Attitude toward mathematics among the students at Nazarbayev University Foundation Year Programme

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73 Mathematical-Physics (MP), 22 Biology-Chemistry (BC) and 13 International Relations-Economics (IRE) students. Generally, they have a positive attitude toward mathematics, with the score mean and standard deviation are 3.999 and 0.531 out of five, respectively. We confirm a hypothesis on a positive correlation between previous high achievement in mathematics and favorable attitude toward it. The correlation value is r = 0.300, its effect size is medium and it is extremely significant (p-value = 0.0008 < 0.001). There is no significant difference between male and female students in terms of their attitude toward mathematics (t = 0.6804, p-value = 002489 > 0.05). There is a very significant difference between students who specialize in IRE and MP in terms of their attitude toward mathematics (F(2, 105) = 5.6848, p-value = 0.0045 < 0.01).     

Attitude towards mathematics: a bridge between beliefs and emotions

Recent research in the field of affect has highlighted the need to theoretically clarify constructs such as beliefs, emotions and attitudes, and to better investigate the relationships among them. As regards the definition of attitude, in a previous study we proposed a characterization of attitude towards mathematics grounded in students’ experiences, investigating how students express their own relationship with mathematics. The data collected suggest a three-dimensional model of attitude towards mathematics that includes students’ emotional disposition, their vision of mathematics, and their perceived competence. In this paper, we discuss the relationship between beliefs and emotions, investigating the interplay among the three dimensions in the proposed model of attitude, as emerging in the students’ essays.     

Increasing Student Access to Qualified Science and Mathematics Teachers Through an Urban School‐University Partnership

Urban schools across the United States face a pervasive problem in their science and mathematics programs — a disproportionate number of the teachers in these classrooms are not certified, thus making them underqualified to teach these subject areas. Furthermore, urban schools deal with teacher shortages and attrition in these critical areas. The situation was found to be particularly severe in the Detroit Public School District. In response, Wayne State University and Detroit Public Schools embarked on a school‐university partnership program to prepare teachers in science and mathematics through an alternative pathway to teacher certification program. This partnership program has proven to be successful in recruiting, preparing, and retaining a significant number of qualified minority science and mathematics teachers to serve the students in Detroit schools.     

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.     

Autobiographical Stories from Preservice Elementary Mathematics and Science Students: Implications for K‐16 Teaching

Autobiographies are an effective tool for assessing students' predispositions toward science and mathematics content and identifying any changes in attitude over time. The purpose of this study was to analyze autobiographies of students enrolled in elementary education methods classes to determine the kinds of K‐12 and college content course experiences affecting their perceptions of mathematics or science. Special attention was given to recollections of events that had positive or negative effects on students' interest in and attitudes toward science or mathematics, their confidence in these areas, and transitions in attitude throughout their experiences. Ninety‐eight autobiographies were collected and analyzed, revealing attitudes that were generally more positive than expected, five major emergent themes, and important information about when and why transitions in attitudes occurred.     

The near-peer mathematical mentoring cycle: studying the impact of outreach on high school students’ attitudes toward mathematics

College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to promote higher education in math and science. In this study college students gave dynamic mathematics outreach presentations, MathShows, to minority and low-income high school students in a mid-sized public school district on the U.S. border with Mexico. The study investigated the impacts of this sort of outreach work on high school students’ attitudes towards mathematics using a mathematics attitudes survey. Results, obtained from N = 306 participants, showed statistically significant improvements in almost all components of mathematical attitudes, with less of an effect on the component of self-confidence in doing mathematics. Differences in impacts by specific student subgroups are all discussed.     

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.     

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.     

Non-Euclidean geometry and Weierstrassian mathematics: The background to Killing's work on Lie algebras

A discussion of the manner in which discoveries in non-Euclidean geometry, combined with the Weierstrassian attitude towards mathematics, led Wilhelm Killing, one of Weierstrass' students, to initiate a research program on foundations of geometry that led to his groundbreaking investigations on the structure of Lie algebras.     

