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.     

Students' attitude towards computer algebra systems (CAS) and their choice of using CAS in problem-solving

We explore students choice of using computer algebra systems (CAS) in problem-solving relative to their self-reported attitude towards learning mathematics with CAS. Our research design is a case study of nine Norwegian upper-secondary mathematics students with a wide range of attitude towards CAS. Our findings on routine problems indicate that (1) students use CAS whenever students perceive the problem as time-consuming regardless of their attitude towards CAS, and (2) students attitude affects their use of CAS whenever students perceive the problem as non-time-consuming. Norway, among other countries, has implemented CAS as an essential digital resource towards learning mathematics in upper-secondary school. Our discussion focuses on the implications of our findings have on local mathematics educators and national policy-makers.     

Dimensions of students’ views of themselves as learners of mathematics

Students’ views of themselves as learners of mathematics are a decisive parameter for their engagement and success in school. We are interested in students’ experiences with mathematics encompassing cognitive, emotional and motivational aspects. In particular, we focus on capturing the structural properties of affect related to mathematics. Participants in our study were 1,436 randomized chosen students of secondary schools from overall Finland. In the Finnish upper secondary school, there are two different syllabi for mathematics: the general and the advanced one. Schools were invited to organize the survey by one of their year 2 general syllabus courses and one of their year 2 advanced syllabus courses in grade 11. By means of factor analysis, we obtained seven dimensions in which students’ hold beliefs and emotions about mathematics partly intertwined with their motivational orientations. These dimensions are described by reliable scales, which allow outlining an average image of Finnish students’ views of themselves as learners of mathematics. Moreover, we analyzed relations between the seven dimensions and what kind of structure they generate. Thereby, a core of three high correlating dimensions could be identified, yielding different accentuations with regard to course choice.     

Gender, technology and attitude towards mathematics: a comparative longitudinal study with Mexican students

In this paper the results of a comparative longitudinal study investigating changes in girls’ and boys’ attitudes towards mathematics, and self-confidence in mathematics are presented. A 5-point Likert scale, AMMEC, was used to measure attitudes towards mathematics (AM), computer-based mathematics (AMC), and self-confidence in mathematics (CM). A total of 430 students using technology for mathematics and 109 students not using it were monitored for 3 years. At the beginning of the study, the participants were aged about 13 years. The statistical analyses of the data showed few gender differences in the way students’ attitudes and self-confidence changed over the 3 years. Significant gender differences favouring boys were found in attitudes towards mathematics in grades 8 and 9 for the group using technology. For the group using technology, significantly more boys than girls got high scores in attitudes towards computer-based mathematics in grade 7. Significantly, more girls using technology than girls not using it got high scores in grade 8. The use of technology did not have a positive impact on students’ self-confidence. Regardless of whether they used computers or not, from grades 7 to 9, there was a decrease in the self-confidence in mathematics of both boys and girls. To enrich these results and detect possible gender differences in the way attitudes were constructed, 12 girls and 13 boys were interviewed at the end of the study. The analysis of the arguments they presented to explain and justify their attitudes towards mathematics, computer-based mathematics, and their self-confidence in working in mathematics provided evidence of important gender differences in the ways in which boys and girls construct their attitude, indicating how their constructions reflect the gender stereotypes within Mexican society.     

Parents’ Attitudes Toward Mathematics and the Influence on Their Students’ Attitudes toward Mathematics: A Quantitative Study

The purpose of this study was to investigate parents’ attitudes toward mathematics, their students' attitude toward mathematics, and the influence of the parents’ attitude on the students' attitude toward mathematics. Data analyses revealed statistically significant positive correlations between parents’ and students’ attitudes toward mathematics. Additionally, parents’ mathematics attitude significantly predicted students’ attitudes toward mathematics (n=146). By understanding the influence of parents’ attitudes on students’ attitudes toward mathematics, school efforts can be geared toward fostering favorable attitudes toward mathematics among parents.     

Mathematical paradoxes as pathways into beliefs and polymathy: an experimental inquiry

This paper addresses the role of mathematical paradoxes in fostering polymathy among pre-service elementary teachers. The results of a 3-year study with 120 students are reported with implications for mathematics pre-service education as well as interdisciplinary education. A hermeneutic-phenomenological approach is used to recreate the emotions, voices and struggles of students as they tried to unravel Russell’s paradox presented in its linguistic form. Based on the gathered evidence some arguments are made for the benefits and dangers in the use of paradoxes in mathematics pre-service education to foster polymathy, change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.     

