Children’s conceptions about mathematics and mathematics education

This paper deals with younger students’ (grade 2 and 5) conceptions about mathematics and mathematics education. The questionnaire consisted of three parts: (1) statements with a Likert-scale; (2) open-end questions where the students could explain further their conceptions; and, (3) a request to draw a picture of yourself doing mathematics. The results from the statements were summarised and the pictures were analysed. Most students in grade 2 had a positive attitude towards mathematics whereas a larger proportion in grade 5 gave negative answers. All students presented mathematics as an individual activity with a focus on the textbook. The elder students narrow the activity down to calculating. A post-questionnaire confirmed the results.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

The Impact of Gender and Pedagogy on the Development of Self-Regulated Learning Strategies in Undergraduate Engineering Classrooms

The purpose of this paper is to examine ways in which pedagogy and gender of instructor impact the development of self-regulated learning strategies as assessed by the Motivated Strategies for Learning Questionnaire (MSLQ) in male and female undergraduate engineering students. Pedagogy was operationalized as two general formats: lecture plus active learning techniques or problem-base/project-based learning. One hundred seventy-six students from four universities participated in the study. Within-group analyses found significant differences with regard to pedagogy, instructors’ gender, and student gender on the learning strategies and motivation subscales as operationalized by the MSLQ. Male and females students reported significant post-test differences with regard to the gender of instructor and the style of pedagogy. The results of this study showed a pattern where more positive responses for students of both genders were found with the same-gendered instructor. The results also suggested that male students responded more positively to project and problem-based courses with changes evidenced in motivation strategies and resource management. Female students showed decreases in resource management in these two types of courses. Further, female students reported increases in the lecture with active learning courses.

Portfolios and pedagogy : an examination of ideology and use

Portfolio use in writing studies contexts is becoming ubiquitous and, as such, portfolios are in danger of being rendered meaningless and thus require that we more fully theorize and historicize portfolios. To this end, I examine portfolios: both the standardized portfolio used for assessment purposes and the personalized portfolio used for entering the job market. I take a critical look at portfolios as a form of technology and acknowledge some of the dangers of blindly using portfolios for gaining employment in the current economic structure of fast capitalism. As educators in the writing studies fields, it is paramount that instructors have a critical awareness of the consequences of portfolio creation on students as designers, lifelong learners, and citizens of a larger society. I argue that a better understanding of the pedagogical implications for portfolio use is imperative before implementing them in the classroom, and that a social-epistemic approach provides a valuable rethinking of portfolio use for assessment purposes. Further, I argue for the notions of meditation and transformation to be added alongside collection, selection, and reflection because they enable portfolio designers and evaluators alike to thoughtfully consider new ways of meaning-making and innovation. Also important and included with meditation and transformation is the understanding that students are ideologically positioned in the educational system. For them to begin recognizing their situatedness is a step toward becoming designers of change. The portfolio can be a site for that change, and a way for them to document their own learning and ways of making meaning over a lifetime.

Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.