Exploring the Responses of Underrepresented Students in Science to an Elementary Classroom Outreach Program

This paper describes a subset of results from a large‐scale two‐year independent evaluation study conducted with the Scientists in School (SiS) outreach program and two large school boards in Ontario, Canada. Specifically, it explores the responses of elementary students (n= 811) from typically underrepresented groups in science (English language learners [ELL], girls, and students at low‐achieving schools) to the SiS outreach program. It explores responses related to enjoyment, interest, perceptions of role modeling, and future career choice in science. Compared to other students, findings suggest that girls and students from low‐achieving schools found the program more enjoyable and reported that it provided positive science role models. Students at schools with high ELL populations also reported higher levels of enjoyment and reported that the program helped get them excited about science.     

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.     

Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

A comparative investigation of the presence of psychological conditions in high achieving eighth graders from TIMSS 2007 Mathematics

This study is a second analysis of Trends in International Mathematics and Science Study (TIMSS) 2007 background questionnaires to investigate high achieving eighth-grade students’ possession of three elements of Krutetskii’s (The Psychology of Mathematical Abilities in Schoolchildren, The University of Chicago, 1976) psychological conditions. Analyses were made between high achieving eighth graders and their lower achieving counterparts, and between Korean high achievers and their high achieving peers across ten high performing TIMSS participating countries. After reviewing 44,643 students across selected countries, we conclude that a larger percentage of students with mathematical talent demonstrate positive attitudes toward mathematics, value mathematics, and have self-confidence in their ability to learn mathematics than their peers without high achievement in mathematics. However, a larger portion of high achieving Korean students displayed low self-confidence and valued mathematics less than their peers from other high performing countries. Findings from this study will provide insight into some educational issues in science, technology, engineering and mathematics education.     

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.     

Relationship Between Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

The purpose of this study was to investigate the change in teacher efficacy beliefs about mathematics and science teaching during participation in methods courses and student teaching, as well as the relationship between mathematics and science teaching efficacy. Data revealed that, as science and mathematics teacher education in a methods course progressed, science and mathematics teaching efficacy significantly increased. This effect appeared to decrease slightly by the end of student teaching. Analysis of data indicated a significant difference in both the personal mathematics and personal science teaching efficacy scores, as well as mathematics outcome expectancy. Additionally, preservice teachers' personal mathematics and science teaching efficacies were directly related, as were their mathematics and science teaching outcome expectancies.     

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.     

Scientific World Building on the Edge of Chaos: High School Students' Beliefs About Mathematics and Science

This study investigated high school students' beliefs about mathematics and science during a four week summer residential mathematics and science program. Beliefs about mathematical and scientific truths, the value and importance of mathematics and science inquiry, gender equity and ability with respect to pursuit of mathematics and science careers, the relationship between mathematics and technology, and the role of science in society were examined. Habermasian ways of knowing were used to categorize student beliefs and determine student world views. Implications of this study include suggested changes in the organizational dynamics of schooling to better prepare our students for surviving in the complexity of the 21st century and reducing dissonance between the “classical” educational viewpoints and the “chaotic” world.     

The Effect of a Horseshoe Crab Citizen Science Program on Middle School Student Science Performance and STEM Career Motivation

The purpose of the present quasi‐experimental study was to examine the impact of a horseshoe crab citizen science program on student achievement and science, technology, engineering, and mathematics (STEM) career motivation with 86 (n = 86) eighth‐grade students. The treatment group conducted fieldwork with naturalists and collected data for a professional biologist studying horseshoe crab speciation and a mock survey. The comparison group studied curriculum related to horseshoe crabs in the science classroom. A series of measures related to self‐efficacy, interest, outcome expectations, choice goals, and content knowledge were given to participants before and after the intervention. It was hypothesized that students would report higher motivational beliefs regarding science and show higher levels of achievement following the intervention than the comparison group. Support was shown for most of the hypotheses. In addition, path analyses indicated that students' motivational beliefs influence content knowledge and outcome expectations, which in turn affect their career goals. These results have implications for incorporating authentic fieldwork within a formal school structure as an effective method for promoting student achievement and STEM career motivation.