Mathematical literacy in undergraduates: role of gender,emotional intelligence and emotional self-efficacy

This empirical study explores the roles that Emotional Intelligence (EI) and Emotional Self-Efficacy (ESE) play in undergraduates’ mathematical literacy, and the influence of EI and ESE on students’ attitudes towards and beliefs about mathematics. A convenience sample of 93 female and 82 male first-year undergraduates completed a test of mathematical literacy, followed by an online survey designed to measure the students’ EI, ESE and factors associated with mathematical literacy. Analysis of the data revealed significant gender differences. Males attained a higher mean test score than females and out-performed the females on most of the individual questions and the associated mathematical tasks. Overall, males expressed greater confidence in their mathematical skills, although both males’ and females’ confidence outweighed their actual mathematical proficiency. Correlation analyses revealed that males and females attaining higher mathematical literacy test scores were more confident and persistent, exhibited lower levels of mathematics anxiety and possessed higher mathematics qualifications. Correlation analyses also revealed that in male students, aspects of ESE were associated with beliefs concerning the learning of mathematics (i.e. that intelligence is malleable and that persistence can facilitate success), but not with confidence or actual performance. Both EI and ESE play a greater role with regard to test performance and attitudes/beliefs regarding mathematics amongst female undergraduates; higher EI and ESE scores were associated with higher test scores, while females exhibiting higher levels of ESE were also more confident and less anxious about mathematics, believed intelligence to be malleable, were more persistent and were learning goal oriented. Moderated regression analyses confirmed mathematics anxiety as a negative predictor of test performance in males and females, but also revealed that in females EI and ESE moderate the effects of anxiety on test performance, with the relationship between anxiety and test performance linked more to emotional management (EI) than to ESE.     

Pupils’ attitudes towards mathematics: a comparative study of Norwegian and English secondary students

Comparing English and Norwegian pupils’ attitude towards mathematics, in this article I develop a deeper understanding of the factors that may shape and influence ‘pupil attitude towards mathematics’, and argue for it as a socio-cultural construct embedded in and shaped by students’ environment and context in which they learn mathematics. The theoretical framework leans on work by Zan and Di Martino (The Montana Mathematics Enthusiast, Monograph 3, pp. 157–168, 2007) to elicit Norwegian and English pupils’ attitude of mathematics as they experience it in their respective environments. Whilst there were differences which could be seen to be accounted for by differently ‘figured’ environments, there are also many similarities. It was interesting to see that, albeit based on a small statistical sample, in both countries students had a positive attitude towards mathematics in year 7/8, which dropped in year 9, and increased again in years 10/11. This result could be explained and compared with other larger scale studies (e.g. Hodgen et al. in Proceedings of the British Society for Research into Learning Mathematics. 29(3), 2009). The analysis of pupils’ qualitative comments (and classroom observations) suggested seven factors that appeared to influence pupil attitude most, and these had ‘superficial’ commonalities, but the perceptions that appeared to underpin these mentions were different, and could be linked to the environments of learning mathematics in their respective classrooms. In summary, it is claimed that it is not enough to identify the factors that may shape and influence pupil attitude, but more importantly, to study how these are ‘lived’ by pupils, what meanings are made in classrooms and in different contexts, and how the factors interrelate and can be understood.     

Puzzle-based learning in engineering mathematics: students’ attitudes

The article reports on the results of two case studies on the impact of the regular use of puzzles as a pedagogical strategy in the teaching and learning of engineering mathematics. The intention of using puzzles is to engage students’ emotions, creativity and curiosity and also to enhance their generic thinking skills and lateral thinking ‘outside the box’. Students’ attitudes towards this pedagogical strategy are evaluated via short questionnaires with two groups of university students taking a second-year engineering mathematics course. Students’ responses to the questionnaire are presented and analyzed in the paper.     

The impact of instructor pedagogy on college calculus students’ attitude toward mathematics

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students’ attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students’ attitudes toward mathematics during a ‘mainstream’ calculus course while controlling for student backgrounds. The attitude measure combines students’ self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted ‘good teaching’ practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational ‘technology’ (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students’ attitudes towards mathematics. (3) ‘Ambitious teaching’ (e.g. group work, word problems, ‘flipped’ reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional ‘good teaching’ practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics.     

Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics

Beliefs constitute a central part of a person’s professional competences as beliefs are crucial to the perception of situations and as they influence our choice of actions. The present article focuses on epistemological beliefs about the nature of mathematics among future teachers and their educators at university and post-university teacher-training institutions in Germany. The data reported are part of a larger sample originating from the MT21 study [supported by the National Science Foundation through a grant to W. S. Schmidt and M. T. Tatto (REC-0231886). MT21 started in 2003] which explores and compares mathematics teacher education in Bulgaria, Germany, Mexico, South Korea, Taiwan, and the United States. In this article, we examine the structure and level of beliefs concerning the nature of mathematics for teacher education students in Germany both at the beginning (n = 368) and the end of their education (n = 286) as well as their educators (n = 77) in three academic disciplines (mathematics, mathematics pedagogy and general pedagogy). In the first part of the article, the literature on epistemological beliefs and their structure will be reviewed. In the empirical part, analyses on the level and the structure of beliefs for our samples and subsamples will be presented. Relations between educators’ and students’ beliefs will be explored.     

