Beliefs and Attitudes Toward Mathematics Among Third- and Fifth-Grade Students: A Descriptive Study

A survey on attitudes toward mathematics of third- and fifth-grade students enrolled in a large urban school district was conducted in the spring of 1994 as part of a review of the mathematics program. Student responses to survey items were analyzed with respect to gender and grade level. Although girls and boys were equally likely to indicate that they like mathematics, in both Grades 3 and 5, boys were more likely than girls to report being good at mathematics. This result has often been reported for older students but has rarely been explored in younger children. Some gender and grade differences were observed in students' attitudes towards the specific strands of mathematics. Both girls and boys in Grade 5 were more likely than students in Grade 3 to believe that mathematics was relevant to their lives. Virtually all children thought that both girls and boys needed to study mathematics. No gender or grade differences in students' beliefs regarding the process of learning mathematics were observed. The results support the need for further research to identify variables that influence the development of student perceptions and attitudes toward mathematics during elementary school.     

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.     

Using Metaphors as a Tool for Examining Preservice Elementary Teachers' Beliefs About Mathematics Teaching and Learning

This study used metaphors as a tool to gain insight about preservice teachers' conceptualizations of the role of the teacher and the learner and held the view that the examination of these metaphors might provide an opportunity for teacher educators to reflectively and critically examine those beliefs. Thus, this research examined possible differences in the reflected beliefs of elementary preservice teachers as depicted in their metaphors about mathematics teaching and learning at three different points throughout their mathematics education methods courses. The results of this study indicated that elementary preservice teachers' beliefs primarily remained static throughout their mathematics methods courses despite ongoing experiences designed to challenge and extend those beliefs.     

Enriching Science and Math Through Engineering

This case study reviewed the collaborative efforts of university engineers, teacher educators, and middle school teachers to advance sixth‐ and seventh‐grade students' learning through a series of project‐based engineering activities. This two‐year project enriched regular school curricula by introducing real‐world applications of science and mathematics concepts that expanded opportunities for creativity and problem‐solving, introduced problem‐based learning, and provided after‐school programming (for girls only) led by engineering students from the local university. This engineering education initiative showed significant impact on students' (1) confidence in science and mathematics; (2) effort toward science and mathematics; (3) awareness of engineering; and (4) interest in engineering as a potential career. With regard to gender, there were no significant differences between boys' and girls' responses. The girls' confidence in their own skills and potential, however, was significantly more positive than the boys' confidence in the girls. These results gave rise to new questions regarding mentor/mentee relationships and the overall effect of “girls only” mentoring.     

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.     

Mathematics teachers’ conceptions about modelling activities and its reflection on their beliefs about mathematics

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.     

The Road to Reform: A Grounded Theory Study of Parents' and Teachers' Influence on Elementary School Science and Mathematics

Though elementary teacher educators introduce new, reform‐based strategies in science and mathematics methods courses, researchers wondered how novices negotiate reform strategies once they enter the elementary school culture. Given that the extent of parents' and veteran teachers' influence on novice teachers is largely unknown, this grounded theory study explored parents' and teachers' expectations of children's optimal science and mathematics learning in the current era of reform. Data consisted of semi‐structured, open‐ended interviews with novice teachers (n = 20), veteran teachers (n = 9), and parents (n = 28). Researchers followed three stages of coding procedures to develop a logic model connecting participants' discrete designations of the landscape, regulating phenomena, contextual orientation, and desired outcomes. This logic model helped researchers develop propositions for future research on the interactive nature of parents' and teachers' influential role in elementary science and mathematics education. Implications encourage science and mathematics teacher educators—as well as school administrators—to explicitly develop and support novice teachers' ability to initiate and sustain parent/family engagement in order to create a school climate where teachers and parents are synergistically motivated to change.     

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.     

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.     

Teachers' funds of knowledge and the teaching and learning of mathematics in multi-ethnic primary schools: Two teachers' views of linking home and school

In this paper we explore two teachers' views on the role(s) of parents, the local community and children's home lives in the learning of mathematics in primary school. We use Moll and Greenberg's concept of ‘funds of knowledge’ and apply it to the case studies of two teachers working in the UK context. Issues of teachers' professional experience, ethnicity, class and gender emerge as significant in examining similarities and differences in the teachers' beliefs, understandings and practices in the area of linking home and school. We end with a discussion of some implications for teacher education and professional development.     

Elementary teachers’ beliefs on the role of struggle in the mathematics classroom

Reform-oriented approaches to mathematics instruction view struggle as critical to learning; however, research suggests many teachers resist providing opportunities for students to struggle. Ninety-three early-years Australian elementary teachers completed a questionnaire about their understanding of the role of struggle in the mathematics classroom. Thematic analysis of data revealed that most teachers (75 %) held positive beliefs about struggle, with four overlapping themes emerging: building resilience, central to learning mathematics, developing problem solving skills and facilitating peer-to-peer learning. Many of the remaining teachers (16 %) held what constituted conditionally positive beliefs about struggle, emphasising that the level of challenge provided needed to be suitable for a given student and adequately scaffolded. The overwhelmingly positive characterisation of student struggle was surprising given prior research but consistent with our contention that an emphasis on growth mindsets in educational contexts over the last decade has seen a shift in teachers’ willingness to embrace struggle.     

