stable during student teaching. The pre‐service teachers also significantly increased their personal efficacy for teaching mathematics throughout the program with these shifts occurring across both methods courses and into student teaching. Pedagogical beliefs and teaching efficacy beliefs were not related at the beginning of the program, but, in general, were positively related throughout the program. In addition, the pre‐service teachers' pedagogical beliefs were positively related to their specialized content knowledge for teaching mathematics at the end of the program.     

Gender‐Related Beliefs and Mathematics Performance of Preservice Primary Teachers

The aim of this study was to examine whether there are gender differences in mathematics achievement and in beliefs about mathematics of preservice teachers over a period of four years. Data were collected from preservice teachers (156 males and 155 females) from the Ad?yaman University Faculty of Education in Turkey. The Mathematics as a Gendered Domain instrument was used to investigate preservice teachers' beliefs about the gender differences in mathematics. The results indicated that gender had no effect on mathematics performances of the preservice primary teachers. Findings of this research show that most of the male and female preservice primary teachers do not gender‐stereotype mathematics and believe that mathematics is gender neutral, although there are gender differences on some types of items of instrument.     

The Relationship Between Teacher and Student Beliefs About Mathematics

In this study the relationship between teacher (n = 7) beliefs about mathematics, the learning and teaching of mathematics and their respective students' beliefs about mathematics (n = 158) are examined. The data were collected by means of two instruments specifically designed to measure belief systems about mathematics. Teacher scores were adjusted so that a higher score reflected beliefs in aligntnent with the National Council of Teachers of Mathematics (NCTM) Standards. Results indicated that the students of teachers whose beliefs were in alignment with the NCTM Standards had significantly different beliefs about factors that lead to success in mathematics than did other students. Specifically these students felt that working hard to solve problems and striving for understanding would lead to success. No student differences were found for subscales of ego orientation, competitiveness, interest and extrinsic factors such as neatness and cooperation. These findings suggest that this group of teachers practiced what they believed and that these practices affected what their students believed about mathematics. We suggest that using these two assessments in tandem give a clearer picture of the mathematical environment within a classroom and can be used in professional development workshops to initiate teacher reflection about classroom practices.     

Assessing Preservice Teachers' Beliefs about the Teaching and Learning of Mathematics and Science

With increased study of teachers' beliefs about science and mathematics teaching in recent years, there is a need for instruments that assess beliefs in both content areas. Moreover, early field experiences in schools and professional development efforts may influence the beliefs that preservice and in‐service teachers develop, and instruments for this purpose are limited. This article describes the development and validation of the Confidence, Commitment, Collaboration, and Student thinking in Mathematics and Science (CCCSMS) beliefs scales, a set of 10 six‐item scales. Collectively, these scales measure teachers' self‐confidence in doing and teaching science and mathematics, confidence in understanding children's thinking and building models of that thinking, commitment to teaching science and mathematics from a standards‐based perspective, and commitment to collaborating with peers. The scales represent an efficient and effective way of assessing beliefs of large groups. Although this article focuses predominantly on development of the scales, results from initial use indicate that there are positive correlations between beliefs related to mathematics and beliefs related to science, but the correlations are low enough to show that many teachers think differently about the two subjects.     

Parent Beliefs about Technology and Innovative Mathematics Instruction

Parent beliefs about roles of education, teachers, computers, and innovative mathematics instruction were examined through factor analysis. Strong relationships between parent beliefs regarding teacher and computer roles were found. The beliefs of parents about the similar roles of teachers and computers in education may impact the implementation of innovations in mathematics education and the uses of computers in education. Reciprocally, the ways computers are implemented in education may impact the beliefs parents have about the purposes of education.     

Perceptions of Mathematics and Gender

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.     

A Problem-Solving Based Mathematics Course and Elementary Teachers' Beliefs

This study examined the impact a problem-solving based mathematics content course for preservice elementary education teachers (PSTs) had on challenging the beliefs they held with respect to mathematics and themselves as doers of mathematics. Nine PSTs were interviewed to gain insight into changes that occurred to their belief systems and what aspect(s) of the course were instrumental in producing those changes. Surveys to measure how strongly PSTs subscribed to five mathematical beliefs were administered to 137 PSTs who were enrolled in the course. Significant positive changes (p < .01) were observed for four of the five beliefs. When changes were studied by achievement level, students with final grades of A or B showed statistically significant changes (p < .005) in three of the five beliefs. Students who were interviewed consistently reported increased confidence in their mathematical abilities as a result of the course.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

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.     

A Mixed‐Method Study: Assessing the BAR Model's Impact on Preservice Teachers' Efficacy Beliefs

This study took place at a mid‐sized, Midwestern university located in a mid‐sized town. The researchers developed the BAR model to teach mathematics methods both in the classroom and in the field. The preservice teachers took Enochs, Smith, and Huinker's Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) on the first and last day of class. A total of 297 responses were collected from the pre‐ and posttests, with 280 matching responses, which were then used for data analysis. Mixed methods were used to analyze qualitative and quantitative data. The researchers sought to determine if the specific teaching methods from the BAR model led to positive changes in preservice teacher efficacy beliefs. They also explored if efficacy beliefs changed as a result of field experiences. Preservice teachers' efficacy scores changed positively on every item on the MTEBI. The researchers also determined that there was an increase in preservice teachers' outputs as a result of their field experiences.     

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.     

Beliefs and Perspectives of First‐Year,Alternative Preparation,Elementary Teachers in Urban Classrooms

Results from an earlier study ( Hart, 2002 ) suggested that a group of 14 teachers participating in an alternative preparation program for elementary teachers had developed beliefs that were consistent with current thinking in mathematics education. The current study follows 8 of those teachers into their first year of teaching in an urban classroom. Qualitative data were collected from three sources: reflection logs, mathematics case discussions, and field notes made during classroom observations. This provided a triangulation of perspectives: the teachers' views of themselves, the teachers' views of others, and the university faculty member's view of them. Also, teachers completed the Standards Belief Instrument (Zollman & Mason, 1996) at the end of Phase I and at the end of Phase II. Results from the instrument and the qualitative analysis suggest that the teachers maintained a strong reform perspective in their beliefs, but they were unable to consistently implement pedagogy that was consistent with those beliefs.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.     

Change in Preservice Teachers' Beliefs: An Evaluation of a Mathematics Methods Course

This study investigated and evaluated the potential impact of an elementary mathematics methods course in promoting teacher beliefs and attitudes that are consistent with the underlying philosophy of current reform efforts in mathematics education. Using the Mathematics Beliefs Instrument (MBI; Hart, 2002 ), data from 89 preservice teachers were used to evaluate the course. Findings from the study suggest a positive relationship between participating in the mathematics methods course and change in teacher beliefs and attitudes. This study also provided additional validation of the MBI.