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.     

Factors affecting student success in a first-year mathematics course: a South African experience

In spite of sustained efforts tertiary institutions implement to try and improve student academic performance, the number of students succeeding in first-year mathematics courses remains disturbingly low. For most students, the gap between their mathematical capability and the competencies they are expected and need to develop to function effectively in these courses persists even after course instruction. In this study, an instrument for identifying and examining factors affecting student performance and success in a first-year Mathematics university course was developed and administered to 86 students. The overall Cronbach's Alpha coefficient for the questionnaire was found to be 0.916. Having identified variables from prior research known to affect student performance, factor analysis was used to identify variables exhibiting the greatest impact on student performance. The variables included prior academic knowledge, workload, student approaches to learning, assessment, student support teaching quality, methods and resources. From the analysis, students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, followed by the matriculation examination score. The findings are discussed and strategies that can be used to improve teaching and contribute to student success in a first-year mathematics course in a South African context are presented.     

‘It takes me longer,but I understand better’ – student feedback on structured derivations

In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach increases the clarity of solutions and facilitates debugging of proofs. It also has potential to increase students' self-perceived level of understanding. Our findings indicate that the main drawbacks experienced by the students are related to time and length. Nevertheless, the overall feedback on the approach was found to be positive, thus encouraging further use of structured derivations in mathematics education.     

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.     

Mathematics identity and achievement among Black students

Employing data from the National Center of Educational Statistics' High School Longitudinal Study and utilizing critical race theory and intersectionality as theoretical frameworks, this article interrogates the relationship between mathematics identity and math success for a nationwide sample of Black secondary school students. More specifically, hierarchical regression modeling is employed to examine the relative impact of math identity, demographic variables, and school/parent social capital variables on the math grade point averages of this sample. The article ends with a discussion of specific steps for teaching mathematics that put the identity of those from traditionally marginalized communities at the center of mathematics instruction. Thus making experiences, histories, culture, and abilities essential elements of students' learning, that are to be supported and built upon.     

Rural teacher leadership in science and mathematics

This study adds to our understanding of science and mathematics teacher leadership in rural schools. Through In Vivo and Concept coding of teacher interviews, we investigated 20 secondary science and mathematics teachers' perceptions of rural teacher leadership during their participation in a three-year professional development program. As the teachers developed as teacher leaders, they broadened their focus from improving their own students' learning to sharing new knowledge learned through the program with other teachers both informally and formally. We compared our program components to the Teacher Leader Model Standards and added an emphasis on the importance of disciplinary content knowledge. We also identified patterns in science and mathematics teacher leadership that are contextually connected to teachers' instruction in rural high poverty schools. Rural teacher leadership included the importance of building strong teacher–student relationships, providing new academic opportunities for students, encouraging students' success, and building community connections.     

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.     

Investigating the association between students' strategy use and mathematics achievement

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm, (b) invented, (c) mixed, and (d) unclassified. We used two-level hierarchical linear regression to investigate the association between students' strategy use and their performance on a standardized test in mathematics. Results indicated that students in the mixed strategy groups had significantly higher mathematics achievement than those in the standard algorithm and the unclassified groups.     

The relationship between mathematicians’ pedagogical goals,orientations, and common teaching practices in advanced mathematics

Despite mathematics educators’ research into more effective modes of teaching, lecture is still the dominant mode of instruction in undergraduate mathematics courses. Surveys suggest this is because most mathematicians believe this is the best way to teach. This paper answers a call by mathematics education researchers to explore mathematicians’ needs and goals concerning teaching. We interviewed eight mathematicians about findings in the mathematics education research literature concerning common pedagogical practices of instructors of advanced mathematics classes: “chalk talk,” the presentation of formal and informal content, and teacher questioning. We then analyzed the responses for resources, orientations, and goals that might influence the participants to engage in these practices. We describe how participants believed common lecturing practices allowed them to achieve their goals and aligned with their orientations. We discuss these findings in depth and consider what implications they may have for researchers that aim to change mathematicians’ teaching practices.     

Searching and exploring properties of geometric configurations using dynamic software

The decline in enrolments and interest in advanced mathematics studies is of growing concern internationally. Previous research suggests that a range of factors can influence students' academic decisions. The focus of the paper is on one of these potential sources of influence— students' perceptions of the tertiary mathematics learning environment. Data from two large-scale surveys (N = 1883) and from a smaller number of interviews (N = 71) with students enrolled in tertiary mathematics courses at five Australian universities are presented and discussed. Collectively, the survey results and the interview data reveal considerable variations in the quality of the teaching and student support available in different mathematics departments. Students' comments were constructive and offered valuable ideas for improving the existing situation, retaining current students and attracting others to mathematics.     