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.     

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.     

Pre-service science teachers’ perceptions of mathematics courses in a science teacher education programme1

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics.     

Post-primary students’ images of mathematics: findings from a survey of Irish ordinary level mathematics students

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for ‘image of mathematics’ was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students’ images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.     

Perceived parental influence and students' dispositions to study mathematically-demanding courses in Higher Education

We explore the influence of family on adolescent students' mathematical habitus by investigating the association between students' perceptions of parental influence and their dispositions towards mathematics. A construct measuring ‘perceived parental influence’ was validated using Rasch methodology on data from 563 Cypriot students on ‘core’ and ‘advanced’ mathematics pre-university courses, and was then used to predict students' dispositions towards future study of mathematically-demanding courses at university. In most of the regression models, perceived parental influence was not associated significantly with students' dispositions towards mathematics, when other variables were included in the models. However, further statistical analysis showed that perceived parental influence is mediated by (i) the mathematics course students are studying and (ii) their mathematical inclination. We suggest that family influences on students' dispositions are significantly accounted for by students' prior choice of mathematics course and the family's inculcation of their mathematical inclination; these are important factors influencing university choices.     

Preparing Pre‐Service Teachers to Teach Mathematics in Inclusive Classrooms: A Three‐Year Case Study

Federal and state regulations mandating inclusion of students with disabilities in general education classes have made it essential to create pathways for pre‐service teachers to develop skills to teach content to diverse groups of students. The study uses a framework suggested by the relationship between teacher attitude and teacher behavior ( Fullan, 1982 ), teacher beliefs and practice, and self‐efficacy and behavioral change ( Bandura, 1977 ). The purpose of the study was to examine changes, if any, in three cohorts of general education teacher candidates' (n=13, n=8, n=5) attitudes toward teaching mathematics to students with disabilities after participating in focused instructional experiences which provided both information and vicarious positive teaching activities in special education. Data collected included pretest and posttest scores for each of the three cohorts and journal entries. Little or no change in attitude towards students with disabilities and mathematics, and efficacy to teach students with disabilities was observed for the year one and year two cohorts. In the third year the modules were combined with a structured field experience. The data collected from the third year cohort suggested a positive trend in attitude as measured by the survey data and field experience journal data. Future study with larger samples is needed.     

Impacting the Science Attitudes of Minority High School Youth

A study involving urban, minority high school students in a supplemental education program was conducted during 1989 to test the null hypothesis that no relationship exists between exposure to program activities and changes in mathematics performance or attitude towards science. The treatment activities integrated science, with language arts, mathematics, computers and counseling and enabled students to discuss matters of concern and the relationship of these concerns to their academic work and to future success in careers based in science and mathematics. Mathematics performance data were analyzed using ANOVA (premath X group, postmath X group), and t-test/pairs (premath vs. postmath). Pre- and postreatment data on attitude towards science were rank ordered, paired and analyzed using the Wilcoxin Matched-Pairs Signed Ranks Test. The findings reveal a significantly positive treatment effect. In spite of the caution suggested by the limited sample, exposure to the treatment has resulted in an increased positive effect, not only upon attitude towards science, but also upon mathematics performance.     

Enhancing elementary-school mathematics teachers' efficacy beliefs: a qualitative action research

Individuals and societies that can use mathematics effectively in this period of rapid changes will have a voice on increasing the opportunities and potentials which can shape their future. This has brought affective characteristics, such as self-efficacy, that affect mathematics achievement into focus of the research. Teacher efficacy refers to the extent to which a teacher feels capable to help students learn, influence students’ performance and commitment, and thus plays a crucial role in developing the student in all aspects. In this study, we used two sources of efficacy beliefs, mastery experiences and physiological and emotional states, in an interesting and challenging seven month workshop, as tools to foster teacher efficacy for six elementary-school teachers who were frustrated and wanted to leave their job. Our aim was to study the nature of these teachers’ efficacy in order to change it. In this qualitative action research, we used open interviews, non-participant observations and field notes. Results show that these teachers became efficacious, their students’ achievements and motivation were enhanced, and the school climate was changed. Qualitative inquiry of this construct sheds light on efficacy beliefs of mathematics teachers. Nurturing teacher efficacy has borne much fruit in the field of mathematics in school.     

A metacognitive intervention in mathematics at university level

The paper reports the main results of an instructional study. The study was aimed at improving the performance in mathematics of a group of university students of biology who repeatedly failed the final examination of a compulsory course in mathematics. The main difficulties of these students seemed to be metacognitive and affective in nature. The training therefore worked on metacognitive and affective features: knowledge about cognition, monitoring, beliefs, emotions and attitudes. The intervention was successful: at the end of the course all students passed the examination that they had failed so often. The results also suggest that it may be possible (and necessary) to ‘teach learning to learn’ mathematics.