Prospective Elementary Teachers' Perceptions of Gender Differences in Children's Attitudes Toward Mathematics

Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these expectations exist for both prospective teachers in a traditional undergraduate degree program and prospective teachers in an alternative licensure graduate degree program. We also found that these expectations do change with the completion of a mathematics methods course and classroom experiences.     

Factors Influencing Elementary Teachers' Positioning of African American Girls as Science and Mathematics Learners

Despite recent progress toward gender equity in science and mathematics education, the underachievement of low‐income African American girls remains a challenge when compared with their white counterparts. Furthermore, the causes of this persistent underachievement have not been explored thoroughly. We have initiated a three‐year longitudinal study of how African American girls position themselves in relation to science and mathematics learning from fifth to seventh grade, including the impact, if any, of the positioning of teachers, counselors, and parents on this process. In this article, we share findings examining science and mathematics teachers' actions and perceptions and their positioning of African American girls. This qualitative study used an interpretive design with multiple data sources including classroom observations, interviews, and field notes. Findings reveal that school‐wide policies and teachers' autonomous decisions impact the regularity of science and mathematics instruction, and that teachers do not always conceptualize the girls as science and mathematics achievers, positioning them in negative ways.     

Teachers attending to student reasoning: Do beliefs matter?

We present the results of a quasi-experimental study of pre-service elementary teachers' learning to recognize students' mathematical reasoning from classroom videos. Researchers examined the nature of participants’ beliefs regarding mathematics education. We found that pre-service elementary teachers whose beliefs were consistent with NCTM Process Standards (NCTM, 2000), or that transitioned in the direction of consistency with the Standards, regarding the teaching and learning of mathematics, were more successful in recognizing students' reasoning than those whose beliefs were generally inconsistent. Predictive Analytics and Generalized Linear Regression modeling were used to quantify the magnitude of experimental pre-service teachers’ reasoning growth and combined pre/post study assessment reasoning success in contrast to that of the comparison groups. The resulting model explained nearly 90% of the variability in success on the reasoning assessment, showing that beliefs do indeed matter for recognition of reasoning.     

Australian teachers’ views of effective mathematics teaching and learning

Thirteen Australian teachers who had been nominated by their professional mathematics teachers’ associations as excellent teachers of elementary school mathematics were interviewed on their beliefs about mathematics, mathematics learning and mathematics teaching. In particular, they were asked to discuss the characteristics of effective teachers of mathematics and excellent mathematics lessons. In spite of their differences in location, experience and teacher education, the teachers displayed a lot of consistency in their responses and in their lists of characteristics. While this group of teachers cannot be claimed to be representative of Australian teachers, they have provided a snapshot of what is regarded as effectiveness in mathematics education in Australian elementary schools.     

Applications of symmetry to problem solving

Symmetry is an important mathematical concept which plays an extremely important role as a problem-solving technique. Nevertheless, symmetry is rarely used in secondary school in solving mathematical problems. Several investigations demonstrate that secondary school mathematics teachers are not aware enough of the importance of this elegant problem-solving tool. In this paper we present examples of problems from several branches of mathematics that can be solved using different types of symmetry. Teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems are discussed.     

Mother and Child Emotions during Mathematics Homework

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the emotions expressed by U.S. mothers and their 11-year-old children while solving pre-algebra tasks in the home. The most notable positive emotions displayed by mothers and children included positive interest, affection, joy, and pride, whereas the most notable negative emotions expressed included tension, frustration, and distress. Reflecting the social aspects of doing homework together, mothers' and children's emotions were highly correlated. Independent of pre-existing differences in knowledge, children's emotions were associated with their performance on a mathematics post-test: tension was linked to poorer performance while positive interest, humor, and pride were linked to better performance. We found no evidence of gender differences in the emotions while working the tasks, although boys responded with more tension following an incorrect solution than did girls.     

Japanese and American teachers' evaluations of mathematics lessons: A new technique for exploring beliefs

In our study, we use a novel technique to explore the beliefs of Japanese and American elementary school teachers. Four American and four Japanese teachers watched a mathematics lesson—videotaped in either Nagano, Japan or Chicago, Illinois—and commented on the lesson's strengths and weaknesses. The major pedagogical issues that differentiated the teachers' comments were: what students should do during a lesson, how instructors should use language, how instructors should pace lessons and address ability differences, and how instructional materials should be used. The specific beliefs of the American and Japanese teachers in this study mapped easily onto common instructional practices in elementary school mathematics classes in the United States and Japan. We conclude that, at least for the teachers in this sample, beliefs are linked to practices and they may help to tie teachers to their culturally preferred method of mathematics instruction.