Trends in basic mathematical competencies of beginning undergraduates in Ireland, 2003–2013

Deficiencies in beginning undergraduate students’ basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning their science-based and technology-based undergraduate courses in the University of Limerick have had their basic mathematics skills tested without any prior warning through a 40 question diagnostic test during their initial service mathematics lecture since 1998. Data gathered through this diagnostic test have been recorded in a database kept at the university and explored to track trends in mathematical competency of these beginning undergraduates. This paper details findings surrounding an analysis of the database between 2003 and 2013, outlining changes in mathematical competencies of these beginning undergraduates in an attempt to determine reasons for such changes. The analysis found that the proportion of students tested through this diagnostic test that are predicted to be at risk of failing their service mathematics end-of-semester examinations has increased significantly between 2003 and 2013. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously.     

A three-year perspective on conceptions of and orientations to learning mathematics of prospective teachers and first year university students

The paper reports a compilation of results from three studies conducted over three years to determine students' conceptions of mathematics, and orientations they follow in learning the subject. Respondents were 459 first year mathematics students from four universities and one teacher college. Results indicated that more than half the sample reported mathematics to be a subject made of numbers and formulae that could be memorized. This suggests a shallow emphasis when learning the subject, with no intention to understand. However, most students passed their examinations. It was concluded that there was no statistically significant relationship between examinations results and students' learning orientations. It is recommended that lecturers should foster students' meta-learning capabilities and an awareness of different learning strategies.     

Pedagogical challenges in making mathematics relevant for Indigenous Australians

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere.     

Rhetoric,Reality, and Possibilities: Interdisciplinary Teaching and Secondary Mathematics

The National Council of Teachers of Mathematics has proposed a broad core mathematics curriculum for all high school students. One emphasis in that core is on “mathematical connections” both among mathematical topics and between mathematics and other disciplines of study. It is suggested that mathematics should become a more integrated part of all students' high school education. In this article, working definitions for the terms curriculum, interdisciplinary, and integrated and a model of three categories of curriculum design based on the work of Harold Alberty are developed. This article then examines how a “connected” mathematics core curriculum might be situated within the different categories of curriculum organization. Examples from research on interdisciplinary education in high schools are presented. Issues arising from this study suggest the need for a greater emphasis on building and using models of curriculum integration both to frame and to give impetus to the work being done by teachers and administrators.     

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.     

Student Reactions to Standards-Based Mathematics Curricula: The Interplay Between Curriculum,Teachers, and Students

As standards-based mathematics curricula are used to guide learning, it is important to capture not just data on achievement but data on the way in which students respond to and interact in a standards-based instructional setting. In this study, sixth and seventh graders reacted through letters to using one of two standards-based curriculum projects (Connected Mathematics Project or Six Through Eight Mathematics). Letters were analyzed by class, by teacher, and by curriculum project. Findings suggest that across classrooms students were positive toward applications, hands-on activities, and working collaboratively. The level of students' enthusiasm for the new curricula varied much from class to class, further documenting the critical role teachers play in influencing students' perceptions of their mathematics learning experiences. The results illustrate that, while these curricula contain rich materials and hold much promise, especially in terms of their activities and applications, their success with students is dependent on the teacher.     

Students' Perceptions of Single‐Gender Science and Mathematics Classroom Experiences

While participating in single‐ and mixed‐gender science and mathematics classes, ninth‐grade urban high school students' (n= 118) academic self‐concept, self‐efficacy, and school climate perceptions were examined. Their perceptions were measured quantitatively from the Fennema‐Sherman Mathematics (modified for Science) Attitude and the Patterns of Adaptive Learning scales. Five factors arose from each instrument: confidence/efficacy, utility, instruction, climate, and anxiety/performance avoidance. Comparative factor analysis of the science‐modified Fennema‐Sherman Scale showed similar constructs within the mathematics scale. Our findings are congruent with reports concerning single‐gender classrooms that find few significant differences in students' attitudes toward science and mathematics, or classroom climate, with regard to single‐gender classes. Lastly, our results supported three structural equation models for the hypothesized factors from each instrument.     

Intentional Integration of Mathematics Content Instruction with Constructivist Pedagogy in Elementary Mathematics Education

The purpose of the research was to improve the effectiveness of instruction in constructivist pedagogy in a college elementary mathematics education course through intentional integration of instruction in mathematics content. Instructors of this course previously used examples involving mathematics content on an ad hoc basis in an attempt to illuminate desirable constructivist pedagogy but discovered that they were ineffective because students experienced difficulty with the mathematics content itself. An instrument was created to assess students' mathematics content knowledge required to understand these examples. Based on the outcome of the assessment, intentional instruction of mathematics content using anchoring examples was integrated with pedagogical instruction. Results showed significant improvement in mathematics content knowledge and confidence in that knowledge with a better understanding of constructivist pedagogy.