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.     

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.     

A quantitative study of the effects of informal mathematics activities on the beliefs of preservice elementary school teachers

This study sought to determine the relationship between participation in informal mathematics activities and the formal-to-informal beliefs of university teacher candidates in elementary education. Three classes of preservice teachers participated in the study through their enrollment in a content mathematics course for elementary education majors. Four informal mathematics activities were employed as part of the course requirements. Before and after formal-to-informal beliefs about mathematics and mathematics instruction were measured using a Likert-scale beliefs assessment instrument used by Collier (J Res Math Educ 3(3):155?C163, 1972) and Seaman et al. (School Sci Math 105(4):197?C210, 2005). Changes in beliefs about mathematics and mathematics instruction were compared to a control group. Student reflection upon personal experience derived from participation in the activities was analyzed for formal and informal belief statements.     

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.     

An Investigation of Relationships between Seventh-Grade Students' Beliefs and Their Participation during Mathematics Discussions in Two Classrooms

As mathematics teachers attempt to promote classroom discourse that emphasizes reasoning about mathematical concepts and supports students' development of mathematical autonomy, not all students will participate similarly. For the purposes of this research report, I examined how 15 seventh-grade students participated during whole-class discussions in two mathematics classrooms. Additionally, I interpreted the nature of students' participation in relation to their beliefs about participating in whole-class discussions, extending results reported previously (Jansen, 2006) about a wider range of students' beliefs and goals in discussion-oriented mathematics classrooms. Students who believed mathematics discussions were threatening avoided talking about mathematics conceptually across both classrooms, yet these students participated by talking about mathematics procedurally. In addition, students' beliefs about appropriate behavior during mathematics class appeared to constrain whether they critiqued solutions of their classmates in both classrooms. Results suggest that coordinating analyses of students' beliefs and participation, particularly focusing on students who participate outside of typical interaction patterns in a classroom, can provide insights for engaging more students in mathematics classroom discussions.     

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.     

Changes in Preservice Teachers' Attitudes and Beliefs: The Net Impact of Two Mathematics Education Units and Intervening Experiences

Preservice teachers in a bachelor of education (Primary and ECE) program were surveyed about their beliefs and attitudes toward mathematics and its teaching and learning, at the beginning of their first mathematics curriculum unit and again at the end of their second mathematics education unit, approximately 18 months later. Significant differences were found for several items. However, in comparison to previously noted changes in the beliefs of similar cohorts from the beginning to end of a single unit, the changes were relatively small. Aspects of the course that students considered valuable and which may have contributed to the changes are also reported.     

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.     

Impacting prospective teachers’ beliefs about mathematics

This study investigated: (1) the changes in the beliefs about mathematics held by 25 prospective elementary teachers as they went through a university mathematics course that aimed, among other things, to promote a problem-solving view about mathematics; and (2) the possible factors that accounted for the observed changes. The course incorporated specific features that prior research suggested reflect successful mechanisms for belief change (e.g., cognitive conflict). The data included students’ reflections, and responses to prompts and interview questions. Analysis of the data revealed the following major trends: (1) a movement towards a problem-solving view from the more traditional Platonist and instrumentalist views; and (2) no change in students’ initial views. Activities creating cognitive conflict, as well as the implementation of instruction valuing group collaboration and explanations, appear to have played important roles in the process of belief change. The findings have implications for research on teacher beliefs and teacher education.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

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.     

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.     

Mathematics and molecules: Exploring connections via programming

This article examines the self-directed activity of two students who learned about molecular structure by writing computer programs. The students wrote programs to display the solution of a mathematics problem and then extended their programs to represent several classes of organic molecules. In the course of this activity, the students learned the standard system for naming organic molecules while maintaining a sense of ownership of their project. We discuss ways to enhance the mathematical connections to chemistry education.     

Issues and Challenges for Middle School Mathematics Teachers in Inclusion Classrooms

The purpose of this qualitative study was to investigate typical middle school general education mathematics teachers' beliefs and knowledge of students with learning disabilities and inclusive instruction and to gain an understanding of the process of inclusion as it is implemented in middle school classrooms. In‐depth interviews, surveys, and classroom observations were conducted with seven teachers. The constant comparative method was used to analyze all interview and observation data. The findings reveal that even teachers who believe that inclusion is being successfully implemented are unclear about their responsibilities towards included students and the learning characteristics and specific mathematics teaching approaches that would be effective. The general educators feel that they were grossly under‐prepared during preservice and inservice for the realities of inclusion teaching. The study provides insights that can be used to enhance preservice and inservice programs for teachers and underscores the necessity for building teamwork and collaboration among general and special education middle school teachers.     

Examining Preservice Teacher Belief Changes in the Context of Coordinated Mathematics Methods Coursework and Classroom Experiences

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30‐minute peer‐teaching sessions, while students in the other group worked for 45 minutes weekly with elementary students in public school classrooms where traditional pedagogy was normally practiced. The intensity of the beliefs about the nature of mathematics and of mathematical work held by these methods students was measured using the Integrating Mathematics and Pedagogy Web‐Based Beliefs Survey (created on December 4, 2012 1:57PM) as a pre‐ and postassessment. While both groups saw significant change in belief intensity across measurement occasions favoring a reform perspective, a significantly greater change was experienced by the group who applied methods in classrooms, despite the traditional practice that usually occurred in them. The authors hypothesize this greater change resulted from the benefits associated with working with children and from the instructor support that may have tended to nullify the effects of teaching in a classroom where traditional pedagogy was the norm.     

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.     

Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

Gender Equity in Mathematics: Beliefs of Students,Parents, and Teachers

The attitudes about mathematics held by girls and boys participating in a regional mathematics contest, their parents, teachers, and mathematics coaches were investigated. Quantitative data regarding mathematics as a male domain, perception of importance of mathematics, confidence in learning mathematics, effectance motivation, and usefulness of mathematics were obtained. It was found that the traditional gender‐based differences in the beliefs regarding mathematics persist even in these mathematically talented students. Furthermore, parents' responses to the questions regarding the role of mathematics revealed that mothers, more than fathers, focused on the computational aspects of mathematics, while fathers more than mothers mentioned the role of mathematics in science or as a language. Boys, fathers, and certain mathematics teachers admitted to a low level of gender stereotyping, as evidenced by their scores on the Mathematics as a Male Domain subscale. However, the girls, mothers, and mathematics coaches did not endorse this stereotyping. Unsolicited responses of girls and mothers, in fact, emphatically denied that gender stereotyping exists. These findings are discussed in terms of the need to resolve the essential conflicts between students', parents', and teachers' deeply held beliefs regarding the nature of mathematics, gender differences in mathematical abilities, and the desire for equity within mathematics education.